diff --git a/105/paper.pdf b/105/paper.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..e401f61fdb3c887196fb8391a1b8b2edc720870e
--- /dev/null
+++ b/105/paper.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f400ea5e7ad9695850fedeb786911509bc15785d2f93f9c5077b3a67df043325
+size 881387
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_gov_bonds.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_gov_bonds.csv
new file mode 100644
index 0000000000000000000000000000000000000000..e8ae17c0fd12e611629efc582c69b5e3452cf4f7
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_gov_bonds.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:847836042b8c20655ccefa8b019995882e1407948b594372a66b0056aadea271
+size 502130
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_liabilities.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_liabilities.csv
new file mode 100644
index 0000000000000000000000000000000000000000..3631d5eff6aa7bccc389612eae25049109296fa2
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/CentralBank_liabilities.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e64747220749fe3eae333298ff678591438ae19a9f08a1aa651c306bc9158853
+size 1153426
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Asset_Details.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Asset_Details.csv
new file mode 100644
index 0000000000000000000000000000000000000000..d35969c349cca49ed4dbf41ccd6ee54473f17c13
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Asset_Details.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:447da03cd373c357bdca599308266247fbe3a3115951d965cb6679dcce8a2df5
+size 1092238
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Safe_Liabilities.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Safe_Liabilities.csv
new file mode 100644
index 0000000000000000000000000000000000000000..22a9a163f482ba0d8c2f4133be94415e7bd6ae4d
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Financial_Safe_Liabilities.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8df4d6cfbfc9415b11754089a1e9a6278d0da1dbeb76ab85e09e8ddfda1572ac
+size 1996412
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/Government_Safe_Liabilities.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Government_Safe_Liabilities.csv
new file mode 100644
index 0000000000000000000000000000000000000000..5453acb268ea1dc5018729939317a237e3bd5d70
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Government_Safe_Liabilities.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f230d212c89375d7252466681a17d53e570673cd976d3e36dfc755d65ff4c431
+size 1268435
diff --git a/105/replication_package/Financial balance sheets non consolidated SNA 2008/Total liabilities.csv b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Total liabilities.csv
new file mode 100644
index 0000000000000000000000000000000000000000..efda2e45f0e49301d3ca4552d7b7b6781413bc96
--- /dev/null
+++ b/105/replication_package/Financial balance sheets non consolidated SNA 2008/Total liabilities.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea484dee1a87689447c1987f5b337acc86f23a02197c833105c8aa49ffe96393
+size 6614345
diff --git a/105/replication_package/GDP/GDP_current_prices.csv b/105/replication_package/GDP/GDP_current_prices.csv
new file mode 100644
index 0000000000000000000000000000000000000000..541f2a9315aecd4906e18c1e6fdc4ee3768ef343
--- /dev/null
+++ b/105/replication_package/GDP/GDP_current_prices.csv
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cea81d95092d1b07bfa92d0b08aa4c802192558d27c10848f3fc24b9cc9ae6d1
+size 803870
diff --git a/105/replication_package/GENERAL_IES/Parameters.m b/105/replication_package/GENERAL_IES/Parameters.m
new file mode 100644
index 0000000000000000000000000000000000000000..2401d108ca2adf43131d06491d8a9e75c30875e9
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/Parameters.m
@@ -0,0 +1,22 @@
+period_length = 0.25;
+
+P = 1 - exp(-.04*period_length); % disaster probability
+
+B = -log(1 - .32); % disaster size
+
+meanB = B;
+
+G = 0.025*period_length; % drift of log output
+
+RHO = 0.04*period_length; % time preference rate
+
+NU = 0.02*period_length; % replacement rate
+
+MU = 0.05; % popoulation share of agent 1
+
+ALPHA = 1/3; % capital share in output
+
+TAU = 0; % bond duration - short-term bonds
+
+GAMMA1 = 1.000001; % start with unit risk aversion
+GAMMA2 = GAMMA1;
diff --git a/105/replication_package/GENERAL_IES/Table_6_theta_half.m b/105/replication_package/GENERAL_IES/Table_6_theta_half.m
new file mode 100644
index 0000000000000000000000000000000000000000..3eac695ce6bbfbff332d4b5030303c01082946f6
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/Table_6_theta_half.m
@@ -0,0 +1,100 @@
+% THETA = 0.5
+
+load('model')
+addpath('files')
+
+Parameters;
+THETA = 0.9999; % start with THETA close to 1, for which we have a good initial guess
+
+% make the vector of parameters
+params = eval(symparams);
+
+% distribution of hatyp
+nodes = exp([G,G-B]); % hatyp
+weights = [1-P,P]; % corresponding probabilities
+
+T = 2000/period_length; % simulate 2000 years
+
+% disaster shock
+rng('default')
+disaster = double(rand(1,T+1)
testF && solve==1
+ t
+ [coeffs,model] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,1); % assume no realized disasters
+
+ if t>burn+10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ newxt = nPhi(:,1);
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt; % solution point
+ coeffs0 = coeffs;
+ end
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/GENERAL_IES/define_model.m b/105/replication_package/GENERAL_IES/define_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..373d5a4c67adf5015676a60f6da144740a905e3d
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/define_model.m
@@ -0,0 +1,152 @@
+%-------------------------------------------------------------------------
+% The model: Safe Assets - the case of general IES (THETA not equal 1)
+%
+% This file defines the model (see Appendix for the full derivation).
+% Bonds are perfectly safe short-term assets.
+%
+% Variables are denoted by small letters and
+% parameters by capital letters. Future values are denoted by suffix p.
+%-------------------------------------------------------------------------
+
+clear,clc
+
+%% Symbolic variables
+
+syms RHO GAMMA1 GAMMA2 NU MU THETA real
+syms f1 f2 f1p f2p x1 x2 x1p x2p real
+syms logq logqp tilp tilpp real
+syms state1 state1p state2 state2p hatyp k1 tilb1 real
+syms tila1 tila2 invtila1 invtila2 invtilp rbp rep c1 c2 c1p c2p q qp real
+syms invc1 invc1p invc2 invc2p invf1 invf2 r1p r2p u1p_power u2p_power u1p u2p logf1 logf1p logf2 logf2p real
+syms term1p term2p invr1p invr2p real
+
+%% Parameters
+
+symparams = [RHO,GAMMA1,GAMMA2,NU,MU,THETA];
+
+%% State variables
+
+state = [state1,state2]; % current period
+statep = [state1p,state2p]; % future period
+
+%% Control variables
+
+control = [f1,f2,x1,x2,logq,tilp]; % current period
+controlp = [f1p,f2p,x1p,x2p,logqp,tilpp]; % future period
+
+%% shocks
+
+shocks = hatyp;
+
+%% auxiliary variables
+
+logc1p = log(c1p);
+logc2p = log(c2p);
+
+invf1_ = 1/f1;
+invf2_ = 1/f2;
+
+logf1p_ = log(f1p);
+logf2p_ = log(f2p);
+
+invr1p_ = 1/r1p;
+invr2p_ = 1/r2p;
+
+q_ = exp(logq);
+qp_ = exp(logqp);
+
+invtila1_ = 1/tila1;
+invtila2_ = 1/tila2;
+
+rep_ = (1 + tilpp)/tilp*hatyp; % return on equity
+rbp_ = 1/q; % return on bond
+
+%% MODEL CONDITIONS
+
+invc1_ = 1 + 1/RHO*f1^(1 - THETA);
+
+c1_ = 1/invc1;
+
+invc1p_ = 1 + 1/RHO*f1p^(1 - THETA);
+
+c1p_ = 1/invc1p;
+
+invc2_ = 1 + 1/RHO*f2^(1-THETA);
+
+c2_ = 1/invc2;
+
+invc2p_ = 1 + 1/RHO*f2p^(1 - THETA);
+
+c2p_ = 1/invc2p;
+
+tila1_ = (1 + tilp)*state1 + state2;
+
+tila2_ = tilp + 1 - tila1;
+
+k1_ = x1*(1 - c1)*tila1/tilp;
+
+eq0 = -(1 - k1) + x2*(1 - c2)*tila2/tilp;
+
+tilb1_ = (1 - x1)*(1 - c1)*tila1;
+
+eq1 = tilb1*invtila2 + (1 - x2)*(1 - c2);
+
+r1p_ = x1*rep + (1 - x1)*rbp;
+
+r2p_ = x2*rep + (1 - x2)*rbp;
+
+term1p_ = ((invc1 - 1)*r1p*invf1)^(1 - GAMMA1)*((1 - NU*(1 - MU))*u1p^(1 - GAMMA1)...
+ + NU*(1 - MU)*u2p^(1 - GAMMA1));
+
+term2p_ = ((invc2 - 1)*r2p*invf2)^(1 - GAMMA2)*((1 - NU*MU)*u2p^(1 - GAMMA2)...
+ + NU*MU*u1p^(1 - GAMMA2));
+
+eq2 = -1 + term1p;
+
+eq3 = -1 + term2p;
+
+u1p_power_ = RHO/(1 + RHO)*c1p^(1 - THETA) + 1/(1 + RHO)*c1p^(1 - THETA)*f1p^(1 - THETA);
+
+u2p_power_ = RHO/(1 + RHO)*c2p^(1 - THETA) + 1/(1 + RHO)*c2p^(1 - THETA)*f2p^(1 - THETA);
+
+u1p_ = u1p_power^(1/(1 - THETA));
+
+u2p_ = u2p_power^(1/(1 - THETA));
+
+eq4 = (rep - rbp)*term1p*invr1p;
+
+eq5 = (rep - rbp)*term2p*invr2p;
+
+%% Function f (Ef = 0 imposes model conditions)
+
+f_fun = [eq0;eq1;eq2;eq3;eq4;eq5];
+
+%% law of motion of state variables
+
+Phi_fun = [k1 - NU*(k1 - MU); % law of motion of state1p
+ (1 - NU)*tilb1/(hatyp*q)]; % law of motion of state2p
+
+%% collect auxiliary variables and functions
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns;tempfun];
+ auxvars=[auxvars;tempvar];
+ end
+end
+
+%% Approximation order (<=4)
+
+order = 4;
+
+%% Preprocess model and save
+
+model = prepare_tp(f_fun,Phi_fun,controlp,control,statep,state,shocks,symparams,order,auxfuns,auxvars);
+
+save('model')
+
diff --git a/105/replication_package/GENERAL_IES/make_Table_6_part_1.m b/105/replication_package/GENERAL_IES/make_Table_6_part_1.m
new file mode 100644
index 0000000000000000000000000000000000000000..cc7e22aa1220500f4d7f486f4afc69a0b3dc752e
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/make_Table_6_part_1.m
@@ -0,0 +1,44 @@
+Table_6_theta_half;
+Table_6_theta_two;
+
+%% Display Table 6 (part 1)
+clc
+homefolder = pwd;
+cd ..
+
+diary on
+
+disp('********** Table 6 **********')
+
+load([homefolder '\Table_6_theta_half'])
+
+Table_6 = [round(Table(:,[1,2,4,5]),3),Table_vol,round(Table_labor(:,[3,4,5]),3),round(Table_labor(:,[6]),2)];
+
+disp('THETA = 0.5')
+disp(Table_6(3,:))
+
+load([homefolder '\Table_6_theta_two'])
+
+Table_6 = [round(Table(:,[1,2,4,5]),3),Table_vol,round(Table_labor(:,[3,4,5]),3),round(Table_labor(:,[6]),2)];
+
+disp('THETA = 2')
+disp(Table_6(3,:))
+
+%% Accuracy Measures
+disp('Appendix Table 2: Accuracy Measures for Table 6')
+
+load([homefolder '\Table_6_theta_half'])
+Accuarcy = [round(Table(:,1),3),round(log10(Table(:,end-1:end)),1)];
+
+disp('THETA = 0.5')
+disp(Accuarcy(3,2:end))
+
+load([homefolder '\Table_6_theta_two'])
+Accuarcy = [round(Table(:,1),3),round(log10(Table(:,end-1:end)),1)];
+
+disp('THETA = 2')
+disp(Accuarcy(3,2:end))
+
+diary off
+
+cd(homefolder)
\ No newline at end of file
diff --git a/105/replication_package/GENERAL_IES/simulate_with_disasters.m b/105/replication_package/GENERAL_IES/simulate_with_disasters.m
new file mode 100644
index 0000000000000000000000000000000000000000..f424aa4e4f620e4434e7f1622854becd925284a0
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/simulate_with_disasters.m
@@ -0,0 +1,19 @@
+% Simulate with disasters
+y_results = zeros(model.n_y,T+1);
+x_results = zeros(model.n_x,T+1);
+R_results = zeros(model.n_f,T+1);
+
+x_results(:,1) = state0;
+
+for t = 1:T
+t
+ xt = x_results(:,t);
+
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ % store results
+ R_results(:,t) = R;
+ y_results(:,t) = g;
+
+ x_results(:,t+1) = nPhi(:,disaster(t+1));
+end
\ No newline at end of file
diff --git a/105/replication_package/GENERAL_IES/solve_and_simulate.m b/105/replication_package/GENERAL_IES/solve_and_simulate.m
new file mode 100644
index 0000000000000000000000000000000000000000..c70927c73a0c797bd5b4684b38fc5e079a8ce3f3
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/solve_and_simulate.m
@@ -0,0 +1,84 @@
+% This file performs the following:
+% 1. Solve the model by Taylor projection at the initial state.
+% 2. Simulate the model without realized disasters.
+
+%% make initial guess for a deterministic version of the model
+
+% in a deterministic economy, the following variables are constant:
+
+x1 = 1; % agents invests only in equity
+x2 = 1;
+tilp = 1/RHO; % price/earning ratio
+hatyp = exp(G-meanB*P); % average growth
+haty = hatyp;
+rep = (1+tilp)/tilp*hatyp; % asset return
+logq = log(1/rep); % price of bond
+c1 = RHO/(1+RHO); % consumption/wealth ratio
+c2 = c1;
+logu1 = (RHO*log(c1)+log(1-c1)+log(rep))/RHO;
+u1 = exp(logu1);
+logu2 = (RHO*log(c2)+log(1-c2)+log(rep))/RHO;
+u2 = exp(logu2);
+f1 = (rep*u1);
+f2 = (rep*u2);
+
+k1 = MU;
+
+tila1 = k1*(1+tilp);
+
+state0 = [k1;0];
+c0 = state0;
+
+derivs0 = [f1;f2;x1;x2;logq;tilp];
+
+derivs1 = zeros(model.n_f,model.n_x);
+derivs2 = zeros(model.n_f,model.n_x^2);
+derivs3 = zeros(model.n_f,model.n_x^3);
+derivs4 = zeros(model.n_f,model.n_x^4);
+
+if order==1
+ [ initial_guess ] = derivs2coeffs( model,derivs0,derivs1 );
+elseif order==2
+ [ initial_guess ] = derivs2coeffs( model,derivs0,derivs1,derivs2);
+elseif order==3
+ [ initial_guess ] = derivs2coeffs( model,derivs0,derivs1,derivs2,derivs3 );
+elseif order==4
+ [ initial_guess ] = derivs2coeffs( model,derivs0,derivs1,derivs2,derivs3,derivs4 );
+end
+
+%% solve the model
+
+[coeffs,model] = tpsolve(initial_guess,state0,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+
+%% simulate the model
+
+solve = 1;
+stop = 0;
+t = 0;
+xt = state0;
+while stop==0
+ t = t+1;
+ % evaluate the previous solution at the new point xt
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ % if residuals are too large solve again
+ if norm(R(:))>testF && solve==1
+ t
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,disaster(t+1)); % new state
+
+ if t>=10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt;
+ coeffs0 = coeffs;
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/GENERAL_IES/summarize_results.m b/105/replication_package/GENERAL_IES/summarize_results.m
new file mode 100644
index 0000000000000000000000000000000000000000..7c0bffe0c0beff6fcf10fb1a36a303f6b44ac52a
--- /dev/null
+++ b/105/replication_package/GENERAL_IES/summarize_results.m
@@ -0,0 +1,61 @@
+
+normal = logical(disaster==1); % normal periods
+d = logical(disaster>1); % disaster periods
+
+state1 = x_results(1,1:T);
+state2 = x_results(2,1:T);
+
+f1 = y_results(1,1:T);
+x1 = y_results(3,1:T);
+logq = y_results(5,1:T);
+tilp=y_results(6,1:T);
+
+invc1 = 1 + 1/RHO*f1.^(1 - THETA);
+c1 = 1./invc1;
+
+q = exp(logq);
+
+tila1 = (1 + tilp).*state1(1:T) + state2(1:T);
+
+k1 = x1.*(1 - c1).*tila1./tilp;
+tilb1 = (1 - x1).*(1 - c1).*tila1;
+
+
+W1_share = k1 - NU*(k1 - MU) + (1 - NU)*tilb1./tilp; % wealth share after type changes
+equity = k1 - NU*(k1 - MU);
+
+debt_to_assets = -(1 - NU)*tilb1./tilp; % debt ratio (after type changes)
+debt_to_GDP = -(1 - NU)*tilb1*period_length;
+
+haty = nodes(1,double(disaster(1:T)));
+
+% compute means by iterated expectations
+
+roe = ((1 + tilp(2:T))./tilp(1:T-1).*haty(2:T)); % this is actual return from t to t+1.
+mean_roe = 1/period_length*log((1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)))); % mean return
+
+period_mean_roe = (1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)));
+period_var_roe = (1-P)*mean((roe(normal(2:T)) - period_mean_roe).^2)+P*mean((roe(d(2:T)) - period_mean_roe).^2);
+vol_roe = sqrt(period_var_roe/period_length);
+
+rb = log(1./q(1:T-1))/period_length; % this is log return on bonds
+mean_rb = (1-P)*mean(rb(normal(1:T-1)))+P*mean(rb(d(1:T-1)));
+
+Rb = 1./q(2:T-1);
+period_mean_rb = (1-P)*mean(Rb(normal(2:T-1)))+P*mean(Rb(d(2:T-1)));
+period_var_rb = (1-P)*mean((Rb(normal(2:T-1)) - period_mean_rb).^2)+P*mean((Rb(d(2:T-1)) - period_mean_rb).^2);
+vol_rb = sqrt(period_var_rb/period_length);
+
+mean_equity = (1-P)*mean(equity(normal(1:T))) + P*mean(equity(d(1:T)));
+mean_debt_to_assets = (1-P)*mean(debt_to_assets(normal(1:T))) + P*mean(debt_to_assets(d(1:T)));
+mean_debt_to_GDP = (1-P)*mean(debt_to_GDP(normal(1:T))) + P*mean(debt_to_GDP(d(1:T)));
+mean_W1_share = (1-P)*mean(W1_share(normal(1:T))) + P*mean(W1_share(d(1:T)));
+
+% mean_W1_share_excluding_labor = mean_W1_share*(1+L) - MU*L;
+% mean_debt_to_assets_excluding_labor = mean_debt_to_assets*(1+L);
+% mean_debt_to_GDP_including_labor = mean_debt_to_GDP/(1+L);
+% mean_equity_excluding_labor = mean_equity*(1+L) - MU*L;
+
+mean_equity_excluding_labor = mean_equity/ALPHA - MU*(1 - ALPHA)/ALPHA;
+mean_debt_to_assets_excluding_labor = mean_debt_to_assets/ALPHA;
+mean_W1_share_excluding_labor = mean_equity_excluding_labor - mean_debt_to_assets_excluding_labor;
\ No newline at end of file
diff --git a/105/replication_package/Make_OECD_data.do b/105/replication_package/Make_OECD_data.do
new file mode 100644
index 0000000000000000000000000000000000000000..dc3c083f493c9b3b22fb78f12fe1353baafc677c
--- /dev/null
+++ b/105/replication_package/Make_OECD_data.do
@@ -0,0 +1,684 @@
+clear
+
+*set matsize 3000
+set matsize 800
+clear mata
+set mem 500m
+set more off
+set logtype text
+capture log close
+*set linesize 255
+
+// IMPORTANT!!! change working directory to the folder of this file
+
+* cd "folder name"
+
+// GDP current prices
+clear
+
+local folder="GDP"
+
+insheet using "`folder'\GDP_current_prices.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - current price and ppp */
+tab Transaction
+
+keep if Measure=="Current prices"
+
+keep Country Year Value
+
+rename Value GDP
+
+rename Country country
+rename Year year
+
+
+label var GDP "GDP current prices, Million of national currency"
+
+save GDP, replace
+
+
+// Step 1: make dataset.dta
+
+clear
+
+local folder="Financial balance sheets non consolidated SNA 2008"
+
+* Total liabilities - all sectors
+
+insheet using "`folder'\Total liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+
+keep if Measure=="National currency, current prices"
+
+keep Country Sector Time Value
+
+rename Time Year
+rename Value totliab
+
+gen Sec=""
+
+replace Sec="Total" if Sector=="Total economy"
+replace Sec="World" if Sector=="Rest of the world"
+replace Sec="Households" if Sector=="Households and NPISH"
+replace Sec="Financials" if Sector=="Financial corporations"
+replace Sec="nonFinancials" if Sector=="Non-financial corporations"
+replace Sec="Gov" if Sector=="General Government"
+
+keep if Sec~=""
+
+keep Country Year Sec totliab
+
+rename Country country
+rename Year year
+rename Sec sector
+rename totliab totliab_
+
+reshape wide totliab_, i(country year) j(sector) string
+
+label var totliab_Total "Tota Liabilities - Total Economy"
+label var totliab_World "Tota Liabilities - Rest of the World"
+label var totliab_Households "Tota Liabilities - Households and NPISH"
+label var totliab_Financials "Tota Liabilities - Financial corporations"
+label var totliab_nonFinancials "Tota Liabilities - Non-financial corporations"
+
+save total_liabilities, replace
+
+
+//* Financial Corporations - safe liabilities
+clear
+
+insheet using "`folder'\Financial_Safe_Liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only financial corporations */
+
+keep if Measure=="National currency, current prices" & Sector=="Financial corporations"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value fin_
+
+reshape wide fin_, i(country year) j(tran) string
+
+label var fin_dep "Currency and deposits - Financial corporations"
+label var fin_secur "Debt securities - Financial corporations"
+label var fin_loan "Loans - Financial corporations"
+label var fin_mmf "Money market fund shares /units - Financial corporations"
+label var fin_trade "Trade credits and advances - Financial corporations"
+
+
+save financials_safe_items, replace
+
+
+//* General Government - safe liabilities
+
+clear
+
+insheet using "`folder'\Government_Safe_Liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only general government */
+
+keep if Measure=="National currency, current prices" & Sector=="General Government"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value gov_
+
+reshape wide gov_, i(country year) j(tran) string
+
+
+label var gov_dep "Currency and deposits - General Government"
+label var gov_secur "Debt securities - General Government"
+label var gov_loan "Loans - General Government"
+label var gov_mmf "Money market fund shares /units - General Government"
+label var gov_trade "Trade credits and advances - General Government"
+
+save government_safe_items, replace
+
+//* Central bank holdings of bonds (assume most of these holdings are government bonds)
+
+clear
+
+insheet using "`folder'\CentralBank_gov_bonds.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only general government */
+
+keep if Measure=="National currency, current prices" & Sector=="Central Bank"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="lbond" if Transaction=="Long-term debt securities"
+replace tran="sbond" if Transaction=="Short-term debt securities"
+
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value cb_
+
+reshape wide cb_, i(country year) j(tran) string
+
+save central_bank_bonds, replace
+
+//* Central bank - safe and total liabilities
+
+clear
+
+insheet using "`folder'\CentralBank_liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only Central Bank */
+
+keep if Measure=="National currency, current prices" & Sector=="Central Bank"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+replace tran="totliab_Total" if Transaction=="Financial liabilities"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value cb_
+
+reshape wide cb_, i(country year) j(tran) string
+
+
+label var cb_dep "Currency and deposits - Central Bank"
+label var cb_secur "Debt securities - Central Bank"
+label var cb_loan "Loans - Central Bank"
+label var cb_mmf "Money market fund shares /units - Central Bank"
+label var cb_trade "Trade credits and advances - Central Bank"
+label var cb_totliab_Total "Financial liabilities - Central Bank"
+
+save cb_safe_items, replace
+
+clear
+
+use total_liabilities, replace
+
+joinby country year using financials_safe_items, unmatched(both)
+cap drop _merge
+
+joinby country year using government_safe_items, unmatched(both)
+cap drop _merge
+
+joinby country year using central_bank_bonds, unmatched(both)
+cap drop _merge
+
+joinby country year using GDP, unmatched(master)
+cap drop _merge
+
+joinby country year using cb_safe_items, unmatched(master)
+cap drop _merge
+
+* replace missing values with zeros
+foreach var of varlist fin_* gov_* cb_* {
+replace `var'=0 if `var'==.
+}
+
+label var cb_lbond "Long-term debt securities held by the central bank"
+label var cb_sbond "Short-term debt securities held by the central bank"
+
+
+encode country, gen(countrys)
+
+drop country
+rename countrys country
+
+tsset country year
+
+save dataset, replace
+
+//* Compute variables in USD
+* Total liabilities - all sectors
+
+clear
+
+insheet using "`folder'\Total liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+
+
+*keep if Measure=="National currency, current prices"
+keep if Measure=="US $, current prices, current exchange rates, end of period"
+
+keep Country Sector Time Value
+
+rename Time Year
+rename Value totliab
+
+gen Sec=""
+
+replace Sec="Total" if Sector=="Total economy"
+replace Sec="World" if Sector=="Rest of the world"
+replace Sec="Households" if Sector=="Households and NPISH"
+replace Sec="Financials" if Sector=="Financial corporations"
+replace Sec="nonFinancials" if Sector=="Non-financial corporations"
+replace Sec="Gov" if Sector=="General Government"
+
+keep if Sec~=""
+
+keep Country Year Sec totliab
+
+rename Country country
+rename Year year
+rename Sec sector
+rename totliab totliab_
+
+reshape wide totliab_, i(country year) j(sector) string
+
+label var totliab_Total "Tota Liabilities - Total Economy"
+label var totliab_World "Tota Liabilities - Rest of the World"
+label var totliab_Households "Tota Liabilities - Households and NPISH"
+label var totliab_Financials "Tota Liabilities - Financial corporations"
+label var totliab_nonFinancials "Tota Liabilities - Non-financial corporations"
+
+save total_liabilitiesUSD, replace
+
+*/
+
+//* Financial Corporations - safe liabilities
+clear
+
+insheet using "`folder'\Financial_Safe_Liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only financial corporations */
+
+*keep if Measure=="National currency, current prices" & Sector=="Financial corporations"
+keep if Measure=="US $, current prices, current exchange rates, end of period"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value fin_
+
+reshape wide fin_, i(country year) j(tran) string
+
+label var fin_dep "Currency and deposits - Financial corporations"
+label var fin_secur "Debt securities - Financial corporations"
+label var fin_loan "Loans - Financial corporations"
+label var fin_mmf "Money market fund shares /units - Financial corporations"
+label var fin_trade "Trade credits and advances - Financial corporations"
+
+
+save financials_safe_itemsUSD, replace
+
+//* General Government - safe liabilities
+
+clear
+
+insheet using "`folder'\Government_Safe_Liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only general government */
+
+*keep if Measure=="National currency, current prices" & Sector=="General Government"
+keep if Measure=="US $, current prices, current exchange rates, end of period"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value gov_
+
+reshape wide gov_, i(country year) j(tran) string
+
+
+label var gov_dep "Currency and deposits - General Government"
+label var gov_secur "Debt securities - General Government"
+label var gov_loan "Loans - General Government"
+label var gov_mmf "Money market fund shares /units - General Government"
+label var gov_trade "Trade credits and advances - General Government"
+
+save government_safe_itemsUSD, replace
+
+
+//* Central bank holdings of bonds (assume most of these holdings are government bonds)
+
+clear
+
+insheet using "`folder'\CentralBank_gov_bonds.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only general government */
+
+*keep if Measure=="National currency, current prices" & Sector=="Central Bank"
+keep if Measure=="US $, current prices, current exchange rates, end of period"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="lbond" if Transaction=="Long-term debt securities"
+replace tran="sbond" if Transaction=="Short-term debt securities"
+
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value cb_
+
+reshape wide cb_, i(country year) j(tran) string
+
+save central_bank_bondsUSD, replace
+
+
+//* Central bank - safe and total liabilities
+
+clear
+
+insheet using "`folder'\CentralBank_liabilities.csv", n c case
+
+des
+
+tab PowerCode /* all number in millions */
+tab Measure /* two types of measures - national currency and USD */
+tab Transaction
+tab Sector /* only Central Bank */
+
+*keep if Measure=="National currency, current prices" & Sector=="Central Bank"
+keep if Measure=="US $, current prices, current exchange rates, end of period"
+
+keep Country Time Transaction Value
+
+gen tran=""
+
+replace tran="dep" if Transaction=="Currency and deposits"
+replace tran="secur" if Transaction=="Debt securities"
+replace tran="loan" if Transaction=="Loans"
+replace tran="mmf" if Transaction=="Money market fund shares /units"
+replace tran="trade" if Transaction=="Trade credits and advances"
+replace tran="totliab_Total" if Transaction=="Financial liabilities"
+
+drop if tran==""
+
+keep Country Time tran Value
+rename Country country
+rename Time year
+rename Value cb_
+
+reshape wide cb_, i(country year) j(tran) string
+
+
+label var cb_dep "Currency and deposits - Central Bank"
+label var cb_secur "Debt securities - Central Bank"
+label var cb_loan "Loans - Central Bank"
+label var cb_mmf "Money market fund shares /units - Central Bank"
+label var cb_trade "Trade credits and advances - Central Bank"
+label var cb_totliab_Total "Financial liabilities - Central Bank"
+
+save cb_safe_itemsUSD, replace
+
+***
+
+clear
+
+use total_liabilitiesUSD, replace
+
+joinby country year using financials_safe_itemsUSD, unmatched(both)
+cap drop _merge
+
+joinby country year using government_safe_itemsUSD, unmatched(both)
+cap drop _merge
+
+joinby country year using central_bank_bondsUSD, unmatched(both)
+cap drop _merge
+
+joinby country year using cb_safe_itemsUSD, unmatched(both)
+cap drop _merge
+
+
+* replace missing values with zeros
+foreach var of varlist fin_* gov_* cb_* {
+replace `var'=0 if `var'==.
+}
+
+label var cb_lbond "Long-term debt securities held by the central bank"
+label var cb_sbond "Short-term debt securities held by the central bank"
+
+
+encode country, gen(countrys)
+
+drop country
+rename countrys country
+
+tsset country year
+
+save datasetUSD, replace
+
+*** do USD aggregates
+
+use datasetUSD, clear
+
+
+gen fin_safeUSD=fin_dep+fin_loan+fin_mmf+fin_secur // remove trade credit and advances - it's a small part of financial debt and seems unrelated
+gen cb_safeUSD=cb_dep+cb_loan+cb_mmf+cb_secur // remove trade credit and advances - it's a small part of financial debt and seems unrelated
+
+
+gen gov_safeUSD=gov_dep+gov_loan+gov_mmf+gov_secur // remove trade credit and advnaces
+
+
+rename totliab_Total totliab_TotalUSD
+
+keep country year fin_safeUSD gov_safeUSD cb_safeUSD totliab_TotalUSD
+
+sort country year
+tsset country year
+
+
+save safeUSD, replace
+
+// Make world table
+
+use safeUSD, clear
+
+gen tempvar=fin_safeUSD+gov_safeUSD+totliab_TotalUSD
+
+bysort country: egen minyear=min(year) if tempvar<.
+bysort country: egen maxyear=max(year) if tempvar<.
+
+keep if minyear<=1995
+keep if year>=1995
+
+keep if maxyear>=2017
+keep if year<=2017
+
+sort country year
+tsset country year // panel is balanced
+
+
+if r(balanced)!="strongly balanced" {
+di "WARNING!!!! panel is not balanced"
+ }
+
+preserve
+
+keep if year==2017
+
+keep country
+
+gen OECD=1
+
+save OECD, replace
+
+restore
+
+
+decode country, g(country_name)
+
+bysort year: egen fin_safeWorld=total(fin_safeUSD)
+bysort year: egen gov_safeWorld=total(gov_safeUSD)
+bysort year: egen new_totalWorld=total(totliab_TotalUSD)
+
+bysort year: egen cb_safeWorld=total(cb_safeUSD)
+
+gen fin_shareWorld=fin_safeWorld/new_totalWorld
+gen gov_shareWorld=gov_safeWorld/new_totalWorld
+gen shareWorld=fin_shareWorld+gov_shareWorld
+
+gen cb_shareWorld=cb_safeWorld/new_totalWorld
+
+bysort year: egen fin_safeNonUS=total(fin_safeUSD) if country_name!="United States"
+bysort year: egen gov_safeNonUS=total(gov_safeUSD) if country_name!="United States"
+bysort year: egen new_totalNonUS=total(totliab_TotalUSD) if country_name!="United States"
+
+bysort year: egen cb_safeNonUS=total(cb_safeUSD) if country_name!="United States"
+
+gen fin_shareNonUS=fin_safeNonUS/new_totalNonUS
+gen gov_shareNonUS=gov_safeNonUS/new_totalNonUS
+gen shareNonUS=fin_shareNonUS+gov_shareNonUS
+
+gen cb_shareNonUS=cb_safeNonUS/new_totalNonUS
+
+sort country year
+
+keep if country==country[1]
+
+keep fin_shareWorld gov_shareWorld shareWorld cb_shareWorld fin_shareNonUS gov_shareNonUS shareNonUS cb_shareNonUS year
+
+
+keep year fin_shareWorld gov_shareWorld shareWorld cb_shareWorld fin_shareNonUS gov_shareNonUS shareNonUS cb_shareNonUS
+
+save World, replace
+
+
+// Make final dataset
+
+use dataset // non-consolidated data
+
+joinby country year using safeUSD, unmatched(both)
+cap drop _merge
+
+joinby year using World, unmatched(both)
+cap drop _merge
+
+joinby country using OECD, unmatched(both)
+cap drop _merge
+
+cap drop fin_safe
+cap drop cb_safe
+
+label var gov_safeUSD "government safe liabilities in USD"
+label var fin_shareWorld "financial liabilities (as share of total assets) for the whole world"
+label var gov_shareWorld "government liabilities (as share of total assets) for the whole world"
+label var cb_shareWorld "central bank liabilities (as share of total assets) for the whole world"
+label var shareWorld "safe liabilities (as share of total assets) for the whole world"
+
+label var fin_shareNonUS "financial liabilities (as share of total assets) for non-US sample"
+label var gov_shareNonUS "government liabilities (as share of total assets) for non-US sample"
+label var cb_shareNonUS "central bank liabilities (as share of total assets) for non-US sample"
+label var shareNonUS "safe liabilities (as share of total assets) for non-US sample"
+
+label var totliab_Gov "Tota Liabilities - Government"
+label var OECD "dummy for OECD countries"
+
+save OECD_data, replace
+
diff --git a/105/replication_package/ReadMe.pdf b/105/replication_package/ReadMe.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..411b0922f234db6171b506074f386e907428468d
--- /dev/null
+++ b/105/replication_package/ReadMe.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9068400c5ca91682b0dd81943ea676402c4cd3e4a0083709b46a65c0d502af1f
+size 42724
diff --git a/105/replication_package/Replicate_Empirical_Results.do b/105/replication_package/Replicate_Empirical_Results.do
new file mode 100644
index 0000000000000000000000000000000000000000..81c488972425daffbe7dc7554239d7a4ec88ee72
--- /dev/null
+++ b/105/replication_package/Replicate_Empirical_Results.do
@@ -0,0 +1,16 @@
+*************************************************************************************************************
+* Replicate Tables 1-4 and Figures 1-2 of "Safe Assets" by Barro, Fernandez-Villaverde, Levintal and Mollerus
+*************************************************************************************************************
+
+clear all
+
+clear mata
+set mem 500m
+set maxvar 32767
+set more off
+set linesize 255
+cap log close
+
+do make_Tables_1_to_3_Figures_1_and_2
+
+do make_Table_4
diff --git a/105/replication_package/Replicate_Simulation_Results.m b/105/replication_package/Replicate_Simulation_Results.m
new file mode 100644
index 0000000000000000000000000000000000000000..c04034d0d1a34e97bfe690cf2281e925ab3a1a9e
--- /dev/null
+++ b/105/replication_package/Replicate_Simulation_Results.m
@@ -0,0 +1,40 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Replicate Tables 5-7 and Figure 3 of "Safe Assets" by Barro, Fernandez-Villaverde, Levintal and Mollerus
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+clear
+
+%% open diary file
+
+FID = fopen('Tables_5_to_7.txt','w');
+fclose(FID);
+
+diary Tables_5_to_7.txt
+diary off
+
+%% add folders to search path
+homefolder = pwd;
+
+addpath(genpath([homefolder '\solution_methods']));
+
+%% define models
+
+run('UNIT_IES\define_model'); % THETA = 1
+run('GENERAL_IES\define_model'); % THETA ~= 1
+run('Variable_Disaster_Size\define_model'); % THETA = 1, variable disaster size, defaultable long-term bonds
+
+
+%% replicate Table 5
+run('UNIT_IES\make_Table_5.m')
+
+%% replicate Table 6
+run('GENERAL_IES\make_Table_6_part_1.m')
+run('UNIT_IES\make_Table_6_part_2.m')
+
+%% replicate Table 7
+run('Variable_Disaster_Size\make_Table_7.m')
+
+%% replicate Figure 3
+run('UNIT_IES\Disaster_IRF.m')
+
+
diff --git a/105/replication_package/UNIT_IES/Disaster_IRF.m b/105/replication_package/UNIT_IES/Disaster_IRF.m
new file mode 100644
index 0000000000000000000000000000000000000000..6098efaee7047147b85c2a9c4242df58d5b1e477
--- /dev/null
+++ b/105/replication_package/UNIT_IES/Disaster_IRF.m
@@ -0,0 +1,46 @@
+% Disaster Impulse response function
+
+clear,clc,close all
+addpath('files')
+
+load('benchmark')
+
+state0 = mean(tila1);
+mean_W1_share0 = mean_W1_share;
+
+T = 10/period_length + 1;
+
+disaster = ones(1,T+1);
+disaster(2) = 2;
+
+simulate_with_disasters;
+summarize_results;
+
+W1_share = [mean_W1_share0;W1_share(:)];
+
+% adjust for human capital
+equity = equity/ALPHA - MU*(1 - ALPHA)/ALPHA;
+debt_to_assets = debt_to_assets/ALPHA;
+W1_share = W1_share/ALPHA - (1 - ALPHA)/ALPHA*MU;
+
+set(0, 'defaultFigurePaperPosition', [0 0 20 21.5]*30);
+h = figure('color', [1 1 1], 'PaperType', 'A4');
+
+subplot(2,2,1);
+plot(W1_share);
+title('W1/W')
+
+subplot(2,2,2)
+plot(rb);
+title('rf')
+
+subplot(2,2,3)
+plot(equity);
+title('K1')
+
+subplot(2,2,4)
+plot(debt_to_assets);
+title('B1/assets')
+
+cd ..
+saveas(h,'Figure_3','jpg')
\ No newline at end of file
diff --git a/105/replication_package/UNIT_IES/Parameters.m b/105/replication_package/UNIT_IES/Parameters.m
new file mode 100644
index 0000000000000000000000000000000000000000..2401d108ca2adf43131d06491d8a9e75c30875e9
--- /dev/null
+++ b/105/replication_package/UNIT_IES/Parameters.m
@@ -0,0 +1,22 @@
+period_length = 0.25;
+
+P = 1 - exp(-.04*period_length); % disaster probability
+
+B = -log(1 - .32); % disaster size
+
+meanB = B;
+
+G = 0.025*period_length; % drift of log output
+
+RHO = 0.04*period_length; % time preference rate
+
+NU = 0.02*period_length; % replacement rate
+
+MU = 0.05; % popoulation share of agent 1
+
+ALPHA = 1/3; % capital share in output
+
+TAU = 0; % bond duration - short-term bonds
+
+GAMMA1 = 1.000001; % start with unit risk aversion
+GAMMA2 = GAMMA1;
diff --git a/105/replication_package/UNIT_IES/Table_6_MU.m b/105/replication_package/UNIT_IES/Table_6_MU.m
new file mode 100644
index 0000000000000000000000000000000000000000..fc572545cc9978208a737f280b088ce72c38785d
--- /dev/null
+++ b/105/replication_package/UNIT_IES/Table_6_MU.m
@@ -0,0 +1,94 @@
+% MU = 0.1
+
+load('model')
+addpath('files')
+
+Parameters;
+MU = 0.1; % popoulation share of agent 1
+
+% make the vector of parameters
+params = eval(symparams);
+
+% distribution of hatyp
+nodes = exp([G,G-B]); % hatyp
+weights = [1-P,P]; % corresponding probabilities
+
+T = 2000/period_length; % simulate 2000 years
+
+% disaster shock
+rng('default')
+disaster = double(rand(1,T+1)
testF && solve==1
+ t
+ [coeffs,model] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,1); % assume no realized disasters
+
+ if t>burn+10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ newxt = nPhi(:,1);
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt; % solution point
+ coeffs0 = coeffs;
+ end
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/UNIT_IES/define_model.m b/105/replication_package/UNIT_IES/define_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..b454c9702d9ba6e773d1b66c362d7a9cafd7df3d
--- /dev/null
+++ b/105/replication_package/UNIT_IES/define_model.m
@@ -0,0 +1,139 @@
+%-------------------------------------------------------------------------
+% The model: Safe Assets - the case of unit IES (THETA = 1)
+%
+% This file defines the baseline model (see Appendix for the full derivation).
+% Bonds are short term perfectly safe.
+%
+% Variables are denoted by small letters and
+% parameters by capital letters. Future values are denoted by suffix p.
+%-------------------------------------------------------------------------
+
+clear,clc
+
+%% Symbolic variables
+
+syms RHO GAMMA1 GAMMA2 NU MU TAU real
+syms f1 f2 f1p f2p x1 x2 x1p x2p real
+syms logq logqp tilp tilpp real
+syms state1 state1p state2 state2p hatyp deltap k1 tilb1 real
+syms tila1 tila1p tila2 invtila1 invtila2 invtilp rbp rep c1 c2 c1p c2p q qp real
+syms invc1 invc1p invc2 invc2p invf1 invf2 r1p r2p logu1p logu2p u1p u2p logf1 logf1p logf2 logf2p real
+syms term1p term2p invr1p invr2p real
+
+%% Parameters
+
+symparams = [RHO,GAMMA1,GAMMA2,NU,MU];
+
+%% State variables
+
+state = [tila1]; % current period
+statep = [tila1p]; % future period
+
+%% Control variables
+
+control = [f1,f2,x1,x2,logq]; % current period
+controlp = [f1p,f2p,x1p,x2p,logqp]; % future period
+
+%% shocks
+
+shocks = [hatyp];
+
+%% auxiliary variables
+
+tilp = 1/RHO; % price-dividend ratio for unit IES
+tilpp = tilp; % next period
+
+c1 = RHO/(1 + RHO); % consumption/wealth ratio of agent 1 for unit IES
+c1p = c1; % next period
+
+c2 = c1; % consumption/wealth ratio of agent 2 for unit IES
+c2p = c2; % next period
+
+logc1p = log(c1p);
+logc2p = log(c2p);
+
+invf1_ = 1/f1;
+invf2_ = 1/f2;
+
+logf1p_ = log(f1p);
+logf2p_ = log(f2p);
+
+invr1p_ = 1/r1p;
+invr2p_ = 1/r2p;
+
+q_ = exp(logq);
+qp_ = exp(logqp);
+
+invtila1_ = 1/tila1;
+invtila2_ = 1/tila2;
+
+rep_ = (1 + tilpp)/tilp*hatyp; % return on equity
+rbp_ = 1/q; % return on bond
+
+u1p_ = exp(logu1p);
+u2p_ = exp(logu2p);
+
+%% MODEL CONDITIONS
+
+tila2_ = tilp + 1 - tila1;
+
+k1_ = x1*(1 - c1)*tila1/tilp;
+
+tilb1_ = (1 - x1)*(1 - c1)*tila1;
+
+eq1 = tilb1*invtila2 + (1 - x2)*(1 - c2);
+
+r1p_ = x1*rep + (1 - x1)*rbp;
+
+r2p_ = x2*rep + (1 - x2)*rbp;
+
+term1p_ = r1p^(1 - GAMMA1)*((1 - NU*(1 - MU))*u1p^(1 - GAMMA1)...
+ + NU*(1 - MU)*u2p^(1 - GAMMA1))*invf1^(1 - GAMMA1);
+
+term2p_ = r2p^(1 - GAMMA2)*((1 - NU*MU)*u2p^(1 - GAMMA2)...
+ +NU*MU*u1p^(1 - GAMMA2))*invf2^(1 - GAMMA2);
+
+eq2 = -1 + term1p; % define f1 = (E(r1p*u1p)^(1-GAMMA1))^(1/(1-GAMMA1))
+
+eq3 = -1 + term2p; % define f2 similarly
+
+logu1p_ = RHO/(1 + RHO)*logc1p + 1/(1 + RHO)*log(1 - c1p) + 1/(1 + RHO)*logf1p;
+
+logu2p_ = RHO/(1 + RHO)*logc2p + 1/(1 + RHO)*log(1 - c2p) + 1/(1 + RHO)*logf2p;
+
+eq4 = (rep - rbp)*term1p*invr1p;
+
+eq5 = (rep - rbp)*term2p*invr2p;
+
+%% Function f (Ef = 0 imposes model conditions)
+
+f_fun = [eq1;eq2;eq3;eq4;eq5];
+
+%% law of motion of state variables
+
+Phi_fun = (1 + tilp)*(k1 - NU*(k1 - MU)) + (1 - NU)*tilb1/(hatyp*q); % law of motion of tila1
+
+%% collect auxiliary variables and functions
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns;tempfun];
+ auxvars=[auxvars;tempvar];
+ end
+end
+
+%% Approximation order (<=4)
+
+order = 4;
+
+%% Preprocess model and save
+
+model = prepare_tp(f_fun,Phi_fun,controlp,control,statep,state,shocks,symparams,order,auxfuns,auxvars);
+
+save('model')
+
diff --git a/105/replication_package/UNIT_IES/make_Table_5.m b/105/replication_package/UNIT_IES/make_Table_5.m
new file mode 100644
index 0000000000000000000000000000000000000000..cf43b050b59082c9593cc3d582954a673ef236b6
--- /dev/null
+++ b/105/replication_package/UNIT_IES/make_Table_5.m
@@ -0,0 +1,210 @@
+% Table 5
+
+clear,clc
+
+load('model')
+addpath('files')
+
+Parameters;
+
+% make the vector of parameters
+params = eval(symparams);
+
+% distribution of hatyp
+nodes = exp([G,G-B]); % hatyp
+weights = [1-P,P]; % corresponding probabilities
+
+T = 2000/period_length; % simulate 2000 years
+
+% disaster shock
+rng('default')
+disaster = double(rand(1,T+1)
testF && solve==1
+ t
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,disaster(t+1)); % new state
+
+ if t>=10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt;
+ coeffs0 = coeffs;
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/UNIT_IES/summarize_results.m b/105/replication_package/UNIT_IES/summarize_results.m
new file mode 100644
index 0000000000000000000000000000000000000000..eb8cdabc39a920fa151d0c10b1b5fea33b5eaa4a
--- /dev/null
+++ b/105/replication_package/UNIT_IES/summarize_results.m
@@ -0,0 +1,56 @@
+
+normal = logical(disaster==1); % normal periods
+d = logical(disaster>1); % disaster periods
+
+tila1 = x_results(1,1:T);
+
+x1 = y_results(3,1:T);
+logq = y_results(5,1:T);
+
+c1 = RHO/(1+RHO);
+tilp = 1/RHO;
+tilp = repmat(tilp,1,T);
+q = exp(logq);
+
+k1 = x1.*(1 - c1).*tila1./tilp;
+tilb1 = (1 - x1).*(1 - c1).*tila1;
+
+
+W1_share = k1 - NU*(k1 - MU) + (1 - NU)*tilb1./tilp; % wealth share after type changes
+equity = k1 - NU*(k1 - MU);
+
+debt_to_assets = -(1 - NU)*tilb1./tilp; % debt ratio (after type changes)
+debt_to_GDP = -(1 - NU)*tilb1*period_length;
+
+haty = nodes(1,double(disaster(1:T)));
+
+% compute means by iterated expectations
+
+roe = ((1 + tilp(2:T))./tilp(1:T-1).*haty(2:T)); % this is actual return from t to t+1.
+mean_roe = 1/period_length*log((1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)))); % mean return
+
+period_mean_roe = (1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)));
+period_var_roe = (1-P)*mean((roe(normal(2:T)) - period_mean_roe).^2)+P*mean((roe(d(2:T)) - period_mean_roe).^2);
+vol_roe = sqrt(period_var_roe/period_length);
+
+rb = log(1./q(1:T-1))/period_length; % this is log return on bonds
+mean_rb = (1-P)*mean(rb(normal(1:T-1)))+P*mean(rb(d(1:T-1)));
+
+Rb = 1./q(2:T-1);
+period_mean_rb = (1-P)*mean(Rb(normal(2:T-1)))+P*mean(Rb(d(2:T-1)));
+period_var_rb = (1-P)*mean((Rb(normal(2:T-1)) - period_mean_rb).^2)+P*mean((Rb(d(2:T-1)) - period_mean_rb).^2);
+vol_rb = sqrt(period_var_rb/period_length);
+
+mean_equity = (1-P)*mean(equity(normal(1:T))) + P*mean(equity(d(1:T)));
+mean_debt_to_assets = (1-P)*mean(debt_to_assets(normal(1:T))) + P*mean(debt_to_assets(d(1:T)));
+mean_debt_to_GDP = (1-P)*mean(debt_to_GDP(normal(1:T))) + P*mean(debt_to_GDP(d(1:T)));
+mean_W1_share = (1-P)*mean(W1_share(normal(1:T))) + P*mean(W1_share(d(1:T)));
+
+% mean_W1_share_excluding_labor = mean_W1_share*(1+L) - MU*L;
+% mean_debt_to_assets_excluding_labor = mean_debt_to_assets*(1+L);
+% mean_debt_to_GDP_including_labor = mean_debt_to_GDP/(1+L);
+% mean_equity_excluding_labor = mean_equity*(1+L) - MU*L;
+
+mean_equity_excluding_labor = mean_equity/ALPHA - MU*(1 - ALPHA)/ALPHA;
+mean_debt_to_assets_excluding_labor = mean_debt_to_assets/ALPHA;
+mean_W1_share_excluding_labor = mean_equity_excluding_labor - mean_debt_to_assets_excluding_labor;
\ No newline at end of file
diff --git a/105/replication_package/User Guide.pdf b/105/replication_package/User Guide.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..472c53d6556de6364aee7049056746e176869cb9
--- /dev/null
+++ b/105/replication_package/User Guide.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4ae3ea65d6ead2e1e273aabe94a8a1f913ec926e7b77f7f75784b25d6db4748f
+size 161394
diff --git a/105/replication_package/Variable_Disaster_Size/Parameters.m b/105/replication_package/Variable_Disaster_Size/Parameters.m
new file mode 100644
index 0000000000000000000000000000000000000000..a6fe9ac05166cc4ddbc618313b5bdcccdc4e2f83
--- /dev/null
+++ b/105/replication_package/Variable_Disaster_Size/Parameters.m
@@ -0,0 +1,46 @@
+period_length = 0.25;
+
+P = 1 - exp(-.04*period_length); % disaster probability
+
+% variable disaster size
+B = -log(1 - [0.1384074;
+ 0.2375926;
+ 0.335;
+ 0.4331111;
+ 0.5516667;
+ 0.653]);
+
+% distribution of disaster size
+probB = [0.6;
+ 0.2;
+ 0.088888889;
+ 0.066666667;
+ 0.022222222;
+ 0.022222222];
+
+
+meanB = B(:)'*probB;
+
+Size = 1 - exp(-B(:)');
+meanSize = Size*probB;
+sdSize = sqrt((Size - meanSize).^2*probB(:));
+
+G = 0.021*period_length; % drift of log output
+
+RHO = 0.04*period_length; % time preference rate
+
+NU = 0.02*period_length; % replacement rate
+
+MU = 0.05; % popoulation share of agent 1
+
+ALPHA = 1/3; % capital share in output
+
+TAU = 0; % bond duration - start with short-term bonds
+
+GAMMA1 = 1.000001; % start with unit risk aversion
+GAMMA2 = GAMMA1;
+
+delta_prob = 0.4; % default probability
+delta_size = 0; % default size
+
+
diff --git a/105/replication_package/Variable_Disaster_Size/correct_params.m b/105/replication_package/Variable_Disaster_Size/correct_params.m
new file mode 100644
index 0000000000000000000000000000000000000000..f3a4df1c176c5a6163e633593681f37f0fae6039
--- /dev/null
+++ b/105/replication_package/Variable_Disaster_Size/correct_params.m
@@ -0,0 +1,45 @@
+% This file changes the parameters gradually from their initival value to
+% the target value
+
+solve = 1;
+stop = 0;
+t = 0;
+
+xt = state0;
+params0 = params;
+while stop==0
+ t = t + 1;
+
+ if t<=burn
+ factor = t/burn;
+ params = (1 - factor)*params0 + factor*newparams;
+ end
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ % if residuals are too large solve again
+ if norm(R(:))>testF && solve==1
+ t
+ [coeffs,model] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,1); % assume no realized disasters
+
+ if t>burn+10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+
+ newxt = nPhi(:,1);
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt; % solution point
+ coeffs0 = coeffs;
+ end
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/Variable_Disaster_Size/define_model.m b/105/replication_package/Variable_Disaster_Size/define_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..ccc424df9ddbff9ebfc0f7ba5d09b32140fd5334
--- /dev/null
+++ b/105/replication_package/Variable_Disaster_Size/define_model.m
@@ -0,0 +1,142 @@
+%-------------------------------------------------------------------------
+% The model: Safe Assets - the case of unit IES (THETA = 1)
+% Bonds are long term and subject to a default shock deltap
+%
+% This file defines the model (see Appendix for the full derivation).
+%
+% Variables are denoted by small letters and
+% parameters by capital letters. Future values are denoted by suffix p.
+%-------------------------------------------------------------------------
+
+clear,clc
+
+%% Symbolic variables
+
+syms RHO GAMMA1 GAMMA2 NU MU TAU real
+syms f1 f2 f1p f2p x1 x2 x1p x2p real
+syms logq logqp tilp tilpp real
+syms state1 state1p state2 state2p hatyp deltap k1 tilb1 real
+syms tila1 tila2 invtila1 invtila2 invtilp rbp rep c1 c2 c1p c2p q qp real
+syms invc1 invc1p invc2 invc2p invf1 invf2 r1p r2p logu1p logu2p u1p u2p logf1 logf1p logf2 logf2p real
+syms term1p term2p invr1p invr2p real
+
+%% Parameters
+
+symparams = [RHO,GAMMA1,GAMMA2,NU,MU,TAU];
+
+%% State variables
+
+state = [state1,state2]; % current period
+statep = [state1p,state2p]; % future period
+
+%% Control variables
+
+control = [f1,f2,x1,x2,logq]; % current period
+controlp = [f1p,f2p,x1p,x2p,logqp]; % future period
+
+%% shocks
+
+shocks = [hatyp,deltap];
+
+%% auxiliary variables
+
+tilp = 1/RHO; % price-dividend ratio for unit IES
+tilpp = tilp; % next period
+
+c1 = RHO/(1 + RHO); % consumption/wealth ratio of agent 1 for unit IES
+c1p = c1; % next period
+
+c2 = c1; % consumption/wealth ratio of agent 2 for unit IES
+c2p = c2; % next period
+
+logc1p = log(c1p);
+logc2p = log(c2p);
+
+invf1_ = 1/f1;
+invf2_ = 1/f2;
+
+logf1p_ = log(f1p);
+logf2p_ = log(f2p);
+
+invr1p_ = 1/r1p;
+invr2p_ = 1/r2p;
+
+q_ = exp(logq);
+qp_ = exp(logqp);
+
+invtila1_ = 1/tila1;
+invtila2_ = 1/tila2;
+
+rep_ = (1 + tilpp)/tilp*hatyp; % return on equity
+rbp_ = (1 + TAU*qp)/q*(1 - deltap); % return on bond
+
+u1p_ = exp(logu1p);
+u2p_ = exp(logu2p);
+
+%% MODEL CONDITIONS
+
+tila1_ = (1 + tilp)*state1 + state2*(1 + TAU*q);
+
+tila2_ = tilp + 1 - tila1;
+
+k1_ = x1*(1 - c1)*tila1/tilp;
+
+tilb1_ = (1 - x1)*(1 - c1)*tila1;
+
+eq1 = tilb1*invtila2 + (1 - x2)*(1 - c2);
+
+r1p_ = x1*rep + (1 - x1)*rbp;
+
+r2p_ = x2*rep + (1 - x2)*rbp;
+
+term1p_ = r1p^(1 - GAMMA1)*((1 - NU*(1 - MU))*u1p^(1 - GAMMA1)...
+ + NU*(1 - MU)*u2p^(1 - GAMMA1))*invf1^(1 - GAMMA1);
+
+term2p_ = r2p^(1 - GAMMA2)*((1 - NU*MU)*u2p^(1 - GAMMA2)...
+ +NU*MU*u1p^(1 - GAMMA2))*invf2^(1 - GAMMA2);
+
+eq2 = -1 + term1p; % define f1 = (E(r1p*u1p)^(1-GAMMA1))^(1/(1-GAMMA1))
+
+eq3 = -1 + term2p; % define f2 similarly
+
+logu1p_ = RHO/(1 + RHO)*logc1p + 1/(1 + RHO)*log(1 - c1p) + 1/(1 + RHO)*logf1p;
+
+logu2p_ = RHO/(1 + RHO)*logc2p + 1/(1 + RHO)*log(1 - c2p) + 1/(1 + RHO)*logf2p;
+
+eq4 = (rep - rbp)*term1p*invr1p;
+
+eq5 = (rep - rbp)*term2p*invr2p;
+
+%% Function f (Ef = 0 imposes model conditions)
+
+f_fun = [eq1;eq2;eq3;eq4;eq5];
+
+%% law of motion of state variables
+
+Phi_fun = [k1 - NU*(k1 - MU); % law of motion of state1p
+ (1 - NU)*tilb1*(1 - deltap)/(hatyp*q)]; % law of motion of state2p
+
+%% collect auxiliary variables and functions
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns;tempfun];
+ auxvars=[auxvars;tempvar];
+ end
+end
+
+%% Approximation order (<=4)
+
+order = 4;
+
+%% Preprocess model and save
+
+model = prepare_tp(f_fun,Phi_fun,controlp,control,statep,state,shocks,symparams,order,auxfuns,auxvars);
+
+save('model')
+
diff --git a/105/replication_package/Variable_Disaster_Size/make_Table_7.m b/105/replication_package/Variable_Disaster_Size/make_Table_7.m
new file mode 100644
index 0000000000000000000000000000000000000000..8dd2c43038bb03b365c36016686f87dfe4db1c91
--- /dev/null
+++ b/105/replication_package/Variable_Disaster_Size/make_Table_7.m
@@ -0,0 +1,200 @@
+% Variable disaster size, long-term bonds, default probability
+
+clear,clc
+
+load('model')
+addpath('files')
+
+Parameters;
+
+% make the vector of parameters
+params = eval(symparams);
+
+% distribution of hatyp and deltap
+nodes = [exp([G,kron(G-B(:)',ones(1,2))]);
+ 0,kron(ones(1,numel(B)),[0,delta_size])];% realizations
+
+weights = [1-P,P*kron(probB(:)',[1-delta_prob,delta_prob])]; % corresponding probabilities
+
+rng('default')
+
+T = 1e5;
+
+N_disasters = ceil(T*P);
+ptr = 1 + round(cumsum([0;probB(:)])*N_disasters);
+disaster_state = zeros(1,N_disasters);
+for i = 1:numel(probB)
+ disaster_state(ptr(i):ptr(i+1)-1) = i;
+end
+randorder = rand(1,N_disasters);
+[~,I] = sort(randorder);
+disaster_state = disaster_state(I);
+
+% disaster shock (normal = 1, disaster>1)
+
+disaster = zeros(1,T+1);
+disaster(randperm(T,N_disasters)) = 1;
+
+default = double(rand(1,T+1)testF && solve==1
+ t
+ [coeffs] = tpsolve(coeffs,xt,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS); % solve
+
+ % evaluate the new solution
+ [R,g,nPhi] = residual(coeffs,xt,params,c0,nodes,weights);
+ end
+
+ newxt = nPhi(:,disaster(t+1)); % new state
+
+ if t>=10 % after 10 periods start checking for convergence
+ if max(abs(newxt-xt))<1e-7
+ stop = 1;
+ state0 = xt;
+ coeffs0 = coeffs;
+ end
+ end
+ xt = newxt;
+end
+
diff --git a/105/replication_package/Variable_Disaster_Size/summarize_results.m b/105/replication_package/Variable_Disaster_Size/summarize_results.m
new file mode 100644
index 0000000000000000000000000000000000000000..a1f296f3b25e1ce0a965895568c0c05b92b2c022
--- /dev/null
+++ b/105/replication_package/Variable_Disaster_Size/summarize_results.m
@@ -0,0 +1,55 @@
+
+normal = logical(disaster==1); % normal periods
+d = logical(disaster>1); % disaster periods
+
+state1 = x_results(1,1:T);
+state2 = x_results(2,1:T);
+
+x1 = y_results(3,1:T);
+logq = y_results(5,1:T);
+
+c1 = RHO/(1+RHO);
+tilp = 1/RHO;
+tilp = repmat(tilp,1,T);
+q = exp(logq);
+
+tila1 = (1 + tilp).*state1 + state2.*(1 + TAU*q);
+
+k1 = x1.*(1 - c1).*tila1./tilp;
+tilb1 = (1 - x1).*(1 - c1).*tila1;
+
+
+W1_share = k1 - NU*(k1 - MU) + (1 - NU)*tilb1./tilp; % wealth share after type changes
+equity = k1 - NU*(k1 - MU);
+
+debt_to_assets = -(1 - NU)*tilb1./tilp; % debt ratio (after type changes)
+debt_to_GDP = -(1 - NU)*tilb1*period_length;
+
+haty = nodes(1,double(disaster(1:T)));
+delta = nodes(2,double(disaster(1:T)));
+
+% compute means by iterated expectations
+
+roe = ((1 + tilp(2:T))./tilp(1:T-1).*haty(2:T)); % this is actual return from t to t+1.
+mean_roe = 1/period_length*log((1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)))); % mean return
+
+period_mean_roe = (1-P)*mean(roe(normal(2:T)))+P*mean(roe(d(2:T)));
+period_var_roe = (1-P)*mean((roe(normal(2:T)) - period_mean_roe).^2)+P*mean((roe(d(2:T)) - period_mean_roe).^2);
+vol_roe = sqrt(period_var_roe/period_length);
+
+rb = log((1 + TAU*q(2:T))./q(1:T-1)).*(1 - delta(2:T))/period_length; % this is log return on bonds
+mean_rb = (1-P)*mean(rb(normal(1:T-1)))+P*mean(rb(d(1:T-1)));
+
+Rb = (1 + TAU*q(3:T))./q(2:T-1).*(1 - delta(3:T));
+period_mean_rb = (1-P)*mean(Rb(normal(2:T-1)))+P*mean(Rb(d(2:T-1)));
+period_var_rb = (1-P)*mean((Rb(normal(2:T-1)) - period_mean_rb).^2)+P*mean((Rb(d(2:T-1)) - period_mean_rb).^2);
+vol_rb = sqrt(period_var_rb/period_length);
+
+mean_equity = (1-P)*mean(equity(normal(1:T))) + P*mean(equity(d(1:T)));
+mean_debt_to_assets = (1-P)*mean(debt_to_assets(normal(1:T))) + P*mean(debt_to_assets(d(1:T)));
+mean_debt_to_GDP = (1-P)*mean(debt_to_GDP(normal(1:T))) + P*mean(debt_to_GDP(d(1:T)));
+mean_W1_share = (1-P)*mean(W1_share(normal(1:T))) + P*mean(W1_share(d(1:T)));
+
+mean_equity_excluding_labor = mean_equity/ALPHA - MU*(1 - ALPHA)/ALPHA;
+mean_debt_to_assets_excluding_labor = mean_debt_to_assets/ALPHA;
+mean_W1_share_excluding_labor = mean_equity_excluding_labor - mean_debt_to_assets_excluding_labor;
\ No newline at end of file
diff --git a/105/replication_package/examples/rbc/prepare_model.m b/105/replication_package/examples/rbc/prepare_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..4528eff1b0ca8cf36151739d330c21d922c7ba81
--- /dev/null
+++ b/105/replication_package/examples/rbc/prepare_model.m
@@ -0,0 +1,69 @@
+%------------------------------------------------------------------
+% This script shows how to solve the RBC model by Taylor projection
+%------------------------------------------------------------------
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms k kp c cp z zp epsp real
+syms BETA GAMMA ALPHA RHO DELTA SIGMA real
+
+%-------------------------------------------------
+% Function f (Euler condition) in a unit-free form
+%-------------------------------------------------
+
+f_fun=BETA*(c/cp)^GAMMA*(ALPHA*exp(zp)*kp^(ALPHA-1)+1-DELTA)-1;
+
+%-------------------------------------------------------
+% Function Phi (law of motion of capital and technology)
+%-------------------------------------------------------
+
+Phi_fun=[exp(z)*k^ALPHA+(1-DELTA)*k-c;
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+
+x=[k,z]; % current period
+xp=[kp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+
+y=[c]; % current period
+yp=[cp]; % future period
+
+%-----------------
+% Vector of shocks
+%-----------------
+
+shocks=[epsp];
+
+%---------------------
+% Vector of parameters
+%---------------------
+
+symparams=[BETA,GAMMA,ALPHA,RHO,DELTA,SIGMA];
+
+%--------------------
+% Approximation order
+%--------------------
+
+order=4; % fourth order is the maximum possible
+
+%----------------
+% Call prepare_tp
+%----------------
+
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,symparams,order);
+
+%-----------
+% Save model
+%-----------
+
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc/prepare_model_auxiliary_functions.m b/105/replication_package/examples/rbc/prepare_model_auxiliary_functions.m
new file mode 100644
index 0000000000000000000000000000000000000000..4b595a5f24c2b66b6bcf319edaaa876f16956d0c
--- /dev/null
+++ b/105/replication_package/examples/rbc/prepare_model_auxiliary_functions.m
@@ -0,0 +1,127 @@
+%----------------------------------------------
+% RBC model with auxiliary functions
+%----------------------------------------------
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms k kp c cp z zp epsp real
+syms BETA GAMMA ALPHA RHO DELTA SIGMA real
+
+%-------------------------------
+% Define the auxiliary functions
+%-------------------------------
+
+% Logs of consumption and capital.
+syms logc logcp logk logkp real
+logc_=log(c);
+logcp_=log(cp);
+logk_=log(k);
+logkp_=log(kp);
+
+% Log and level of future mpk.
+syms mpkp logmpkp real
+logmpkp_=log(ALPHA)+zp+(ALPHA-1)*logkp;
+mpkp_=exp(logmpkp);
+
+% Log and level of stochastic discount factor.
+syms mp logmp real
+logmp_=log(BETA)+GAMMA*(logc-logcp);
+mp_=exp(logmp);
+
+% Log and level of output.
+syms logoutput output real
+logoutput_=z+ALPHA*logk;
+output_=exp(logoutput);
+
+%-----------------------------
+% Function f (Euler condition)
+%-----------------------------
+f_fun=mp*(mpkp+1-DELTA)-1;
+
+%-------------------------------------------------------
+% Function Phi (law of motion of capital and technology)
+%-------------------------------------------------------
+
+Phi_fun=[output+(1-DELTA)*k-c;
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+x=[k,z]; % current period
+xp=[kp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+y=[c]; % current period
+yp=[cp]; % future period
+
+%-----------------
+% Vector of shocks
+%-----------------
+shocks=[epsp];
+
+%---------------------
+% Vector of parameters
+%---------------------
+symparams=[BETA,GAMMA,ALPHA,RHO,DELTA,SIGMA];
+
+%-----------------------------------------------------------
+% Vectors of auxiliary functions and corresponding variables
+%-----------------------------------------------------------
+
+% you can do it manually:
+
+% auxfuns=[logc_;logcp_;logk_;logkp_;logmp_;logmpkp_;logoutput_;mp_;mpkp_;output_];
+% auxvars=[logc;logcp;logk;logkp;logmp;logmpkp;logoutput;mp;mpkp;output];
+
+
+% or automatically by the following code (the names of the
+% auxiliary functions must be the same as the auxiliary variables with an
+% underscore suffix):
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns(:);tempfun(:)];
+ auxvars=[auxvars(:);tempvar(:)];
+ end
+end
+
+% Note that f is a function of the model variables and the auxiliary
+% variables. To get f as a function of the model variables only, use the
+% function subsf:
+
+f_noaux = subsf( f_fun,auxvars,auxfuns );
+
+% Compare f with f_noaux
+
+f_fun,f_noaux
+
+% Display the auxiliary equations:
+
+[auxvars,auxfuns]
+
+%--------------------
+% Approximation order
+%--------------------
+order=4; % fourth order is the maximum possible
+
+%----------------
+% Call prepare_tp
+%----------------
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,symparams,order,auxfuns,auxvars);
+
+%-----------
+% Save model
+%-----------
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc/solve_continuation.m b/105/replication_package/examples/rbc/solve_continuation.m
new file mode 100644
index 0000000000000000000000000000000000000000..f4c7203e7703a38122e61f854627061430252224
--- /dev/null
+++ b/105/replication_package/examples/rbc/solve_continuation.m
@@ -0,0 +1,102 @@
+%--------------------------------------------
+% Solve the RBC model by continuation method
+%--------------------------------------------
+
+clear,clc
+
+%---------------------------------------------------------
+% Add folder 'files' to the search path and load the model
+%---------------------------------------------------------
+addpath('files');
+load('model')
+
+%----------------------------------------------------------------------------
+% Provide nodes and weights for the quadrature that approximates expectations
+%----------------------------------------------------------------------------
+n_e=1; % number of shocks.
+[n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e)); % this quadrature function was written by Judd, Maliar, Maliar and Valero (2014).
+nodes=nodes'; % transpose to n_e-by-n_nodes
+
+%----------------------------------------------------
+% Choose parameter values with a closed-form solution
+%----------------------------------------------------
+BETA=.96; GAMMA=1; ALPHA=.3; RHO=.8; DELTA=1; SIGMA=.02;
+params=eval(symparams);
+
+%-----------------------------------------------------------------------
+% The closed-form solution for the case GAMMA=1, DELTA=1 for consumption
+%-----------------------------------------------------------------------
+
+g=(1-ALPHA*BETA)*exp(z)*k^ALPHA;
+
+%---------------------------------------------------------
+% Use the closed-form solution to produce an initial guess
+%---------------------------------------------------------
+
+% differentiate the closed-form solution up to fourth order
+gx=jacobian(g,x);
+gxx=jacobian(gx(:),x);
+gxxx=jacobian(gxx(:),x);
+gxxxx=jacobian(gxxx(:),x);
+
+% choose some arbitrary state - I use the steady state of the model of
+% interest (with DELTA=.1)
+
+k0=((1/BETA-1+.1)/ALPHA)^(1/(ALPHA-1));
+z0=0;
+
+x0=[k0;z0];
+
+% compute g(x) and its derivatives at x0
+
+g0=double(subs(g,x(:),x0));
+gx0=double(subs(gx,x(:),x0));
+gxx0=double(subs(gxx,x(:),x0));
+gxxx0=double(subs(gxxx,x(:),x0));
+gxxxx0=double(subs(gxxxx,x(:),x0));
+
+% transform the derivatives into a vector of coefficients
+
+[ initial_guess ] = derivs2coeffs(model,g0,gx0,gxx0,gxxx0,gxxxx0);
+
+% this is for order=4. for lower orders include only the relevant
+% derivatives, e.g. derivs2coeffs(model,g0,gx0,gxx0) is for second order.
+
+% define the center of the initial guess (this is the point at which we computed
+% the derivatives)
+
+c0=x0;
+
+% now we have the initial guess, and we can proceed to solve the model by
+% continuation
+
+%-------------------------------------------------------------------------------
+% solve by Taylor projection and change the parameters gradually to the
+% required level
+%-------------------------------------------------------------------------------
+tolX=1e-6;
+tolF=1e-6;
+maxiter=10;
+
+[coeffs,model]=tpsolve(initial_guess,x0,model,params,c0,nodes,weights,tolX,tolF,maxiter);
+
+% Now change the parameters GAMMA and DELTA gradually to their required levels:
+
+GAMMA_original=GAMMA;
+GAMMA_target=2;
+
+DELTA_original=DELTA;
+DELTA_target=.1;
+
+for h=0:.1:1 % this is the homotopy parameter
+ GAMMA=(1-h)*GAMMA_original+h*GAMMA_target;
+ DELTA=(1-h)*DELTA_original+h*DELTA_target;
+
+ disp(['GAMMA=' num2str(GAMMA) ' DELTA=' num2str(DELTA)])
+
+ params(2)=GAMMA;
+ params(5)=DELTA;
+ [coeffs,model]=tpsolve(coeffs,x0,model,params,c0,nodes,weights,tolX,tolF,maxiter);
+
+end
+
diff --git a/105/replication_package/examples/rbc/solve_model.m b/105/replication_package/examples/rbc/solve_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..f0e4139ed386a775b98a908d71ac61b6b79a88b8
--- /dev/null
+++ b/105/replication_package/examples/rbc/solve_model.m
@@ -0,0 +1,160 @@
+clear,clc
+
+%---------------------------------------------------------
+% Add folder 'files' to the search path and load the model
+%---------------------------------------------------------
+addpath('files');
+load('model')
+
+%----------------------------------------------------------------------------
+% Provide nodes and weights for the quadrature that approximates expectations
+%----------------------------------------------------------------------------
+n_e=1; % number of shocks.
+[n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e)); % this quadrature function was written by Judd, Maliar, Maliar and Valero (2014).
+nodes=nodes'; % transpose to n_e-by-n_nodes
+
+%----------------------------------
+% Make a vector of parameter values
+%----------------------------------
+BETA=.96; GAMMA=2; ALPHA=.3; RHO=.8; DELTA=.1; SIGMA=.02;
+params=eval(symparams);
+
+%----------------------------------------------------------------------
+% Prepare an initial guess - in this case I use a perturbation solution
+%----------------------------------------------------------------------
+
+% Steady state values
+
+kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
+zss=0;
+css=kss^ALPHA-DELTA*kss;
+
+nxss=[kss;zss];
+nyss=css;
+
+% Cross moments of the shocks
+
+M=get_moments(nodes,weights,model.order(2));
+
+% Compute the perturbation solution (keep the 4 outputs):
+
+[derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss);
+
+% Explanation of outputs:
+% derivs=structure with the perturbation solution as explained in Levintal
+% (2017): "Fifth-Order Perturbation Solution to DSGE Models".
+% stoch_pert=the perturbation solution in the form of unique polynomial coefficients.
+% nonstoch_pert=same as stoch_pert but without correction for the model volatility (i.e. this is a perturbation solution of a deterministic version of the model)
+
+%-------------------------------------
+% Solve the model by Taylor projection
+%-------------------------------------
+
+x0=nxss; % the approximation point (here we use the steady state, but it could be any arbitrary state)
+c0=nxss; % the center of the initial guess
+
+% tolerance parameters for the Newton solver
+tolX=1e-6;
+tolF=1e-6;
+maxiter=10;
+
+% model.jacobian='exact'; % this is the default
+% model.jacobian='approximate'; % for large models try the approximate jacobian.
+
+initial_guess=stoch_pert;
+[coeffs,model]=tpsolve(initial_guess,x0,model,params,c0,nodes,weights,tolX,tolF,maxiter);
+
+%------------------------------------------------------------------
+% Compute the residual function and the model variables at point x0
+%------------------------------------------------------------------
+
+[R_fun0,g_fun0,Phi_fun0,auxvars0]=residual(coeffs,x0,params,c0,nodes,weights);
+
+% R_fun0 is the residual function at x0.
+% g_fun0 is the control variables at x0, namely, g(x0).
+% Phi_fun0 is the function Phi at x0 and each future node, namely, Phi(x0,g(x0),epsp), for each node of the quadrature.
+% auxvars0 is the auxiliary functions at x0 and each future node.
+
+% compute the function g(x) at x0
+y0=evalg(x0,coeffs,c0);
+
+% compute the function Phi(x,y,epsp) at x0, y0 and epsp0
+epsp0=.02;
+xp0=evalPhi(x0,y0,epsp0,params);
+
+%---------------------------------
+% simulate the model for T periods
+%---------------------------------
+T=100;
+shocks=randn(1,T+1); % draw shocks
+
+% preallocate
+x_simul=zeros(model.n_x,T+1);
+y_simul=zeros(model.n_y,T);
+R_simul=zeros(model.n_y,T);
+
+x_simul(:,1)=x0;
+
+% option=1; % compute only simulated variables
+option=2; % compute model residuals
+
+for t=1:T
+ xt=x_simul(:,t);
+ epsp=shocks(t+1);
+
+ % Option 1 - compute only the simulated variables
+ if option==1
+ yt=evalg(xt,coeffs,c0);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,params);
+ else
+ % Option 2 - compute also model residuals
+ [Rt,yt]=residual(coeffs,xt,params,c0,nodes,weights);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,params);
+ R_simul(:,t)=Rt;
+ end
+end
+
+%-------------------------------------------
+% Solve the model again at a different state
+%-------------------------------------------
+% This is useful when the long run domain of the model is far from the
+% initial state, so we need to approximate the solution at the long run state
+% (e.g. the risky steady state or the mean of the ergodic distribution)
+% rather than the steady state.
+
+x1=x0*1.1; % take some arbitrary state
+[coeffs1,model]=tpsolve(coeffs,x1,model,params,c0,nodes,weights,tolX,tolF,maxiter); % solve at x1
+
+%-----------------------
+% Use a different solver
+%-----------------------
+
+% The function tpsolve uses the Newton method for up to maxiter iterations. If it fails, it
+% switches automatically to fsolve for another maxiter iterations. You can
+% control the parameters of the second solver by optimoptions. The
+% supported solvers are fsolve and lsqnonlin.
+
+% For example, do one Newton iteration and switch to lsqnonlin:
+
+x2=x1*1.1;
+maxiter=1; % one Newton iteration
+OPTIONS = optimoptions('lsqnonlin','TolX',tolX,'TolF',tolF,'MaxIter',10,'Display','iter-detailed'); % 10 more iterations by lsqnonlin
+
+[coeffs2,model]=tpsolve(coeffs,x2,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+
+
+% or switch to fsolve:
+
+maxiter=1; % one Newton iteration
+OPTIONS = optimoptions('fsolve','TolX',tolX,'TolF',tolF,'MaxIter',10,'Display','iter-detailed'); % 10 more iterations by fsolve
+
+[coeffs3,model]=tpsolve(coeffs,x2,model,params,c0,nodes,weights,tolX,tolF,maxiter,OPTIONS);
+
+
+
+
+
diff --git a/105/replication_package/examples/rbc_EZ/prepare_model.m b/105/replication_package/examples/rbc_EZ/prepare_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..304c5eafddf3d65bce7e016499ab231474d99eef
--- /dev/null
+++ b/105/replication_package/examples/rbc_EZ/prepare_model.m
@@ -0,0 +1,88 @@
+%------------------------------------------------------------------
+% RBC model with Epstein-Zin preferences
+%------------------------------------------------------------------
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms logk logkp logc logcp z zp logxi logxip logq logqp epsp real
+syms BETA GAMMA PSI ALPHA RHO DELTA SIGMA real
+
+
+%----------------------
+% Substituted variables
+%----------------------
+
+c=exp(logc); cp=exp(logcp);
+
+k=exp(logk); kp=exp(logkp);
+
+xi=exp(logxi); xip=exp(logxip);
+
+q=exp(logq);
+
+Vpowerp=(1-BETA)*cp^(1-PSI)+BETA*xip^(1-PSI); % this is Vp^(1-PSI)
+
+logVp=1/(1-PSI)*log( Vpowerp );
+
+Vp=exp(logVp);
+
+logmp=log(BETA)+PSI*(logc-logcp)+(PSI-GAMMA)*(logVp-logxi);
+
+mp=exp(logmp);
+
+%-----------------------
+% Equilibrium conditions
+%-----------------------
+f1=mp*(ALPHA*exp(zp)*kp^(ALPHA-1)+1-DELTA)-1;
+f2=xi^(GAMMA-1)*Vp^(1-GAMMA)-1;
+f3=mp/q-1;
+
+f_fun=[f1;f2;f3];
+
+%-------------------------------------------------------
+% Function Phi (law of motion of log capital and technology)
+%-------------------------------------------------------
+
+Phi_fun=[log(exp(z)*k^ALPHA+(1-DELTA)*k-c);
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+x=[logk,z]; % current period
+xp=[logkp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+y=[logc,logxi,logq]; % current period
+yp=[logcp,logxip,logqp]; % future period
+
+%-----------------
+% Vector of shocks
+%-----------------
+shocks=[epsp];
+
+%---------------------
+% Vector of parameters
+%---------------------
+symparams=[BETA,GAMMA,PSI,ALPHA,RHO,DELTA,SIGMA];
+
+%--------------------
+% Approximation order
+%--------------------
+order=3; % fourth order is the maximum possible
+
+%----------------
+% Call prepare_tp
+%----------------
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,symparams,order);
+
+%-----------
+% Save model
+%-----------
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc_EZ/prepare_model_auxiliary_functions.m b/105/replication_package/examples/rbc_EZ/prepare_model_auxiliary_functions.m
new file mode 100644
index 0000000000000000000000000000000000000000..59f127fed7187de7e8614246d682b7815fe28549
--- /dev/null
+++ b/105/replication_package/examples/rbc_EZ/prepare_model_auxiliary_functions.m
@@ -0,0 +1,106 @@
+%------------------------------------------------------------------
+% RBC model with Epstein-Zin preferences
+%------------------------------------------------------------------
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms logk logkp logc logcp z zp logxi logxip logq logqp epsp real
+syms BETA GAMMA PSI ALPHA RHO DELTA SIGMA real
+
+
+%-----------------------------------------------------
+% Substituted variables defined by auxiliary functions
+%-----------------------------------------------------
+
+syms c cp k kp xi xip q Vpowerp logVp Vp logmp mp real
+
+c_=exp(logc); cp_=exp(logcp);
+
+k_=exp(logk); kp_=exp(logkp);
+
+xi_=exp(logxi); xip_=exp(logxip);
+
+q_=exp(logq);
+
+Vpowerp_=(1-BETA)*cp^(1-PSI)+BETA*xip^(1-PSI); % this is Vp^(1-PSI)
+
+logVp_=1/(1-PSI)*log( Vpowerp );
+
+Vp_=exp(logVp);
+
+logmp_=log(BETA)+PSI*(logc-logcp)+(PSI-GAMMA)*(logVp-logxi);
+
+mp_=exp(logmp);
+
+%-----------------------
+% Equilibrium conditions
+%-----------------------
+f1=mp*(ALPHA*exp(zp)*kp^(ALPHA-1)+1-DELTA)-1;
+f2=xi^(GAMMA-1)*Vp^(1-GAMMA)-1;
+f3=mp/q-1;
+
+f_fun=[f1;f2;f3];
+
+%-------------------------------------------------------
+% Function Phi (law of motion of log capital and technology)
+%-------------------------------------------------------
+
+Phi_fun=[log(exp(z)*k^ALPHA+(1-DELTA)*k-c);
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+x=[logk,z]; % current period
+xp=[logkp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+y=[logc,logxi,logq]; % current period
+yp=[logcp,logxip,logqp]; % future period
+
+%-----------------
+% Vector of shocks
+%-----------------
+shocks=[epsp];
+
+%---------------------
+% Vector of parameters
+%---------------------
+symparams=[BETA,GAMMA,PSI,ALPHA,RHO,DELTA,SIGMA];
+
+%------------------------------------------
+% Collect auxiliary functions and variables
+%------------------------------------------
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns(:);tempfun(:)];
+ auxvars=[auxvars(:);tempvar(:)];
+ end
+end
+
+%--------------------
+% Approximation order
+%--------------------
+order=4; % fourth order is the maximum possible
+
+%----------------
+% Call prepare_tp
+%----------------
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,symparams,order,auxfuns,auxvars);
+
+%-----------
+% Save model
+%-----------
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc_EZ/solve_model.m b/105/replication_package/examples/rbc_EZ/solve_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..7fb77ea16892b0353e82ec2e91ce281984046943
--- /dev/null
+++ b/105/replication_package/examples/rbc_EZ/solve_model.m
@@ -0,0 +1,104 @@
+clear,clc
+
+%---------------------------------------------------------
+% Add folder 'files' to the search path and load the model
+%---------------------------------------------------------
+addpath('files');
+load('model')
+
+%----------------------------------------------------------------------------
+% Provide nodes and weights for the quadrature that approximates expectations
+%----------------------------------------------------------------------------
+n_e=length(shocks); % number of shocks.
+[n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e)); % this quadrature function was written by Judd, Maliar, Maliar and Valero (2014).
+nodes=nodes'; % transpose to n_e-by-n_nodes
+
+%----------------------------------
+% Make a vector of parameter values
+%----------------------------------
+BETA=.96; GAMMA=2; PSI=1.5; ALPHA=.3; RHO=.8; DELTA=.1; SIGMA=.08;
+params=eval(symparams);
+
+%----------------------------------------------------------------------
+% Prepare an initial guess - in this case I use a perturbation solution
+%----------------------------------------------------------------------
+
+% Steady state values
+
+kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
+zss=0;
+css=kss^ALPHA-DELTA*kss;
+vss=css;
+xiss=vss;
+qss=BETA;
+
+nxss=[log(kss);zss];
+nyss=[log(css);log(xiss);log(qss)];
+
+% Cross moments of the shocks
+
+M=get_moments(nodes,weights,model.order(2));
+
+% Compute the perturbation solution (keep the 4 outputs):
+
+[derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss);
+
+% Explanation of outputs:
+% derivs=structure with the perturbation solution as explained in Levintal
+% (2017): "Fifth-Order Perturbation Solution to DSGE Models".
+% stoch_pert=the perturbation solution in the form of unique polynomial coefficients.
+% nonstoch_pert=same as stoch_pert but without correction for the model volatility (i.e. this is a perturbation solution of a deterministic version of the model)
+
+%-------------------------------------
+% Solve the model by Taylor projection
+%-------------------------------------
+
+x0=nxss; % the approximation point (here we use the steady state, but it could be any arbitrary state)
+c0=nxss; % the center of the initial guess
+
+% tolerance parameters for the Newton solver
+tolX=1e-6;
+tolF=1e-6;
+maxiter=10;
+
+% model.jacobian='exact'; % this is the default
+% model.jacobian='approximate'; % for large models try the approximate jacobian.
+
+initial_guess=stoch_pert;
+[coeffs,model]=tpsolve(initial_guess,x0,model,params,c0,nodes,weights,tolX,tolF,maxiter);
+
+%------------------------------------------------------------------
+% Compute the residual function and the model variables at point x0
+%------------------------------------------------------------------
+
+[R_fun0,g_fun0,Phi_fun0,auxvars0]=residual(coeffs,x0,params,c0,nodes,weights);
+
+%------------------------
+% Check the interest rate
+%------------------------
+
+logq=g_fun0(3);
+Rf=exp(-logq)-1
+
+%----------------------------------------------------------------------------
+% Increase risk aversion (gradually) and see how the interest rate falls
+%----------------------------------------------------------------------------
+
+GAMMAvec=2:4:82;
+
+Rfvec=zeros(size(GAMMAvec));
+
+i=0;
+for GAMMA=GAMMAvec
+ i=i+1;
+ params(2)=GAMMA;
+ [coeffs,model]=tpsolve(coeffs,x0,model,params,c0,nodes,weights,tolX,tolF,maxiter);
+ [R_fun0,g_fun0,Phi_fun0,auxvars0]=residual(coeffs,x0,params,c0,nodes,weights);
+ logq=g_fun0(3);
+ Rfvec(i)=exp(-logq)-1;
+end
+
+
+plot(GAMMAvec,Rfvec)
+xlabel('Risk aversion (GAMMA)')
+ylabel('Risk-free interest rate (Rf)')
\ No newline at end of file
diff --git a/105/replication_package/examples/rbc_MS_parameters/prepare_model.m b/105/replication_package/examples/rbc_MS_parameters/prepare_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..88e3c30acb93c0961d4bb1d1d100697c91d2d739
--- /dev/null
+++ b/105/replication_package/examples/rbc_MS_parameters/prepare_model.m
@@ -0,0 +1,75 @@
+%-------------------------------------------
+% RBC model with Markov-switching parameters
+%-------------------------------------------
+% The parameters that depend on the regime are the discount
+% factor and the depreciation rate.
+% There are 2 regimes.
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms k kp c cp z zp epsp real
+syms BETA BETAp GAMMA ALPHA RHO DELTA DELTAp SIGMA real
+
+%-----------------------------
+% Function f (Euler condition)
+%-----------------------------
+f_fun=BETA*(c/cp)^GAMMA*(ALPHA*exp(zp)*kp^(ALPHA-1)+1-DELTAp)-1; % note the use of future depreciation rate DELTAp
+
+%-------------------------------------------------------
+% Function Phi (law of motion of capital and technology)
+%-------------------------------------------------------
+
+Phi_fun=[exp(z)*k^ALPHA+(1-DELTA)*k-c; % here we use the current depreciation rate DELTA
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+x=[k,z]; % current period
+xp=[kp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+y=[c]; % current period
+yp=[cp]; % future period
+
+%-----------------
+% Vector of shocks
+%-----------------
+shocks=[epsp];
+
+%---------------------------
+% Vector of fixed parameters
+%---------------------------
+symparams=[GAMMA,ALPHA,RHO,SIGMA];
+
+%--------------------------------------
+% Vector of Markov-switching parameters
+%--------------------------------------
+chi=[BETA,DELTA]; % current period
+chip=[BETAp,DELTAp]; % next period
+
+%--------------------
+% Approximation order
+%--------------------
+order=4; % fourth order is the maximum possible
+
+%------------------
+% number of regimes
+%------------------
+n_regimes=2;
+
+%----------------
+% Call prepare_tp
+%----------------
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,chip,chi,symparams,order,n_regimes);
+
+% % if you use auxiliary functions and variables, use the following syntax:
+% model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,chip,chi,symparams,order,n_regimes,auxfuns,auxvars);
+
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc_MS_parameters/solve_model.m b/105/replication_package/examples/rbc_MS_parameters/solve_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..c0fdd1eb899dcbea2dec15d7e86efb0513885c19
--- /dev/null
+++ b/105/replication_package/examples/rbc_MS_parameters/solve_model.m
@@ -0,0 +1,191 @@
+clear,clc
+
+%---------------------------------------------------------
+% Add folder 'files' to the search path and load the model
+%---------------------------------------------------------
+addpath('files');
+load('model')
+
+%----------------------------------------------------------------------------
+% Provide nodes and weights for the quadrature that approximates expectations
+%----------------------------------------------------------------------------
+n_e=1; % number of shocks.
+[n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e)); % this quadrature function was written by Judd, Maliar, Maliar and Valero (2014).
+nodes=nodes'; % transpose to n_e-by-n_nodes
+
+%--------------------------------------------
+% parameter values (for the fixed parameters)
+%--------------------------------------------
+GAMMA=2; ALPHA=.3; RHO=.8; SIGMA=.02;
+params=eval(symparams);
+
+%--------------------------------------------------------------------
+% Start with a perturbation solution for the case of fixed parameters
+%--------------------------------------------------------------------
+BETA=.96; DELTA=.1;
+% Steady state values
+kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
+zss=0;
+css=kss^ALPHA-DELTA*kss;
+
+nxss=[kss;zss];
+nyss=css;
+
+pert_order=model.order(2);
+
+M=get_moments(nodes,weights,pert_order);
+
+% Get a perturbation solution for the case of fixed parameters. You need to
+% provide the fixed value of the ms parameters (the variable chi_fixed)
+
+chi_fixed=eval(chi);
+
+[derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss,chi_fixed);
+
+%---------------------------------------
+% Proceed to Markov-switching parameters
+%---------------------------------------
+
+% The values of the parameters in each regime (there are 2 regimes)
+msparams=[BETA-.02,BETA+.02;% BETA varies across regimes
+ DELTA-.05,DELTA+.05]; % DELTA varies across regimes
+
+transition=[.9,.1;
+ .8,.2];
+
+initial_guess=stoch_pert; % the initial guess has n_regimes columns (one for each regime).
+
+x0=nxss; % evaluate the system at the steady state
+c0=nxss; % the center of the initial guess is the steady state.
+
+tolX=1e-6;
+tolF=1e-6;
+maxiter=10;
+[coeffs,model]=tpsolve(initial_guess,x0,model,params,msparams,transition,c0,nodes,weights,tolX,tolF,maxiter);
+
+
+% compute the model residuals
+
+[R_funMS,g_funMS,Phi_funMS,aux_funMS]=residual(coeffs,x0,params,msparams,transition,c0,nodes,weights);
+
+% R_funMS is a n_y-by-n_regimes matrix of the model residuals.
+% g_funMS is a n_y-by-n_regimes matrix of the endogenous control variables for each current regime.
+% Phi_funMS is a n_x-by-n_nodes-by-n_regimes-by-n_regimes array of next period state variables for each future node and current and future regimes.
+% aux_funMS is a similar array of the auxiliary functions (for each future
+% node and current/future regimes)
+
+% To compute the model residuals only for a specific regime, add the
+% required regime as the last argument
+
+specific_regime=1;
+
+[R_specific,g_specific,Phi_specific,auxvars_specific]=residual(coeffs,x0,params,msparams,transition,c0,nodes,weights,specific_regime);
+
+% Compute the function g given the state x0 and the regime specific_regime
+g_fun=evalg(x0,specific_regime,coeffs,c0);
+
+% Compute the function Phi given the state x0, the control y0, the current
+% and future regimes and the future shock epsp
+y0=g_fun;
+current_regime=1;
+future_regime=2;
+epsp=0;
+Phi_fun=evalPhi(x0,y0,epsp,future_regime,current_regime,params,msparams);
+
+
+%---------------------------------
+% simulate the model for T periods
+%---------------------------------
+
+T=10000;
+shocks=randn(1,T+1);
+rshock=rand(1,T+1); % to determine the regime
+
+x_simul=zeros(model.n_x,T+1);
+regime_simul=zeros(1,T+1);
+y_simul=zeros(model.n_y,T);
+R_simul=zeros(model.n_y,T);
+
+coeffs=reshape(coeffs,[],model.n_regimes);
+
+x_simul(:,1)=x0;
+regime_simul(1)=1;
+
+% option=1; % compute only simulated variables
+option=2; % compute model residuals
+
+for t=1:T
+
+ xt=x_simul(:,t); % current state
+ regimet=regime_simul(t); % current regime
+
+ epsp=shocks(t+1); % future shock
+ % future regime
+ regimet_next=1+model.n_regimes-sum(double(logical((rshock(t+1)-cumsum(transition(regimet,:)))<0)));
+
+ % Option 1 - compute only the simulated variables
+ if option==1
+ yt=evalg(xt,regimet,coeffs,c0);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
+ regime_simul(t+1)=regimet_next;
+ else
+ % Option 2 - compute also model residuals
+ [Rt,yt]=residual(coeffs,xt,params,msparams,transition,c0,nodes,weights,regimet);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
+ regime_simul(t+1)=regimet_next;
+ R_simul(:,t)=Rt;
+ end
+end
+
+% Note that the simulated capital level is considerably different than the
+% initial approximation point that we used. To improve accuracy, we can solve the
+% model at the mean of the ergodic distribution.
+
+meank=mean(x_simul(1,:));
+
+ergodic_x0=[meank;0]; % solve at the mean of the ergodic distribution
+
+[coeffs,model]=tpsolve(coeffs,ergodic_x0,model,params,msparams,transition,c0,nodes,weights,tolX,tolF,maxiter);
+
+% simulate again and store residuals in R_simul2
+
+x_simul(:,1)=ergodic_x0;
+regime_simul(1)=1;
+R_simul2=R_simul;
+for t=1:T
+ xt=x_simul(:,t);
+ regimet=regime_simul(t);
+
+ epsp=shocks(t+1);
+ % future regime
+ regimet_next=1+model.n_regimes-sum(double(logical((rshock(t+1)-cumsum(transition(regimet,:)))<0)));
+
+ % Option 1 - compute only the simulated variables
+ if option==1
+ yt=evalg(xt,regimet,coeffs,c0);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
+ regime_simul(t+1)=regimet_next;
+ else
+ % Option 2 - compute also model residuals
+ [Rt,yt]=residual(coeffs,xt,params,msparams,transition,c0,nodes,weights,regimet);
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
+ regime_simul(t+1)=regimet_next;
+ R_simul2(:,t)=Rt;
+ end
+end
+
+% compare mean errors for the two simulations
+
+mean(abs(R_simul))
+
+mean(abs(R_simul2))
+
+% the second simulation is more accurate
\ No newline at end of file
diff --git a/105/replication_package/examples/rbc_disasters/prepare_model.m b/105/replication_package/examples/rbc_disasters/prepare_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..ba104b0cba365c4723a6d8e065f5010332851529
--- /dev/null
+++ b/105/replication_package/examples/rbc_disasters/prepare_model.m
@@ -0,0 +1,111 @@
+%----------------------------------------
+% RBC with Markov shocks (rare disasters)
+%----------------------------------------
+
+clear,clc
+
+%-----------------------------------------
+% Define symbolic variables and parameters
+%-----------------------------------------
+
+syms logc logcp logk logkp z zp epsp d dp real
+syms BETA GAMMA ALPHA RHO DELTA SIGMA PHI real
+
+%---------------------------
+% Define auxiliary functions
+%---------------------------
+
+syms k kp c cp loga a logap real
+c_=exp(logc);
+cp_=exp(logcp);
+k_=exp(logk);
+kp_=exp(logkp);
+
+loga_=z-PHI*d; % log technology in current period
+a_=exp(loga);
+
+logap_=zp-PHI*dp; % log technology in next period
+
+% Log and level of future mpk.
+syms mpkp logmpkp real
+logmpkp_=log(ALPHA)+logap+(ALPHA-1)*logkp;
+mpkp_=exp(logmpkp);
+
+% Log and level of stochastic discount factor.
+syms mp logmp real
+logmp_=log(BETA)+GAMMA*(logc-logcp);
+mp_=exp(logmp);
+
+%-----------------------------
+% Function f (Euler condition)
+%-----------------------------
+f_fun=mp*(mpkp+1-DELTA)-1;
+
+%----------------------------------------------------------
+% Function Phi (law of motion of log capital and technology)
+%----------------------------------------------------------
+
+Phi_fun=[log(a*k^ALPHA+(1-DELTA)*k-c);
+ RHO*z+SIGMA*epsp];
+
+%--------------------------
+% Vector of state variables
+%--------------------------
+x=[logk,z]; % current period
+xp=[logkp,zp]; % future period
+
+%----------------------------
+% Vector of control variables
+%----------------------------
+y=[logc]; % current period
+yp=[logcp]; % future period
+
+%---------------------
+% Vector of iid shocks
+%---------------------
+shocks=[epsp];
+
+%------------------------
+% Vector of Markov shocks
+%------------------------
+
+markov_shocks=d; % current period
+markov_shocksp=dp; % future period
+
+n_states=2; % number of Markov states
+
+%---------------------
+% Vector of parameters
+%---------------------
+symparams=[BETA,GAMMA,ALPHA,RHO,DELTA,SIGMA,PHI];
+
+%-----------------------------------------------------------
+% Vectors of auxiliary functions and corresponding variables
+%-----------------------------------------------------------
+
+allvars=who;
+auxfuns=[];
+auxvars=[];
+for i=1:length(allvars)
+ if strcmp(allvars{i}(end),'_')
+ eval(['tempfun=' allvars{i} ';'])
+ eval(['tempvar=' allvars{i}(1:end-1) ';'])
+ auxfuns=[auxfuns(:);tempfun(:)];
+ auxvars=[auxvars(:);tempvar(:)];
+ end
+end
+
+%--------------------
+% Approximation order
+%--------------------
+order=3; % fourth order is the maximum possible
+
+%----------------
+% Call prepare_tp
+%----------------
+model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,markov_shocksp,markov_shocks,symparams,order,n_states,auxfuns,auxvars);
+
+%-----------
+% Save model
+%-----------
+save('model') % you will need this later
diff --git a/105/replication_package/examples/rbc_disasters/solve_model.m b/105/replication_package/examples/rbc_disasters/solve_model.m
new file mode 100644
index 0000000000000000000000000000000000000000..4dc81507cbff2e03cfdc41a9d68e3972cc61f8c5
--- /dev/null
+++ b/105/replication_package/examples/rbc_disasters/solve_model.m
@@ -0,0 +1,127 @@
+clear,clc
+
+%---------------------------------------------------------
+% Add folder 'files' to the search path and load the model
+%---------------------------------------------------------
+addpath('files');
+load('model')
+
+%----------------------------------------------------------------------------
+% Provide nodes and weights for the quadrature that approximates expectations
+%----------------------------------------------------------------------------
+n_e=model.n_e; % number of shocks.
+[n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e)); % this quadrature function was written by Judd, Maliar, Maliar and Valero (2014).
+nodes=nodes'; % transpose to n_e-by-n_nodes
+
+%----------------------------------
+% Make a vector of parameter values
+%----------------------------------
+BETA=.96; GAMMA=2; ALPHA=.3; RHO=.8; DELTA=.1; SIGMA=.02; PHI=0.1;
+params=eval(symparams);
+
+%------------------
+% transition matrix
+%------------------
+
+transition=[.95,.05;
+ .5,.5];
+
+%--------------------------------------------------------------------------
+% Prepare an initial guess - perturbation solution of RBC without disasters
+%--------------------------------------------------------------------------
+
+fixed_markov_values=0; % start with a fixed value for the disaster shock (disaster shock is 0 in all states)
+
+% Steady state values
+
+kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
+zss=0;
+css=kss^ALPHA-DELTA*kss;
+
+nxss=[log(kss);zss];
+nyss=log(css);
+
+% Cross moments of the shocks
+
+M=get_moments(nodes,weights,model.order(2));
+
+% Compute the perturbation solution
+
+[derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss,fixed_markov_values);
+
+% the variables stoch_pert and nonstoch_pert have two columns, corresponding to the two Markov states.
+
+%-------------------------------------
+% Taylor projection with Markov shocks
+%-------------------------------------
+
+markov_values=[0,1]; % now the values of the Markov shock depend on the Markov state
+
+x0=nxss; % the approximation point
+c0=nxss; % the center of the initial guess
+
+% tolerance parameters for the Newton solver
+tolX=1e-6;
+tolF=1e-6;
+maxiter=10;
+
+% model.jacobian='exact'; % this is the default
+% model.jacobian='approximate'; % for large models try the approximate jacobian.
+
+initial_guess=stoch_pert;
+[coeffs,model]=tpsolve(initial_guess,x0,model,params,markov_values,transition,c0,nodes,weights,tolX,tolF,maxiter);
+
+%-------------------------------------------------------------------------------------
+% Compute the residual function and the model variables at point x0 for Markov state s
+%-------------------------------------------------------------------------------------
+
+s=1; % Markov state 1
+[R_fun1,g_fun1,Phi_fun1,auxvars1]=residual(coeffs,x0,params,markov_values,transition,c0,nodes,weights,s);
+c1=exp(g_fun1); % consumption in normal state
+inv1=exp(Phi_fun1(1,1))-exp(x0(1))*(1-DELTA);
+
+
+s=2; % Markov state 2
+[R_fun2,g_fun2,Phi_fun2,auxvars2]=residual(coeffs,x0,params,markov_values,transition,c0,nodes,weights,s);
+c2=exp(g_fun2); % consumption in normal state
+inv2=exp(Phi_fun2(1,1))-exp(x0(1))*(1-DELTA);
+
+c2/c1-1 % fall in consumption is smaller than fall in output
+inv2/inv1-1 % fall in investment is larger than fall in output
+
+
+%-------------------
+% Simulate the model
+%-------------------
+
+T=1000;
+shocks=randn(1,T+1); % draw shocks
+
+% simulate a Markov chain from the transition matrix
+ushock=rand(1,T+1); % draw shocks from a uniform distribution to determine the Markov state
+Markov_state=zeros(1,T+1);
+Markov_state(1)=1; % start at state 1
+for t=2:T+1
+ Markov_state(t)=1+(ushock(t)>transition(Markov_state(t-1),1)); % state in period t, given the state in t-1
+end
+
+% preallocate
+x_simul=zeros(model.n_x,T+1);
+y_simul=zeros(model.n_y,T);
+R_simul=zeros(model.n_y,T);
+
+x_simul(:,1)=x0;
+
+for t=1:T
+ xt=x_simul(:,t);
+ st=Markov_state(t);
+
+ [Rt,yt]=residual(coeffs,xt,params,markov_values,transition,c0,nodes,weights,st);
+
+ epsp=shocks(t+1); % future iid shock
+ stp=Markov_state(t+1); % future Markov shock
+
+ y_simul(:,t)=yt;
+ x_simul(:,t+1)=evalPhi(xt,yt,epsp,stp,st,params,markov_values);
+ R_simul(:,t)=Rt;
+end
diff --git a/105/replication_package/make_Table_4.do b/105/replication_package/make_Table_4.do
new file mode 100644
index 0000000000000000000000000000000000000000..b98af0ed730ee07dd4c3e52a70835a519001d743
--- /dev/null
+++ b/105/replication_package/make_Table_4.do
@@ -0,0 +1,87 @@
+******************************************************************************************
+* Replicate Table 4 of "Safe Assets" by Barro, Fernandez-Villaverde, Levintal and Mollerus
+******************************************************************************************
+
+clear all
+
+clear mata
+set mem 500m
+set maxvar 32767
+set more off
+cap log close
+
+clear
+use rscfp2019 // can be downloaded from https://www.federalreserve.gov/econres/files/scfp2019s.zip
+
+gen stockfund = stmutf
+gen stocks_indirect = equity - stocks - stockfund /* the variable equity is generated by SCF to measure all stock holdings, including indirect holdings of stocks. */
+gen realestate_net = houses - mrthel + oresre - resdbt +nnresre
+gen otherphysical = vehic + othnfin
+gen allequity = equity + bus
+
+* percentiles
+
+_pctile networth [aweight = wgt], p(50,75,90,95,99)
+
+local p50 = r(r1)
+local p75 = r(r2)
+local p90 = r(r3)
+local p95 = r(r4)
+local p99 = r(r5)
+
+gen pctile = 0
+
+replace pctile = 1 if networth<=`p50'
+replace pctile = 2 if networth>`p50' & networth<=`p75'
+replace pctile = 3 if networth>`p75' & networth<=`p90'
+replace pctile = 4 if networth>`p90' & networth<=`p95'
+replace pctile = 5 if networth>`p95' & networth<=`p99'
+replace pctile = 6 if networth>`p99'
+
+foreach var in "networth" "allequity" "stocks" "stockfund" "bus" "stocks_indirect" "realestate_net" "othnfin" "vehic" {
+ di "`var'"
+
+ gen sum_`var' = 0
+ gen share_`var' = 0
+ gen port_`var' = 0
+
+ foreach x in 1 2 3 4 5 6 {
+ sum `var' [aweight = wgt] if pctile==`x'
+ replace sum_`var' = r(sum) if _n==`x'
+ }
+
+ * total population
+ sum `var' [aweight = wgt]
+ replace sum_`var' = r(sum) if _n==7
+
+ * bottom 90
+ sum `var' [aweight = wgt] if pctile<=3
+ replace sum_`var' = r(sum) if _n==8
+
+ * p90-p95
+ sum `var' [aweight = wgt] if pctile==4
+ replace sum_`var' = r(sum) if _n==9
+
+ * top 5
+ sum `var' [aweight = wgt] if pctile>=5
+ replace sum_`var' = r(sum) if _n==10
+
+ * top 1
+ sum `var' [aweight = wgt] if pctile==6
+ replace sum_`var' = r(sum) if _n==11
+
+ * share in total population
+ replace share_`var' = sum_`var'/sum_`var'[7]
+
+ }
+
+keep share*
+keep if _n<=11
+
+quietly log using Tables_1_to_4.smcl, append
+
+* Table 4 (transposed)
+
+list share_networth share_allequity share_stocks share_stockfund share_bus share_stocks_indirect share_realestate_net share_othnfin share_vehic if _n>=8, clean noobs
+
+log close
diff --git a/105/replication_package/make_Tables_1_to_3_Figures_1_and_2.do b/105/replication_package/make_Tables_1_to_3_Figures_1_and_2.do
new file mode 100644
index 0000000000000000000000000000000000000000..21cac499024309273da1f7652826473cfb84ce1c
--- /dev/null
+++ b/105/replication_package/make_Tables_1_to_3_Figures_1_and_2.do
@@ -0,0 +1,217 @@
+*************************************************************************************************************
+* Replicate Tables 1-3 and Figures 1-2 of "Safe Assets" by Barro, Fernandez-Villaverde, Levintal and Mollerus
+*************************************************************************************************************
+
+clear
+
+graph drop _all
+set matsize 800
+clear mata
+set mem 500m
+set more off
+
+run Make_OECD_data
+
+use OECD_data // this file is generated by Make_OECD_data.do
+
+
+****
+gen fin_safe=fin_dep+fin_loan+fin_mmf+fin_secur
+gen cb_safe=cb_dep+cb_loan+cb_mmf+cb_secur
+gen gov_safe=gov_dep+gov_loan+gov_mmf+gov_secur
+
+gen gov_secur_safe=gov_secur/gov_safe
+gen gov_loan_safe=gov_loan/gov_safe
+gen gov_dep_safe=gov_dep/gov_safe
+gen gov_mmf_safe=gov_mmf/gov_safe
+
+gen new_total=totliab_Households+totliab_nonFinancials+totliab_Financials+totliab_Gov
+replace new_total=totliab_Total
+
+gen fin_share=fin_safe/new_total
+gen gov_share=gov_safe/new_total
+gen cb_share=cb_safe/new_total
+
+gen finexcb_share=fin_share-cb_share
+gen govcb_share=gov_share+cb_share
+
+gen dep_share=fin_dep/new_total
+
+gen share=fin_share+gov_share
+
+gen asset_gdp=new_total/GDP
+
+decode country, g(country_name)
+
+drop if country_name=="Luxembourg"
+drop if country_name=="Russia"
+drop if country_name=="New Zealand"
+drop if country_name=="Colombia"
+
+log using Tables_1_to_4, replace s
+
+*** Table 1
+
+
+list country_name share gov_share cb_share finexcb_share asset_gdp if year==2015, clean noobs
+
+* means
+
+sum share gov_share cb_share finexcb_share asset_gdp if year==2015
+
+quietly log off
+
+
+bysort year: egen worldassets=sum(totliab_TotalUSD)
+gen assetweight=totliab_TotalUSD/worldassets
+
+quietly log on
+
+*asset weighted means
+
+sum share gov_share cb_share finexcb_share asset_gdp if year==2015 [iweight = assetweight]
+
+quietly log off
+
+* subsample of countries with bond return data
+
+gen subsample = 0
+
+foreach x in "Belgium" "Canada" "Denmark" "Finland" "France" "Germany" "Italy" "Japan" "Netherlands" "Norway" /*
+*/ "Portugal" "Spain" "Sweden" "Switzerland" "United Kingdom" "United States" {
+ replace subsample = 1 if country_name=="`x'"
+ }
+
+quietly log on
+
+* subsample of 16 countries with bond return data
+
+sum share gov_share cb_share finexcb_share asset_gdp if year==2015 & subsample==1 [iweight = assetweight]
+
+quietly log off
+
+*** Table 2
+gen gov_bonds_safe=gov_secur/gov_safe
+gen gov_deposits_safe=(gov_dep+gov_loan)/gov_safe
+
+gen cb_bonds_safe=cb_secur/cb_safe
+gen cb_deposits_safe=(cb_dep+cb_loan)/cb_safe
+
+gen fin_bonds_safe=fin_secur/fin_safe
+gen fin_deposits_safe=(fin_dep+fin_loan)/fin_safe
+gen fin_mmf_safe = fin_mmf/fin_safe
+
+gen finexcb_safe = fin_safe - cb_safe
+
+gen finexcb_bonds_safe = (fin_secur-cb_secur)/finexcb_safe
+gen finexcb_deposits_safe = (fin_loan+fin_dep-cb_loan-cb_dep)/finexcb_safe
+gen finexcb_mmfunds_safe = (fin_mmf-cb_mmf)/finexcb_safe
+
+sort country year
+
+quietly log on
+
+* Table 2
+
+list country gov_bonds_safe gov_deposits_safe cb_bonds_safe cb_deposits_safe finexcb_bonds_safe finexcb_deposits_safe finexcb_mmfunds_safe if year==2015, clean noobs
+
+quietly log off
+
+*** Table 3
+
+gen finexcb_shareNonUS=fin_shareNonUS-cb_shareNonUS
+gen finexcb_shareWorld=fin_shareWorld-cb_shareWorld
+gen govcb_shareNonUS=gov_shareNonUS+cb_shareNonUS
+gen govcb_shareWorld=gov_shareWorld+cb_shareWorld
+
+quietly log on
+
+* Table 3
+
+* US
+reg finexcb_share govcb_share if country_name=="United States"
+sum year if e(sample)
+
+* Non-US
+
+reg finexcb_shareNonUS govcb_shareNonUS if country_name=="United States"
+sum year if e(sample)
+
+* All OECD
+
+reg finexcb_shareWorld govcb_shareWorld if country_name=="United States"
+sum year if e(sample)
+
+* OECD - balanced panel with fixed effects
+xtreg finexcb_share govcb_share if OECD==1 & year<=2017 & year>=1995, fe
+sum year if e(sample)
+
+* OECD - unbalanced panel with fixed effects
+xtreg finexcb_share govcb_share if OECD==1, fe
+sum year if e(sample)
+
+quietly log close
+
+*** Figure 1 - safe asset share for US and non-US
+
+label var share "safe asset share (US)"
+label var gov_share "gov share (US)"
+
+label var cb_share "central bank share (US)"
+
+label var shareNonUS "safe asset share (non US)"
+
+label var gov_shareNonUS "gov share (non US)"
+label var cb_shareNonUS "central bank share (non US)"
+
+label var shareWorld "safe asset share (All)"
+label var gov_shareWorld "gov share (All)"
+label var cb_shareWorld "central bank share (All)"
+
+label var share "U.S."
+label var shareNonUS "Other OECD countries"
+label var shareWorld "All OECD countries"
+
+*twoway (line share shareNonUS year ) if country_name=="United States", ylabel(0 .1 .2 .3 .4 .5) xlabel(1950 1960 1970 1980 1990 2000 2010 2018) name(Figure1)
+twoway (line share year, lcolor(black)) (line shareNonUS year, lcolor(black) lpattern(dash)) if country_name=="United States", ylabel(0 .1 .2 .3 .4 .5) xlabel(1950 1960 1970 1980 1990 2000 2010 2018) name(Figure1)
+
+graph export "Figure1.emf", as(emf) replace name(Figure1)
+
+
+*** Figure 2.a - public and private safe assets - US
+
+label var gov_share "Gov (US)"
+label var gov_shareNonUS "Gov (non US)"
+label var gov_shareWorld "Gov (All)"
+
+label var cb_share "CB (US)"
+label var cb_shareNonUS "CB (non US)"
+label var cb_shareWorld "CB (All)"
+
+label var finexcb_share "Financial (US)"
+label var finexcb_shareNonUS "Financial (non US)"
+label var finexcb_shareWorld "Financial (All)"
+
+gen public_share = gov_share + cb_share
+label var public_share "Public safe assets"
+gen private_share = finexcb_share
+label var private_share "Private safe assets"
+
+gen public_shareNonUS = gov_shareNonUS + cb_shareNonUS
+label var public_shareNonUS "Public safe assets"
+gen private_shareNonUS = finexcb_shareNonUS
+label var private_shareNonUS "Private safe assets"
+
+label var share "Total safe assets"
+label var shareNonUS "Total safe assets"
+twoway (line share year, lcolor(black) ) (line private_share year, lcolor(black) lpattern(dash) ) (line public_share year, lcolor(black) lpattern(dot) lwidth(thick) ) if country_name=="United States" , ylabel(0 .1 .2 .3 .4 .5) xlabel(1950 1960 1970 1980 1990 2000 2010 2018) title("A. U.S. - Public, Private and Total Safe Assets") subtitle("(as shares of Total Assets)") name(Figure2a)
+
+graph export "Figure2a.emf", as(emf) replace name(Figure2a)
+
+*** Figure 2.b - public and private safe assets - non-US
+
+twoway (line shareNonUS year, lcolor(black) ) (line private_shareNonUS year, lcolor(black) lpattern(dash) ) (line public_shareNonUS year, lcolor(black) lpattern(dot) lwidth(thick) ) if country_name=="United States" && year>=1995, ylabel(0 .1 .2 .3 .4 .5) xlabel(1995 2000 2005 2010 2015) title("B. Non-U.S. Countries - Public, Private and Total Safe Assets") subtitle("(as shares of Total Assets)") name(Figure2b)
+
+graph export "Figure2b.emf", as(emf) replace name(Figure2b)
+
+graph drop _all
diff --git a/105/replication_package/scfp2019excel.zip b/105/replication_package/scfp2019excel.zip
new file mode 100644
index 0000000000000000000000000000000000000000..1883a1fcbacf0b109f19388b156bf233e6dc5d80
--- /dev/null
+++ b/105/replication_package/scfp2019excel.zip
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87766da9024f7b6742d277c955234cf6bee439248fbc5f689c81d91880fd1b05
+size 2635565
diff --git a/105/replication_package/scfp2019s.zip b/105/replication_package/scfp2019s.zip
new file mode 100644
index 0000000000000000000000000000000000000000..4ab6f1d8d164d9f394267ff23774f790c0b27ad9
--- /dev/null
+++ b/105/replication_package/scfp2019s.zip
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4a2ffd493eeb6388766b5f828edf9409d900168d91677c5bd25e4648007baa0
+size 3437486
diff --git a/105/replication_package/solution_methods/Perturbation/AU_fifth_order.m b/105/replication_package/solution_methods/Perturbation/AU_fifth_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..b8f9a62489b9a3d9c4cd3f2263b21d2b1b6cf0b6
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/AU_fifth_order.m
@@ -0,0 +1,69 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+fvvvvvEvx5U5;
+
+A=result;
+
+
+fvvvvEvx3_vxx;
+
+
+derivs=[1,4];
+perms1=[1,2,4,3;1,4,2,3];
+perms2=[1;1];
+Matrix=kron(kron(hx,Ezeta2),Ix);
+tempresult= permutekron2(derivs,4,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxxx1);
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta3,Ix);
+tempresult=tempresult+permutekron2(derivs,4,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxxx1);
+
+result=result+tempresult*(kron(Ix3,hxx));
+clear tempresult Matrix
+
+A=A+result*(OMEGA_x.OMEGA5*fullU5);
+
+
+fvvvEvx2_vxxx;
+
+
+derivs=[1,3];
+struct=[0,0,1];
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta2,Ix);
+
+tempresult= permutekron2(derivs,3,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxx1);
+
+result=result+tempresult*kron(Ix2,hxxx);
+clear tempresult Matrix
+
+A=A+result*OMEGA_x.OMEGA6;
+
+
+fvvvEvx_vxx2;
+
+
+A=A+result*OMEGA_x.OMEGA7;
+
+
+fvvEvx_vxxxx;
+
+
+A=A+result*OMEGA_x.OMEGA8;
+
+
+fvvEvxx_vxxxU5;
+
+A=A+result*OMEGA_x.OMEGA9;
+
+clear result
+
+A=reshape(A,n_f,n_x^5);
+
+A=A+fyp*reshape(chain5(gx,gxx,gxxx,gxxxx,[],hx,hxx,hxxx,hxxxx,[],OMEGA_x.OMEGA5,OMEGA_x.OMEGA6,OMEGA_x.OMEGA7,...
+ OMEGA_x.OMEGA8,OMEGA_x.OMEGA9),n_y,n_x^5);
+
+clear result
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/A_fifth_order.m b/105/replication_package/solution_methods/Perturbation/A_fifth_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..8391bcde5ba908fecc3727c5e9b42d86c62c0c3e
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/A_fifth_order.m
@@ -0,0 +1,69 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+fvvvvvEvx5;
+
+A=result;
+
+
+fvvvvEvx3_vxx;
+
+
+derivs=[1,4];
+perms1=[1,2,4,3;1,4,2,3];
+perms2=[1;1];
+Matrix=kron(kron(hx,Ezeta2),Ix);
+tempresult= permutekron2(derivs,4,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxxx1);
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta3,Ix);
+tempresult=tempresult+permutekron2(derivs,4,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxxx1);
+
+result=result+tempresult*kron(Ix3,hxx);
+clear tempresult Matrix
+
+A=A+result*OMEGA_x.OMEGA5;
+
+
+fvvvEvx2_vxxx;
+
+
+derivs=[1,3];
+struct=[0,0,1];
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta2,Ix);
+
+tempresult= permutekron2(derivs,3,perms1,perms2,n_v,n_x,n_f,Matrix,fv,Vxxx1);
+
+result=result+tempresult*kron(Ix2,hxxx);
+clear tempresult Matrix
+
+A=A+result*OMEGA_x.OMEGA6;
+
+
+fvvvEvx_vxx2;
+
+
+A=A+result*OMEGA_x.OMEGA7;
+
+
+fvvEvx_vxxxx;
+
+
+A=A+result*OMEGA_x.OMEGA8;
+
+
+fvvEvxx_vxxx;
+
+A=A+result*OMEGA_x.OMEGA9;
+
+clear result
+
+A=reshape(A,n_f,n_x^5);
+
+A=A+fyp*reshape(chain5(gx,gxx,gxxx,gxxxx,[],hx,hxx,hxxx,hxxxx,[],OMEGA_x.OMEGA5,OMEGA_x.OMEGA6,OMEGA_x.OMEGA7,...
+ OMEGA_x.OMEGA8,OMEGA_x.OMEGA9),n_y,n_x^5);
+
+clear result
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/A_fourth_order.m b/105/replication_package/solution_methods/Perturbation/A_fourth_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..48eef3b6d5a3b52d9e264f8c78ee4cdda8bbe928
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/A_fourth_order.m
@@ -0,0 +1,24 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+fvvvvEvx4;
+A=result;
+
+
+fvvvEvx2_vxx;
+
+result=result+fv*Vxxx1*kron(Ezeta2,hxx);
+
+A=A+result*OMEGA_x.OMEGA2;
+
+fvvEvx_vxxx;
+
+A=A+result*OMEGA_x.OMEGA3;
+saveA=A;
+
+fvvEvxx2;
+
+A=A+result*OMEGA_x.OMEGA4;
+
+A=A+fyp*chain4(gx,gxx,gxxx,[],hx,hxx,hxxx,[],OMEGA_x.OMEGA2,OMEGA_x.OMEGA3,OMEGA_x.OMEGA4);
+
diff --git a/105/replication_package/solution_methods/Perturbation/A_third_order.m b/105/replication_package/solution_methods/Perturbation/A_third_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..00ae4e4fccd5fd2114484088d6330471190a244a
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/A_third_order.m
@@ -0,0 +1,11 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+fvvvEvx3;
+A=result;
+
+fvvEvx_vxx;
+
+A=A+(result+fyp*innerkron(n_y,n_x,gxx,hx,hxx))*OMEGA_x.OMEGA1;
+
+
diff --git a/105/replication_package/solution_methods/Perturbation/AkronkC.m b/105/replication_package/solution_methods/Perturbation/AkronkC.m
new file mode 100644
index 0000000000000000000000000000000000000000..b59b33299ba17091e76bba70487d6273d086bfc5
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/AkronkC.m
@@ -0,0 +1,16 @@
+function R=AkronkC(A,C,k)
+%Perform R=A*kron(C,...,C), where C is multiplied k times by the Kronecker operator.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+n=size(A,1);
+m=size(C,1);
+for j=1:k
+ A=reshape(A,numel(A)/m,m);
+ A=(A*C)';
+end
+
+R=reshape(A,numel(A)/n,n)';
+
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/LICENSE.txt b/105/replication_package/solution_methods/Perturbation/LICENSE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f4c9cef9508120c4a8d47df9505e92a2d3ac0cd
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/LICENSE.txt
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fb9263af0dd9125a9f518d09c39d28dd177728acc9ac56a0f3c7fdb2594c00d0
+size 1019
diff --git a/105/replication_package/solution_methods/Perturbation/Treshape.m b/105/replication_package/solution_methods/Perturbation/Treshape.m
new file mode 100644
index 0000000000000000000000000000000000000000..e82e4b69fee14aed7b6ace7079620c10f1664401
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/Treshape.m
@@ -0,0 +1,15 @@
+function [ rmat ] = Treshape( mat,m,n )
+%Treshape(A,m,n) transposes matrix A and then reshapes it into m,n
+%dimensions.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+[j0,i0,s]=find(mat);
+[n0,m0]=size(mat);
+
+ind=(j0-1)*m0+i0;
+[i1,j1]=ind2sub([m,n],ind);
+rmat=sparse(i1,j1,s,m,n);
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/WBU_fifth_order.m b/105/replication_package/solution_methods/Perturbation/WBU_fifth_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..67ed1e8e7cefe23511199738c119f4d26def5610
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/WBU_fifth_order.m
@@ -0,0 +1,29 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+
+temp1=(reshape(W5, unique*n_x^3,n_x^2)*kron_hx_hx);
+temp1=reshape(temp1,unique,n_x^5);
+temp2=kron(hx,kron_hx_hx)*reshape(U5,n_x^3,n_x^2*unique);
+temp2=reshape(temp2,n_x^5,unique);
+W5BU5=temp1*temp2;
+
+order=5;
+Matrix=hx3_Ezeta2;
+perms1=[1,3,2,4,5;1,3,4,2,5;1,3,4,5,2;3,1,2,4,5;3,1,4,2,5;3,1,4,5,2;3,4,1,2,5;3,4,1,5,2;3,4,5,1,2];
+tempresult = permutekronB2(order,perms1,n_x,Matrix,W5 );
+
+Matrix=hx2_Ezeta3;
+perms1=[1,2,4,3,5;1,2,4,5,3;1,4,2,3,5;1,4,2,5,3;1,4,5,2,3;4,1,2,3,5;4,1,2,5,3;4,1,5,2,3;4,5,1,2,3];
+tempresult = tempresult+permutekronB2(order,perms1,n_x,Matrix,W5 );
+
+Matrix=hx_Ezeta4;
+perms1=[1,2,3,5,4;1,2,5,3,4;1,5,2,3,4;5,1,2,3,4];
+tempresult = tempresult+permutekronB2(order,perms1,n_x,Matrix,W5);
+
+tempresult = tempresult+W5*Ezeta5;
+
+W5BU5=W5BU5+tempresult*U5;
+
+clear tempresult
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/WBU_fourth_order.m b/105/replication_package/solution_methods/Perturbation/WBU_fourth_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..3f28e7e8a6fcd73b07a5c226b38d59ea59e5a411
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/WBU_fourth_order.m
@@ -0,0 +1,21 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+temp1=reshape(W4, unique*n_x^2,n_x^2)*kron_hx_hx;
+temp1=reshape(temp1,unique,n_x^4);
+temp2=kron_hx_hx*reshape(U4,n_x^2,n_x^2*unique);
+temp2=reshape(temp2,n_x^4,unique);
+W4BU4=temp1*temp2;
+
+
+Matrix=hx2_Ezeta2;
+perms1=[1,3,2,4;1,3,4,2;3,1,2,4;3,1,4,2;3,4,1,2];
+tempresult = permutekronB2(4,perms1,n_x,Matrix,W4);
+
+Matrix=hx_Ezeta3;
+perms1=[1,2,4,3;1,4,2,3;4,1,2,3];
+tempresult = tempresult+permutekronB2(4,perms1,n_x,Matrix,W4 );
+
+tempresult=tempresult+W4*Ezeta4;
+
+W4BU4=W4BU4+tempresult*U4;
diff --git a/105/replication_package/solution_methods/Perturbation/WBU_third_order.m b/105/replication_package/solution_methods/Perturbation/WBU_third_order.m
new file mode 100644
index 0000000000000000000000000000000000000000..2928dc285304283a5faed4d882b4aec4aa7aa796
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/WBU_third_order.m
@@ -0,0 +1,17 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+% W3(hx^3)U3
+W3BU3=reshape([reshape(reshape([reshape(W3, unique*n_x^2,n_x)*hx]',n_x*unique*n_x,n_x)*hx,n_x,unique*n_x^2)]',unique,n_x^3)...
+ *reshape(hx*reshape(U3, n_x,n_x^2*unique),n_x^3,unique);
+
+% W3*E(P(kron(hx,zeta,zeta)))+W3*E(kron(zeta,zeta,zeta))
+Matrix=kron(hx,Ezeta2);
+perms1=[1,3,2;3,1,2];
+tempresult = permutekronB2(3,perms1,n_x,Matrix,W3);
+
+tempresult=tempresult+W3*Ezeta3;
+
+% final result
+W3BU3=W3BU3+tempresult*U3;
+
diff --git a/105/replication_package/solution_methods/Perturbation/bigprod.m b/105/replication_package/solution_methods/Perturbation/bigprod.m
new file mode 100644
index 0000000000000000000000000000000000000000..4a6266bea2984c071f951d2711348e5168682704
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/bigprod.m
@@ -0,0 +1,30 @@
+function result=bigprod(bigmat,smallmat)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+try
+ result=bigmat*smallmat;
+catch
+ m=size(bigmat,1);
+ n=size(smallmat,2);
+ if nnz(bigmat)==0 || nnz(smallmat)==0
+ result=sparse(m,n);
+ else
+ [i,j,s]=find(bigmat);
+ clear bigmat
+
+ temp=repmat(s,1,n).*smallmat(j,:); clear j s smallmat
+ [sorti,indI] = sort(i,1); clear i
+ Di=[(abs(diff(sorti))~=0);1];
+ cumtemp=cumsum(temp(indI,:)); clear temp indI
+ sumtemp=cumtemp(Di==1,:); clear cumtemp
+ sumtemp=[sumtemp(1,:);diff(sumtemp)];
+ Di=[1;Di(1:end-1)];
+ newi=repmat(sorti(Di==1),n,1);
+ newj=repmat(1:n,length(sorti(Di==1)),1); clear sorti Di
+ newj=newj(:);
+ result=sparse(newi,newj,sumtemp(:),m,n);
+ end
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/chain2.m b/105/replication_package/solution_methods/Perturbation/chain2.m
new file mode 100644
index 0000000000000000000000000000000000000000..b07b22a9dd71de937dd356dcfdd17a4a5e4e8149
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/chain2.m
@@ -0,0 +1,31 @@
+function [ fxx ] = chain2(fv,fvv,vx,vxx)
+%chain2 calculates a 3-dimensional array of second derivatives of the composite
+%function f(v(x)) with respect to x, using the second order multivariate chain
+%rule derived in Levintal, Oren, "Fifth Order Perturbation Solutions
+%to DSGE Models".
+%
+% Input arguments:
+% fv is the Jacobian matrix of f(v) wrt v.
+% fvv is an array of the second derivatives of f wrt v.
+% vx is the Jacobian matrix of v(x) wrt x.
+% vxx is an array of the second derivatives of v wrt x.
+%
+% All arguments, except fv and vx, can be reshaped in any form by the
+% reshape.m function. fv and vx must be in matrix form, where the rows of
+% fv correspond to the rows of f(v), and the row of vx correspond to the
+% rows of v(x).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+[n_f,n_v]=size(fv);
+n_x=size(vx,2);
+
+term1=innerkron(n_f,n_v,fvv,vx,vx);
+term2=fv*reshape(vxx,n_v,n_x^2);
+
+fxx=term1+term2;
+
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/chain3.m b/105/replication_package/solution_methods/Perturbation/chain3.m
new file mode 100644
index 0000000000000000000000000000000000000000..befdea5fb6c8da9a0ba1601d15cd9197d88ef3e1
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/chain3.m
@@ -0,0 +1,65 @@
+function [ fxxx ] = chain3(fv,fvv,fvvv,vx,vxx,vxxx,varargin)
+%chain3 calculates the matrix of third derivatives of the composite
+%function f(v(x)) with respect to x, using the third order multivariate chain
+%rule derived in Levintal, Oren, "Fifth Order Perturbation Solution
+%to DSGE Models", July 6, 2014.
+%
+% Input arguments:
+% fv is the Jacobian matrix of f(v) wrt v.
+% fvv is an array of the second derivatives of f wrt v.
+% fvvv is an array of the third derivatives of f wrt v.
+% vx is the Jacobian matrix of v(x) wrt x.
+% vxx is an array of the second derivatives of v wrt x.
+% vxxx is an array of the third derivatives of v wrt x.
+%
+% All arguments, except fv and vx, can be reshaped in any form by the
+% reshape.m function. fv and vx must be in matrix form, where the rows of
+% fv correspond to the rows of f(v), and the row of vx correspond to the
+% rows of v(x).
+%
+% [ fxxx ] = chain3(fv,fvv,fvvv,vx,vxx,vxxx,OMEGA1) uses the user-defined
+% OMEGA1 matrix.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+[n_f,n_v]=size(fv);
+n_x=size(vx,2);
+
+if isempty(varargin)==0
+ OMEGA1=varargin{1};
+end
+
+% fvvv(vx^3)
+
+if isempty(fvvv)
+ term1=sparse(1,1);
+else
+ term1=innerkron(n_f,n_v,fvvv,vx,vx,vx);
+end
+
+% fvv(vx*vxx)
+
+term2=innerkron(n_f,n_v,fvv,vx,vxx);
+
+if isempty(varargin)
+ term2=reshape(full(term2),n_f,n_x,n_x,n_x);
+ term2_OMEGA1=ipermute(term2,[1,3,4,2])+ipermute(term2,[1,2,4,3])+ipermute(term2,[1,2,3,4]);
+ term2_OMEGA1=reshape(term2_OMEGA1,n_f,n_x^3);
+else
+ term2_OMEGA1=term2*OMEGA1;
+end
+
+% fv(vxxx)
+
+if isempty(vxxx)
+ term3=sparse(1,1);
+else
+ term3=innerkron(n_f,n_v,fv,vxxx);
+end
+
+fxxx=term1+term2_OMEGA1+term3;
+
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/chain4.m b/105/replication_package/solution_methods/Perturbation/chain4.m
new file mode 100644
index 0000000000000000000000000000000000000000..26c5dac93227c34e08bc77580629bc78d1ee3c75
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/chain4.m
@@ -0,0 +1,87 @@
+function [ fxxxx ] = chain4(fv,fvv,fvvv,fvvvv,vx,vxx,vxxx,vxxxx,varargin)
+%chain4 calculates a 5-dimensional array of fourth derivatives of the composite
+%function f(v(x)) with respect to x, using the fourth order multivariate chain
+%rule derived in Levintal, Oren, "Fifth Order Perturbation Solution
+%to DSGE Models".
+%
+% Input arguments:
+% fv is the Jacobian matrix of f(v) wrt v.
+% fvv is an array of the second derivatives of f wrt v.
+% fvvv is an array of the third derivatives of f wrt v.
+% fvvvv is an array of the fourth derivatives of f wrt v.
+% vx is the Jacobian matrix of v(x) wrt x.
+% vxx is an array of the second derivatives of v wrt x.
+% vxxx is an array of the third derivatives of v wrt x.
+% vxxxx is an array of the fourth derivatives of v wrt x.
+%
+% All arguments, except fv and vx, can be reshaped in any form by the
+% reshape.m function. fv and vx must be in matrix form, where the rows of
+% fv correspond to the rows of f(v), and the row of vx correspond to the
+% rows of v(x).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+
+[n_f,n_v]=size(fv);
+n_x=size(vx,2);
+
+if isempty(varargin)==0
+ OMEGA2=varargin{1};
+ OMEGA3=varargin{2};
+ OMEGA4=varargin{3};
+end
+
+if isempty(fvvvv)
+ term1=sparse(1,1);
+else
+ term1=innerkron(n_f,n_v,fvvvv,vx,vx,vx,vx);
+end
+
+% fvvv(vx^2*vxx)
+
+term2=innerkron(n_f,n_v,fvvv,vx,vx,vxx);
+
+if isempty(varargin)
+ term2=reshape(full(term2),n_f,n_x,n_x,n_x,n_x);
+ term2_OMEGA2=ipermute(term2,[1,4,5,3,2])+ipermute(term2,[1,3,5,4,2])+ipermute(term2,[1,2,5,4,3])...
+ +ipermute(term2,[1,3,4,5,2])+ipermute(term2,[1,2,4,5,3])+ipermute(term2,[1,2,3,5,4]);
+ term2_OMEGA2=reshape(term2_OMEGA2,n_f,n_x^4);
+else
+ term2_OMEGA2=term2*OMEGA2;
+end
+
+% fvv(vx*vxxx)
+
+term3=innerkron(n_f,n_v,fvv,vx,vxxx);
+
+if isempty(varargin)
+ term3=reshape(full(term3),n_f,n_x,n_x,n_x,n_x);
+ term3_OMEGA3=ipermute(term3,[1,3,4,5,2])+ipermute(term3,[1,2,4,5,3])+ipermute(term3,[1,2,3,5,4])+ipermute(term3,[1,2,3,4,5]);
+ term3_OMEGA3=reshape(term3_OMEGA3,n_f,n_x^4);
+else
+ term3_OMEGA3=term3*OMEGA3;
+end
+
+% fvv(vxx^2)
+
+term4=innerkron(n_f,n_v,fvv,vxx,vxx);
+
+if isempty(varargin)
+ term4=reshape(full(term4),n_f,n_x,n_x,n_x,n_x);
+ term4_OMEGA4=ipermute(term4,[1,3,4,2,5])+ipermute(term4,[1,2,4,3,5])+ipermute(term4,[1,2,3,4,5]);
+ term4_OMEGA4=reshape(term4_OMEGA4,n_f,n_x^4);
+else
+ term4_OMEGA4=term4*OMEGA4;
+end
+
+if isempty(vxxxx)
+ term5=sparse(1,1);
+else
+ term5=innerkron(n_f,n_v,fv,vxxxx);
+end
+
+fxxxx=term1+term2_OMEGA2+term3_OMEGA3+term4_OMEGA4+term5;
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/chain5.m b/105/replication_package/solution_methods/Perturbation/chain5.m
new file mode 100644
index 0000000000000000000000000000000000000000..c1d20265987d3f46f2d276320f72c8d07d4d7571
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/chain5.m
@@ -0,0 +1,133 @@
+function [ fxxxxx ] = chain5(fv,fvv,fvvv,fvvvv,fvvvvv,vx,vxx,vxxx,vxxxx,vxxxxx,varargin)
+%chain5 calculates a 6-dimensional array of fifth derivatives of the composite
+%function f(v(x)) with respect to x, using the fifth order multivariate chain
+%rule derived in Levintal, Oren, "Fifth Order Perturbation Solution
+%to DSGE Models".
+%
+% Input arguments:
+% fv is the Jacobian matrix of f(v) wrt v.
+% fvv is an array of the second derivatives of f wrt v.
+% fvvv is an array of the third derivatives of f wrt v.
+% fvvvv is an array of the fourth derivatives of f wrt v.
+% fvvvvv is an array of the fifth derivatives of f wrt v.
+% vx is the Jacobian matrix of v(x) wrt x.
+% vxx is an array of the second derivatives of v wrt x.
+% vxxx is an array of the third derivatives of v wrt x.
+% vxxxx is an array of the fourth derivatives of v wrt x.
+% vxxxxx is an array of the fifth derivatives of v wrt x.
+%
+% All arguments, except fv and vx, can be reshaped in any form by the
+% reshape.m function. fv and vx must be in matrix form, where the rows of
+% fv correspond to the rows of f(v), and the rows of vx correspond to the
+% rows of v(x).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+[n_f,n_v]=size(fv);
+n_x=size(vx,2);
+
+if isempty(varargin)==0
+ OMEGA5=varargin{1};
+ OMEGA6=varargin{2};
+ OMEGA7=varargin{3};
+ OMEGA8=varargin{4};
+ OMEGA9=varargin{5};
+end
+
+% fvvvvv(vx^5)
+
+if isempty(fvvvvv)
+ term1=sparse(1,1);
+else
+ term1=innerkron(n_f,n_v,fvvvvv,vx,vx,vx,vx,vx);
+end
+
+% fvvvv(vx^3*vxx)
+
+term2=innerkron(n_f,n_v,fvvvv,vx,vx,vx,vxx);
+
+if isempty(varargin)
+ term2=reshape(full(term2),n_f,n_x,n_x,n_x,n_x,n_x);
+ term2_OMEGA5=ipermute(term2,[1,5,6,4,3,2])+ipermute(term2,[1,4,6,5,3,2])+ipermute(term2,[1,3,6,5,4,2])+ipermute(term2,[1,2,6,5,4,3])...
+ +ipermute(term2,[1,4,5,6,3,2])+ipermute(term2,[1,3,5,6,4,2])...
+ +ipermute(term2,[1,2,5,6,4,3])+ipermute(term2,[1,3,4,6,5,2])+ipermute(term2,[1,2,4,6,5,3])+ipermute(term2,[1,2,3,6,5,4]);
+ term2_OMEGA5=reshape(term2_OMEGA5,n_f,n_x^5);
+else
+ term2_OMEGA5=term2*OMEGA5;
+ clear term2 OMEGA5
+end
+
+% fvvv(vx^2*vxxx)
+
+term3=innerkron(n_f,n_v,fvvv,vx,vx,vxxx);
+
+if isempty(varargin)
+ term3=reshape(full(term3),n_f,n_x,n_x,n_x,n_x,n_x);
+ term3_OMEGA6=ipermute(term3,[1,4,5,6,3,2])+ipermute(term3,[1,3,5,6,4,2])+ipermute(term3,[1,2,5,6,4,3])+ipermute(term3,[1,3,4,6,5,2])...
+ +ipermute(term3,[1,2,4,6,5,3])+ipermute(term3,[1,2,3,6,5,4])+ipermute(term3,[1,3,4,5,6,2])...
+ +ipermute(term3,[1,2,4,5,6,3])+ipermute(term3,[1,2,3,5,6,4])+ipermute(term3,[1,2,3,4,6,5]);
+ term3_OMEGA6=reshape(term3_OMEGA6,n_f,n_x^5);
+else
+ term3_OMEGA6=term3*OMEGA6;
+ clear term3 OMEGA6
+end
+
+% fvvv(vx*vxx^2)
+
+term4=innerkron(n_f,n_v,fvvv,vx,vxx,vxx);
+
+if isempty(varargin)
+ term4=reshape(full(term4),n_f,n_x,n_x,n_x,n_x,n_x);
+ term4_OMEGA7=ipermute(term4,[1,4,5,3,6,2])+ipermute(term4,[1,3,5,4,6,2])+ipermute(term4,[1,2,5,4,6,3])...
+ +ipermute(term4,[1,3,4,5,6,2])+ipermute(term4,[1,2,4,5,6,3])+ipermute(term4,[1,2,3,5,6,4])...
+ +ipermute(term4,[1,4,5,2,6,3])+ipermute(term4,[1,3,5,2,6,4])+ipermute(term4,[1,2,5,3,6,4])...
+ +ipermute(term4,[1,3,4,2,6,5])+ipermute(term4,[1,2,4,3,6,5])+ipermute(term4,[1,2,3,4,6,5])...
+ +ipermute(term4,[1,3,4,2,5,6])+ipermute(term4,[1,2,4,3,5,6])+ipermute(term4,[1,2,3,4,5,6]);
+ term4_OMEGA7=reshape(term4_OMEGA7,n_f,n_x^5);
+else
+ term4_OMEGA7=term4*OMEGA7;
+ clear term4 OMEGA7
+end
+
+% fvv(vx*vxxxx)
+
+term5=innerkron(n_f,n_v,fvv,vx,vxxxx);
+
+if isempty(varargin)
+ term5=reshape(full(term5),n_f,n_x,n_x,n_x,n_x,n_x);
+ term5_OMEGA8=ipermute(term5,[1,3,4,5,6,2])+ipermute(term5,[1,2,4,5,6,3])+ipermute(term5,[1,2,3,5,6,4])...
+ +ipermute(term5,[1,2,3,4,6,5])+ipermute(term5,[1,2,3,4,5,6]);
+ term5_OMEGA8=reshape(term5_OMEGA8,n_f,n_x^5);
+else
+ term5_OMEGA8=term5*OMEGA8;
+ clear term5 OMEGA8
+end
+
+% fvv(vxx*vxxx)
+
+term6=innerkron(n_f,n_v,fvv,vxx,vxxx);
+
+if isempty(varargin)
+ term6=reshape(full(term6),n_f,n_x,n_x,n_x,n_x,n_x);
+ term6_OMEGA9=ipermute(term6,[1,3,4,5,2,6])+ipermute(term6,[1,2,4,5,3,6])+ipermute(term6,[1,2,3,5,4,6])+ipermute(term6,[1,2,3,4,5,6])...
+ +ipermute(term6,[1,3,4,6,2,5])+ipermute(term6,[1,2,4,6,3,5])+ipermute(term6,[1,2,3,6,4,5])...
+ +ipermute(term6,[1,2,5,6,3,4])+ipermute(term6,[1,3,5,6,2,4])+ipermute(term6,[1,4,5,6,2,3]);
+ term6_OMEGA9=reshape(term6_OMEGA9,n_f,n_x^5);
+else
+ term6_OMEGA9=term6*OMEGA9;
+ clear term6 OMEGA9
+end
+
+% fv(vxxxxx)
+
+if isempty(vxxxxx)
+ lastterm=sparse(1,1);
+else
+ lastterm=innerkron(n_f,n_v,fv,vxxxxx);
+end
+
+fxxxxx=term1+term2_OMEGA5+term3_OMEGA6+term4_OMEGA7+term5_OMEGA8+term6_OMEGA9+lastterm;
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/compderivs.m b/105/replication_package/solution_methods/Perturbation/compderivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..613e38923961e3efebcc302ea1d43e609c316339
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/compderivs.m
@@ -0,0 +1,157 @@
+function [derivs,uncomp]=compderivs(f,x,order)
+
+% [derivs,uncomp,U,W]=compderivs(f,x,order) differentiates f with respect to x
+% serveral times (given by order). The differentiation is done in
+% a compressed manner, by exploiting sparsity and symmetry of mixed derivatives.
+% The function returns two cell arrays. The first output contains the
+% nonzero unique derivatives up to the order defined by the user. The
+% second array contains matrices that uncompress the nonzero unique derivatives
+% into the full arrays of derivatives. U and W are compress/uncompress
+% matrices to unique elements.
+%
+% For details on the compressed differentiation routine see:
+% Levintal, Oren, "Fifth Order Perturbation Solution to DSGE Models".
+%
+% Input arguments:
+% f - a symbolic scalar.
+% x - a symbolic vector.
+% order - the maximum order of derivatives. For example, order=3 returns
+% the first, second and third derivatives.
+%
+% Output arguments:
+% derivs - a cell array of the nonzero unique derivatives. For example,
+% derivs{1} is a symbolic vector of the nonzero first derivatives, derivs{2} is a
+% symbolic vector of the nonzero unique second derivatives and so on.
+% uncomp - a cell array of sparse matrices that are used to uncompress the
+% compressed derivatives. For example, the full array of second order
+% derivatives is obtained by uncomp{2}*derivs{2}.
+%
+% Example: f=x1^3*x2^4, and x=[x1,x2], both are symbolic variables.
+% [derivs,uncomp]=compderivs(f,x,3) returns the first, second and third
+% compressed derivatives. The full array of third derivatives is obtained
+% by uncomp{3}*derivs{3}. This array can be reshaped into a 2-by-2-by-2
+% array by the reshape function.
+% The i,j,l element of this array is the third derivative of f
+% w.r.t xi, xj and xl.
+%
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+n_x=length(x);
+derivs=cell(order,1);
+uncomp=cell(order,1);
+
+if n_x==1
+ tempderiv=f;
+ for k=1:order
+ tempderiv=jacobian(tempderiv,x);
+ derivs{k}=tempderiv;
+ if logical(tempderiv==0)
+ uncomp{k}=sparse(0);
+ else
+ uncomp{k}=sparse(1);
+ end
+ end
+else
+ tempderiv=jacobian(f,x);
+ tempderiv=tempderiv(:);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ tempind=find(nnztempderiv);
+ countdf=sparse(tempind,ones(length(tempind),1),ones(length(tempind),1),numel(tempderiv),1); % counts nonzero derivatives.
+ N1=sparse(tempind,1:sum(countdf),ones(1,sum(countdf)),n_x,sum(countdf));
+ uncomp{1}=N1;
+ derivs{1}=tempderiv(countdf==1);
+
+ for k=2:order
+ tempderiv=jacobian(derivs{k-1}, x);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ [i,j]=find(nnztempderiv);
+
+ countdf_short=sparse(i,j,ones(length(i),1),size(tempderiv,1),size(tempderiv,2));
+ countdf=uncomp{k-1}*countdf_short;
+ countdf=countdf(:);
+ if nnz(countdf)>0
+ [U,W]=create_UW(n_x,k,countdf);
+ N=sparse(find(countdf),1:sum(countdf),ones(1,sum(countdf)),n_x^k,sum(countdf));
+ tempmat=[U'*(N'*kron(speye(n_x),uncomp{k-1}))];
+ [i,j]=find(tempmat');
+ tempderiv=tempderiv(i);
+ [colM,rowM]=find(N);
+ [rowW,colW]=find(W);
+ tempuncomp=sparse(size(N,1),size(W,1));
+ tempeye=speye(size(W,1));
+ tempuncomp(colM,:)=tempeye(rowW,:);
+ else
+ tempderiv=sym(0);
+ tempuncomp=sparse(n_x^k,1);
+ end
+ derivs{k}=tempderiv;
+ uncomp{k}=tempuncomp;
+ end
+end
+
+end
+
+function [U,W]=create_UW(n,k,varargin)
+% [U,W]=create_UW(n,k) creates two sparse matrices, U and W, that compress and
+% uncompress a symmetric array A with k dimensions and n^k elements.
+% A(:)'*U is a row vector that contains the unique elements of A,
+% and A(:)'=(A(:)'*U)*W.
+% [U,W]=create_UW(n,k,N) creates matrices U and W of a sparse symmetric
+% array A with k dimensions and n^k elements. N is a vector of size n^k,
+% where N(j)=1 if A(j)~=0 and zero otherwise. If B is a row
+% vector with the nonzero elements of the row vector A(:)', then B*U
+% is a row vector of the unique nonzero elements of A, and B=(B*U)*W.
+%
+% This code can be used freely for non commercial purposes, provided that
+% it is not altered.
+%
+% (c) Oren Levintal, December 20, 2013
+
+if isempty(varargin)
+% nonzero=ones(n^k,1);
+ I=[1:n^k];
+else
+ nonzero=varargin{1};
+ I=find(nonzero);
+end
+
+if isempty(I)
+ error('The symmetric array is all zero')
+end
+
+I=I(:);
+% nonzero(nonzero~=0)=1; nonzero=nonzero(:);
+sizeM='n';
+subind='I1';
+for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+end
+
+eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+eval(['M=[' subind '];']);
+
+M=sort(M,2); % sort columns
+[M,I]=sortrows(M); % sort rows
+if size(M,1)==1
+ DM=1;
+else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+end
+group=cumsum(DM);
+minI=accumarray(group,I,[],@min);
+newi=minI(group);
+
+unique=newi(DM>0); % index of unique nonzero elements
+
+n_unique=length(unique);
+
+U= sparse(unique,[1:n_unique]',ones(n_unique,1),length(I),n_unique);
+
+W= sparse(group,I,ones(length(I),1),n_unique,length(I));
+
+end
diff --git a/105/replication_package/solution_methods/Perturbation/create_OMEGA.m b/105/replication_package/solution_methods/Perturbation/create_OMEGA.m
new file mode 100644
index 0000000000000000000000000000000000000000..5d52e9f9310d08448e201238c59af2041fccb56c
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/create_OMEGA.m
@@ -0,0 +1,53 @@
+function [ OMEGA ] = create_OMEGA( n_x,varargin )
+%The function creates sparse matrices OMEGA1,..,OMEGA9, that are used for
+%the high-order multivariate chain rules described in Levintal, Oren,
+%"Fifth Order Perturbation Solution to DSGE Models", 2014.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if length(varargin)==1
+ order=varargin{1}; % do only specified order
+else
+ order=0; % do orders 3,4,5
+end
+
+if order==3 || order==0
+ ind=[1:n_x^3];
+ M=reshape(ind,1,n_x,n_x,n_x);
+ Ix=speye(n_x^3);
+ OMEGA.OMEGA1=Ix(:,ipermute(M,[1,3,4,2]))+Ix(:,ipermute(M,[1,2,4,3]))+Ix(:,ipermute(M,[1,2,3,4]));
+end
+
+if order==4 || order==0
+ ind=[1:n_x^4];
+ M=reshape(ind,1,n_x,n_x,n_x,n_x);
+ Ix=speye(n_x^4);
+ OMEGA.OMEGA2=Ix(:,ipermute(M,[1,4,5,3,2]))+Ix(:,ipermute(M,[1,3,5,4,2]))+Ix(:,ipermute(M,[1,2,5,4,3]))...
+ +Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]));
+ OMEGA.OMEGA3=Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]))+Ix(:,ipermute(M,[1,2,3,4,5]));
+ OMEGA.OMEGA4=Ix(:,ipermute(M,[1,3,4,2,5]))+Ix(:,ipermute(M,[1,2,4,3,5]))+Ix(:,ipermute(M,[1,2,3,4,5]));
+end
+
+if order==5 || order==0
+ ind=[1:n_x^5];
+ M=reshape(ind,1,n_x,n_x,n_x,n_x,n_x);
+ Ix=speye(n_x^5);
+ OMEGA.OMEGA5=Ix(:,ipermute(M,[1,5,6,4,3,2]))+Ix(:,ipermute(M,[1,4,6,5,3,2]))+Ix(:,ipermute(M,[1,3,6,5,4,2]))+Ix(:,ipermute(M,[1,2,6,5,4,3]))...
+ +Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))...
+ +Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))+Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]));
+ OMEGA.OMEGA6=Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))+Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))...
+ +Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]))+Ix(:,ipermute(M,[1,3,4,5,6,2]))...
+ +Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]));
+ OMEGA.OMEGA7=Ix(:,ipermute(M,[1,4,5,3,6,2]))+Ix(:,ipermute(M,[1,3,5,4,6,2]))+Ix(:,ipermute(M,[1,2,5,4,6,3]))...
+ +Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))...
+ +Ix(:,ipermute(M,[1,4,5,2,6,3]))+Ix(:,ipermute(M,[1,3,5,2,6,4]))+Ix(:,ipermute(M,[1,2,5,3,6,4]))...
+ +Ix(:,ipermute(M,[1,3,4,2,6,5]))+Ix(:,ipermute(M,[1,2,4,3,6,5]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))...
+ +Ix(:,ipermute(M,[1,3,4,2,5,6]))+Ix(:,ipermute(M,[1,2,4,3,5,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
+ OMEGA.OMEGA8=Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
+ OMEGA.OMEGA9=Ix(:,ipermute(M,[1,3,4,5,2,6]))+Ix(:,ipermute(M,[1,2,4,5,3,6]))+Ix(:,ipermute(M,[1,2,3,5,4,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]))...
+ +Ix(:,ipermute(M,[1,3,4,6,2,5]))+Ix(:,ipermute(M,[1,2,4,6,3,5]))+Ix(:,ipermute(M,[1,2,3,6,4,5]))...
+ +Ix(:,ipermute(M,[1,2,5,6,3,4]))+Ix(:,ipermute(M,[1,3,5,6,2,4]))+Ix(:,ipermute(M,[1,4,5,6,2,3]));
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/create_OMEGA_x.m b/105/replication_package/solution_methods/Perturbation/create_OMEGA_x.m
new file mode 100644
index 0000000000000000000000000000000000000000..0fece30f88267e470d628ab239037de8984bd881
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/create_OMEGA_x.m
@@ -0,0 +1,23 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+OMEGA_x=[];
+if approx>=3
+ tempOMEGA = create_OMEGA( n_x,3 );
+ OMEGA_x.OMEGA1=tempOMEGA.OMEGA1;
+end
+
+if approx>=4
+ tempOMEGA = create_OMEGA( n_x,4 );
+ OMEGA_x.OMEGA2=tempOMEGA.OMEGA2;
+ OMEGA_x.OMEGA3=tempOMEGA.OMEGA3;
+ OMEGA_x.OMEGA4=tempOMEGA.OMEGA4;
+end
+if approx>=5
+ tempOMEGA = create_OMEGA( n_x,5 );
+ OMEGA_x.OMEGA5=tempOMEGA.OMEGA5;
+ OMEGA_x.OMEGA6=tempOMEGA.OMEGA6;
+ OMEGA_x.OMEGA7=tempOMEGA.OMEGA7;
+ OMEGA_x.OMEGA8=tempOMEGA.OMEGA8;
+ OMEGA_x.OMEGA9=tempOMEGA.OMEGA9;
+end
diff --git a/105/replication_package/solution_methods/Perturbation/create_UW.m b/105/replication_package/solution_methods/Perturbation/create_UW.m
new file mode 100644
index 0000000000000000000000000000000000000000..0560026cde9504572ee1e2a37619c85cea3f2563
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/create_UW.m
@@ -0,0 +1,59 @@
+function [U,W]=create_UW(n,k,varargin)
+% [U,W]=create_UW(n,k) creates two sparse matrices, U and W, that compress and
+% uncompress a symmetric array A with k dimensions and n^k elements.
+% A(:)'*U is a row vector that contains the unique elements of A,
+% and A(:)'=(A(:)'*U)*W.
+% [U,W]=create_UW(n,k,N) creates matrices U and W of a sparse symmetric
+% array A with k dimensions and n^k elements. N is a vector of size n^k,
+% where N(j)=1 if A(j)~=0 and zero otherwise. If B is a row
+% vector with the nonzero elements of the row vector A(:)', then B*U
+% is a row vector of the unique nonzero elements of A, and B=(B*U)*W.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(varargin)
+% nonzero=ones(n^k,1);
+ I=[1:n^k];
+else
+ nonzero=varargin{1};
+ I=find(nonzero);
+end
+
+if isempty(I)
+ error('The symmetric array is all zero')
+end
+
+I=I(:);
+% nonzero(nonzero~=0)=1; nonzero=nonzero(:);
+sizeM='n';
+subind='I1';
+for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+end
+
+eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+eval(['M=[' subind '];']);
+
+M=sort(M,2); % sort columns
+[M,I]=sortrows(M); % sort rows
+if size(M,1)==1
+ DM=1;
+else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+end
+group=cumsum(DM);
+minI=accumarray(group,I,[],@min);
+newi=minI(group);
+
+unique=newi(DM>0); % index of unique nonzero elements
+
+n_unique=length(unique);
+
+U= sparse(unique,[1:n_unique]',ones(n_unique,1),length(I),n_unique);
+
+W= sparse(group,I,ones(length(I),1),n_unique,length(I));
+
+end
+
+
diff --git a/105/replication_package/solution_methods/Perturbation/create_compression_matrices_nonzero.m b/105/replication_package/solution_methods/Perturbation/create_compression_matrices_nonzero.m
new file mode 100644
index 0000000000000000000000000000000000000000..3ec5214e462b7a390937ac65b4b287e26d008541
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/create_compression_matrices_nonzero.m
@@ -0,0 +1,75 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if approx>=2
+ k=2;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x);
+ nonzero(end,1:end-1)=0;
+ nonzero(1:end-1,end)=0;
+ [U2,W2]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N2=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U2=N2*U2;
+ W2=W2*N2';
+end
+
+if approx>=3
+ k=3;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end)=0;
+ [U3,W3]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N3=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U3=N3*U3;
+ W3=W3*N3';
+end
+
+if approx>=4
+ k=4;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,end)=0;
+ [U4,W4]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N4=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U4=N4*U4;
+ W4=W4*N4';
+end
+
+if approx>=5
+ k=5;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,1:end-1,end)=0;
+ [U5,W5]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N5=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U5=N5*U5;
+ W5=W5*N5';
+end
+
+if approx==1
+ UW=struct([]);
+elseif approx==2
+ UW.U2=U2; UW.W2=W2;
+elseif approx==3
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+elseif approx==4
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+ UW.U4=U4; UW.W4=W4;
+elseif approx==5
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+ UW.U4=U4; UW.W4=W4;
+ UW.U5=U5; UW.W5=W5;
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/differentiate_dsge.m b/105/replication_package/solution_methods/Perturbation/differentiate_dsge.m
new file mode 100644
index 0000000000000000000000000000000000000000..599057320ec16aad796a1874cb1f3d2658407143
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/differentiate_dsge.m
@@ -0,0 +1,77 @@
+function model=differentiate_dsge(f,yp,y,xp,x,symparams,approx,Phi)
+%differentiate_dsge(f,yp,y,xp,x,symparams,approx,Phi,ufun,u)
+%This function differentiates the dsge model and prepares all the files
+%necessary to run solve_dsge.m.
+%Input variables:
+%f,yp,y,xp,x: the model conditions and variable as in Schmitt-Grohe and Uribe (2004)
+%symparams: a symbolic array that lists all parameters.
+%approx: order of perturbation
+%Phi: expected value of exgoenous variables (leave empty if not
+%used)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+disp('Preparing perturbation...')
+
+currentFolder = pwd;
+mkdir('files');
+cd('files')
+
+syms sigma_perturbation sigmap_perturbation real
+Phi=sym(Phi);
+f=sym(f);
+
+x=[x(:);sigma_perturbation];
+xp=[xp(:);sigmap_perturbation];
+
+v=[yp(:); y(:); xp(:); x(:)];
+
+n_f=length(f);
+n_x=length(x);
+n_y=length(y);
+n_x2=size(Phi,1);
+n_x1=n_f-n_y;
+n_v=length(v);
+
+model.f=f;
+model.yp=yp;
+model.y=y;
+model.xp=xp;
+model.x=x;
+model.v=v;
+model.n_f=n_f;
+model.n_x=n_x;
+model.n_y=n_y;
+model.n_x2=n_x2;
+model.n_x1=n_x1;
+model.n_v=n_v;
+
+create_compression_matrices_nonzero;
+
+if approx>=1
+ model.f_ind=getderivs_vector(f,v,approx,symparams,'f');
+end
+
+% Create an m file for Phi and its derivatives w.r.t x
+
+gen_fun(Phi,symparams,x,'Phi');
+if approx>=1
+ model.Phi_ind=getderivs(Phi,x,approx,symparams,'Phi');
+end
+
+create_OMEGA_x;
+
+model.UW=UW;
+
+if approx<3
+ OMEGA_x=[];
+end
+model.OMEGA_x=OMEGA_x;
+
+rehash;
+
+disp('Perturbation prepared successfully.')
+
+cd(currentFolder)
+
diff --git a/105/replication_package/solution_methods/Perturbation/disp_deriv.m b/105/replication_package/solution_methods/Perturbation/disp_deriv.m
new file mode 100644
index 0000000000000000000000000000000000000000..9522591797c3cbe244c564a1bb4732838dfcf0f6
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/disp_deriv.m
@@ -0,0 +1,45 @@
+function disp_deriv( fun_string,i,fun_sym , varargin)
+%disp_deriv breaks derivativs into several lines if the length of derivative is
+%higher than 1000 characters.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(varargin)
+ texp=char(fun_sym(i));
+else
+ texp=char(fun_sym(varargin{1}));
+end
+if length(texp)<1000
+ disp([fun_string '(' num2str(i) ')=' texp ';']);
+ texp='';
+else
+ itexp=1000;
+ while strcmp(texp(itexp),'+')+strcmp(texp(itexp),'-')+strcmp(texp(itexp),'*')+strcmp(texp(itexp),'/')==0 & itexp0
+ itexp=min(1000,length(texp));
+ while strcmp(texp(itexp),'+')+strcmp(texp(itexp),'-')+strcmp(texp(itexp),'*')+strcmp(texp(itexp),'/')==0 & itexp1)=perms2(perms2>1)-1;
+Matrix=kron(Ix_Ezeta2,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X2)(X)(Vxx1*P(zeta(X)hx)
+
+perms1=[2,1,3,4];
+perms2=[1,2,3];
+Matrix=kron(Ezeta3,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxx1);
+
+% Vx0^(X2)(X)(Vxx1*zeta^(X2))
+
+perms1=[];
+perms2=[];
+Matrix=Ix2_Ezeta2;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx0,Vxx1);
+
+% P(Vx0(X)(Vx1*zeta))(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,4,3];
+perms2=[1,3,2];
+Matrix=Ix_Ezeta3;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X2)(X)(Vxx1*zeta^(X2))
+
+perms1=[];
+perms2=[];
+Matrix=Ezeta4;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxx1);
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvEvx2_vxxx.m b/105/replication_package/solution_methods/Perturbation/fvvvEvx2_vxxx.m
new file mode 100644
index 0000000000000000000000000000000000000000..bd60736778c5b3a99390d93a297df0ee8ec65891
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvEvx2_vxxx.m
@@ -0,0 +1,120 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0^(X2)(X)Vxxx0
+
+derivs=[3,1,1,3];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx0,Vxxx0);
+
+% Vx0^(X2)(X)(Vxxx1*P(zeta^(X2)(X)hx))
+
+perms1=[2,1,3,4,5;2,3,1,4,5];
+perms2=[1,2,3;1,2,3];
+Matrix=kron(Ix2_Ezeta2,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx0,Vxxx1);
+
+% Vx0^(X2)(X)(Vxxx1*zeta^(X3))
+
+perms1=[];
+perms2=[];
+Matrix=Ix2_Ezeta3;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx0,Vxxx1);
+
+% P(Vx0(X)(Vx1*zeta))(X)(Vxxx1*P(zeta(X)hx^(X2)))
+
+perms1=[1,3,2,4,5;3,1,2,4,5;1,2,3,5,4;1,3,2,5,4;3,1,2,5,4];
+perms2=perms1(:,[1,4,5]); perms2(perms2<=3)=1; perms2(perms2>1)=perms2(perms2>1)-2;
+Matrix=kron(Ix_Ezeta2,hx2);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxxx1);
+
+% P(Vx0(X)(Vx1*zeta))(X)(Vxxx1*P(zeta^(X2)(X)hx)
+
+perms1=[2,1,3,4,5;2,3,1,4,5;1,2,3,5,4;2,1,3,5,4;2,3,1,5,4];
+perms2=perms1(:,[1,4,5]); perms2(perms2<=3)=1; perms2(perms2>1)=perms2(perms2>1)-2;
+Matrix=kron(Ix_Ezeta3,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxxx1);
+
+% P(Vx0(X)(Vx1*zeta))(X)(Vxxx1*zeta^(X3))
+
+perms1=[1,2,3,5,4];
+perms2=perms1(:,[1,4,5]); perms2(perms2<=3)=1; perms2(perms2>1)=perms2(perms2>1)-2;
+Matrix=Ix_Ezeta4;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxxx1);
+
+% P(Vx0(X)(Vx1*zeta))(X)(Vxx1*(zeta(X)hxx)*Omega1
+
+perms1=[1,2,4,3];
+perms2=perms1(:,[1,3,4]); perms2(perms2<=2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix_Ezeta2,Ix);
+
+tempresult=permutekron2([3,1,1,2],4,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vxx1);
+
+tempmat_Omega1=reshape(kron(Ix,hxx),n_x^2,n_x^3)*OMEGA_x.OMEGA1;
+
+clear tempmat
+
+tempmat_Omega1=reshape(tempmat_Omega1,n_x^2,n_x^3);
+
+tempresult=reshape([reshape(tempresult,n_f*n_x^2,n_x^2)]',n_x^2*n_f,n_x^2);
+tempresult=[reshape([tempresult*tempmat_Omega1]',n_x^5,n_f)]';
+
+result=result+tempresult;
+
+clear tempresult
+
+% (Vx1*zeta)^(X2)(X)Vxxx0
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta2,Ix3);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxxx0);
+
+% (Vx1*zeta)^(X2)(X)(Vxxx1*P(zeta(X)hx^(X2))
+
+perms1=[1,3,2,4,5;3,1,2,4,5];
+perms2=[1,2,3;1,2,3];
+Matrix=kron(Ezeta3,hx2);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxxx1);
+% (Vx1*zeta)^(X2)(X)(Vxxx1*P(zeta^(X2)(X)hx)
+
+perms1=[2,1,3,4,5;2,3,1,4,5];
+perms2=[1,2,3;1,2,3];
+Matrix=kron(Ezeta4,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxxx1);
+
+% (Vx1*zeta)^(X2)(X)(Vxxx1*zeta^(X3))
+
+perms1=[];
+perms2=[];
+Matrix=Ezeta5;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxxx1);
+
+% (Vx1*zeta)^(X2)(X)(Vxx1*(zeta(X)hxx)*Omega1
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta3,Ix);
+
+tempresult=permutekron2([3,1,1,2],4,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vxx1);
+
+tempresult=reshape([reshape(tempresult,n_f*n_x^2,n_x^2)]',n_x^2*n_f,n_x^2);
+tempresult=[reshape([tempresult*tempmat_Omega1]',n_x^5,n_f)]';
+
+result=result+tempresult;
+
+clear tempresult tempmat_Omega1
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvEvx3.m b/105/replication_package/solution_methods/Perturbation/fvvvEvx3.m
new file mode 100644
index 0000000000000000000000000000000000000000..ed5161f6dbcbce27d40f5a1315646df49710004f
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvEvx3.m
@@ -0,0 +1,33 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=3;
+
+% Vx0^(X3)
+
+derivs=[3,1,1,1];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx0,Vx0);
+
+% P(Vx0(X)[Vx1*zeta)^(X2)]
+
+perms1=[1,3,2;3,1,2];
+perms2=perms1;
+Matrix=Ix_Ezeta2;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vx1,Vx1);
+
+% (Vx1*zeta)^(X3)
+
+perms1=[];
+perms2=perms1;
+Matrix=Ezeta3;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vx1,Vx1);
+
+
+
+
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvEvx_vxx2.m b/105/replication_package/solution_methods/Perturbation/fvvvEvx_vxx2.m
new file mode 100644
index 0000000000000000000000000000000000000000..5e7bf158aecc04d71833956c3119400de605354d
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvEvx_vxx2.m
@@ -0,0 +1,92 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0(X)Vxx0^(X2)
+derivs=[3,1,2,2];
+
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vxx0,Vxx0);
+
+% Vx0(X)P(Vxx0(X)(Vxx1*zeta^(X2))
+
+perms1=[3,4,1,2,5];
+perms2=[2,1,3];
+Matrix=Ix3_Ezeta2;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vxx0,Vxx1);
+
+% Vx0(X)P(Vxx1*P(hx(X)zeta))(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,4,3,5;3,4,1,2,5;4,3,1,2,5];
+perms2=[1,2,3;1,2,3;1,2,3];
+Matrix=kron(kron(Ix,hx),Ezeta3);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vxx1,Vxx1);
+
+% Vx0(X)(Vxx1*P(hx(X)zeta))(X)(Vxx1*P(zeta(X)hx))
+
+perms1=[2,1,3,4,5;1,2,4,3,5;2,1,4,3,5];
+perms2=[1,2,3;1,2,3;1,2,3];
+Matrix=kron(kron(Ix,hx),kron(Ezeta2,hx));
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vxx1,Vxx1);
+
+% Vx0(X)(Vxx1*zeta^(X2)(X)(Vxx1*zeta^(X2))
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ix,Ezeta4);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx0,Vxx1,Vxx1);
+
+% (Vx1*zeta)(X)P((Vxx1*P(zeta(X)hx))(X)Vxx0)
+
+perms1=[1,2,4,3,5;3,4,1,2,5;4,3,1,2,5];
+perms2=[1,2,3;2,1,3;2,1,3];
+Matrix=kron(kron(Ezeta2,hx),Ix2);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vxx1,Vxx0);
+
+% (Vx1*zeta)(X)P((Vxx1*zeta^(X2)(X)Vxx0)
+
+perms1=[3,4,1,2,5];
+perms2=[2,1,3];
+Matrix=kron(Ezeta3,Ix2);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vxx1,Vxx0);
+
+% (Vx1*zeta)(X)P((Vxx1*zeta^(X2))(X)(Vxx1*P(zeta(X)hx)))
+
+perms1=[2,1,3,4,5;3,4,1,2,5;3,4,2,1,5];
+perms2=[1,2,3;2,1,3;2,1,3];
+Matrix=kron(Ezeta4,hx);
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vxx1,Vxx1);
+
+% (Vx1*zeta)(X)(Vxx1*P(zeta(X)hx))^(X2): this one is different, because the structrue of the
+% unpermuted Matrix does not have all zeta's in a row.
+
+% To calculate expected value of the stochastic Matrix, use
+% kron(Ix,Ix,zeta,zeta,zeta) and permute it.
+Matrix=kron(Ezeta3,hx2);
+tempindex=permute(reshape([1:n_x^5],n_x,n_x,n_x,n_x,n_x),[1,3,2,4,5]);
+Matrix=Matrix(tempindex,tempindex);
+clear tempindex
+
+perms1=[2,1,3,4,5;1,2,4,3,5;2,1,4,3,5;];
+perms2=[1,2,3;1,2,3;1,2,3];
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vxx1,Vxx1);
+
+% (Vx1*zeta)(X)(Vxx1*zeta^(X2))^(X2)
+
+perms1=[];
+perms2=[];
+Matrix=Ezeta5;
+
+result=result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvv,Vx1,Vxx1,Vxx1);
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxx.m b/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxx.m
new file mode 100644
index 0000000000000000000000000000000000000000..2efe5a08561dd1195608499fb888adb7b68602c3
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxx.m
@@ -0,0 +1,85 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0^(X3)(X)Vxx0
+
+derivs=[4,1,1,1,2];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx0,Vxx0);
+
+% Vx0^(X3)(X)(Vxx1*zeta^(X2))
+
+perms1=[];
+perms2=perms1;
+Matrix=Ix3_Ezeta2;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx0,Vxx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)(X)(Vxx1*P(zeta(X)hx))
+
+perms1=[1,2,4,3,5;1,2,4,5,3;2,1,3,4,5;2,1,4,3,5;2,1,4,5,3;];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix2,kron(Ezeta2,hx));
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx1,Vxx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,4,3,5;1,2,4,5,3];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=Ix2_Ezeta3;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx1,Vxx1);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)Vxx0)
+
+perms1=[1,2,3,5,4;1,2,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix,kron(Ezeta2,Ix2));
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx1,Vx1,Vxx0);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)(Vxx1*P(zeta(X)hx))
+
+perms1=[1,2,3,5,4;1,2,5,3,4;2,1,3,4,5;2,1,3,5,4;2,1,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix,kron(Ezeta3,hx));
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx1,Vx1,Vxx1);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,3,5,4;1,2,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=Ix_Ezeta4;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx1,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X3)(X)Vxx0
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta3,Ix2);
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx1,Vx1,Vx1,Vxx0);
+
+% (Vx1*zeta)^(X3)(X)(Vxx1*P(zeta(X)hx)
+
+perms1=[2,1,3,4,5];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ezeta4,hx);
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx1,Vx1,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X3)(X)(Vxx1*zeta2^(X2))
+
+perms1=[];
+perms2=[];
+Matrix=Ezeta5;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx1,Vx1,Vx1,Vxx1);
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxxU5.m b/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxxU5.m
new file mode 100644
index 0000000000000000000000000000000000000000..6efce66fb795677a9afe3d053b945faf508ee61b
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvvEvx3_vxxU5.m
@@ -0,0 +1,85 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0^(X3)(X)Vxx0
+
+derivs=[4,1,1,1,2];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx0,Vx0,Vxx0);
+
+% Vx0^(X3)(X)(Vxx1*zeta^(X2))
+
+perms1=[];
+perms2=perms1;
+Matrix=Ix3_Ezeta2;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx0,Vx0,Vxx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)(X)(Vxx1*P(zeta(X)hx))
+
+perms1=[1,2,4,3,5;1,2,4,5,3;2,1,3,4,5;2,1,4,3,5;2,1,4,5,3;];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix2,kron(Ezeta2,hx));
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx0,Vx1,Vxx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,4,3,5;1,2,4,5,3];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=Ix2_Ezeta3;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx0,Vx1,Vxx1);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)Vxx0)
+
+perms1=[1,2,3,5,4;1,2,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix,kron(Ezeta2,Ix2));
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx1,Vx1,Vxx0);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)(Vxx1*P(zeta(X)hx))
+
+perms1=[1,2,3,5,4;1,2,5,3,4;2,1,3,4,5;2,1,3,5,4;2,1,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ix,kron(Ezeta3,hx));
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx1,Vx1,Vxx1);
+
+% P(Vx0(X)(Vx1*zeta^(X2)(X)(Vxx1*zeta^(X2))
+
+perms1=[1,2,3,5,4;1,2,5,3,4];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=Ix_Ezeta4;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx0,Vx1,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X3)(X)Vxx0
+
+perms1=[];
+perms2=[];
+Matrix=kron(Ezeta3,Ix2);
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx1,Vx1,Vx1,Vxx0);
+
+% (Vx1*zeta)^(X3)(X)(Vxx1*P(zeta(X)hx)
+
+perms1=[2,1,3,4,5];
+perms2=perms1(:,[1,3,4,5]); perms2(perms2==2)=1; perms2(perms2>1)=perms2(perms2>1)-1;
+Matrix=kron(Ezeta4,hx);
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx1,Vx1,Vx1,Vxx1);
+
+% (Vx1*zeta)^(X3)(X)(Vxx1*zeta2^(X2))
+
+perms1=[];
+perms2=[];
+Matrix=Ezeta5;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvv,Vx1,Vx1,Vx1,Vxx1);
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvvEvx4.m b/105/replication_package/solution_methods/Perturbation/fvvvvEvx4.m
new file mode 100644
index 0000000000000000000000000000000000000000..bf60c7f8cb8b4f96d3bb90f73e171a48ecbec4f0
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvvEvx4.m
@@ -0,0 +1,38 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=4;
+
+% Vx0^(X4)
+
+derivs=[4,1,1,1,1];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx0,Vx0);
+
+% P(Vx0(X)[Vx1*zeta)^(X3)]
+
+perms1=[1,2,4,3;1,4,2,3;4,1,2,3];
+perms2=perms1;
+Matrix=Ix_Ezeta3;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx1,Vx1,Vx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)^(X2))
+
+perms1=[1,3,2,4;1,3,4,2;3,1,2,4;3,1,4,2;3,4,1,2];
+perms2=perms1;
+Matrix=Ix2_Ezeta2;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx0,Vx0,Vx1,Vx1);
+
+% (Vx1*zeta)^(X4)
+
+perms1=[];
+perms2=perms1;
+Matrix=Ezeta4;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvv,Vx1,Vx1,Vx1,Vx1);
+
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5.m b/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5.m
new file mode 100644
index 0000000000000000000000000000000000000000..3ac53c9ea03bb80ab3af34fe3b0c590f0f3a3990
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5.m
@@ -0,0 +1,46 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0^(X5)
+
+derivs=[5,1,1,1,1,1];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvvv,Vx0,Vx0,Vx0,Vx0,Vx0);
+
+% P(Vx0(X)[Vx1*zeta)^(X4)]
+
+perms1=[1,2,3,5,4;1,2,5,3,4;1,5,2,3,4;5,1,2,3,4];
+perms2=perms1;
+Matrix=Ix_Ezeta4;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvvv,Vx0,Vx1,Vx1,Vx1,Vx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)^(X3))
+
+perms1=[1,2,4,3,5;1,2,4,5,3;1,4,2,3,5;1,4,2,5,3;1,4,5,2,3;4,1,2,3,5;4,1,2,5,3;4,1,5,2,3;4,5,1,2,3];
+perms2=perms1;
+Matrix=Ix2_Ezeta3;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvvv,Vx0,Vx0,Vx1,Vx1,Vx1);
+
+% P(Vx0^(X3)(X)(Vx1*zeta)^(X2))
+
+perms1=[1,3,2,4,5;1,3,4,2,5;1,3,4,5,2;3,1,2,4,5;3,1,4,2,5;3,1,4,5,2;3,4,1,2,5;3,4,1,5,2;3,4,5,1,2];
+perms2=perms1;
+Matrix=Ix3_Ezeta2;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvvv,Vx0,Vx0,Vx0,Vx1,Vx1);
+
+% (Vx1*zeta)^(X5)
+
+perms1=[];
+perms2=perms1;
+Matrix=Ezeta5;
+
+result= result+permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,fvvvvv,Vx1,Vx1,Vx1,Vx1,Vx1);
+
diff --git a/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5U5.m b/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5U5.m
new file mode 100644
index 0000000000000000000000000000000000000000..5a78247239d1fba7a5f69662f67b0cd7b94ec735
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/fvvvvvEvx5U5.m
@@ -0,0 +1,46 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=5;
+
+% Vx0^(X5)
+
+derivs=[5,1,1,1,1,1];
+perms1=[];
+perms2=perms1;
+Matrix=[];
+
+result= permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvvv,Vx0,Vx0,Vx0,Vx0,Vx0);
+
+% P(Vx0(X)[Vx1*zeta)^(X4)]
+
+perms1=[1,2,3,5,4;1,2,5,3,4;1,5,2,3,4;5,1,2,3,4];
+perms2=perms1;
+Matrix=Ix_Ezeta4;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvvv,Vx0,Vx1,Vx1,Vx1,Vx1);
+
+% P(Vx0^(X2)(X)(Vx1*zeta)^(X3))
+
+perms1=[1,2,4,3,5;1,2,4,5,3;1,4,2,3,5;1,4,2,5,3;1,4,5,2,3;4,1,2,3,5;4,1,2,5,3;4,1,5,2,3;4,5,1,2,3];
+perms2=perms1;
+Matrix=Ix2_Ezeta3;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvvv,Vx0,Vx0,Vx1,Vx1,Vx1);
+
+% P(Vx0^(X3)(X)(Vx1*zeta)^(X2))
+
+perms1=[1,3,2,4,5;1,3,4,2,5;1,3,4,5,2;3,1,2,4,5;3,1,4,2,5;3,1,4,5,2;3,4,1,2,5;3,4,1,5,2;3,4,5,1,2];
+perms2=perms1;
+Matrix=Ix3_Ezeta2;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvvv,Vx0,Vx0,Vx0,Vx1,Vx1);
+
+% (Vx1*zeta)^(X5)
+
+perms1=[];
+perms2=perms1;
+Matrix=Ezeta5;
+
+result= result+permutekron3(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,Ui,fvvvvv,Vx1,Vx1,Vx1,Vx1,Vx1);
+
diff --git a/105/replication_package/solution_methods/Perturbation/gaussian_moments.m b/105/replication_package/solution_methods/Perturbation/gaussian_moments.m
new file mode 100644
index 0000000000000000000000000000000000000000..c0f9493a0e199d2013f0f8b12d7f8b656a6f072d
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/gaussian_moments.m
@@ -0,0 +1,29 @@
+function [ M ] = gaussian_moments( n_e )
+%Calculate cross moments of a stochastic vector of size n_e-by-1
+%distributed normally with mean zero(n_e,1) and variance matrix eye(n_e).
+%The cross moments are defined:
+%M2=E(kron(x,x))
+%M3=E(kron(x,x,x))
+%M4=E(kron(x,x,x,x))
+%M5=E(kron(x,x,x,x,x))
+%They are stored as fields of struct M.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+M.M2=speye(n_e); M.M2=M.M2(:);
+M.M3=sparse(n_e^3,1);
+M.M4=sparse(n_e^4,1);
+for i=1:n_e
+ M.M4(sub2ind([n_e,n_e,n_e,n_e],i,i,i,i))=3;
+end
+for i=1:n_e-1
+ for j=i+1:n_e
+ tempP=perms([i,i,j,j]);
+ M.M4(sub2ind([n_e,n_e,n_e,n_e],tempP(:,1),tempP(:,2),tempP(:,3),tempP(:,4)))=1;
+ end
+end
+
+M.M5=sparse(n_e^5,1);
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/gen_fun.m b/105/replication_package/solution_methods/Perturbation/gen_fun.m
new file mode 100644
index 0000000000000000000000000000000000000000..1db402ced1c90c83c24e75b492e9b8512ca7ba7e
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/gen_fun.m
@@ -0,0 +1,49 @@
+function gen_fun(f,symparams,v,fname,varargin)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+rowformat=0; % function returns a column vector (number of columns>1 in vectorized form)
+if ~isempty(varargin)
+ if strcmp(varargin{1},'row')
+ rowformat=1; % function returns a row vector (number of rows>1 in vectorized form)
+ end
+end
+
+f=f(:);
+if numel(f)>1
+ nnzf=1-logical(f==0);
+ index=find(nnzf);
+else
+ index=1;
+end
+fid = fopen([fname '_fun.m'], 'w');
+fprintf(fid,'%s\n', ['function function_f=' fname '_fun(variables_v,parameters)']);
+for i=1:length(symparams)
+ if strcmp(char(symparams(i)),'function_f') || strcmp(char(symparams(i)),'variables_v') || strcmp(char(symparams(i)),'parameters')
+ error([char(symparams(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ fprintf(fid,'%s\n', [char(symparams(i)) '=parameters(' num2str(i) ');']);
+end
+for i=1:length(v)
+ if strcmp(char(v(i)),'function_f') || strcmp(char(v(i)),'variables_v') || strcmp(char(v(i)),'parameters')
+ error([char(v(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ fprintf(fid,'%s\n', [char(v(i)) '=variables_v(' num2str(i) ',:);']);
+end
+if isempty(f)
+ fprintf(fid,'%s\n', ['function_f=[];']);
+else
+ if rowformat==0
+ fprintf(fid,'%s\n', ['function_f=zeros(' num2str(numel(f)) ',size(variables_v,2));']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', ['function_f=zeros(size(variables_v,2),' num2str(numel(f)) ');']);
+ end
+ for i=index(:)'
+ if rowformat==0
+ disp_fun('function_f',f(i),i,fid);
+ elseif rowformat==1
+ disp_fun_row('function_f',f(i),i,fid);
+ end
+ end
+end
+fclose(fid);
diff --git a/105/replication_package/solution_methods/Perturbation/getderivs.m b/105/replication_package/solution_methods/Perturbation/getderivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..6e2965368964286e78345011cd19f50653e71047
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/getderivs.m
@@ -0,0 +1,104 @@
+function [index]=getderivs(f,v,order,symparams,fname)
+%This function differentiates f w.r.t v up to order, and generates
+%vectorized functions that calculate these derivatives. The derivatives are
+%stored in a sparse matrix of dimensions n_f,n_v^order, where n_f
+%is the size of f and n_v is the size of v.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+if order<1
+ error('order must be at least 1')
+end
+
+f=f(:);
+v=v(:);
+
+n_f=length(f);
+n_v=length(v);
+
+uncomp=cell(n_f,order);
+derivs=cell(n_f,order);
+
+% differentiate rows of f separately w.r.t to relevant variables ONLY
+relevant_v=logical(jacobian(f(:),v)~=0);
+for frow=1:n_f
+ [derivs(frow,:),uncomp(frow,:)]=compderivs(f(frow),v(relevant_v(frow,:)),order);
+end
+
+% transform uncompression matrices into indices, and create totalloc.
+% totalloc(frow,k) stores the total number of nonzero k-order derivatives of f(frow), including all (nonzero) mixed derivatives.
+index=[];
+totalloc=zeros(n_f,order);
+for k=1:order
+ for frow=1:n_f
+ [index.loc{frow,k},index.nnz{frow,k}]=find(uncomp{frow,k});
+ totalloc(frow,k)=length(index.loc{frow,k});
+ if isempty(index.loc{frow,k})
+ index.loc{frow,k}=0;
+ end
+ end
+end
+
+% create matlab functions to calculate the derivatives
+for k=1:order
+ fun_name=[fname '_d' num2str(k)];
+ fid = fopen([fun_name '.m'], 'w');
+ fprintf(fid,'%s\n', ['function derivs=' fun_name '(vars,params,index)']);
+% fprintf(fid,'%s\n', 'n_s=size(vars,1);');
+ for i=1:length(v)
+ fprintf(fid,'%s\n', [char(v(i)) '=vars(' num2str(i) ');']);
+ end
+ for i=1:length(symparams)
+ fprintf(fid,'%s\n', [char(symparams(i)) '=params(' num2str(i) ');']);
+ end
+ fprintf(fid,'%s\n', ['full_rows=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_cols=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_vals=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+
+ for frow=1:n_f
+ if totalloc(frow,k)>0
+ tempderiv=derivs{frow,k};
+ fprintf(fid,'%s\n', ['compressed_deriv=zeros(' num2str(length(tempderiv)) ',1);']);
+ for i=1:length(tempderiv)
+ disp_fun('compressed_deriv',tempderiv(i),i,fid);
+ end
+ fprintf(fid,'%s\n', ['uncompressed_deriv=compressed_deriv(index.nnz{' num2str(frow) ',' num2str(k) '});']);
+ tempstart=sum(totalloc(1:frow-1,k));
+ tempend=sum(totalloc(1:frow,k));
+ fprintf(fid,'%s\n', ['full_vals(' num2str(tempstart+1) ':' num2str(tempend) ')=uncompressed_deriv;']);
+
+ % transform columns to n-dimensions
+ tempcols='tempcol1';
+ n_relevant_v=sum(relevant_v(frow,:));
+ tempdim=num2str(n_relevant_v);
+ for tempk=2:k
+ tempcols=[tempcols ',tempcol' num2str(tempk)];
+ tempdim=[tempdim ',' num2str(n_relevant_v)];
+ end
+ eval(['[' tempcols ']=ind2sub([' tempdim '],index.loc{' num2str(frow) ',' num2str(k) '});']);
+ tempcols=eval(['[' tempcols ']']);
+ % each row of f was differentiated w.r.t relevant variables.
+ % now, translate dimensions to the full vector of variables.
+ tempv=1:n_v;
+ takev=tempv(relevant_v(frow,:));
+ tempcols=takev(tempcols);
+ % return to linear index
+ tempdims='tempcols(:,1)';
+ for tempi=2:size(tempcols,2)
+ tempdims=[tempdims,',tempcols(:,' num2str(tempi) ')'];
+ end
+ if k>1
+ eval(['tempcols=sub2ind(repmat(' num2str(n_v) ',1,' num2str(k) '),' tempdims ');']);
+ end
+ index.loc{frow,k}=tempcols;
+ fprintf(fid,'%s\n', ['full_cols(' num2str(tempstart+1) ':' num2str(tempend) ')=index.loc{' num2str(frow) ',' num2str(k) '};']);
+
+ fprintf(fid,'%s\n', ['full_rows(' num2str(tempstart+1) ':' num2str(tempend) ')=' num2str(frow) ';']);
+ end
+ end
+ fprintf(fid,'%s\n', ['derivs=sparse(full_rows,full_cols,full_vals,' num2str(n_f) ',' num2str(n_v^k) ');']);
+ fclose(fid);
+end
+
+
diff --git a/105/replication_package/solution_methods/Perturbation/getderivs_vector.m b/105/replication_package/solution_methods/Perturbation/getderivs_vector.m
new file mode 100644
index 0000000000000000000000000000000000000000..65b46fb783a35b4da0f250e91f0f64fc0962cd63
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/getderivs_vector.m
@@ -0,0 +1,102 @@
+function [index]=getderivs_vector(f,v,order,symparams,fname)
+%This function differentiates f w.r.t v up to order, and generates
+%vectorized functions that calculate these derivatives. The derivatives are
+%stored in a sparse column vector of length n_f*n_v^order, where n_f
+%is the size of f and n_v is the size of v.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+if order<1
+ error('order must be at least 1')
+end
+
+f=f(:);
+v=v(:);
+
+n_f=length(f);
+n_v=length(v);
+
+uncomp=cell(n_f,order);
+derivs=cell(n_f,order);
+
+% differentiate rows of f separately w.r.t to relevant variables ONLY
+relevant_v=logical(jacobian(f(:),v)~=0);
+for frow=1:n_f
+ [derivs(frow,:),uncomp(frow,:)]=compderivs(f(frow),v(relevant_v(frow,:)),order);
+end
+
+% transform uncompression matrices into indices, and create totalloc.
+% totalloc(frow,k) stores the total number of nonzero k-order derivatives of f(frow), including all (nonzero) mixed derivatives.
+index=[];
+totalloc=zeros(n_f,order);
+for k=1:order
+ for frow=1:n_f
+ [index.loc{frow,k},index.nnz{frow,k}]=find(uncomp{frow,k});
+ totalloc(frow,k)=length(index.loc{frow,k});
+ if isempty(index.loc{frow,k})
+ index.loc{frow,k}=0;
+ end
+ end
+end
+
+% create matlab functions to calculate the derivatives
+for k=1:order
+ fun_name=[fname '_d' num2str(k)];
+ fid = fopen([fun_name '.m'], 'w');
+ fprintf(fid,'%s\n', ['function derivs=' fun_name '(vars,params,index)']);
+ for i=1:length(v)
+ fprintf(fid,'%s\n', [char(v(i)) '=vars(' num2str(i) ');']);
+ end
+ for i=1:length(symparams)
+ fprintf(fid,'%s\n', [char(symparams(i)) '=params(' num2str(i) ');']);
+ end
+ fprintf(fid,'%s\n', ['full_rows=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_vals=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+
+ for frow=1:n_f
+ if totalloc(frow,k)>0
+ tempderiv=derivs{frow,k};
+ fprintf(fid,'%s\n', ['compressed_deriv=zeros(' num2str(length(tempderiv)) ',1);']);
+ for i=1:length(tempderiv)
+ disp_fun('compressed_deriv',tempderiv(i),i,fid);
+ end
+ fprintf(fid,'%s\n', ['uncompressed_deriv=compressed_deriv(index.nnz{' num2str(frow) ',' num2str(k) '});']);
+ tempstart=sum(totalloc(1:frow-1,k));
+ tempend=sum(totalloc(1:frow,k));
+ fprintf(fid,'%s\n', ['full_vals(' num2str(tempstart+1) ':' num2str(tempend) ')=uncompressed_deriv;']);
+
+ % transform columns to n-dimensions
+ tempcols='tempcol1';
+ n_relevant_v=sum(relevant_v(frow,:));
+ tempdim=num2str(n_relevant_v);
+ for tempk=2:k
+ tempcols=[tempcols ',tempcol' num2str(tempk)];
+ tempdim=[tempdim ',' num2str(n_relevant_v)];
+ end
+ eval(['[' tempcols ']=ind2sub([' tempdim '],index.loc{' num2str(frow) ',' num2str(k) '});']);
+ tempcols=eval(['[' tempcols ']']);
+ % each row of f was differentiated w.r.t relevant variables.
+ % now, translate dimensions to the full vector of variables.
+ tempv=1:n_v;
+ takev=tempv(relevant_v(frow,:));
+ tempcols=takev(tempcols);
+ % create a linear index
+ tempdims='tempcols(:,1)';
+ for tempi=2:size(tempcols,2)
+ tempdims=[tempdims,',tempcols(:,' num2str(tempi) ')'];
+ end
+ if k>1
+ eval(['tempcols=sub2ind(repmat(' num2str(n_v) ',1,' num2str(k) '),' tempdims ');']);
+ end
+ index.loc{frow,k}=sub2ind([n_f,n_v^k],repmat(frow,length(tempcols),1),tempcols(:));
+
+ fprintf(fid,'%s\n', ['full_rows(' num2str(tempstart+1) ':' num2str(tempend) ')=index.loc{' num2str(frow) ',' num2str(k) '};']);
+
+ end
+ end
+ fprintf(fid,'%s\n', ['derivs=sparse(full_rows,ones(length(full_vals),1),full_vals,' num2str(n_f*n_v^k) ',1);']);
+ fclose(fid);
+end
+
+
diff --git a/105/replication_package/solution_methods/Perturbation/innerkron.m b/105/replication_package/solution_methods/Perturbation/innerkron.m
new file mode 100644
index 0000000000000000000000000000000000000000..b0566a60ab28947945e38ed1fff2ed78466fd834
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/innerkron.m
@@ -0,0 +1,21 @@
+function [ R ] = innerkron( n_f,n_v,fmat, varargin )
+%innerkron Calculates expressions such as fmat(A*B*C....), where fmat is a
+%matrix with symmetric columns. A, B, C, ..., are matrices, and * is a
+%Kronecker product. These expressions arise in high order multivariate
+%chain rules of the composite function f(v(x)). In this case, fmat is an
+%array of high derivatives of f w.r.t v, reshaped into a matrix with the
+%same number of rows as f. A, B, C, etc would be derivatives of v w.r.t x.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+R=fmat;
+
+for j=1:length(varargin)
+ R=reshape(R,numel(R)/n_v,n_v);
+ R=(R*reshape(varargin{j},n_v,numel(varargin{j})/n_v))';
+end
+
+R=reshape(R,numel(R)/n_f,n_f)';
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/permutekron2.m b/105/replication_package/solution_methods/Perturbation/permutekron2.m
new file mode 100644
index 0000000000000000000000000000000000000000..aab9fa8d0358584d2563f7bbafa7e600f073f15a
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/permutekron2.m
@@ -0,0 +1,142 @@
+function [ R ] = permutekron2(derivs,order,perms1,perms2,n_v,n_x,n_f,Matrix,varargin )
+%permutekron: This function calculates expressions such as
+%(fvvv*kron(Vx0,Vx1,Vx1))*E(kron(hx,zeta,zeta)), or
+%(fvvv*kron(Vx0,Vx1,Vx1))*E(kron(I,zeta,zeta))*(kron(hx,I,I)), which is
+%equivalent. The function also calculates permutations of these
+%expressions. The permutations are in perms1 and perms2. The output is the sum
+%of all permutations.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(Matrix) % no stochastic matrix
+ stochastic_matrix_exists=0;
+ Matrix=1;
+else
+ stochastic_matrix_exists=1;
+end
+
+if nnz(Matrix)==0 % stochastic matrix is all zero
+ R=sparse(n_f,n_x^order);
+else
+ if isempty(perms2)
+ perms2_exists=0; % no permutation for nonstochastic part
+ perms2_trivial=1;
+ elseif nnz(perms2-repmat(1:size(perms2,2),size(perms2,1),1))==0
+ perms2_exists=0; % permutation for nonstochastic part are degenerate
+ perms2_trivial=1;
+ else
+ perms2_exists=1;
+ perms2_order=size(perms2,2);
+ end
+
+ % 2. The second term is the stochastic matrix
+
+ R=Matrix;
+ stochR=R;
+ % 3. Prepare an index for the permutations.
+
+ if order>1 && ~isempty(perms1)
+ tempind=[1:n_x^order];
+ ind1=reshape(tempind,repmat(n_x,1,order));
+ if perms2_exists==1
+ ind2=reshape(tempind,[n_x.^derivs(end:-1:2),1]);
+ end
+ clear tempind
+
+% sparseM=speye(n_x^order);
+ end
+
+ % 4. Calculate permutations and sum.
+
+ for i=1:size(perms1,1)
+ % a. Permute
+ if isequal(perms1(i,:),1:order)
+ perms1_trivial=1;
+ else
+ permute_ind1=permute(ind1,perms1(i,:));
+ perms1_trivial=0;
+ end
+ if perms2_exists==1
+ if isequal(perms2(i,:),1:perms2_order)
+ perms2_trivial=1;
+ else
+% permute_ind2=permute(ind2,perms2(i,:));
+ ipermute_ind2=ipermute(ind2,perms2(i,:));
+ perms2_trivial=0;
+ end
+ end
+ if perms1_trivial==0
+ if perms2_trivial==0
+% permute_stochR=sparseM(:,permute_ind2)*sparseM(:,permute_ind1)'*stochR(:,permute_ind1);%P2*P1'*M*P1
+ permute_stochR=stochR(:,permute_ind1);
+
+ permute_stochR=permute_stochR(permute_ind1(ipermute_ind2),:);
+% max(max(abs(permute_stochR-ipermute_stochR)))
+% isequal(permute_stochR,ipermute_stochR)
+ else
+% permute_stochR=sparseM(:,permute_ind1)'*stochR(:,permute_ind1);
+ permute_stochR=stochR(:,permute_ind1);
+ permute_stochR=permute_stochR(permute_ind1,:);
+% isequal(permute_stochR,ipermute_stochR)
+ end
+ else
+ if perms2_trivial==0
+% permute_stochR=sparseM(:,permute_ind2)*stochR;
+ permute_stochR=stochR(ipermute_ind2,:);
+ else
+ permute_stochR=stochR;
+ end
+ end
+ % b. Sum
+ R=R+permute_stochR;
+ end
+
+
+ % 1. Calculate the nonstochastic part: For example:
+ % fvvv*kron(Vx0,Vx1,Vx1).
+ if stochastic_matrix_exists==0
+ fmat=varargin{1};
+
+ temp=reshape(fmat,numel(fmat)/n_v,n_v);
+ for j=1:length(derivs)-2
+ temp=Treshape(bigprod(temp,sparse(varargin{j+1})),numel(temp)/n_v^2*n_x^derivs(j+1),n_v);
+ end
+
+ j=length(derivs)-1;
+ nonstoch=[reshape([temp*sparse(varargin{j+1})]',numel(temp)/n_v*n_x^derivs(j+1)/n_f,n_f)]';
+ R=nonstoch*R;
+ else
+ nnzx=logical(sum(logical(R),2));
+
+ fmat=varargin{1};
+ temp=reshape(fmat,numel(fmat)/n_v,n_v);
+ for j=1:length(derivs)-2
+ vmat=sparse(varargin{j+1});
+ % choose nonzero columns of vmat
+ nnzx=reshape(nnzx,n_x^(order-derivs(j+1)),n_x^derivs(j+1));
+ tempind=logical(sum(nnzx,1)); % identify relevant columns
+ vmat=vmat(:,tempind); % extract relevant columns
+ % add the zero columns
+ [temprow,tempcol,tempvals]=find(vmat);
+ ztempind=find(tempind);
+ vmat=sparse(temprow,ztempind(tempcol),tempvals,size(vmat,1),n_x^derivs(j+1));
+
+ temp=Treshape(bigprod(temp,vmat),numel(temp)/n_v^2*n_x^derivs(j+1),n_v);
+ nnzx=nnzx';
+ end
+
+ j=length(derivs)-1;
+ vmat=sparse(varargin{j+1});
+ % choose nonzero columns of vmat
+ nnzx=reshape(nnzx,n_x^(order-derivs(j+1)),n_x^derivs(j+1));
+ tempind=logical(sum(nnzx,1)); % identify relevant columns
+ vmat=vmat(:,tempind); % extract relevant columns
+ % add the zero columns
+ [temprow,tempcol,tempvals]=find(vmat);
+ ztempind=find(tempind);
+ vmat=sparse(temprow,ztempind(tempcol),tempvals,size(vmat,1),n_x^derivs(j+1));
+ nonstoch=[reshape([bigprod(temp,vmat)]',numel(temp)/n_v*n_x^derivs(j+1)/n_f,n_f)]';
+ R=nonstoch*R;
+ end
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/permutekronB2.m b/105/replication_package/solution_methods/Perturbation/permutekronB2.m
new file mode 100644
index 0000000000000000000000000000000000000000..e4c3e7d641ad256a6d652b5c4dc24875dda086cf
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/permutekronB2.m
@@ -0,0 +1,40 @@
+
+function [ R ] = permutekronB2(order,perms1,n_x,Matrix,varargin )
+%permutekronB: This function calculates product of two or three matrices of
+%the form:W3*E(kron(hx,zeta,zeta)) or W3*E(kron(hx,zeta,zeta))*(hx*I*I), and
+%permutations of this expression, and sums everything.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+W=varargin{1};
+unique=size(W,1);
+
+if nnz(Matrix)==0
+ R=sparse(unique,n_x^order);
+else
+ % 1. Calculate product of first two terms.
+
+ R=W*Matrix;
+
+ % 2. Prepare an index for the permutations.
+
+ if order>1
+ ind=reshape([1:n_x^order],repmat(n_x,1,order));
+ end
+
+ % 4. Calculate permutations and sum.
+
+ for i=1:size(perms1,1)
+ % a. permute the (expected value of the) stochastic part by permutation
+ % indices.
+ permute_ind=permute(ind,perms1(i,:));
+ permute_Matrix=Matrix(permute_ind,permute_ind);
+
+ tempresult=W*permute_Matrix;
+
+ % b. Sum everything.
+ R=R+tempresult;
+ end
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/policy.m b/105/replication_package/solution_methods/Perturbation/policy.m
new file mode 100644
index 0000000000000000000000000000000000000000..b9fc1f9beed8d0d7bfef7240e0a878540e1e8acc
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/policy.m
@@ -0,0 +1,56 @@
+function [ g,h ] = policy( nx,nyss,nxss,derivs,approx,varargin )
+%[g,h]=policy(nx,nxss,derivs,approx) evaluates the policy functions g and h
+% at state nx, given the steady state values nyss and nxss, the structure
+% derivs and the approximation order approx.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+[n_y,n_x]=size(derivs.gx);
+
+
+xhat=[nx(:)-nxss(:);1];
+
+pf=[derivs.gx;derivs.hx]*xhat;
+
+n_f=length(pf);
+
+if isempty(varargin)
+
+ if approx>=2
+ xhat2=kron(xhat,xhat);
+ pf=pf+[derivs.gxx;derivs.hxx]*xhat2/2;
+ end
+ if approx>=3
+ xhat3=kron(xhat2,xhat);
+ pf=pf+[derivs.gxxx;derivs.hxxx]*xhat3/6;
+ end
+ if approx>=4
+ xhat4=kron(xhat3,xhat);
+ pf=pf+[derivs.gxxxx;derivs.hxxxx]*xhat4/24;
+ end
+ if approx>=5
+ xhat5=kron(xhat4,xhat);
+ pf=pf+[derivs.gxxxxx;derivs.hxxxxx]*xhat5/120;
+ end
+else
+ derivsc=varargin{1};
+ if approx>=2
+ pf=pf+innerkron(n_f,n_x,[derivsc.gxx;derivsc.hxx],xhat,xhat)/2;
+ end
+ if approx>=3
+ pf=pf+innerkron(n_f,n_x,[derivsc.gxxx;derivsc.hxxx],xhat,xhat,xhat)/6;
+ end
+ if approx>=4
+ pf=pf+innerkron(n_f,n_x,[derivsc.gxxxx;derivsc.hxxxx],xhat,xhat,xhat,xhat)/24;
+ end
+ if approx>=5
+ pf=pf+innerkron(n_f,n_x,[derivsc.gxxxxx;derivsc.hxxxxx],xhat,xhat,xhat,xhat,xhat)/120;
+ end
+end
+R=pf+[nyss;nxss];
+
+g=R(1:n_y);
+h=R(n_y+1:end);
+
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/simul.m b/105/replication_package/solution_methods/Perturbation/simul.m
new file mode 100644
index 0000000000000000000000000000000000000000..e7fc15be47741fb89dae034941c858de9abaf555
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/simul.m
@@ -0,0 +1,169 @@
+function [yt,xt]=simul(x0,shocks,nyss,nxss,eta,derivs,approx,pruning,varargin)
+% [yt,xt]=simul(x0,shocks,nyss,nxss,eta,derivs,approx,pruning) simulates
+% the model from the initial state x0. shocks is a matrix with n_e rows
+% and T columns, where n_e is the number of shocks (corresponds to the
+% columns of eta), and T is the length of the simulation. The function
+% returns yt and xt for T+1 periods. The first period is the initial state
+% and the rest T periods correspond to the shocks. pruning=0 is a simple
+% simulation without pruning. pruning=1 is a pruned simulation. The
+% pruning algorithm follows Andreasen, Fernandez-Villaverde and
+% Rubio-Ramirez (2013) "The Pruned State-Space System for Non-Linear DSGE Models:
+% Theory and Empirical Applications".
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if ~isempty(varargin)
+ model=varargin{1};
+ if approx>=2
+ tempmat=model.UW.U2*model.UW.W2*model.UW.W2'*model.UW.U2';
+ derivsc.gxx=sparse(derivs.gxx)*tempmat;
+ derivsc.hxx=sparse(derivs.hxx)*tempmat;
+ end
+ if approx>=3
+ tempmat=model.UW.U3*model.UW.W3*model.UW.W3'*model.UW.U3';
+ derivsc.gxxx=sparse(derivs.gxxx)*tempmat;
+ derivsc.hxxx=sparse(derivs.hxxx)*tempmat;
+ end
+ if approx>=4
+ tempmat=model.UW.U4*model.UW.W4*model.UW.W4'*model.UW.U4';
+ derivsc.gxxxx=sparse(derivs.gxxxx)*tempmat;
+ derivsc.hxxxx=sparse(derivs.hxxxx)*tempmat;
+ end
+ if approx>=5
+ tempmat=model.UW.U5*model.UW.W5*model.UW.W5'*model.UW.U5';
+ derivsc.gxxxxx=sparse(derivs.gxxxxx)*tempmat;
+ derivsc.hxxxxx=sparse(derivs.hxxxxx)*tempmat;
+ end
+end
+
+if approx>=2
+ n_x=length(nxss)+1;
+ derivs.gxx=reshape(derivs.gxx,[],n_x^2);
+ derivs.hxx=reshape(derivs.hxx,[],n_x^2);
+end
+if approx>=3
+ derivs.gxxx=reshape(derivs.gxxx,[],n_x^3);
+ derivs.hxxx=reshape(derivs.hxxx,[],n_x^3);
+end
+if approx>=4
+ derivs.gxxxx=reshape(derivs.gxxxx,[],n_x^4);
+ derivs.hxxxx=reshape(derivs.hxxxx,[],n_x^4);
+end
+if approx>=5
+ derivs.gxxxxx=reshape(derivs.gxxxxx,[],n_x^5);
+ derivs.hxxxxx=reshape(derivs.hxxxxx,[],n_x^5);
+end
+
+T=size(shocks,2);
+n_y=size(derivs.gx,1);
+n_x=size(derivs.hx,1);
+n_e=size(shocks,1);
+shocks=[zeros(n_e,1),shocks,zeros(n_e,1)];
+if pruning==0
+ yt=zeros(n_y,T+2);
+ xt=zeros(n_x,T+2);
+ xt(:,1)=x0;
+ for t=1:T+1
+ nx=xt(:,t);
+ if isempty(varargin)
+ [g,h]=policy( nx,nyss,nxss,derivs,approx );
+ else
+ [g,h]=policy( nx,nyss,nxss,derivs,approx,derivsc );
+ end
+ yt(:,t)=g;
+ xt(:,t+1)=h+eta*shocks(:,t+1);
+ end
+ xt=xt(:,1:T+1);
+ yt=yt(:,1:T+1);
+elseif pruning==1
+ xt_f=zeros(n_x+1,T+2);
+ yt=zeros(n_y,T+2);
+ if approx>=2
+ xt_s=zeros(n_x+1,T+2);
+ end
+ if approx>=3
+ xt_rd=zeros(n_x+1,T+2);
+ end
+ if approx>=4
+ xt_4th=zeros(n_x+1,T+2);
+ end
+ if approx>=5
+ xt_5th=zeros(n_x+1,T+2);
+ end
+
+ xt_f(1:end-1,1)=x0-nxss;
+ xt_f(end,:)=1;
+
+ for t=1:T+1
+ x_f=xt_f(:,t);
+ xt_f(1:end-1,t+1)=derivs.hx*x_f+eta*shocks(:,t+1);
+ if approx>=2
+ x_s=xt_s(:,t);
+ x_f2=kron(x_f,x_f);
+ xt_s(1:end-1,t+1)=derivs.hx*x_s+derivs.hxx*x_f2/2;
+ end
+ if approx>=3
+ x_rd=xt_rd(:,t);
+ x_f3=kron(x_f2,x_f);
+ x_f_x_s=kron(x_f,x_s);
+ xt_rd(1:end-1,t+1)=derivs.hx*x_rd+derivs.hxx*(2*x_f_x_s)/2+derivs.hxxx*x_f3/6;
+ end
+ if approx>=4
+ x_4th=xt_4th(:,t);
+ x_f4=kron(x_f3,x_f);
+ x_f2_x_s=kron(x_f,x_f_x_s);
+ x_s2=kron(x_s,x_s);
+ x_f_x_rd=kron(x_f,x_rd);
+ xt_4th(1:end-1,t+1)=derivs.hx*x_4th+derivs.hxx*(2*x_f_x_rd+x_s2)/2 ...
+ +derivs.hxxx*(3*x_f2_x_s)/6 ...
+ +derivs.hxxxx*x_f4/24;
+ end
+ if approx>=5
+ x_5th=xt_5th(:,t);
+ x_f5=kron(x_f4,x_f);
+ x_f3_x_s=kron(x_f,x_f2_x_s);
+ x_f_x_s2=kron(x_f,x_s2);
+ x_f2_x_rd=kron(x_f,x_f_x_rd);
+ x_s_x_rd=kron(x_s,x_rd);
+ x_f_x_4th=kron(x_f,x_4th);
+ xt_5th(1:end-1,t+1)=derivs.hx*x_5th+derivs.hxx*(2*x_f_x_4th+2*x_s_x_rd)/2 ...
+ +derivs.hxxx*(3*x_f2_x_rd+3*x_f_x_s2)/6 ...
+ +derivs.hxxxx*(4*x_f3_x_s)/24 ...
+ +derivs.hxxxxx*x_f5/120;
+ end
+ if approx==1
+ yt(:,t)=derivs.gx*(x_f);
+ elseif approx==2
+ yt(:,t)=derivs.gx*(x_f+x_s)+derivs.gxx*(x_f2)/2;
+ elseif approx==3
+ yt(:,t)=derivs.gx*(x_f+x_s+x_rd)+derivs.gxx*(x_f2+2*x_f_x_s)/2 ...
+ +derivs.gxxx*(x_f3)/6;
+ elseif approx==4
+ yt(:,t)=derivs.gx*(x_f+x_s+x_rd+x_4th)+derivs.gxx*(x_f2+2*x_f_x_s+2*x_f_x_rd+x_s2)/2 ...
+ +derivs.gxxx*(x_f3+3*x_f2_x_s)/6 ...
+ +derivs.gxxxx*x_f4/24;
+ elseif approx==5
+ yt(:,t)=derivs.gx*(x_f+x_s+x_rd+x_4th+x_5th)+derivs.gxx*(x_f2+2*x_f_x_s+2*x_f_x_rd+2*x_f_x_4th+x_s2+2*x_s_x_rd)/2 ...
+ +derivs.gxxx*(x_f3+3*x_f2_x_s+3*x_f2_x_rd+3*x_f_x_s2)/6 ...
+ +derivs.gxxxx*(x_f4+4*x_f3_x_s)/24 ...
+ +derivs.gxxxxx*x_f5/120;
+ end
+ end
+ yt=yt(:,1:T+1);
+ xt=xt_f(:,1:T+1);
+ if approx>=2
+ xt=xt+xt_s(:,1:T+1);
+ end
+ if approx>=3
+ xt=xt+xt_rd(:,1:T+1);
+ end
+ if approx>=4
+ xt=xt+xt_4th(:,1:T+1);
+ end
+ if approx>=5
+ xt=xt+xt_5th(:,1:T+1);
+ end
+ yt=yt+repmat(nyss,1,T+1);
+ xt=xt(1:end-1,:)+repmat(nxss,1,T+1);
+end
+
diff --git a/105/replication_package/solution_methods/Perturbation/solve_dsge.m b/105/replication_package/solution_methods/Perturbation/solve_dsge.m
new file mode 100644
index 0000000000000000000000000000000000000000..2d140d42d1ec61beb3a72d4745ab4626c3a20a42
--- /dev/null
+++ b/105/replication_package/solution_methods/Perturbation/solve_dsge.m
@@ -0,0 +1,1002 @@
+function [derivs,sol_time,deriv_time]=solve_dsge(model,params,M,eta,nxss,nyss,approx,algo,varargin)
+%solve_dsge(model,params,M,eta,nxss,nyss,approx,algo,gx,hx)
+%This function solves the dsge model with perturbation up to a fifth
+%order.
+%Input variables:
+%model: a structure that is generated automatically by the function
+%differentiate_dsge.m
+%params: a vector of all parameter values ordered in the same order of symparams.
+%M: a structure that contains all the cross moments of the shocks. The fields of
+%this structure should be M2,M3,M4,M5.
+%eta: The matrix eta as defined in Schmitt-Grohe and Uribe (2004).
+%nxss,nyss: steady state values of x and y
+%algo: algorithm type. 'dlyap' for dlyap or 'vectorize' for vectorization.
+%gx,hx: first order solutions. These arguments are optional. If not supplied, the first order solution is calculated
+%by the function gx_hx.m written by Schmitt-Grohe and Uribe (2004).
+%
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if strcmpi(algo,'binning')
+ kamenik_type=1;
+ algo='Kamenik';
+elseif strcmpi(algo,'gensylv')
+ kamenik_type=2;
+ algo='Kamenik';
+elseif ~strcmpi(algo,'dlyap') && ~strcmpi(algo,'vectorize')
+ error('wrong algorithm')
+end
+
+sol_time=0;
+
+n_f=model.n_f;
+n_x=model.n_x;
+n_y=model.n_y;
+n_x2=model.n_x2;
+n_x1=model.n_x1;
+n_v=model.n_v;
+
+f_ind=model.f_ind;
+UW=model.UW; % IMPORTANT: THESE COMPRESSION MATRICES ASSUME A CERTAIN NONZERO PATTERN.
+OMEGA_x=model.OMEGA_x;
+
+if isempty(OMEGA_x)
+ create_OMEGA_x;
+end
+
+n_e=size(eta,2);
+eta=[eta;zeros(1,n_e)];
+
+nxss=[nxss(:);0]; % add steady state value of the perturbation variable.
+nyss=nyss(:);
+
+nPhi=Phi_fun(nxss,params);
+if approx>=1
+ nPhix=Phi_d1(nxss',params,model.Phi_ind);
+end
+if approx>=2
+ W2=UW.W2; U2=UW.U2;
+ nPhixx=Phi_d2(nxss',params,model.Phi_ind);
+end
+if approx>=3
+ W3=UW.W3; U3=UW.U3;
+ nPhixxx=Phi_d3(nxss',params,model.Phi_ind);
+end
+if approx>=4
+ W4=UW.W4; U4=UW.U4;
+ nPhixxxx=Phi_d4(nxss',params,model.Phi_ind);
+end
+if approx>=5
+ W5=UW.W5; U5=UW.U5;
+ nPhixxxxx=Phi_d5(nxss',params,model.Phi_ind);
+end
+
+nv=[nyss;nyss;nxss;nxss];
+
+start=tic;
+fv=f_d1(nv',params,model.f_ind);
+deriv_time=toc(start);
+fv=reshape(fv,n_f,n_v);
+
+
+fyp=fv(:,1:n_y); fy=fv(:,n_y+1:2*n_y); fxp=fv(:,2*n_y+1:2*n_y+n_x); fx=fv(:,2*n_y+n_x+1:end);
+
+% First Order
+
+% If first order solution not provided, use the function gx_hx of Schmitt-Grohe and Uribe (2004)
+if isempty(varargin)
+ tic
+ [gx,hx,exitflag]=gx_hx(full([fy;zeros(n_x2,n_y)]),full([fx(:,1:end-1);nPhix(:,1:end-1)]),full([fyp;zeros(n_x2,n_y)]),full([fxp(:,1:end-1);[zeros(n_x2,n_x1),-eye(n_x2)]]));
+ time=toc;
+ sol_time=sol_time+time;
+ gx=[gx,zeros(n_y,1)];
+ hx=[hx;zeros(1,n_x-1)];
+ hx=[hx,zeros(n_x,1)];
+ hx(end,end)=1;
+ % replace relevant rows of hx with nPhix which is more numerically accurate
+ hx(n_x1+1:n_x1+n_x2,:)=nPhix;
+else
+ gx=zeros(n_y,n_x);
+ gx(1:size(varargin{1},1),1:size(varargin{1},2))=varargin{1};
+ hx=zeros(n_x,n_x);
+ hx(end,end)=1;
+ hx(1:size(varargin{2},1),1:size(varargin{2},2))=varargin{2};
+end
+
+hx=sparse(hx);
+gx=sparse(gx);
+
+% Second Order
+if approx>=2
+ M2=M.M2;
+ eta2_M2=reshape([eta*reshape(M2,n_e,n_e)]',n_e,n_x);
+ eta2_M2=reshape([eta*eta2_M2]',n_x^2,1);
+
+ start=tic;
+ fvv=f_d2(nv',params,model.f_ind);
+ deriv_time=deriv_time+toc(start);
+
+ unique=nchoosek(n_x+2-1,2);
+ unique=unique-nchoosek(n_x-1+1-1,1);
+
+ Vx0=[gx*hx;gx;hx;speye(n_x)];
+ Vx1=[gx;sparse(n_y,n_x);speye(n_x,n_x);sparse(n_x,n_x)];
+
+ Ezeta2=[ sparse(n_x^2,n_x^2-1) , eta2_M2 ];
+
+ A=innerkron(n_f,n_v,fvv,Vx0,Vx0)+innerkron(n_f,n_v,fvv,Vx1,Vx1)*Ezeta2;
+
+ fy_fxp_fypgx=[fv(:,n_y+1:2*n_y) fv(:,2*n_y+1:2*n_y+n_x)+fv(:,1:n_y)*gx];
+
+ G=fy_fxp_fypgx(:,1:n_f);
+ H=fy_fxp_fypgx(:,n_f+1:n_f+n_x2);
+
+ D=sparse(n_f,n_f);
+ D(:,1:n_y)=fv(:,1:n_y);
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixx);
+ end
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2=logical(choosex2==1);
+ tempeye=speye(n_x^2);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ hx_hat=hx(1:end-1,1:end-1);
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,2 );
+ time=toc;
+ else
+ G=full(G);
+ D=full(D);
+ hx_hat=full(hx_hat);
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-CZ) );
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^2);
+ X(:,choosex2)=full(Xtemp);
+ gxx_hat=Xtemp(1:n_y,:);
+ hat_eta2_M2=eta2_M2(choosex2,:);
+ %Block 2: ss
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2=logical(choosex2==1);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ tic
+ Xtemp=-(D+G)\(CZ+(fyp*gxx_hat)*hat_eta2_M2);
+ time=toc;
+ sol_time=sol_time+time;
+
+ acc=norm(full(CZ+(fyp*gxx_hat)*hat_eta2_M2+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex2)=full(Xtemp); clear Xtemp
+ else
+ if n_x2==0
+ CU2=A*U2;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ CU2=A*U2+H*(nPhixx*U2);
+ end
+ W2BU2=(innerkron(unique,n_x,W2,hx,hx)+W2*Ezeta2)*U2;
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ CU2Z=CU2*Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(full(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U2,2));
+ X(:,choosex2U)=full(Xtemp); clear Xtemp ZTW2BU2Z
+ %Block 2
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ W2BU2Z=W2BU2*Z;
+ CU2Z=CU2*Z+D*X*W2BU2Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z);
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex2U)=full(Xtemp); clear Xtemp W2BU2Z ZTW2BU2Z
+ X=X*W2;
+ end
+ gxx=X(1:n_y,:);
+ hxx=[X(n_y+1:end,:);nPhixx;zeros(1,n_x^2)];
+end
+
+% Third Order
+if approx>=3
+ Vxx0=[chain2(gx,gxx,hx,hxx);gxx;hxx;sparse(n_x,n_x^2)];
+ Vxx1=[gxx;sparse(n_y+2*n_x,n_x^2)];
+
+ M3=M.M3(:);
+
+ eta3_M3=reshape([eta*reshape(M3,n_e,n_e^2)]',n_e,n_e*n_x);
+ eta3_M3=reshape([eta*eta3_M3]',n_e,n_x^2);
+ eta3_M3=reshape([eta*eta3_M3]',n_x^3,1);
+
+ Ezeta3=[ sparse(n_x^3,n_x^3-1) , eta3_M3 ];
+ Ix=speye(n_x);
+ Ix_Ezeta2=kron(Ix,Ezeta2);
+
+ start=tic;
+ fvvv=f_d3(nv',params,model.f_ind);
+ deriv_time=deriv_time+toc(start);
+
+ unique=nchoosek(n_x+3-1,3);
+ unique=unique-nchoosek(n_x-1+2-1,2);
+ A_third_order; % create matrix A of a third order solution
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxx);
+ end
+ %Block 1:xxx
+ choosex3=kron(spx,kron(spx,spx));
+ choosex3=logical(choosex3==1);
+ tempeye=speye(n_x^3);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,3 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 3,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,3)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^3);
+ X(:,choosex3)=full(Xtemp);
+ gxxx_hat=Xtemp(1:n_y,:);
+ hat_eta3_M3=eta3_M3(choosex3,:);
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxx_hat,n_f*(n_x-1),(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f,n_x-1)*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ %Block 2:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=(fyp*gxxx_hat)*hat_eta3_M3;
+ cons=CZ+term2;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+ sol_time=sol_time+time;
+
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices, because the
+ % compression matrices assume i1>=i2>=i3, while block xss has
+ % i11e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U3,2));
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=choosex3+kron(kron(sps,spx),sps);
+ choosex3=choosex3+kron(kron(spx,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 3:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z W3BU3
+ X=X*W3;
+ end
+
+ gxxx=X(1:n_y,:);
+ hxxx=[X(n_y+1:end,:);nPhixxx;zeros(1,n_x^3)];
+end
+
+% Fourth Order
+if approx>=4
+ Vxxx0=[chain3(gx,gxx,gxxx,hx,hxx,hxxx,OMEGA_x.OMEGA1);gxxx;hxxx;sparse(n_x,n_x^3)];
+ Vxxx1=[gxxx;sparse(n_y+2*n_x,n_x^3)];
+
+ M4=M.M4(:);
+
+ eta4_M4=reshape([eta*reshape(M4,n_e,n_e^3)]',n_e,n_e^2*n_x);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_e*n_x^2);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_x^3);
+ eta4_M4=reshape([eta*eta4_M4]',n_x^4,1);
+
+ Ezeta4=[ sparse(n_x^4,n_x^4-1) , eta4_M4 ];
+ Ix_Ezeta3=kron(Ix,Ezeta3);
+ Ix2=speye(n_x^2);
+ Ix2_Ezeta2=kron(Ix2,Ezeta2);
+
+ hx2=kron(hx,hx);
+ hx_Ezeta2_hx=kron(kron(hx,Ezeta2),hx);
+ hx_Ezeta3=kron(hx,Ezeta3);
+ hx2_Ezeta2=kron(hx2,Ezeta2);
+
+ start=tic;
+ fvvvv=f_d4(nv',params,model.f_ind);
+ deriv_time=deriv_time+toc(start);
+
+ unique=nchoosek(n_x+4-1,4);
+ unique=unique-nchoosek(n_x-1+3-1,3);
+
+ clear result R
+ A_fourth_order; % create matrix A of a fourth order solution
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxxx);
+ end
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ tempeye=speye(n_x^4);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,4 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 4,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,4)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^4);
+ X(:,choosex4)=full(Xtemp);
+ gxxxx_hat=Xtemp(1:n_y,:);
+ hat_eta4_M4=eta4_M4(choosex4,:);
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1)^2,(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f*(n_x-1),(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)*n_f,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^2,n_f);
+ term2=term2';
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,2 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ gxxss_hat=Xtemp(1:n_y,:);
+ %Block 2:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1),(n_x-1)^3)*hat_eta3_M3;
+ term2=reshape(term2',n_f,(n_x-1))*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ %Block 2:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=(6*fyp*gxxss_hat)*hat_eta2_M2;
+ term3=(fyp*gxxxx_hat)*hat_eta4_M4;
+ cons=CZ+term2+term3;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+ sol_time=sol_time+time;
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices.
+ X=reshape(permute(reshape(X,[],n_x,n_x,n_x,n_x),[1,5,4,3,2]),[],n_x^4)*U4*W4;
+ else
+ if n_x2==0
+ CU4=A*U4;
+ else
+ CU4=A*U4+H*(nPhixxxx*U4);
+ end
+ kron_hx_hx=kron(hx,hx);
+ WBU_fourth_order; % create the matrix W4BU4
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4U=logical(U4'*choosex4~=0);
+ tempeye=speye(size(U4,2));
+ Z=tempeye(:,choosex4U);
+ CU4Z=CU4*Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U4,2));
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(spx,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,spx),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 3:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 4:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ X=X*W4;
+ end
+
+ gxxxx=X(1:n_y,:);
+ hxxxx=[X(n_y+1:end,:);nPhixxxx;zeros(1,n_x^4)];
+end
+
+% Fifth Order
+if approx>=5
+ Vxxxx0=[chain4(gx,gxx,gxxx,gxxxx,hx,hxx,hxxx,hxxxx,OMEGA_x.OMEGA2,OMEGA_x.OMEGA3,OMEGA_x.OMEGA4);gxxxx;hxxxx;sparse(n_x,n_x^4)];
+ Vxxxx1=[gxxxx;sparse(n_y+2*n_x,n_x^4)];
+
+ M5=M.M5(:);
+ eta5_M5=reshape([eta*reshape(M5,n_e,n_e^4)]',n_e,n_e^3*n_x);
+ eta5_M5=reshape([eta*eta5_M5]',n_e,n_e^2*n_x^2);
+ eta5_M5=reshape([eta*eta5_M5]',n_e,n_e^1*n_x^3);
+ eta5_M5=reshape([eta*eta5_M5]',n_e,n_x^4);
+ eta5_M5=reshape([eta*eta5_M5]',n_x^5,1);
+
+ start=tic;
+ fvvvvv=f_d5(nv',params,model.f_ind);
+ deriv_time=deriv_time+toc(start);
+
+ clearvars -except n_f n_v n_x n_y n_x2 eta5_M5 Ix* *Ezeta* OMEGA_x U5 W5 gx* hx* nPhix* Vx* fv* fyp algo D G H approx sps spx kron_hx_hx hat_eta2_M2 hat_eta3_M3 hat_eta4_M4 sol_time deriv_time kamenik_type
+
+ Ezeta5=[ sparse(n_x^5,n_x^5-1) , eta5_M5 ];
+ Ix_Ezeta4=kron(Ix,Ezeta4);
+ Ix2_Ezeta3=kron(Ix2,Ezeta3);
+ Ix3=speye(n_x^3);
+ Ix3_Ezeta2=kron(Ix3,Ezeta2);
+
+ hx3=kron(hx2,hx);
+ hx3_Ezeta2=kron(hx3,Ezeta2);
+ hx2_Ezeta3=kron(hx2,Ezeta3);
+ hx_Ezeta4=kron(hx,Ezeta4);
+
+ unique=nchoosek(n_x+5-1,5);
+ unique=unique-nchoosek(n_x-1+4-1,4);
+
+ A_fifth_order; % create matrix A of a fifth order solution
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxxxx);
+ end
+ %Block 1:xxxxx
+ choosex5=kron(kron(spx,kron(spx,spx)),kron(spx,spx));
+ choosex5=logical(choosex5==1);
+ tempeye=speye(n_x^5);
+ Z=tempeye(:,choosex5);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,5 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 5,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,5)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^5);
+ X(:,choosex5)=full(Xtemp);
+ gxxxxx_hat=Xtemp(1:n_y,:);
+ hat_eta5_M5=eta5_M5(choosex5,:);
+ %Block 2:xxxss
+ choosex5=kron(kron(sps,sps),kron(spx,kron(spx,spx)));
+ choosex5=logical(choosex5==1);
+ Z=tempeye(:,choosex5);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxxx_hat,n_f*(n_x-1)^3,(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f*(n_x-1)^2,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)*n_f*(n_x-1),(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^2*n_f,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^3,n_f);
+ term2=term2';
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,3 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 3,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,3)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex5)=full(Xtemp);
+ gxxxss_hat=Xtemp(1:n_y,:);
+ %Block 3:xxsss
+ choosex5=kron(kron(sps,sps),kron(sps,kron(spx,spx)));
+ choosex5=logical(choosex5==1);
+ Z=tempeye(:,choosex5);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxxx_hat,n_f*(n_x-1)^2,(n_x-1)^3)*hat_eta3_M3;
+ term2=reshape(term2',n_f*(n_x-1),(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)*n_f,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^2,n_f);
+ term2=term2';
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,2 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex5)=full(Xtemp);
+ gxxsss_hat=Xtemp(1:n_y,:);
+ %Block 2:xssss
+ choosex5=kron(kron(sps,sps),kron(kron(sps,sps),spx));
+ choosex5=logical(choosex5==1);
+ Z=tempeye(:,choosex5);
+ CZ=C*Z;
+ term2=reshape(6*fyp*gxxxss_hat,n_f*(n_x-1),(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f,(n_x-1))*hx_hat;
+ term3=reshape(fyp*gxxxxx_hat,n_f*(n_x-1),(n_x-1)^4)*hat_eta4_M4;
+ term3=reshape(term3',n_f,(n_x-1))*hx_hat;
+ cons=CZ+term2+term3;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ sol_time=sol_time+time;
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex5)=full(Xtemp);
+ %Block 5:sssss
+ choosex5=kron(kron(sps,sps),kron(kron(sps,sps),sps));
+ choosex5=logical(choosex5==1);
+ Z=tempeye(:,choosex5);
+ CZ=C*Z;
+ term2=(10*fyp*gxxsss_hat)*hat_eta2_M2;
+ term3=(10*fyp*gxxxss_hat)*hat_eta3_M3;
+ term4=(fyp*gxxxxx_hat)*hat_eta5_M5;
+ cons=CZ+term2+term3+term4;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+ sol_time=sol_time+time;
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex5)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices.
+ X=reshape(permute(reshape(X,[],n_x,n_x,n_x,n_x,n_x),[1,6,5,4,3,2]),[],n_x^5)*U5*W5;
+ else
+ if n_x2==0
+ CU5=A*U5;
+ else
+ CU5=A*U5+H*(nPhixxxxx*U5);
+ end
+ WBU_fifth_order; % create the matrix W5BU5
+ clearvars -except G D W5BU5 CU5 W5 gx* hx hxx* algo n_y nPhixxxxx n_x n_f unique approx spx sps U5
+ %Block 1:xxxxx
+ choosex5=kron(kron(kron(spx,spx),kron(spx,spx)),spx);
+ choosex5U=logical(U5'*choosex5~=0);
+ tempeye=speye(size(U5,2));
+ Z=tempeye(:,choosex5U);
+ CU5Z=CU5*Z;
+ ZTW5BU5Z=Z'*W5BU5*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW5BU5Z',D)+kron(speye(size(Z,2)),G))\CU5Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW5BU5Z',(-G\D)',(-G\CU5Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW5BU5Z'),full((G\D)'),full((-G\CU5Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW5BU5Z+CU5Z);
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U5,2));
+ X(:,choosex5U)=full(Xtemp); clear Xtemp ZTW5BU5Z
+ %Block 2:xxxss
+ choosex5=kron(kron(kron(sps,sps),kron(spx,spx)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(sps,spx)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(spx,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(spx,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(sps,spx)),spx);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(spx,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(spx,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,spx),kron(sps,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(spx,spx),kron(sps,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,spx),kron(spx,sps)),sps);
+ choosex5U=logical(U5'*choosex5~=0);
+ Z=tempeye(:,choosex5U);
+ W5BU5Z=W5BU5*Z;
+ CU5Z=CU5*Z+D*X*W5BU5Z;
+ ZTW5BU5Z=Z'*W5BU5*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW5BU5Z',D)+kron(speye(size(Z,2)),G))\CU5Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW5BU5Z',(-G\D)',(-G\CU5Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW5BU5Z'),full((G\D)'),full((-G\CU5Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW5BU5Z+CU5Z);
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex5U)=full(Xtemp); clear Xtemp ZTW5BU5Z
+ %Block 3:xxsss
+ choosex5=kron(kron(kron(spx,spx),kron(sps,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(spx,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(sps,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(spx,sps),kron(sps,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(spx,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(sps,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(sps,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(spx,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(spx,sps)),spx);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(sps,spx)),spx);
+ choosex5U=logical(U5'*choosex5~=0);
+ Z=tempeye(:,choosex5U);
+ W5BU5Z=W5BU5*Z;
+ CU5Z=CU5*Z+D*X*W5BU5Z;
+ ZTW5BU5Z=Z'*W5BU5*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW5BU5Z',D)+kron(speye(size(Z,2)),G))\CU5Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW5BU5Z',(-G\D)',(-G\CU5Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW5BU5Z'),full((G\D)'),full((-G\CU5Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW5BU5Z+CU5Z);
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex5U)=full(Xtemp); clear Xtemp ZTW5BU5Z
+ %Block 4:xssss
+ choosex5=kron(kron(kron(spx,sps),kron(sps,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,spx),kron(sps,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(spx,sps)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(sps,spx)),sps);
+ choosex5=choosex5+kron(kron(kron(sps,sps),kron(sps,sps)),spx);
+ choosex5U=logical(U5'*choosex5~=0);
+ Z=tempeye(:,choosex5U);
+ W5BU5Z=W5BU5*Z;
+ CU5Z=CU5*Z+D*X*W5BU5Z;
+ ZTW5BU5Z=Z'*W5BU5*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW5BU5Z',D)+kron(speye(size(Z,2)),G))\CU5Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW5BU5Z',(-G\D)',(-G\CU5Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW5BU5Z'),full((G\D)'),full((-G\CU5Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW5BU5Z+CU5Z);
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex5U)=full(Xtemp); clear Xtemp ZTW5BU5Z
+ %Block 5:sssss
+ choosex5=kron(kron(kron(sps,sps),kron(sps,sps)),sps);
+ choosex5U=logical(U5'*choosex5~=0);
+ Z=tempeye(:,choosex5U);
+ W5BU5Z=W5BU5*Z;
+ CU5Z=CU5*Z+D*X*W5BU5Z;
+ ZTW5BU5Z=Z'*W5BU5*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW5BU5Z',D)+kron(speye(size(Z,2)),G))\CU5Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW5BU5Z',(-G\D)',(-G\CU5Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW5BU5Z'),full((G\D)'),full((-G\CU5Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW5BU5Z+CU5Z);
+ if acc>1e-8
+ warning(['Fifth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex5U)=full(Xtemp); clear Xtemp ZTW5BU5Z W5BU5
+ X=X*W5;
+ end
+
+ gxxxxx=X(1:n_y,:);
+ hxxxxx=[X(n_y+1:end,:);nPhixxxxx;zeros(1,n_x^5)];
+end
+
+clear derivs
+derivs.gx=full(gx);
+derivs.hx=full(hx(1:end-1,:));
+if approx>=2
+ derivs.gxx=full(gxx);
+ derivs.hxx=full(hxx(1:end-1,:));
+end
+if approx>=3
+ derivs.gxxx=full(gxxx);
+ derivs.hxxx=full(hxxx(1:end-1,:));
+end
+if approx>=4
+ derivs.gxxxx=full(gxxxx);
+ derivs.hxxxx=full(hxxxx(1:end-1,:));
+end
+if approx>=5
+ derivs.gxxxxx=full(gxxxxx);
+ derivs.hxxxxx=full(hxxxxx(1:end-1,:));
+end
+
+end
+
+
+
diff --git a/105/replication_package/solution_methods/extrenal files/First order solution/gx_hx.m b/105/replication_package/solution_methods/extrenal files/First order solution/gx_hx.m
new file mode 100644
index 0000000000000000000000000000000000000000..4ecf0949ced012672d705ab239a0ccaaa972f87d
--- /dev/null
+++ b/105/replication_package/solution_methods/extrenal files/First order solution/gx_hx.m
@@ -0,0 +1,70 @@
+function [gx,hx,exitflag]=gx_hx(fy,fx,fyp,fxp,stake);
+%[gx,hx,exitflag]=gx_hx(fy,fx,fyp,fxp,stake);
+%computes the matrices gx and hx that define the first-order approximation to the solution
+%of a dynamic stochastic general equilibrium model.
+%Following the notation in Schmitt-Grohe and Uribe (JEDC, 2004), the model's equilibrium conditions
+%take the form
+%E_t[f(yp,y,xp,x)=0.
+%The solution is of the form
+%xp = h(x,sigma) + sigma * eta * ep
+%y = g(x,sigma).
+%The first-order approximations to the functions g and h around the point (x,sigma)=(xbar,0), where xbar=h(xbar,0), are:
+%h(x,sigma) = xbar + hx (x-xbar)
+%and
+%g(x,sigma) = ybar + gx * (x-xbar),
+%where ybar=g(xbar,0).
+%The variable exitflag takes the values 0 (no solution), 1 (unique solution), 2 (indeterminacy), or 3 (z11 is not invertible).
+%Inputs: fy fyp fx fxp stake
+% The parameter stake ensures that all eigenvalues of hx are less than stake in modulus (the default is stake=1).
+%Outputs: gx hx exitflag
+%This program is a modified version of solab.m by Paul Klein (JEDC, 2000).
+%Modified on August 30 2009 by Ryan Chahrour (rc2374@columbia.edu) to replace qzdiv.m by ordqz.m to increase speed.
+%(c) Stephanie Schmitt-Grohe and Martin Uribe
+%Date July 17, 2001, May 11 2006, November 19, 2009
+
+if nargin<5
+ stake=1;
+end
+exitflag = 1;
+
+%Create system matrices A,B
+A = [-fxp -fyp];
+B = [fx fy];
+NK = size(fx,2);
+
+%Complex Schur Decomposition
+[s,t,q,z] = qz(A,B);
+
+%Pick non-explosive (stable) eigenvalues
+slt = (abs(diag(t))NK
+ warning('The Equilibrium is Locally Indeterminate')
+ exitflag=2;
+elseif nk=1;
+% "vcv" is the variance-covariance matrix; N-by-N
+
+% Outputs: "n_nodes" is the total number of integration nodes; 2*N;
+% "epsi_nodes" are the integration nodes; n_nodes-by-N;
+% "weight_nodes" are the integration weights; n_nodes-by-1
+% -------------------------------------------------------------------------
+% Copyright � 2011 by Lilia Maliar and Serguei Maliar. All rights reserved.
+% The code may be used, modified and redistributed under the terms provided
+% in the file "License_Agreement.txt".
+% -------------------------------------------------------------------------
+
+function [n_nodes,epsi_nodes,weight_nodes] = Monomials_1(N,vcv)
+
+n_nodes = 2*N; % Total number of integration nodes
+
+% 1. N-dimensional integration nodes for N uncorrelated random variables with
+% zero mean and unit variance
+% ---------------------------------------------------------------------------
+z1 = zeros(n_nodes,N); % A supplementary matrix for integration nodes;
+ % n_nodes-by-N
+
+for i = 1:N % In each node, random variable i takes value either
+ % 1 or -1, and all other variables take value 0
+ z1(2*(i-1)+1:2*i,i) = [1; -1];
+end % For example, for N = 2, z1 = [1 0; -1 0; 0 1; 0 -1]
+
+% z = z1*sqrt(N); % Integration nodes
+
+% 2. N-dimensional integration nodes and weights for N correlated random
+% variables with zero mean and variance-covaraince matrix vcv
+% ----------------------------------------------------------------------
+sqrt_vcv = chol(vcv); % Cholesky decomposition of the variance-covariance
+ % matrix
+
+R = sqrt(N)*sqrt_vcv; % Variable R; see condition (B.7) in the Supplement
+ % to JMM (2011)
+
+epsi_nodes = z1*R; % Integration nodes; see condition ((B.7) in the
+ % Supplement% to JMM (2011); n_nodes-by-N
+
+% 3. Integration weights
+%-----------------------
+weight_nodes = ones(n_nodes,1)/n_nodes;
+ % Integration weights are equal for all integration
+ % nodes; n_nodes-by-1; the weights are the same for
+ % the cases of correlated and uncorrelated random
+ % variables
diff --git a/105/replication_package/solution_methods/extrenal files/Maliar codes/Monomials_2.m b/105/replication_package/solution_methods/extrenal files/Maliar codes/Monomials_2.m
new file mode 100644
index 0000000000000000000000000000000000000000..2dd7be9c72b489305e249e64e33b8fa0f9b7928a
--- /dev/null
+++ b/105/replication_package/solution_methods/extrenal files/Maliar codes/Monomials_2.m
@@ -0,0 +1,87 @@
+% Monomials_2.m is a routine that constructs integration nodes and weights
+% under N-dimensional monomial (non-product) integration rule with 2N^2+1
+% nodes; see supplement to "Numerically Stable and Accurate Stochastic
+% Simulation Approaches for Solving Dynamic Economic Models" by Kenneth L.
+% Judd, Lilia Maliar and Serguei Maliar, (2011), Quantitative Economics 2/2,
+% 173�210 (henceforth, JMM, 2011).
+%
+% This version: July 14, 2011. First version: August 27, 2009.
+% -------------------------------------------------------------------------
+% Inputs: "N" is the number of random variables; N>=1;
+% "vcv" is the variance-covariance matrix; N-by-N;
+
+% Outputs: "n_nodes" is the total number of integration nodes; 2*N^2+1;
+% "epsi_nodes" are the integration nodes; n_nodes-by-N;
+% "weight_nodes" are the integration weights; n_nodes-by-1
+% -------------------------------------------------------------------------
+% Copyright � 2011 by Lilia Maliar and Serguei Maliar. All rights reserved.
+% The code may be used, modified and redistributed under the terms provided
+% in the file "License_Agreement.txt".
+% -------------------------------------------------------------------------
+
+
+function [n_nodes,epsi_nodes,weight_nodes] = Monomials_2(N,vcv)
+
+n_nodes = 2*N^2+1; % Total number of integration nodes
+
+% 1. N-dimensional integration nodes for N uncorrelated random variables with
+% zero mean and unit variance
+% ---------------------------------------------------------------------------
+
+% 1.1 The origin point
+% --------------------
+z0 = zeros(1,N); % A supplementary matrix for integration nodes: the
+ % origin point
+
+% 1.2 Deviations in one dimension
+% -------------------------------
+z1 = zeros(2*N,N); % A supplementary matrix for integration nodes;
+ % n_nodes-by-N
+
+for i = 1:N % In each node, random variable i takes value either
+ % 1 or -1, and all other variables take value 0
+ z1(2*(i-1)+1:2*i,i) = [1; -1];
+end % For example, for N = 2, z1 = [1 0; -1 0; 0 1; 0 -1]
+
+% 1.3 Deviations in two dimensions
+% --------------------------------
+z2 = zeros(2*N*(N-1),N); % A supplementary matrix for integration nodes;
+ % 2N(N-1)-by-N
+
+i=0; % In each node, a pair of random variables (p,q)
+ % takes either values (1,1) or (1,-1) or (-1,1) or
+ % (-1,-1), and all other variables take value 0
+for p = 1:N-1
+ for q = p+1:N
+ i=i+1;
+ z2(4*(i-1)+1:4*i,p) = [1;-1;1;-1];
+ z2(4*(i-1)+1:4*i,q) = [1;1;-1;-1];
+ end
+end % For example, for N = 2, z2 = [1 1;1 -1;-1 1;-1 1]
+
+% z = [z0;z1*sqrt(N+2);z2*sqrt((N+2)/2)]; % Integration nodes
+
+% 2. N-dimensional integration nodes and weights for N correlated random
+% variables with zero mean and variance-covaraince matrix vcv
+% ----------------------------------------------------------------------
+sqrt_vcv = chol(vcv); % Cholesky decomposition of the variance-
+ % covariance matrix
+
+R = sqrt(N+2)*sqrt_vcv; % Variable R; see condition (B.8) in the
+ % Supplement to JMM (2011)
+
+S = sqrt((N+2)/2)* sqrt_vcv; % Variable S; see condition (B.8) in the
+ % Supplement to JMM (2011)
+
+epsi_nodes = [z0;z1*R;z2*S];
+ % Integration nodes; see condition (B.8)
+ % in the Supplement to JMM (2011);
+ % n_nodes-by-N
+
+% 3. Integration weights
+%-----------------------
+weight_nodes = [2/(N+2)*ones(size(z0,1),1);(4-N)/2/(N+2)^2*ones(size(z1,1),1);1/(N+2)^2*ones(size(z2,1),1)];
+ % See condition in (B.8) in the Supplement
+ % to JMM (2011); n_nodes-by-1; the weights
+ % are the same for the cases of correlated
+ % and uncorrelated random variables
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/extrenal files/gensylv/gensylv.mexw64 b/105/replication_package/solution_methods/extrenal files/gensylv/gensylv.mexw64
new file mode 100644
index 0000000000000000000000000000000000000000..1cda78ac91ee81f5e27a872ed9b64497c2bfd84e
Binary files /dev/null and b/105/replication_package/solution_methods/extrenal files/gensylv/gensylv.mexw64 differ
diff --git a/105/replication_package/solution_methods/extrenal files/gensylv/license.txt b/105/replication_package/solution_methods/extrenal files/gensylv/license.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8e1c2f1d5b551da7170ce12c83cd1144ec695d41
--- /dev/null
+++ b/105/replication_package/solution_methods/extrenal files/gensylv/license.txt
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bfaf86e8f67a59725bc688982e2aae5db5bad761d9cd72c921b4716f6e689060
+size 13778
diff --git a/105/replication_package/solution_methods/taylor_projection/GetInitial.m b/105/replication_package/solution_methods/taylor_projection/GetInitial.m
new file mode 100644
index 0000000000000000000000000000000000000000..2ac183ccf0a211eeed6e67a876d15f35a79c30a5
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/GetInitial.m
@@ -0,0 +1,75 @@
+function [ pert_coeffs,power_coeffs ] = GetInitial( order,derivs,choose,nyss,nxss,n_x,n_x1 )
+%This function transforms a pertrubation solution to an initial guess for Taylor
+%Projection. Two types of guess are available: pert_coeffs includes
+%correction for volatility. power_coeffs does not include correction for
+%volatility.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+if order==1
+ [GH0,GH1]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)]);
+ pert_coeffs=[GH0,GH1];
+ if nargout==2
+ [GH0,GH1]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)]);
+ power_coeffs=[GH0,GH1];
+ end
+elseif order==2
+ [GH0,GH1,GH2]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2);
+ [U2,~]=create_UW(n_x,2);
+ pert_coeffs=[GH0,GH1,GH2*U2];
+ if nargout==2
+ [GH0,GH1,GH2]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2);
+ power_coeffs=[GH0,GH1,GH2*U2];
+ end
+elseif order==3
+ [GH0,GH1,GH2,GH3]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3];
+ if nargout==2
+ [GH0,GH1,GH2,GH3]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3));
+ power_coeffs=[GH0,GH1,GH2*U2,GH3*U3];
+ end
+elseif order==4
+ [GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ [U4,~]=create_UW(n_x,4);
+ pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
+ if nargout==2
+ [GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4));
+ power_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
+ end
+elseif order==5
+ [GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx(choose,:);derivs.hxxxxx(1:n_x1,:)]/factorial(5));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ [U4,~]=create_UW(n_x,4);
+ [U5,~]=create_UW(n_x,5);
+ pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
+ if nargout==2
+ [GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
+ [derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx(choose,:);derivs.hxxxxx(1:n_x1,:)]/factorial(5));
+ power_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
+ end
+end
+pert_coeffs=pert_coeffs(:);
+
+if nargout==2
+ power_coeffs=power_coeffs(:);
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/LICENSE.txt b/105/replication_package/solution_methods/taylor_projection/LICENSE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d46926707a031aac19829334b7671dbd9270759d
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/LICENSE.txt
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:55dad499f94ec1db4229ecb667529e5ed4b118e5d5fc96a70ff4ecb5d5652e3a
+size 1043
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..73cf48aea647e6c34df2702680f7634f007b6eda
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2IC_mex.F
@@ -0,0 +1,228 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,m,n,IA,JA
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows,ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 7) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '7 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(6))
+ JBrows = mxGetM(prhs(7))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ IB = mxGetPr(prhs(6))
+ JB = mxGetPr(prhs(7))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(4))
+
+ complexflag = 0
+ ndim=1
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),%VAL(n),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB),%VAL(JB),
+ + %VAL(IC_1),%VAL(IC_2),
+ + IArows,JArows,IBrows,JBrows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,
+ + IB,JB,
+ + IC_1,IC_2,
+ + IArows,JArows,
+ + IBrows,JBrows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,2)
+
+ mwSize, target :: IB(IBrows)
+ mwSize JB(JBrows)
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,vp,v1,v2,nz
+ mwSize kpstart
+
+ integer AllocateStatus
+
+C first contraction
+
+ allocate (w(m,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB(kp)
+ if (w(k1,k2)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB(kp)
+ if (w(k1,k2)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=pJB(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n),
+ + x(min(sC,maxload),n,n),
+ + tempJC1(JCrows_1,2),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>tempJC1
+
+ sA=sC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (pJB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (pJB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2)
+ x(1,v1,v2)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2,tempJC1)
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..6baa828e0bfbcfb3b9a8989a76508717b206456e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU2vec_mex.F
@@ -0,0 +1,428 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = AkronBU2vec_mex(l,m,n,IA,JA,NA,...
+C IB,JB,NB,...
+C IC_1,JC_1,IC_2,JC_2,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m,n
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2
+ mwPointer JC_1,JC_2
+ mwPointer maxload,dosum
+ mwPointer NA,NB
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows
+ mwSize ICrows_1,ICrows_2
+ mwSize JCrows_1,JCrows_2
+
+ mwSize s,sC,sA,sB
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 15) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '19 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(7))
+ JBrows = mxGetM(prhs(8))
+
+ ICrows_1 = mxGetM(prhs(10))
+ JCrows_1 = mxGetM(prhs(11))
+
+ ICrows_2 = mxGetM(prhs(12))
+ JCrows_2 = mxGetM(prhs(13))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ NA = mxGetPr(prhs(6))
+ IB = mxGetPr(prhs(7))
+ JB = mxGetPr(prhs(8))
+ NB = mxGetPr(prhs(9))
+ IC_1 = mxGetPr(prhs(10))
+ JC_1 = mxGetPr(prhs(11))
+ IC_2 = mxGetPr(prhs(12))
+ JC_2 = mxGetPr(prhs(13))
+ maxload = mxGetPr(prhs(14))
+
+C Get number of states
+ sA = mxGetM(prhs(6))
+ sB = mxGetM(prhs(9))
+
+C check compatibility of states
+ s=max(sA,sB)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB.ne.s .and. sB.ne.1))
+ + then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(15))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),
+ + %VAL(n),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB),%VAL(JB),%VAL(NB),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(maxload),
+ + %VAL(NC),
+ + IArows,JArows,IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,NA,
+ + IB,JB,NB,
+ + IC_1,JC_1,IC_2,JC_2,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n,sC,sA,sB
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+ mwSize ICrows_1,ICrows_2
+ mwSize JCrows_1,JCrows_2
+
+ mwSize s,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB(sB,JBrows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:)
+ logical, allocatable :: w(:,:)
+
+C two temporary crs var is needed, 2
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,2)
+
+ mwSize, target :: IB(IBrows)
+ mwSize, target :: JB(JBrows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,3)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,2)
+
+ mwSize i,jp,j,kp,k1,k2,vp,v1,v2
+ mwSize is,js,nz
+
+ mwSize mati,k,kpstart,loc,j2
+ real*8 mat(2,2), fact(2), prod1
+
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C prepare matrices for factorials and products
+ k=2
+ mat(1,1:k)=(/ (mati, mati = n+1, n+k) /)
+ mat(2,1:k)=(/ (mati, mati = n, n+k-1) /)
+
+ fact(1)=1
+ do j=2,k
+ fact(j)=fact(j-1)*j
+ end do
+ prod1=product(mat(2,:))
+
+C first contraction
+ sC2=max(sA,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m,n),
+ + x(min(sC2,maxload),m,n),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2)==.false.) then
+ w(k1,k2)=.true.
+ x(:,k1,k2)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n),
+ + x(min(sC,maxload),n,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ sA=sC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (pJB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (pJB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,2)
+ v2=pJC(vp,3)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2)
+ x(1,v1,v2)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..89bd30f93cd9deedea407bb878d14f14b5ded674
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3IC_mex.F
@@ -0,0 +1,322 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2,IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,m,n,IA,JA
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows,ndim
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 7) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '14 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(6))
+ JBrows = mxGetM(prhs(7))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ IB = mxGetPr(prhs(6))
+ JB = mxGetPr(prhs(7))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(4))
+
+ complexflag = 0
+ ndim=1
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_3 = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),%VAL(n),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB),%VAL(JB),
+ + %VAL(IC_1),%VAL(IC_2),%VAL(IC_3),
+ + IArows,JArows,IBrows,JBrows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,
+ + IB,JB,
+ + IC_1,IC_2,IC_3,
+ + IArows,JArows,
+ + IBrows,JBrows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,3)
+
+ mwSize, target :: IB(IBrows)
+ mwSize JB(JBrows)
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+ mwSize, target :: IC_3(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+ mwSize, target,allocatable :: JC_3(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,k3,vp,v1,v2,v3,nz
+
+ mwSize kpstart
+
+ integer AllocateStatus
+
+C first contraction
+ allocate (w(m,m,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ IC_3(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB(kp)
+ if (w(k1,k2,k3)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB(kp)
+ if (w(k1,k2,k3)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>tempJC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=pJB(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m,n,n),
+ + x(min(sC2,maxload),m,n,n),
+ + tempNC2(sC2,rows),
+ + tempJC2(rows,3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_3
+ pJA=>tempJC3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ sA=sC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3,tempJC3)
+
+C third contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n),
+ + x(min(sC,maxload),n,n,n),
+ + tempJC1(JCrows_1,3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>tempJC1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3)
+ x(1,v1,v2,v3)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2,tempJC1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..cdd1aea5bccf4b2208397c69dd550c2dd8965908
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU3vec_mex.F
@@ -0,0 +1,545 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = AkronBU3vec_mex(l,m,n,IA,JA,NA,...
+C IB,JB,NB,...
+C IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m,n
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3
+ mwPointer JC_1,JC_2,JC_3
+ mwPointer maxload,dosum
+ mwPointer NA,NB
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3
+ mwSize JCrows_1,JCrows_2,JCrows_3
+
+ mwSize s,sC,sA,sB
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 17) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '17 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(7))
+ JBrows = mxGetM(prhs(8))
+
+ ICrows_1 = mxGetM(prhs(10))
+ JCrows_1 = mxGetM(prhs(11))
+
+ ICrows_2 = mxGetM(prhs(12))
+ JCrows_2 = mxGetM(prhs(13))
+
+ ICrows_3 = mxGetM(prhs(14))
+ JCrows_3 = mxGetM(prhs(15))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ NA = mxGetPr(prhs(6))
+ IB = mxGetPr(prhs(7))
+ JB = mxGetPr(prhs(8))
+ NB = mxGetPr(prhs(9))
+ IC_1 = mxGetPr(prhs(10))
+ JC_1 = mxGetPr(prhs(11))
+ IC_2 = mxGetPr(prhs(12))
+ JC_2 = mxGetPr(prhs(13))
+ IC_3 = mxGetPr(prhs(14))
+ JC_3 = mxGetPr(prhs(15))
+ maxload = mxGetPr(prhs(16))
+
+C Get number of states
+ sA = mxGetM(prhs(6))
+ sB = mxGetM(prhs(9))
+
+C check compatibility of states
+ s=max(sA,sB)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB.ne.s .and. sB.ne.1))
+ + then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(17))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1,complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),
+ + %VAL(n),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB),%VAL(JB),%VAL(NB),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(IC_3),%VAL(JC_3),%VAL(maxload),
+ + %VAL(NC),
+ + IArows,JArows,IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,
+ + sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,NA,
+ + IB,JB,NB,
+ + IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,
+ + sC,sA,sB)
+
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n,sC,sA,sB
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3
+ mwSize JCrows_1,JCrows_2,JCrows_3
+
+ mwSize s,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB(sB,JBrows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:)
+ logical, allocatable :: w(:,:,:)
+
+C two temporary crs vars are needed, 2 and 3
+ real*8, target, allocatable :: tempNC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,3)
+
+ mwSize, target :: IB(IBrows)
+ mwSize, target :: JB(JBrows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,4)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,3)
+
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: JC_3(JCrows_3,3)
+
+ mwSize i,jp,j,kp,k1,k2,k3,vp,v1,v2,v3
+ mwSize is,js,nz
+
+ mwSize mati,k,kpstart,loc,j2
+ real*8 mat(2,2), fact(2), prod1
+
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C prepare matrices for factorials and products
+
+ mat(1,1:k)=(/ (mati, mati = n+1, n+k) /)
+ mat(2,1:k)=(/ (mati, mati = n, n+k-1) /)
+ do j=2,k-1
+ mat(j+1,1:k-j+1)=(/ (mati, mati = n+k-j+1, n+1, -1) /)
+ end do
+ fact(1)=1
+ do j=2,k
+ fact(j)=fact(j-1)*j
+ end do
+ prod1=product(mat(2,:))
+
+C first contraction
+ sC3=max(sA,sB)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m,m,n),
+ + x(min(sC3,maxload),m,m,n),
+ + tempNC3(sC3,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>JC_3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2,k3)==.false.) then
+ w(k1,k2,k3)=.true.
+ x(:,k1,k2,k3)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m,n,n),
+ + x(min(sC2,maxload),m,n,n),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ sA=sC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3)
+
+C third contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n),
+ + x(min(sC,maxload),n,n,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,2)
+ v2=pJC(vp,3)
+ v3=pJC(vp,4)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3)
+ x(1,v1,v2,v3)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..e54505824cb4581aebb6e241fb06b9efa2191b32
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4IC_mex.F
@@ -0,0 +1,414 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2,IC_3,IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,m,n,IA,JA
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3,IC_4
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows,ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 7) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '7 inputs required.')
+ endif
+ if(nlhs .gt. 4) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 4 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(6))
+ JBrows = mxGetM(prhs(7))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ IB = mxGetPr(prhs(6))
+ JB = mxGetPr(prhs(7))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(4))
+ ndim=1
+ complexflag = 0
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_3 = mxGetPr(plhs(3))
+
+ plhs(4) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_4 = mxGetPr(plhs(4))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),%VAL(n),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB),%VAL(JB),
+ + %VAL(IC_1),%VAL(IC_2),%VAL(IC_3),%VAL(IC_4),
+ + IArows,JArows,IBrows,JBrows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,
+ + IB,JB,
+ + IC_1,IC_2,IC_3,IC_4,
+ + IArows,JArows,
+ + IBrows,JBrows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:,:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,2)
+
+ mwSize, target :: IB(IBrows)
+ mwSize JB(JBrows)
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+ mwSize, target :: IC_3(IArows)
+ mwSize, target :: IC_4(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+ mwSize, target,allocatable :: JC_3(:,:)
+ mwSize, target,allocatable :: JC_4(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4,nz
+
+ mwSize kpstart
+
+ integer AllocateStatus
+
+C first contraction
+ allocate (w(m,m,m,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ IC_4(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+
+ do i=1,l
+ IC_3(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ IC_4(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ k3=convertind(i,pJA(jp,3))
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+
+ do i=1,l
+ IC_3(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ k3=convertind(i,pJA(jp,3))
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_4
+ pJC=>tempJC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ k3=convertind(i,pJA(jp,3))
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3,k4)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=convertind(i,pJC(vp,2))
+ v3=convertind(i,pJC(vp,3))
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(smallm,smallm,n,n),
+ + x(min(sC3,maxload),smallm,smallm,n,n),
+ + tempNC3(sC3,rows),
+ + tempJC3(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_4
+ pJA=>tempJC4
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>tempJC3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=convertind(i,pJC(vp,2))
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4,tempJC4)
+
+C third contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(smallm,n,n,n),
+ + x(min(sC2,maxload),smallm,n,n,n),
+ + tempNC2(sC2,rows),
+ + tempJC2(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_3
+ pJA=>tempJC3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3,tempJC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n,n),
+ + x(min(sC,maxload),n,n,n,n),
+ + tempJC1(JCrows_1,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>tempJC1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2,tempJC1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4ivec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4ivec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..43c9c78213a2f9f66b7cbff24d8d4d12934e3f62
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4ivec_mex.F
@@ -0,0 +1,675 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = AkronBU4ivec_mex(l,m,n,IA,JA,NA,...
+C IB,JB,NB,...
+C IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+C maxload,dosum,convertind,maxind)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m,n
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3,IC_4
+ mwPointer JC_1,JC_2,JC_3,JC_4
+ mwPointer maxload,dosum
+ mwPointer NA,NB
+ mwPointer convertind,maxind
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows
+
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC,sA,sB
+ real*8 do_sum
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 21) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '21 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(7))
+ JBrows = mxGetM(prhs(8))
+
+ ICrows_1 = mxGetM(prhs(10))
+ JCrows_1 = mxGetM(prhs(11))
+
+ ICrows_2 = mxGetM(prhs(12))
+ JCrows_2 = mxGetM(prhs(13))
+
+ ICrows_3 = mxGetM(prhs(14))
+ JCrows_3 = mxGetM(prhs(15))
+
+ ICrows_4 = mxGetM(prhs(16))
+ JCrows_4 = mxGetM(prhs(17))
+
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ NA = mxGetPr(prhs(6))
+ IB = mxGetPr(prhs(7))
+ JB = mxGetPr(prhs(8))
+ NB = mxGetPr(prhs(9))
+
+ IC_1 = mxGetPr(prhs(10))
+ JC_1 = mxGetPr(prhs(11))
+ IC_2 = mxGetPr(prhs(12))
+ JC_2 = mxGetPr(prhs(13))
+ IC_3 = mxGetPr(prhs(14))
+ JC_3 = mxGetPr(prhs(15))
+ IC_4 = mxGetPr(prhs(16))
+ JC_4 = mxGetPr(prhs(17))
+ maxload = mxGetPr(prhs(18))
+
+ convertind = mxGetPr(prhs(20))
+ maxind = mxGetPr(prhs(21))
+
+C Get number of states
+ sA = mxGetM(prhs(6))
+ sB = mxGetM(prhs(9))
+
+C check compatibility of states
+ s=max(sA,sB)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB.ne.s .and. sB.ne.1))
+ + then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(19))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1,complexflag)
+ NC = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),
+ + %VAL(n),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB),%VAL(JB),%VAL(NB),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(IC_3),%VAL(JC_3),%VAL(IC_4),%VAL(JC_4),
+ + %VAL(maxload),%VAL(NC),
+ + %VAL(convertind),%VAL(maxind),
+ + IArows,JArows,IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,NA,
+ + IB,JB,NB,
+ + IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,
+ + maxload,
+ + NC,
+ + convertind,maxind,
+ + IArows,JArows,
+ + IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n,sC,sA,sB,smallm
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC4,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB(sB,JBrows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:,:)
+ logical, allocatable :: w(:,:,:,:)
+
+C three temporary crs vars are needed
+ real*8, target, allocatable :: tempNC4(:,:)
+ real*8, target, allocatable :: tempNC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,4)
+
+ mwSize, target :: IB(IBrows)
+ mwSize, target :: JB(JBrows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,5)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,4)
+
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: JC_3(JCrows_3,4)
+
+ mwSize, target :: IC_4(ICrows_4)
+ mwSize, target :: JC_4(JCrows_4,4)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4
+ mwSize is,js,nz
+
+ mwSize mati,k,kpstart,loc,j2,maxind
+ mwSize convertind(l,m)
+
+ real*8 mat(2,2), fact(2), prod1
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C prepare matrices for factorials and products
+
+ mat(1,1:k)=(/ (mati, mati = n+1, n+k) /)
+ mat(2,1:k)=(/ (mati, mati = n, n+k-1) /)
+ do j=2,k-1
+ mat(j+1,1:k-j+1)=(/ (mati, mati = n+k-j+1, n+1, -1) /)
+ end do
+ fact(1)=1
+ do j=2,k
+ fact(j)=fact(j-1)*j
+ end do
+ prod1=product(mat(2,:))
+
+ smallm=maxind ! here is the memory saving
+
+C first contraction
+ sC4=max(sA,sB)
+ rows=IC_4(ICrows_4)-1
+ allocate (w(smallm,smallm,smallm,n),
+ + x(min(sC4,maxload),smallm,smallm,smallm,n),
+ + tempNC4(sC4,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_4
+ pJC=>JC_4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ k3=convertind(i,pJA(jp,3))
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=convertind(i,pJC(vp,2))
+ v3=convertind(i,pJC(vp,3))
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(smallm,smallm,n,n),
+ + x(min(sC3,maxload),smallm,smallm,n,n),
+ + tempNC3(sC3,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>JC_3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ k2=convertind(i,pJA(jp,2))
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=convertind(i,pJC(vp,2))
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4)
+
+C third contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(smallm,n,n,n),
+ + x(min(sC2,maxload),smallm,n,n,n),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=convertind(i,pJA(jp,1))
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=convertind(i,pJC(vp,1))
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n,n),
+ + x(min(sC,maxload),n,n,n,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,2)
+ v2=pJC(vp,3)
+ v3=pJC(vp,4)
+ v4=pJC(vp,5)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vecI_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vecI_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..bad83e99446e63f9bb0fdff9f5c458a15093e2cd
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vecI_mex.F
@@ -0,0 +1,706 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC,JC_1] = AkronBU4vecI_mex(l,m,n,IA,JA,NA,...
+C IB,JB,NB,...
+C IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m,n
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3,IC_4
+ mwPointer maxload,dosum
+ mwPointer NA,NB
+
+ mwPointer NC,JC_1
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1
+
+ mwSize s,sC,sA,sB
+ real*8 do_sum
+
+ mwSize rows
+ mwSize JCdims(2),ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 16) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '16 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(7))
+ JBrows = mxGetM(prhs(8))
+
+ ICrows_1 = mxGetM(prhs(10))
+ ICrows_2 = mxGetM(prhs(11))
+ ICrows_3 = mxGetM(prhs(12))
+ ICrows_4 = mxGetM(prhs(13))
+
+ rows = mxGetScalar(prhs(14))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ NA = mxGetPr(prhs(6))
+ IB = mxGetPr(prhs(7))
+ JB = mxGetPr(prhs(8))
+ NB = mxGetPr(prhs(9))
+
+ IC_1 = mxGetPr(prhs(10))
+ IC_2 = mxGetPr(prhs(11))
+ IC_3 = mxGetPr(prhs(12))
+ IC_4 = mxGetPr(prhs(13))
+ JCrows_1 = mxGetPr(prhs(14))
+ maxload = mxGetPr(prhs(15))
+
+C Get number of states
+ sA = mxGetM(prhs(6))
+ sB = mxGetM(prhs(9))
+
+C check compatibility of states
+ s=max(sA,sB)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB.ne.s .and. sB.ne.1))
+ + then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(16))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag = 0
+
+ plhs(1) = mxCreateDoubleMatrix(sC,rows,complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for JC_1.
+
+ classid = mxGetClassID(prhs(5))
+
+ JCdims(1)=rows
+ JCdims(2)=1
+ ndim=2
+ plhs(2) = mxCreateNumericArray(ndim, JCdims,
+ + classid,
+ + complexflag)
+
+ JC_1 = mxGetPr(plhs(2))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),
+ + %VAL(n),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB),%VAL(JB),%VAL(NB),
+ + %VAL(IC_1),%VAL(IC_2),%VAL(IC_3),%VAL(IC_4),
+ + %VAL(JCrows_1),%VAL(maxload),
+ + %VAL(NC),%VAL(JC_1),
+ + IArows,JArows,IBrows,JBrows,
+ + ICrows_1,ICrows_2,ICrows_3,ICrows_4,
+ + sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,NA,
+ + IB,JB,NB,
+ + IC_1,IC_2,IC_3,IC_4,
+ + JCrows_1,maxload,
+ + NC,JC_1,
+ + IArows,JArows,
+ + IBrows,JBrows,
+ + ICrows_1,ICrows_2,ICrows_3,ICrows_4,
+ + sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n,sC,sA,sB
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC4,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB(sB,JBrows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:,:)
+ mwSize, allocatable :: w(:,:,:,:)
+
+C three temporary crs vars are needed
+ real*8, target, allocatable :: tempNC4(:,:)
+ mwSize, target, allocatable :: tempJC4(:,:)
+ real*8, target, allocatable :: tempNC3(:,:)
+ mwSize, target, allocatable :: tempJC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+ mwSize, target, allocatable :: tempJC2(:,:)
+
+ mwSize, target, allocatable :: tempJC1(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,4)
+
+ mwSize, target :: IB(IBrows)
+ mwSize, target :: JB(JBrows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,1)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: IC_4(ICrows_4)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4
+ mwSize is,js,nz
+
+ mwSize mati,k,kpstart,loc,j2
+ parameter (k=4)
+ real*8 mat(k,k), fact(k), prod1
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C prepare matrices for factorials and products
+
+ mat(1,1:k)=(/ (mati, mati = n+1, n+k) /)
+ mat(2,1:k)=(/ (mati, mati = n, n+k-1) /)
+ do j=2,k-1
+ mat(j+1,1:k-j+1)=(/ (mati, mati = n+k-j+1, n+1, -1) /)
+ end do
+ fact(1)=1
+ do j=2,k
+ fact(j)=fact(j-1)*j
+ end do
+ prod1=product(mat(2,:))
+
+C first contraction
+ sC4=max(sA,sB)
+ rows=IC_4(ICrows_4)-1
+ allocate (w(m,m,m,n),
+ + x(min(sC4,maxload),m,m,m,n),
+ + tempNC4(sC4,rows),
+ + tempJC4(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_4
+ pJC=>tempJC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB(kp)
+
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3,k4)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m,m,n,n),
+ + x(min(sC3,maxload),m,m,n,n),
+ + tempNC3(sC3,rows),
+ + tempJC3(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_4
+ pJA=>tempJC4
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>tempJC3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4,tempJC4)
+
+C third contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m,n,n,n),
+ + x(min(sC2,maxload),m,n,n,n),
+ + tempNC2(sC2,rows),
+ + tempJC2(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_3
+ pJA=>tempJC3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3,tempJC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n,n),
+ + x(min(sC,maxload),n,n,n,n),
+ + tempJC1(JCrows_1,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>tempJC1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2,tempJC1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..a2e454685ddab3293973c426ecededdf93d1671a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/AkronBU4vec_mex.F
@@ -0,0 +1,665 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = AkronBU4vec_mex(l,m,n,IA,JA,NA,...
+C IB,JB,NB,...
+C IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m,n
+ mwPointer IB,JB
+ mwPointer IC_1,IC_2,IC_3,IC_4
+ mwPointer JC_1,JC_2,JC_3,JC_4
+ mwPointer maxload,dosum
+ mwPointer NA,NB
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IBrows, JBrows
+
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC,sA,sB
+ real*8 do_sum
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 19) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '19 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(4))
+ JArows = mxGetM(prhs(5))
+
+ IBrows = mxGetM(prhs(7))
+ JBrows = mxGetM(prhs(8))
+
+ ICrows_1 = mxGetM(prhs(10))
+ JCrows_1 = mxGetM(prhs(11))
+
+ ICrows_2 = mxGetM(prhs(12))
+ JCrows_2 = mxGetM(prhs(13))
+
+ ICrows_3 = mxGetM(prhs(14))
+ JCrows_3 = mxGetM(prhs(15))
+
+ ICrows_4 = mxGetM(prhs(16))
+ JCrows_4 = mxGetM(prhs(17))
+
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m = mxGetPr(prhs(2))
+ n = mxGetPr(prhs(3))
+ IA = mxGetPr(prhs(4))
+ JA = mxGetPr(prhs(5))
+ NA = mxGetPr(prhs(6))
+ IB = mxGetPr(prhs(7))
+ JB = mxGetPr(prhs(8))
+ NB = mxGetPr(prhs(9))
+
+ IC_1 = mxGetPr(prhs(10))
+ JC_1 = mxGetPr(prhs(11))
+ IC_2 = mxGetPr(prhs(12))
+ JC_2 = mxGetPr(prhs(13))
+ IC_3 = mxGetPr(prhs(14))
+ JC_3 = mxGetPr(prhs(15))
+ IC_4 = mxGetPr(prhs(16))
+ JC_4 = mxGetPr(prhs(17))
+ maxload = mxGetPr(prhs(18))
+
+C Get number of states
+ sA = mxGetM(prhs(6))
+ sB = mxGetM(prhs(9))
+
+C check compatibility of states
+ s=max(sA,sB)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB.ne.s .and. sB.ne.1))
+ + then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(19))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1,complexflag)
+ NC = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m),
+ + %VAL(n),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB),%VAL(JB),%VAL(NB),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(IC_3),%VAL(JC_3),%VAL(IC_4),%VAL(JC_4),
+ + %VAL(maxload),%VAL(NC),
+ + IArows,JArows,IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m,n,IA,JA,NA,
+ + IB,JB,NB,
+ + IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IBrows,JBrows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,m,n,sC,sA,sB
+ mwSize IArows,JArows
+ mwSize IBrows,JBrows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC4,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB(sB,JBrows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:,:)
+ logical, allocatable :: w(:,:,:,:)
+
+C three temporary crs vars are needed
+ real*8, target, allocatable :: tempNC4(:,:)
+ real*8, target, allocatable :: tempNC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,4)
+
+ mwSize, target :: IB(IBrows)
+ mwSize, target :: JB(JBrows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,5)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,4)
+
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: JC_3(JCrows_3,4)
+
+ mwSize, target :: IC_4(ICrows_4)
+ mwSize, target :: JC_4(JCrows_4,4)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4
+ mwSize is,js,nz
+
+ mwSize mati,k,kpstart,loc,j2
+ real*8 mat(2,2), fact(2), prod1
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C prepare matrices for factorials and products
+
+ mat(1,1:k)=(/ (mati, mati = n+1, n+k) /)
+ mat(2,1:k)=(/ (mati, mati = n, n+k-1) /)
+ do j=2,k-1
+ mat(j+1,1:k-j+1)=(/ (mati, mati = n+k-j+1, n+1, -1) /)
+ end do
+ fact(1)=1
+ do j=2,k
+ fact(j)=fact(j-1)*j
+ end do
+ prod1=product(mat(2,:))
+
+C first contraction
+ sC4=max(sA,sB)
+ rows=IC_4(ICrows_4)-1
+ allocate (w(m,m,m,n),
+ + x(min(sC4,maxload),m,m,m,n),
+ + tempNC4(sC4,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_4
+ pJC=>JC_4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m,m,n,n),
+ + x(min(sC3,maxload),m,m,n,n),
+ + tempNC3(sC3,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_4
+ pJA=>JC_4
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_3
+ pJC=>JC_3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k4)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4)
+
+C third contraction
+ sC2=max(sC3,sB)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m,n,n,n),
+ + x(min(sC2,maxload),m,n,n,n),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_3
+ pJA=>JC_3
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k3)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n,n,n,n),
+ + x(min(sC,maxload),n,n,n,n),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB
+ pJB=>JB
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB>1) then
+ pNB=>NB(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ if ((pIB(j).le.(pIB(j+1)-1)) .and. (JB(pIB(j+1)-1).ge.k2)) then
+ kpstart=pIB(j)
+ do while (JB(kpstart)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ endif
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,2)
+ v2=pJC(vp,3)
+ v3=pJC(vp,4)
+ v4=pJC(vp,5)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/col2ptr_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/col2ptr_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..f569473bee021cebb6d1714d9411602537c29d7e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/col2ptr_mex.F
@@ -0,0 +1,204 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+
+C [ newptr,newcols,newvals ] = col2ptr_mex( ptr,cols,vals,l,coldim,colptr,ptrcoldim )
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ mwPointer mxGetM, mxGetN
+ real*8 mxGetScalar
+ integer*4 mexPrintf
+
+ mwPointer ptr,cols,vals,l,coldim,colptr
+ mwPointer newcols,newvals
+
+ mwSize ptrM,colsM,colsN,valsM,valsN,coldimM,coldimN
+ mwSize newptrM,newptrN
+ mwSize ptrcoldim
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+ mwSize ndim
+ mwSize dims(2)
+ mwSize newptr
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 7) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nInput',
+ + '7 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nOutput',
+ + '3 outputs required.')
+ endif
+
+
+C Create Fortran array from the input arguments.
+
+ ptr = mxGetPr(prhs(1))
+ cols = mxGetPr(prhs(2))
+ vals = mxGetPr(prhs(3))
+ l = mxGetPr(prhs(4))
+ coldim = mxGetPr(prhs(5))
+ colptr = mxGetPr(prhs(6))
+
+ ptrM = mxGetM(prhs(1))
+
+ colsM = mxGetM(prhs(2))
+ colsN = mxGetN(prhs(2))
+
+ valsM = mxGetM(prhs(3))
+ valsN = mxGetN(prhs(3))
+
+ coldimM = mxGetM(prhs(5))
+ coldimN = mxGetN(prhs(5))
+ coldimN = coldimM*coldimN
+
+C Create matrix for the return arguments.
+C 2 dimensional ptr
+
+ ptrcoldim=mxGetScalar(prhs(7)) ! second dimension of newptr
+
+
+ newptrM=ptrM-1
+ newptrN=ptrcoldim
+
+ classid = mxGetClassID(prhs(1))
+ ndim=2
+ dims(1)=newptrM
+ dims(2)=newptrN
+ complexflag = 0
+
+ plhs(1) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+ newptr = mxGetPr(plhs(1))
+
+ classid = mxGetClassID(prhs(2))
+ ndim = 2
+ dims(1) = colsM
+ dims(2) = colsN-1
+ plhs(2) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+ newcols = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateDoubleMatrix(valsM,valsN,complexflag)
+
+ newvals = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(ptr),%VAL(cols),%VAL(vals),
+ + %VAL(l),%VAL(coldim),%VAL(colptr),
+ + ptrM,colsM,colsN,valsM,valsN,coldimN,
+ + %VAL(newptr),%VAL(newcols),%VAL(newvals),
+ + newptrM,newptrN)
+
+ return
+ end
+
+
+ subroutine compute(ptr,cols,vals,l,coldim,colptr,
+ + ptrM,colsM,colsN,valsM,valsN,coldimN,
+ + newptr,newcols,newvals,
+ + newptrM,newptrN)
+ implicit none
+
+ mwSize ptrM,colsM,colsN,valsM,valsN,coldimN,newptrM,newptrN
+ mwSize ptr(ptrM),coldim(coldimN)
+
+ mwSize l,colptr,colptrdim,newcolsind(colsN-1)
+ mwSize, target :: cols(colsM,colsN)
+ mwSize, pointer :: pcol(:,:)
+
+ mwSize newptr(newptrM,newptrN),newcols(colsM,colsN-1)
+ real*8 vals(valsM,valsN),newvals(valsM,valsN)
+
+ mwSize i,n_vals,j,temploc1,temploc2,n_valsi
+
+ mwSize, allocatable :: countcol(:),z(:),loc(:),ind(:),tempptr(:)
+
+ integer AllocateStatus
+
+ colptrdim=coldim(colptr)
+ n_vals=ptr(ptrM)-1
+ newcolsind(1:colptr-1)=(/(i,i=1,colptr-1)/)
+ newcolsind(colptr:colsN-1)=(/(i,i=colptr+1,colsN)/)
+
+ allocate (countcol(colptrdim),z(colptrdim+1),
+ + tempptr(colptrdim+1),loc(colptrdim),ind(n_vals),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+ do i=1,l
+ n_valsi=ptr(i+1)-ptr(i)
+C count cols
+ countcol=0
+ do j=ptr(i),ptr(i+1)-1
+ countcol(cols(j,colptr))=countcol(cols(j,colptr))+1
+ end do
+
+C create ptr for the column dimension
+ z(1)=1
+ z(2:colptrdim+1)=countcol
+ call cumsum(tempptr,z,colptrdim+1)
+
+C assign in newptr
+ newptr(i,:)=tempptr+ptr(i)-1
+
+C create sort index
+ loc=tempptr(1:colptrdim)
+ do j=1,n_valsi
+ temploc1=ptr(i)+j-1
+ ind(j)=loc(cols(temploc1,colptr))
+ loc(cols(temploc1,colptr))=loc(cols(temploc1,colptr))+1
+ end do
+
+C sort
+ do j=1,n_valsi
+ temploc1=ptr(i)+ind(j)-1
+ temploc2=ptr(i)+j-1
+ newvals(:,temploc1)=vals(:,temploc2)
+ newcols(temploc1,1:colsN-1)=cols(temploc2,newcolsind)
+ end do
+ end do
+
+ deallocate(countcol,z,
+ + tempptr,loc,ind,
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'cannot deallocate.')
+ endif
+
+ return
+ end
+
+ subroutine cumsum(cumx, x, n_x)
+ implicit none
+
+ mwSize i, n_x
+ mwSize cumx(n_x), x(n_x)
+
+ cumx(1)=x(1)
+ do i=2,n_x
+ cumx(i)=cumx(i-1)+x(i)
+ end do
+
+ return
+ end
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diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/compress_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/compress_mex.F
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index 0000000000000000000000000000000000000000..c4d5d641023d3df784748bdc83527e3d3e528e47
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/compress_mex.F
@@ -0,0 +1,193 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+
+C [ newvals,ptr,newcols ] = compress( vals,row,cols,rowdim,n_vals )
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxClassIDFromClassName
+ mwPointer mxGetM, mxGetN
+ real*8 mxGetScalar
+ integer*4 mexPrintf
+
+ mwPointer vals,row,cols
+ mwPointer rowdim, n_vals
+
+ mwPointer newvals,ptr,newcols
+ mwSize n_ptr
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+ mwSize ndim
+ mwSize dims(2)
+
+ mwSize valsM, valsN, colsM, colsN
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 5) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nInput',
+ + '5 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nOutput',
+ + '3 outputs required.')
+ endif
+
+
+C Create Fortran array from the input arguments.
+ vals = mxGetPr(prhs(1))
+ row = mxGetPr(prhs(2))
+ cols = mxGetPr(prhs(3))
+ rowdim = mxGetPr(prhs(4))
+ n_vals = mxGetPr(prhs(5))
+
+ valsM = mxGetM(prhs(1))
+ valsN = mxGetN(prhs(1))
+
+ colsM = mxGetM(prhs(3))
+ colsN = mxGetN(prhs(3))
+
+C Create matrix for the return arguments.
+ plhs(1) = mxCreateDoubleMatrix(valsM, valsN, 0)
+
+ n_ptr=mxGetScalar(prhs(4))+1
+
+ if (sizeof (n_ptr) == 4 ) then
+ classid = mxClassIDFromClassName('int32')
+ else if (sizeof (n_ptr) == 8 ) then
+ classid = mxClassIDFromClassName('int64')
+ else
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'failed')
+ end if
+
+
+ complexflag = 0
+ plhs(2) = mxCreateNumericArray(1, n_ptr,
+ + classid,
+ + complexflag)
+
+ ndim = 2
+ dims(1) = colsM
+ dims(2) = colsN
+ plhs(3) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+
+ newvals = mxGetPr(plhs(1))
+ ptr = mxGetPr(plhs(2))
+ newcols = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(vals),%VAL(row),%VAL(cols),
+ + %VAL(n_vals),%VAL(rowdim),
+ + valsM,valsN,colsM,colsN,
+ + %VAL(newvals),%VAL(ptr),%VAL(newcols))
+
+
+
+ return
+ end
+
+
+ subroutine compute(vals,row,cols, n_vals, rowdim,
+ + valsM,valsN,colsM,colsN,
+ + newvals,ptr,newcols)
+ implicit none
+
+ mwSize i, n, size, valsM, valsN, colsM, colsN
+ mwSize n_vals, rowdim
+
+ real*8 vals(valsM,valsN), newvals(valsM,valsN)
+ mwSize cols(colsM,colsN), newcols(colsM,colsN)
+ mwSize row(n_vals), ptr(rowdim+1)
+
+
+
+ mwSize, allocatable :: countrow(:), z(:), loc(:), ind(:)
+
+ integer AllocateStatus
+
+ allocate (countrow(rowdim),z(rowdim+1),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ call countdim(countrow, row, n_vals, rowdim)
+
+
+ z(1)=1
+ z(2:rowdim+1)=countrow
+
+ deallocate(countrow)
+
+ call cumsum(ptr,z,rowdim+1)
+
+ deallocate(z)
+ allocate (loc(rowdim), ind(n_vals),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ loc=ptr(1:rowdim)
+
+ do i=1,n_vals
+ ind(i)=loc(row(i))
+ loc(row(i))=loc(row(i))+1
+ end do
+
+ do i=1,n_vals
+ newvals(1:valsM,ind(i))=vals(1:valsM,i)
+ newcols(ind(i),1:colsN)=cols(i,1:colsN)
+ end do
+
+ deallocate(loc,ind,STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'cannot deallocate.')
+ endif
+
+ return
+ end
+
+ subroutine countdim(countd, d, n_d, dim)
+ implicit none
+
+ mwSize i, n_d, dim
+ mwSize countd(dim), d(n_d)
+
+ countd=0
+ do i=1,n_d
+ countd(d(i))=countd(d(i))+1
+ end do
+
+ return
+ end
+
+ subroutine cumsum(cumx, x, n_x)
+ implicit none
+
+ mwSize i, n_x
+ mwSize cumx(n_x), x(n_x)
+
+ cumx(1)=x(1)
+ do i=2,n_x
+ cumx(i)=cumx(i-1)+x(i)
+ end do
+
+ return
+ end
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1IC2D_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1IC2D_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..8fdc20abe8f3fa24e8528d0865d53dcdf48c9535
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1IC2D_mex.F
@@ -0,0 +1,148 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1] = contraction1IC2D_mex(l,n1,IA,JA,IB1,JB1)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,n1,IA,JA,IB1,JB1
+ mwPointer IC_1
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows,IB1cols,JB1rows,ndim,dims(2)
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 6) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '6 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + '1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(5))
+ IB1cols = mxGetN(prhs(5))
+ JB1rows = mxGetM(prhs(6))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ n1 = mxGetPr(prhs(2))
+ IA = mxGetPr(prhs(3))
+ JA = mxGetPr(prhs(4))
+ IB1 = mxGetPr(prhs(5))
+ JB1 = mxGetPr(prhs(6))
+
+C Create matrix for the return arguments.
+
+ classid = mxGetClassID(prhs(3))
+ complexflag = 0
+ ndim=2
+ dims(1)=IArows-1
+ dims(2)=IB1cols
+ plhs(1) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(n1),
+ + %VAL(IA),%VAL(JA),%VAL(IB1),%VAL(JB1),
+ + %VAL(IC_1),
+ + IArows,JArows,IB1rows,IB1cols,JB1rows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,IA,JA,IB1,JB1,
+ + IC_1,
+ + IArows,JArows,IB1rows,IB1cols,JB1rows)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1
+ mwSize IArows,JArows
+ mwSize IB1rows,IB1cols,JB1rows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: pIB(:,:)
+
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows,IB1cols)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(IArows-1,IB1cols)
+
+ mwSize i,jp,j,kp,k1,vp,v1,nz,i2
+
+ integer AllocateStatus
+
+ allocate (w(n1),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB1
+
+ do i=1,l
+ w=0
+ do i2=1,IB1cols-1
+ IC_1(i,i2)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j,i2),pIB(j,i2+1)-1
+ k1=JB1(kp)
+ if (w(k1)IA
+ pJA=>JA
+
+ pIB=>IB1
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1)IA
+ pJA=>JA
+
+ pIB=>IB1
+
+ do i=1,l
+ w=0
+ do i2=1,IB1cols-1
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j,i2),pIB(j,i2+1)-1
+ k1=JB1(kp)
+ if (w(k1)IA
+ pJA=>JA
+
+ pIB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1)sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(min(sC,maxload),n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ x1=0.0
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ do loadi=1,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ if (sB>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+ pIB=>IB1
+
+ do i=1,l
+ do i2=1,IB1cols-1
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j,i2),pIB(j,i2+1)-1
+ k1=JB1(kp)
+ if (sC>1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i,i2),pIC(i,i2+1)-1
+ v1=pJC(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+ end do
+ end do
+ end do
+ deallocate (vecload)
+ deallocate (x1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI2D_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI2D_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..8efb3a16faf34311f226930b4ae8770c6004acf6
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI2D_mex.F
@@ -0,0 +1,406 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC,JC] = contraction1IC2D_mex(l,n1,IA,JA,NA,IB1,JB1,NB1,IC_1,JCrows_1,maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,n1,IA,JA,NA,IB1,JB1,NB1
+ mwPointer IC_1,JCrows_1
+ mwPointer maxload, dosum
+
+ mwPointer NC,JC1_1
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows,IB1cols,JB1rows
+ mwSize ICrows_1,ICcols_1,rows
+
+ mwSize sC,sA,sB,ndim,dims(2)
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 12) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '12 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(6))
+ IB1cols = mxGetN(prhs(6))
+ JB1rows = mxGetM(prhs(7))
+
+ ICrows_1 = mxGetM(prhs(9))
+ ICcols_1 = mxGetN(prhs(9))
+ rows = mxGetScalar(prhs(10))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ n1 = mxGetPr(prhs(2))
+ IA = mxGetPr(prhs(3))
+ JA = mxGetPr(prhs(4))
+ NA = mxGetPr(prhs(5))
+ IB1 = mxGetPr(prhs(6))
+ JB1 = mxGetPr(prhs(7))
+ NB1 = mxGetPr(prhs(8))
+ IC_1 = mxGetPr(prhs(9))
+ JCrows_1 = mxGetPr(prhs(10))
+ maxload = mxGetPr(prhs(11))
+ dosum = mxGetPr(prhs(12))
+
+C Get number of states
+ sA = mxGetM(prhs(5))
+ sB = mxGetM(prhs(8))
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(12))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=max(sA,sB)
+ endif
+C Create matrix for NC.
+ complexflag = 0
+
+ plhs(1) = mxCreateDoubleMatrix(sC,rows, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for JC1_1.
+
+ classid = mxGetClassID(prhs(4))
+
+ ndim=1
+ plhs(2) = mxCreateNumericArray(ndim, rows,
+ + classid,
+ + complexflag)
+
+ JC1_1 = mxGetPr(plhs(2))
+
+
+C Call the computational routine.
+ call compute(%VAL(l), %VAL(n1),
+ + %VAL(IA), %VAL(JA),%VAL(NA),
+ + %VAL(IB1), %VAL(JB1),%VAL(NB1),
+ + %VAL(IC_1), %VAL(JCrows_1),
+ + %VAL(maxload),
+ + IArows,JArows,
+ + IB1rows,IB1cols,JB1rows,
+ + ICrows_1,ICcols_1,
+ + %VAL(NC),%VAL(JC1_1),sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,
+ + IA,JA,NA,
+ + IB1,JB1,NB1,
+ + IC_1,JCrows_1,
+ + maxload,
+ + IArows,JArows,
+ + IB1rows,IB1cols,JB1rows,
+ + ICrows_1,ICcols_1,
+ + NC,JC_1,sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1,s,sC,sA,sB,maxload,n_vecload,loadi,load_
+ mwSize IArows,JArows,temp
+ mwSize IB1rows,IB1cols,JB1rows
+ mwSize ICrows_1,ICcols_1,JCrows_1
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB,JB1rows)
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:)
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: pIC(:,:)
+ mwSize, pointer :: pJC(:)
+ real*8, pointer :: NB(:,:)
+ mwSize, pointer :: pIB(:,:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x1(:,:)
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows,IB1cols)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(ICrows_1,ICcols_1)
+ mwSize, target :: JC_1(JCrows_1)
+
+ mwSize i,jp,j,kp,k1,vp,v1,is,js,nz,i2
+
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+ s=max(sA,sB)
+
+ if ((sA>sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(min(sC,maxload),n1),w(n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),w(n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ x1=0.0
+ w=0
+ nz=1
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C Run first time and calculate JC
+ do loadi=1,2-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ if (sB>1) then
+ NB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ NB=>NB1
+ endif
+ pIB=>IB1
+
+ do i=1,l
+ w=0
+ do i2=1,IB1cols-1
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j,i2),pIB(j,i2+1)-1
+ k1=JB1(kp)
+C collect information for JC_1
+ if (w(k1)1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ endif
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i,i2),pIC(i,i2+1)-1
+ v1=pJC(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+ end do
+
+ end do
+ end do
+
+C If n_vecload>2 run again but don't calculate JC this time
+
+ do loadi=2,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ if (sB>1) then
+ NB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ NB=>NB1
+ endif
+ pIB=>IB1
+
+ do i=1,l
+ do i2=1,IB1cols-1
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=pIB(j,i2),pIB(j,i2+1)-1
+ k1=JB1(kp)
+ if (sC>1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ endif
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i,i2),pIC(i,i2+1)-1
+ v1=pJC(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+ end do
+
+ end do
+ end do
+
+ deallocate (vecload)
+ deallocate (x1,w)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecIW_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecIW_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..6e8308278fc87de1af5cce3da85de9da31c6d6c3
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecIW_mex.F
@@ -0,0 +1,302 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C Gateway subroutine
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+
+C Declarations
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxClassIDFromClassName
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer pr_in1,pr_in2
+ mwPointer pr_in3,pr_in4,pr_in5,pr_in6
+ mwPointer pr_in7,pr_in8,pr_in9,pr_in10
+ mwPointer pr_in11, dosum
+
+ mwPointer NC,JC1_1
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ mwSize sC,sA,sB
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 12) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '12 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(6))
+ JB1rows = mxGetM(prhs(7))
+
+ ICrows_1 = mxGetM(prhs(9))
+ JCrows_1 = mxGetScalar(prhs(10))
+
+
+
+C Create Fortran array from the input arguments.
+ pr_in1 = mxGetPr(prhs(1))
+ pr_in2 = mxGetPr(prhs(2))
+ pr_in3 = mxGetPr(prhs(3))
+ pr_in4 = mxGetPr(prhs(4))
+ pr_in5 = mxGetPr(prhs(5))
+ pr_in6 = mxGetPr(prhs(6))
+ pr_in7 = mxGetPr(prhs(7))
+ pr_in8 = mxGetPr(prhs(8))
+ pr_in9 = mxGetPr(prhs(9))
+ pr_in10 = mxGetPr(prhs(10))
+ pr_in11 = mxGetPr(prhs(11))
+
+C Get number of states
+ sA = mxGetM(prhs(5))
+ sB = 1 ! B1 is a W matrix
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(12))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=max(sA,sB)
+ endif
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for JC1_1.
+
+ classid = mxGetClassID(prhs(4))
+
+ plhs(2) = mxCreateNumericArray(1, JCrows_1,
+ + classid,
+ + complexflag)
+
+ JC1_1 = mxGetPr(plhs(2))
+
+
+C Call the computational routine.
+ call compute(%VAL(pr_in1), %VAL(pr_in2),
+ + %VAL(pr_in3), %VAL(pr_in4),
+ + %VAL(pr_in5), %VAL(pr_in6),
+ + %VAL(pr_in7), %VAL(pr_in8),
+ + %VAL(pr_in9),%VAL(pr_in10),
+ + %VAL(pr_in11),
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + %VAL(NC),%VAL(JC1_1),sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,
+ + IA,JA,NA,
+ + IB1,JB1,NB1,
+ + IC_1,temp,
+ + maxload,
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + NC,JC1_1,sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1,s,sC,sA,sB,maxload,n_vecload,loadi,load_
+ mwSize IArows,JArows,temp
+ mwSize IB1rows,JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB,JB1rows)
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:)
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: IC(:)
+ mwSize, pointer :: JC1(:)
+ real*8, pointer :: NB(:,:)
+ mwSize, pointer :: IB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x1(:,:)
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC1_1(JCrows_1)
+
+ mwSize i,jp,j,kp,k1,vp,v1,is,js,nz
+
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+ s=max(sA,sB)
+
+ if ((sA>sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(maxload,n1),w(n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),w(n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+C x1=0.0
+C w=0
+ nz=1
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ do loadi=1,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ IC=>IC_1
+ JC1=>JC1_1
+
+ IB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=IB(j),IB(j+1)-1
+ k1=JB1(kp)
+C collect information for JC_1
+C if (w(k1)1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA.ge.sB) then
+ !DEC$ simd
+ do is=1,load_
+ NC(is,nz)=pNA(is,jp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ NC(is,nz)=pNA(1,jp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA.ge.sB) then
+ !DEC$ simd
+ do is=1,load_
+ NC(1,nz)=NC(1,nz)+pNA(is,jp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ NC(1,nz)=NC(1,nz)+pNA(1,jp)
+ end do
+ endif
+ endif
+ nz=nz+1
+ end do
+ end do
+
+#if 0
+C assign the result in NC
+ do vp=IC(i),IC(i+1)-1
+ v1=JC1(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+#endif
+
+ end do
+
+ end do
+ deallocate (vecload)
+ deallocate (x1,w)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..fd98d47bdd73fd2674ff790977b6e2e707811fee
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecI_mex.F
@@ -0,0 +1,309 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC,JC] = contraction1IC_mex(l,n1,IA,JA,NA,IB1,JB1,NB1,IC_1,JCrows_1,maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,n1,IA,JA,NA,IB1,JB1,NB1
+ mwPointer IC_1,JCrows_1
+ mwPointer maxload, dosum
+
+ mwPointer NC,JC1_1
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize ICrows_1,rows
+
+ mwSize sC,sA,sB,ndim
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 12) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '12 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(6))
+ JB1rows = mxGetM(prhs(7))
+
+ ICrows_1 = mxGetM(prhs(9))
+ rows = mxGetScalar(prhs(10))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ n1 = mxGetPr(prhs(2))
+ IA = mxGetPr(prhs(3))
+ JA = mxGetPr(prhs(4))
+ NA = mxGetPr(prhs(5))
+ IB1 = mxGetPr(prhs(6))
+ JB1 = mxGetPr(prhs(7))
+ NB1 = mxGetPr(prhs(8))
+ IC_1 = mxGetPr(prhs(9))
+ JCrows_1 = mxGetPr(prhs(10))
+ maxload = mxGetPr(prhs(11))
+ dosum = mxGetPr(prhs(12))
+
+C Get number of states
+ sA = mxGetM(prhs(5))
+ sB = mxGetM(prhs(8))
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(12))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=max(sA,sB)
+ endif
+C Create matrix for NC.
+ complexflag = 0
+
+ plhs(1) = mxCreateDoubleMatrix(sC,rows, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for JC1_1.
+
+ classid = mxGetClassID(prhs(4))
+
+ ndim=1
+ plhs(2) = mxCreateNumericArray(ndim, rows,
+ + classid,
+ + complexflag)
+
+ JC1_1 = mxGetPr(plhs(2))
+
+
+C Call the computational routine.
+ call compute(%VAL(l), %VAL(n1),
+ + %VAL(IA), %VAL(JA),%VAL(NA),
+ + %VAL(IB1), %VAL(JB1),%VAL(NB1),
+ + %VAL(IC_1), %VAL(JCrows_1),
+ + %VAL(maxload),
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,
+ + %VAL(NC),%VAL(JC1_1),sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,
+ + IA,JA,NA,
+ + IB1,JB1,NB1,
+ + IC_1,JCrows_1,
+ + maxload,
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,
+ + NC,JC1_1,sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1,s,sC,sA,sB,maxload,n_vecload,loadi,load_
+ mwSize IArows,JArows,temp
+ mwSize IB1rows,JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB,JB1rows)
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:)
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: IC(:)
+ mwSize, pointer :: JC1(:)
+ real*8, pointer :: NB(:,:)
+ mwSize, pointer :: IB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x1(:,:)
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC1_1(JCrows_1)
+
+ mwSize i,jp,j,kp,k1,vp,v1,is,js,nz
+
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+ s=max(sA,sB)
+
+ if ((sA>sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(min(sC,maxload),n1),w(n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),w(n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ x1=0.0
+ w=0
+ nz=1
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ do loadi=1,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ IC=>IC_1
+ JC1=>JC1_1
+
+ if (sB>1) then
+ NB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ NB=>NB1
+ endif
+ IB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=IB(j),IB(j+1)-1
+ k1=JB1(kp)
+C collect information for JC_1
+ if (w(k1)1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ endif
+ end do
+ end do
+
+C assign the result in NC
+ do vp=IC(i),IC(i+1)-1
+ v1=JC1(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+ end do
+
+ end do
+ deallocate (vecload)
+ deallocate (x1,w)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecW_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecW_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..f6ddbc0c58139f39b94a57556faf92b6dcd9c68b
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vecW_mex.F
@@ -0,0 +1,274 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C Gateway subroutine
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+
+C Declarations
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxGetM, mxGetN
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer pr_in1,pr_in2
+ mwPointer pr_in3,pr_in4,pr_in5,pr_in6
+ mwPointer pr_in7,pr_in8,pr_in9,pr_in10
+ mwPointer pr_in11, dosum
+
+ mwPointer pr_out
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ mwSize sC,sA,sB
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 12) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '12 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'One output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(6))
+ JB1rows = mxGetM(prhs(7))
+
+ ICrows_1 = mxGetM(prhs(9))
+ JCrows_1 = mxGetM(prhs(10))
+
+
+
+C Create Fortran array from the input arguments.
+ pr_in1 = mxGetPr(prhs(1))
+ pr_in2 = mxGetPr(prhs(2))
+ pr_in3 = mxGetPr(prhs(3))
+ pr_in4 = mxGetPr(prhs(4))
+ pr_in5 = mxGetPr(prhs(5))
+ pr_in6 = mxGetPr(prhs(6))
+ pr_in7 = mxGetPr(prhs(7))
+ pr_in8 = mxGetPr(prhs(8))
+ pr_in9 = mxGetPr(prhs(9))
+ pr_in10 = mxGetPr(prhs(10))
+ pr_in11 = mxGetPr(prhs(11))
+
+C Get number of states
+ sA = mxGetM(prhs(5))
+ sB = 1 ! B1 is a W matrix
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(12))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=max(sA,sB)
+ endif
+C Create matrix for the return argument.
+ complexflag = 0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ pr_out = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(pr_in1), %VAL(pr_in2),
+ + %VAL(pr_in3), %VAL(pr_in4),
+ + %VAL(pr_in5), %VAL(pr_in6),
+ + %VAL(pr_in7), %VAL(pr_in8),
+ + %VAL(pr_in9), %VAL(pr_in10),
+ + %VAL(pr_in11),
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + %VAL(pr_out),sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,
+ + IA,JA,NA,
+ + IB1,JB1,NB1,
+ + IC_1,JC1_1,
+ + maxload,
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + NC,sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1,s,sC,sA,sB,maxload,n_vecload,loadi,load_
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB,JB1rows)
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:)
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: IC(:)
+ mwSize, pointer :: JC1(:)
+ real*8, pointer :: NB(:,:)
+ mwSize, pointer :: IB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x1(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC1_1(JCrows_1)
+
+ mwSize i,jp,j,kp,k1,vp,v1,is,js,nz
+
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+ s=max(sA,sB)
+
+ if ((sA>sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(maxload,n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+C x1=0.0
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ do loadi=1,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ IC=>IC_1
+ JC1=>JC1_1
+
+ IB=>IB1
+ nz=1
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=IB(j),IB(j+1)-1
+C k1=JB1(kp)
+ if (sC>1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA.ge.sB) then
+ !DEC$ simd
+ do is=1,load_
+ NC(is,nz)=pNA(is,jp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ NC(is,nz)=pNA(1,jp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA.ge.sB) then
+ !DEC$ simd
+ do is=1,load_
+ NC(1,nz)=NC(1,nz)+pNA(is,jp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ NC(1,nz)=NC(1,nz)+pNA(1,jp)
+ end do
+ endif
+ endif
+ nz=nz+1
+ end do
+ end do
+#if 0
+C assign the result in NC
+ do vp=IC(i),IC(i+1)-1
+ v1=JC1(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+#endif
+
+ end do
+ end do
+ deallocate (vecload)
+ deallocate (x1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..1b7152772e496f080f896548302f2a0b1832098e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction1vec_mex.F
@@ -0,0 +1,280 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = contraction1IC_mex(l,n1,IA,JA,NA,IB1,JB1,NB1,IC_1,JC_1,maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxGetM, mxGetN
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,n1,IA,JA,NA,IB1,JB1,NB1
+ mwPointer IC_1,JC_1
+ mwPointer maxload, dosum
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ mwSize sC,sA,sB
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 12) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '12 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'One output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(3))
+ JArows = mxGetM(prhs(4))
+
+ IB1rows = mxGetM(prhs(6))
+ JB1rows = mxGetM(prhs(7))
+
+ ICrows_1 = mxGetM(prhs(9))
+ JCrows_1 = mxGetM(prhs(10))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ n1 = mxGetPr(prhs(2))
+ IA = mxGetPr(prhs(3))
+ JA = mxGetPr(prhs(4))
+ NA = mxGetPr(prhs(5))
+ IB1 = mxGetPr(prhs(6))
+ JB1 = mxGetPr(prhs(7))
+ NB1 = mxGetPr(prhs(8))
+ IC_1 = mxGetPr(prhs(9))
+ JC_1 = mxGetPr(prhs(10))
+ maxload = mxGetPr(prhs(11))
+
+C Get number of states
+ sA = mxGetM(prhs(5))
+ sB = mxGetM(prhs(8))
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(12))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=max(sA,sB)
+ endif
+C Create matrix for the return argument.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(l), %VAL(n1),
+ + %VAL(IA), %VAL(JA),%VAL(NA),
+ + %VAL(IB1), %VAL(JB1),%VAL(NB1),
+ + %VAL(IC_1), %VAL(JC_1),
+ + %VAL(maxload),
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + %VAL(NC),sC,sA,sB)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,n1,
+ + IA,JA,NA,
+ + IB1,JB1,NB1,
+ + IC_1,JC_1,
+ + maxload,
+ + IArows,JArows,
+ + IB1rows,JB1rows,
+ + ICrows_1,JCrows_1,
+ + NC,sC,sA,sB)
+
+C Declarations
+ implicit none
+
+ mwSize l,n1,s,sC,sA,sB,maxload,n_vecload,loadi,load_
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows
+ mwSize ICrows_1,JCrows_1
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB,JB1rows)
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:)
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:)
+ mwSize, pointer :: IC(:)
+ mwSize, pointer :: JC(:)
+ real*8, pointer :: NB(:,:)
+ mwSize, pointer :: IB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x1(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1)
+
+ mwSize i,jp,j,kp,k1,vp,v1,is,js
+
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+ s=max(sA,sB)
+
+ if ((sA>sB .and. sB.ne.1) .or. (sA1) then
+ allocate (x1(min(sC,maxload),n1),
+ + STAT = AllocateStatus)
+ else
+ allocate (x1(1,n1),
+ + STAT = AllocateStatus)
+ endif
+
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ x1=0.0
+
+C NC=0.0, mxCreateDoubleMatrix already initializes to zero
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ do loadi=1,n_vecload-1
+
+ load_=vecload(loadi+1)-vecload(loadi)
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+ pIA=>IA
+ pJA=>JA
+
+ IC=>IC_1
+ JC=>JC_1
+
+ if (sB>1) then
+ NB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ NB=>NB1
+ endif
+ IB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp)
+ do kp=IB(j),IB(j+1)-1
+ k1=JB1(kp)
+ if (sC>1) then
+C Choose among three options and do not sum across rows: 1. A and B are both vectorized. 2. Only A is vectorized. 3. only B is vectorized.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(is,k1)=x1(is,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(is,jp)*NB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x1(1,k1)=x1(1,k1)+pNA(1,jp)*NB(is,kp)
+ end do
+ endif
+ endif
+ end do
+ end do
+
+C assign the result in NC
+ do vp=IC(i),IC(i+1)-1
+ v1=JC(vp)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x1(is,v1)
+ x1(is,v1)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x1(1,v1)
+ x1(1,v1)=0.0
+ endif
+
+ end do
+ end do
+ end do
+ deallocate (vecload)
+ deallocate (x1)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..ce96d3a90ed5f0a01d72c8544da431f4b89cab02
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2IC_mex.F
@@ -0,0 +1,229 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,m1,n1,n2,IA,JA
+ mwPointer IB1,JB1,IB2,JB2
+ mwPointer IC_1,IC_2
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows,ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 10) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '10 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 2 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(5))
+ JArows = mxGetM(prhs(6))
+
+ IB1rows = mxGetM(prhs(7))
+ JB1rows = mxGetM(prhs(8))
+ IB2rows = mxGetM(prhs(9))
+ JB2rows = mxGetM(prhs(10))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ n1 = mxGetPr(prhs(3))
+ n2 = mxGetPr(prhs(4))
+ IA = mxGetPr(prhs(5))
+ JA = mxGetPr(prhs(6))
+ IB1 = mxGetPr(prhs(7))
+ JB1 = mxGetPr(prhs(8))
+ IB2 = mxGetPr(prhs(9))
+ JB2 = mxGetPr(prhs(10))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(5))
+ ndim=1
+ complexflag = 0
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),%VAL(n1),%VAL(n2),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB1),%VAL(JB1),%VAL(IB2),%VAL(JB2),
+ + %VAL(IC_1),%VAL(IC_2),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,n1,n2,IA,JA,
+ + IB1,JB1,IB2,JB2,
+ + IC_1,IC_2,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,n1,n2
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,2)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize JB2(JB2rows)
+
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,vp,v1,v2,nz
+
+ integer AllocateStatus
+
+C first contraction
+
+ allocate (w(m1,n2),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB2
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2)IA
+ pJA=>JA
+
+ pIB=>IB2
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2)IA
+ pJA=>JA
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=pJB(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2),
+ + x(min(sC,maxload),n1,n2),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ sA=sC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=pJB(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2)
+ x(1,v1,v2)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..f47d9d63cb88ddad109ffd6bab1ea5f9d93ee8db
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction2vec_mex.F
@@ -0,0 +1,425 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = contraction2vec_mex(l,m1,n1,n2,IA,JA,NA,...
+C IB1,JB1,NB1,IB2,JB2,NB2,...
+C IC_1,JC_1,IC_2,JC_2,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ integer*4 complexflag
+ real*8 mxGetScalar
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m1,n1,n2
+ mwPointer IB1,JB1,IB2,JB2
+ mwPointer IC_1,IC_2
+ mwPointer JC_1,JC_2
+ mwPointer maxload,dosum
+ mwPointer NA,NB1,NB2
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize ICrows_1,ICrows_2
+ mwSize JCrows_1,JCrows_2
+
+ mwSize s,sC,sA,sB1,sB2
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 19) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '19 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(5))
+ JArows = mxGetM(prhs(6))
+
+ IB1rows = mxGetM(prhs(8))
+ JB1rows = mxGetM(prhs(9))
+ IB2rows = mxGetM(prhs(11))
+ JB2rows = mxGetM(prhs(12))
+
+ ICrows_1 = mxGetM(prhs(14))
+ JCrows_1 = mxGetM(prhs(15))
+
+ ICrows_2 = mxGetM(prhs(16))
+ JCrows_2 = mxGetM(prhs(17))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ n1 = mxGetPr(prhs(3))
+ n2 = mxGetPr(prhs(4))
+ IA = mxGetPr(prhs(5))
+ JA = mxGetPr(prhs(6))
+ NA = mxGetPr(prhs(7))
+ IB1 = mxGetPr(prhs(8))
+ JB1 = mxGetPr(prhs(9))
+ NB1 = mxGetPr(prhs(10))
+ IB2 = mxGetPr(prhs(11))
+ JB2 = mxGetPr(prhs(12))
+ NB2 = mxGetPr(prhs(13))
+ IC_1 = mxGetPr(prhs(14))
+ JC_1 = mxGetPr(prhs(15))
+ IC_2 = mxGetPr(prhs(16))
+ JC_2 = mxGetPr(prhs(17))
+ maxload = mxGetPr(prhs(18))
+
+C Get number of states
+ sA = mxGetM(prhs(7))
+ sB1 = mxGetM(prhs(10))
+ sB2 = mxGetM(prhs(13))
+
+C check compatibility of states
+ s=max(sA,sB1,sB2)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB1.ne.s .and. sB1.ne.1)
+ + .or. (sB1.ne.sB2)) then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(19))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag = 0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),
+ + %VAL(n1),%VAL(n2),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB1),%VAL(JB1),%VAL(NB1),
+ + %VAL(IB2),%VAL(JB2),%VAL(NB2),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(maxload),
+ + %VAL(NC),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + sC,sA,sB1,sB2)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,n1,n2,IA,JA,NA,
+ + IB1,JB1,NB1,IB2,JB2,NB2,
+ + IC_1,JC_1,IC_2,JC_2,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + sC,sA,sB1,sB2)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,n1,n2,sC,sA,sB1,sB2
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize ICrows_1,ICrows_2
+ mwSize JCrows_1,JCrows_2
+
+ mwSize s,sB,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB1,JB1rows)
+ real*8, target :: NB2(sB2,JB2rows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:)
+ logical, allocatable :: w(:,:)
+
+C one temporary crs var is needed, 2
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,2)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize, target :: JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize, target :: JB2(JB2rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,2)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,2)
+
+ mwSize i,jp,j,kp,k1,k2,vp,v1,v2
+ mwSize is,js,nz
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB1,sB2)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ sB=sB1 ! sB1 and sB2 must all be equal
+
+C first contraction
+ sC2=max(sA,sB2)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m1,n2),
+ + x(min(sC2,maxload),m1,n2),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,2)
+ k1=pJA(jp,1)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2)==.false.) then
+ w(k1,k2)=.true.
+ x(:,k1,k2)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2),
+ + x(min(sC,maxload),n1,n2),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ sA=sC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=pJB(kp)
+C initialize x to zero
+ if (w(k1,k2)==.false.) then
+ w(k1,k2)=.true.
+ x(:,k1,k2)=0
+ endif
+
+ if (sC>1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2)=x(is,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2)=x(1,k1,k2)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2)
+ x(is,v1,v2)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2)
+ x(1,v1,v2)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..80f07167f75a8f467676bbb920b8fb587c3ac8bc
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3IC_mex.F
@@ -0,0 +1,324 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2,IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m1,m2,n1,n2,n3
+ mwPointer IB1,JB1,IB2,JB2,IB3,JB3
+ mwPointer IC_1,IC_2,IC_3
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize IB3rows, JB3rows,ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 14) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '14 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(7))
+ JArows = mxGetM(prhs(8))
+
+ IB1rows = mxGetM(prhs(9))
+ JB1rows = mxGetM(prhs(10))
+ IB2rows = mxGetM(prhs(11))
+ JB2rows = mxGetM(prhs(12))
+ IB3rows = mxGetM(prhs(13))
+ JB3rows = mxGetM(prhs(14))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ m2 = mxGetPr(prhs(3))
+ n1 = mxGetPr(prhs(4))
+ n2 = mxGetPr(prhs(5))
+ n3 = mxGetPr(prhs(6))
+ IA = mxGetPr(prhs(7))
+ JA = mxGetPr(prhs(8))
+ IB1 = mxGetPr(prhs(9))
+ JB1 = mxGetPr(prhs(10))
+ IB2 = mxGetPr(prhs(11))
+ JB2 = mxGetPr(prhs(12))
+ IB3 = mxGetPr(prhs(13))
+ JB3 = mxGetPr(prhs(14))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(7))
+
+ ndim=1
+ complexflag = 0
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_3 = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),%VAL(m2),
+ + %VAL(n1),%VAL(n2),%VAL(n3),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB1),%VAL(JB1),%VAL(IB2),%VAL(JB2),
+ + %VAL(IB3),%VAL(JB3),
+ + %VAL(IC_1),%VAL(IC_2),%VAL(IC_3),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,m2,n1,n2,n3,IA,JA,
+ + IB1,JB1,IB2,JB2,IB3,JB3,
+ + IC_1,IC_2,IC_3,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,m2,n1,n2,n3
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize IB3rows,JB3rows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,3)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize JB2(JB2rows)
+ mwSize, target :: IB3(IB3rows)
+ mwSize JB3(JB3rows)
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+ mwSize, target :: IC_3(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+ mwSize, target,allocatable :: JC_3(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,k3,vp,v1,v2,v3,nz
+
+ integer AllocateStatus
+
+C first contraction
+ allocate (w(m1,m2,n3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB3
+
+ do i=1,l
+ IC_3(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+ if (w(k1,k2,k3)IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2,k3)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2,k3)IA
+ pJA=>JA
+
+ pIB=>IB3
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+ if (w(k1,k2,k3)IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2,k3)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2,k3)IA
+ pJA=>JA
+
+ pIB=>IB3
+ pJB=>JB3
+
+ pIC=>IC_3
+ pJC=>tempJC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB3>1) then
+ pNB=>NB3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB3
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC2=max(sC3,sB2)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m1,n2,n3),
+ + x(min(sC2,maxload),m1,n2,n3),
+ + tempNC2(sC2,rows),
+ + tempJC2(rows,3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_3
+ pJA=>tempJC3
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ sA=sC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+C collect information for pJC and initializes x to zero
+ if (w(k1,k2,k3)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3,tempJC3)
+
+C third contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2,n3),
+ + x(min(sC,maxload),n1,n2,n3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+C collect information for pJC and initializes x to zero
+ if (w(k1,k2,k3)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3)
+ x(1,v1,v2,v3)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..c49585445a8db9ddd822dda828b407f070f1839f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction3vec_mex.F
@@ -0,0 +1,551 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = contraction3vec_mex(l,m1,m2,n1,n2,n3,IA,JA,NA,...
+C IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,...
+C IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m1,m2,n1,n2,n3
+ mwPointer IB1,JB1,IB2,JB2,IB3,JB3
+ mwPointer IC_1,IC_2,IC_3
+ mwPointer JC_1,JC_2,JC_3
+ mwPointer maxload,dosum
+ mwPointer NA,NB1,NB2,NB3
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize IB3rows, JB3rows
+ mwSize ICrows_1,ICrows_2,ICrows_3
+ mwSize JCrows_1,JCrows_2,JCrows_3
+
+ mwSize s,sC,sA,sB1,sB2,sB3
+ real*8 do_sum
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 26) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '26 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(7))
+ JArows = mxGetM(prhs(8))
+
+ IB1rows = mxGetM(prhs(10))
+ JB1rows = mxGetM(prhs(11))
+ IB2rows = mxGetM(prhs(13))
+ JB2rows = mxGetM(prhs(14))
+ IB3rows = mxGetM(prhs(16))
+ JB3rows = mxGetM(prhs(17))
+
+ ICrows_1 = mxGetM(prhs(19))
+ JCrows_1 = mxGetM(prhs(20))
+
+ ICrows_2 = mxGetM(prhs(21))
+ JCrows_2 = mxGetM(prhs(22))
+
+ ICrows_3 = mxGetM(prhs(23))
+ JCrows_3 = mxGetM(prhs(24))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ m2 = mxGetPr(prhs(3))
+ n1 = mxGetPr(prhs(4))
+ n2 = mxGetPr(prhs(5))
+ n3 = mxGetPr(prhs(6))
+ IA = mxGetPr(prhs(7))
+ JA = mxGetPr(prhs(8))
+ NA = mxGetPr(prhs(9))
+ IB1 = mxGetPr(prhs(10))
+ JB1 = mxGetPr(prhs(11))
+ NB1 = mxGetPr(prhs(12))
+ IB2 = mxGetPr(prhs(13))
+ JB2 = mxGetPr(prhs(14))
+ NB2 = mxGetPr(prhs(15))
+ IB3 = mxGetPr(prhs(16))
+ JB3 = mxGetPr(prhs(17))
+ NB3 = mxGetPr(prhs(18))
+ IC_1 = mxGetPr(prhs(19))
+ JC_1 = mxGetPr(prhs(20))
+ IC_2 = mxGetPr(prhs(21))
+ JC_2 = mxGetPr(prhs(22))
+ IC_3 = mxGetPr(prhs(23))
+ JC_3 = mxGetPr(prhs(24))
+ maxload = mxGetPr(prhs(25))
+
+C Get number of states
+ sA = mxGetM(prhs(9))
+ sB1 = mxGetM(prhs(12))
+ sB2 = mxGetM(prhs(15))
+ sB3 = mxGetM(prhs(18))
+
+C check compatibility of states
+ s=max(sA,sB1,sB2,sB3)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB1.ne.s .and. sB1.ne.1)
+ + .or. (sB1.ne.sB2) .or. (sB1.ne.sB3)) then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(26))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),%VAL(m2),
+ + %VAL(n1),%VAL(n2),%VAL(n3),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB1),%VAL(JB1),%VAL(NB1),
+ + %VAL(IB2),%VAL(JB2),%VAL(NB2),
+ + %VAL(IB3),%VAL(JB3),%VAL(NB3),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(IC_3),%VAL(JC_3),%VAL(maxload),
+ + %VAL(NC),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,
+ + sC,sA,sB1,sB2,sB3)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,m2,n1,n2,n3,IA,JA,NA,
+ + IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,
+ + IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,
+ + sC,sA,sB1,sB2,sB3)
+
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,m2,n1,n2,n3,sC,sA,sB1,sB2,sB3
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize IB3rows,JB3rows
+ mwSize ICrows_1,ICrows_2,ICrows_3
+ mwSize JCrows_1,JCrows_2,JCrows_3
+
+ mwSize s,sB,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB1,JB1rows)
+ real*8, target :: NB2(sB2,JB2rows)
+ real*8, target :: NB3(sB3,JB3rows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:)
+ logical, allocatable :: w(:,:,:)
+
+C two temporary crs vars are needed, 2 and 3
+ real*8, target, allocatable :: tempNC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,3)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize, target :: JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize, target :: JB2(JB2rows)
+ mwSize, target :: IB3(IB3rows)
+ mwSize, target :: JB3(JB3rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,3)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,3)
+
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: JC_3(JCrows_3,3)
+
+ mwSize i,jp,j,kp,k1,k2,k3,vp,v1,v2,v3
+ mwSize is,js,nz
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB1,sB2,sB3)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ sB=sB1 ! sB1, sB2 and sB3 must all be equal
+
+C first contraction
+ sC3=max(sA,sB3)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m1,m2,n3),
+ + x(min(sC3,maxload),m1,m2,n3),
+ + tempNC3(sC3,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB3
+ pJB=>JB3
+
+ pIC=>IC_3
+ pJC=>JC_3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB3>1) then
+ pNB=>NB3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB3
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+C initialize x to zero
+ if (w(k1,k2,k3)==.false.) then
+ w(k1,k2,k3)=.true.
+ x(:,k1,k2,k3)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC2=max(sC3,sB2)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m1,n2,n3),
+ + x(min(sC2,maxload),m1,n2,n3),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ sA=sC3
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+C initialize x to zero
+ if (w(k1,k2,k3)==.false.) then
+ w(k1,k2,k3)=.true.
+ x(:,k1,k2,k3)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3)
+
+C third contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2,n3),
+ + x(min(sC,maxload),n1,n2,n3),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+C initialize x to zero
+ if (w(k1,k2,k3)==.false.) then
+ w(k1,k2,k3)=.true.
+ x(:,k1,k2,k3)=0
+ endif
+
+ if (sC>1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3)=x(is,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3)=x(1,k1,k2,k3)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3)
+ x(is,v1,v2,v3)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3)
+ x(1,v1,v2,v3)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4IC_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4IC_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..69b44ac7c51c710e391c70b1e8b6a080923e31c4
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4IC_mex.F
@@ -0,0 +1,414 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC_1,IC_2,IC_3,IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m1,m2,m3,n1,n2,n3,n4
+ mwPointer IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4
+ mwPointer IC_1,IC_2,IC_3,IC_4
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize IB3rows, JB3rows
+ mwSize IB4rows, JB4rows,ndim
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 18) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '18 inputs required.')
+ endif
+ if(nlhs .gt. 4) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 4 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(9))
+ JArows = mxGetM(prhs(10))
+
+ IB1rows = mxGetM(prhs(11))
+ JB1rows = mxGetM(prhs(12))
+ IB2rows = mxGetM(prhs(13))
+ JB2rows = mxGetM(prhs(14))
+ IB3rows = mxGetM(prhs(15))
+ JB3rows = mxGetM(prhs(16))
+ IB4rows = mxGetM(prhs(17))
+ JB4rows = mxGetM(prhs(18))
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ m2 = mxGetPr(prhs(3))
+ m3 = mxGetPr(prhs(4))
+ n1 = mxGetPr(prhs(5))
+ n2 = mxGetPr(prhs(6))
+ n3 = mxGetPr(prhs(7))
+ n4 = mxGetPr(prhs(8))
+ IA = mxGetPr(prhs(9))
+ JA = mxGetPr(prhs(10))
+ IB1 = mxGetPr(prhs(11))
+ JB1 = mxGetPr(prhs(12))
+ IB2 = mxGetPr(prhs(13))
+ JB2 = mxGetPr(prhs(14))
+ IB3 = mxGetPr(prhs(15))
+ JB3 = mxGetPr(prhs(16))
+ IB4 = mxGetPr(prhs(17))
+ JB4 = mxGetPr(prhs(18))
+
+C Create matrix for the return arguments.
+ classid = mxGetClassID(prhs(9))
+ ndim=1
+ complexflag = 0
+ plhs(1) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_1 = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_2 = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_3 = mxGetPr(plhs(3))
+
+ plhs(4) = mxCreateNumericArray(ndim, IArows,
+ + classid,
+ + complexflag)
+
+ IC_4 = mxGetPr(plhs(4))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),%VAL(m2),%VAL(m3),
+ + %VAL(n1),%VAL(n2),%VAL(n3),%VAL(n4),
+ + %VAL(IA),%VAL(JA),
+ + %VAL(IB1),%VAL(JB1),%VAL(IB2),%VAL(JB2),
+ + %VAL(IB3),%VAL(JB3),%VAL(IB4),%VAL(JB4),
+ + %VAL(IC_1),%VAL(IC_2),%VAL(IC_3),%VAL(IC_4),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,IB4rows,JB4rows)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,
+ + IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4,
+ + IC_1,IC_2,IC_3,IC_4,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,IB4rows,JB4rows)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,m2,m3,n1,n2,n3,n4
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize IB3rows,JB3rows,IB4rows,JB4rows
+
+ mwSize, pointer :: pIA(:)
+ mwSize, pointer :: pJA(:,:)
+ mwSize, pointer :: pIB(:)
+
+ mwSize, allocatable :: w(:,:,:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,4)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize JB2(JB2rows)
+ mwSize, target :: IB3(IB3rows)
+ mwSize JB3(JB3rows)
+ mwSize, target :: IB4(IB4rows)
+ mwSize JB4(JB4rows)
+
+ mwSize, target :: IC_1(IArows)
+ mwSize, target :: IC_2(IArows)
+ mwSize, target :: IC_3(IArows)
+ mwSize, target :: IC_4(IArows)
+
+ mwSize, target,allocatable :: JC_2(:,:)
+ mwSize, target,allocatable :: JC_3(:,:)
+ mwSize, target,allocatable :: JC_4(:,:)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4,nz
+
+ integer AllocateStatus
+
+C first contraction
+ allocate (w(m1,m2,m3,n4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB4
+
+ do i=1,l
+ IC_4(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB4(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB3
+
+ do i=1,l
+ IC_3(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+ if (w(k1,k2,k3,k4)IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+
+ do i=1,l
+ IC_2(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2,k3,k4)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+ IC_1(i)=nz
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2,k3,k4)IA
+ pJA=>JA
+
+ pIB=>IB4
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB4(kp)
+ if (w(k1,k2,k3,k4)IC_4
+ pJA=>JC_4
+
+ pIB=>IB3
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+ if (w(k1,k2,k3,k4)IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+ if (w(k1,k2,k3,k4)IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+ if (w(k1,k2,k3,k4)IA
+ pJA=>JA
+
+ pIB=>IB4
+ pJB=>JB4
+
+ pIC=>IC_4
+ pJC=>tempJC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB4>1) then
+ pNB=>NB4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB4
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB4(kp)
+
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3,k4)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB3)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m1,m2,n3,n4),
+ + x(min(sC3,maxload),m1,m2,n3,n4),
+ + tempNC3(sC3,rows),
+ + tempJC3(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_4
+ pJA=>tempJC4
+
+ pIB=>IB3
+ pJB=>JB3
+
+ pIC=>IC_3
+ pJC=>tempJC3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB3>1) then
+ pNB=>NB3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB3
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+C collect information for pJC and initialize x to zero
+ if (w(k1,k2,k3,k4)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4,tempJC4)
+
+C third contraction
+ sC2=max(sC3,sB2)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m1,n2,n3,n4),
+ + x(min(sC2,maxload),m1,n2,n3,n4),
+ + tempNC2(sC2,rows),
+ + tempJC2(rows,4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_3
+ pJA=>tempJC3
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>tempJC2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+C collect information for pJC and initializes x to zero
+ if (w(k1,k2,k3,k4)sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3,tempJC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2,n3,n4),
+ + x(min(sC,maxload),n1,n2,n3,n4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=0
+ nz=1
+
+ pIA=>IC_2
+ pJA=>tempJC2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+C collect information for pJC and initializes x to zero
+ if (w(k1,k2,k3,k4)1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2,tempJC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4vec_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4vec_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..44a67f52a61c45251b5ef4bd1878096c08042ed6
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/contraction4vec_mex.F
@@ -0,0 +1,676 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC] = contraction4vec_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,NA,...
+C IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,IB4,JB4,NB4,...
+C IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+C maxload,dosum)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ real*8 mxGetScalar
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,IA,JA
+ mwPointer m1,m2,m3,n1,n2,n3,n4
+ mwPointer IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4
+ mwPointer IC_1,IC_2,IC_3,IC_4
+ mwPointer JC_1,JC_2,JC_3,JC_4
+ mwPointer maxload,dosum
+ mwPointer NA,NB1,NB2,NB3,NB4
+
+ mwPointer NC
+
+C Array information:
+ mwSize IArows,JArows
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize IB3rows, JB3rows
+ mwSize IB4rows, JB4rows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sC,sA,sB1,sB2,sB3,sB4
+ real*8 do_sum
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 33) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '33 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(9))
+ JArows = mxGetM(prhs(10))
+
+ IB1rows = mxGetM(prhs(12))
+ JB1rows = mxGetM(prhs(13))
+ IB2rows = mxGetM(prhs(15))
+ JB2rows = mxGetM(prhs(16))
+ IB3rows = mxGetM(prhs(18))
+ JB3rows = mxGetM(prhs(19))
+ IB4rows = mxGetM(prhs(21))
+ JB4rows = mxGetM(prhs(22))
+
+ ICrows_1 = mxGetM(prhs(24))
+ JCrows_1 = mxGetM(prhs(25))
+
+ ICrows_2 = mxGetM(prhs(26))
+ JCrows_2 = mxGetM(prhs(27))
+
+ ICrows_3 = mxGetM(prhs(28))
+ JCrows_3 = mxGetM(prhs(29))
+
+ ICrows_4 = mxGetM(prhs(30))
+ JCrows_4 = mxGetM(prhs(31))
+
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ m2 = mxGetPr(prhs(3))
+ m3 = mxGetPr(prhs(4))
+ n1 = mxGetPr(prhs(5))
+ n2 = mxGetPr(prhs(6))
+ n3 = mxGetPr(prhs(7))
+ n4 = mxGetPr(prhs(8))
+ IA = mxGetPr(prhs(9))
+ JA = mxGetPr(prhs(10))
+ NA = mxGetPr(prhs(11))
+ IB1 = mxGetPr(prhs(12))
+ JB1 = mxGetPr(prhs(13))
+ NB1 = mxGetPr(prhs(14))
+ IB2 = mxGetPr(prhs(15))
+ JB2 = mxGetPr(prhs(16))
+ NB2 = mxGetPr(prhs(17))
+ IB3 = mxGetPr(prhs(18))
+ JB3 = mxGetPr(prhs(19))
+ NB3 = mxGetPr(prhs(20))
+ IB4 = mxGetPr(prhs(21))
+ JB4 = mxGetPr(prhs(22))
+ NB4 = mxGetPr(prhs(23))
+ IC_1 = mxGetPr(prhs(24))
+ JC_1 = mxGetPr(prhs(25))
+ IC_2 = mxGetPr(prhs(26))
+ JC_2 = mxGetPr(prhs(27))
+ IC_3 = mxGetPr(prhs(28))
+ JC_3 = mxGetPr(prhs(29))
+ IC_4 = mxGetPr(prhs(30))
+ JC_4 = mxGetPr(prhs(31))
+ maxload = mxGetPr(prhs(32))
+
+C Get number of states
+ sA = mxGetM(prhs(11))
+ sB1 = mxGetM(prhs(14))
+ sB2 = mxGetM(prhs(17))
+ sB3 = mxGetM(prhs(20))
+ sB4 = mxGetM(prhs(23))
+
+C check compatibility of states
+ s=max(sA,sB1,sB2,sB3,sB4)
+ if ((sA.ne.s .and. sA.ne.1) .or. (sB1.ne.s .and. sB1.ne.1)
+ + .or. (sB1.ne.sB2) .or. (sB1.ne.sB3) .or. (sB1.ne.sB4)) then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C sum across rows of C if dosum==1
+ do_sum=mxGetScalar(prhs(33))
+
+ if (do_sum==1) then
+ sC=1
+ else
+ sC=s
+ endif
+
+C Create matrix for NC.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(sC,JCrows_1, complexflag)
+ NC = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),%VAL(m2),%VAL(m3),
+ + %VAL(n1),%VAL(n2),%VAL(n3),%VAL(n4),
+ + %VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(IB1),%VAL(JB1),%VAL(NB1),
+ + %VAL(IB2),%VAL(JB2),%VAL(NB2),
+ + %VAL(IB3),%VAL(JB3),%VAL(NB3),
+ + %VAL(IB4),%VAL(JB4),%VAL(NB4),
+ + %VAL(IC_1),%VAL(JC_1),%VAL(IC_2),%VAL(JC_2),
+ + %VAL(IC_3),%VAL(JC_3),%VAL(IC_4),%VAL(JC_4),
+ + %VAL(maxload),%VAL(NC),
+ + IArows,JArows,IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,IB4rows,JB4rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB1,sB2,sB3,sB4)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,NA,
+ + IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,IB4,JB4,NB4,
+ + IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,
+ + maxload,
+ + NC,
+ + IArows,JArows,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + IB3rows,JB3rows,IB4rows,JB4rows,
+ + ICrows_1,JCrows_1,ICrows_2,JCrows_2,
+ + ICrows_3,JCrows_3,ICrows_4,JCrows_4,
+ + sC,sA,sB1,sB2,sB3,sB4)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,m2,m3,n1,n2,n3,n4,sC,sA,sB1,sB2,sB3,sB4
+ mwSize IArows,JArows
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize IB3rows,JB3rows,IB4rows,JB4rows
+ mwSize ICrows_1,ICrows_2,ICrows_3,ICrows_4
+ mwSize JCrows_1,JCrows_2,JCrows_3,JCrows_4
+
+ mwSize s,sB,sC4,sC3,sC2,rows
+ mwSize maxload,n_vecload,loadi,load_
+
+ real*8, target :: NA(sA,JArows)
+ real*8, target :: NB1(sB1,JB1rows)
+ real*8, target :: NB2(sB2,JB2rows)
+ real*8, target :: NB3(sB3,JB3rows)
+ real*8, target :: NB4(sB4,JB4rows)
+
+ real*8 NC(sC,JCrows_1)
+
+ real*8, pointer :: pNA(:,:),pNB(:,:)
+ mwSize, pointer :: pIA(:),pIB(:),pIC(:)
+ mwSize, pointer :: pJA(:,:),pJC(:,:)
+ mwSize, pointer :: pJB(:)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:,:,:,:)
+ logical, allocatable :: w(:,:,:,:)
+
+C three temporary crs vars are needed
+ real*8, target, allocatable :: tempNC4(:,:)
+ real*8, target, allocatable :: tempNC3(:,:)
+ real*8, target, allocatable :: tempNC2(:,:)
+
+ mwSize, target :: IA(IArows)
+ mwSize, target :: JA(JArows,4)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize, target :: JB1(JB1rows)
+ mwSize, target :: IB2(IB2rows)
+ mwSize, target :: JB2(JB2rows)
+ mwSize, target :: IB3(IB3rows)
+ mwSize, target :: JB3(JB3rows)
+ mwSize, target :: IB4(IB4rows)
+ mwSize, target :: JB4(JB4rows)
+
+ mwSize, target :: IC_1(ICrows_1)
+ mwSize, target :: JC_1(JCrows_1,4)
+
+ mwSize, target :: IC_2(ICrows_2)
+ mwSize, target :: JC_2(JCrows_2,4)
+
+ mwSize, target :: IC_3(ICrows_3)
+ mwSize, target :: JC_3(JCrows_3,4)
+
+ mwSize, target :: IC_4(ICrows_4)
+ mwSize, target :: JC_4(JCrows_4,4)
+
+ mwSize i,jp,j,kp,k1,k2,k3,k4,vp,v1,v2,v3,v4
+ mwSize is,js,nz
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+C vecload
+ s=max(sA,sB1,sB2,sB3,sB4)
+
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+ sB=sB1 ! sB1, sB2, sB3 and sB4 must all be equal
+
+C first contraction
+ sC4=max(sA,sB4)
+ rows=IC_4(ICrows_4)-1
+ allocate (w(m1,m2,m3,n4),
+ + x(min(sC4,maxload),m1,m2,m3,n4),
+ + tempNC4(sC4,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IA
+ pJA=>JA
+
+ pIB=>IB4
+ pJB=>JB4
+
+ pIC=>IC_4
+ pJC=>JC_4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sA>1) then
+ pNA=>NA(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>NA
+ endif
+
+ if (sB4>1) then
+ pNB=>NB4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB4
+ endif
+
+ do i=1,l
+
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ j=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k4=JB4(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC4
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC4(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+
+C second contraction
+ sC3=max(sC4,sB3)
+ rows=IC_3(ICrows_3)-1
+ allocate (w(m1,m2,n3,n4),
+ + x(min(sC3,maxload),m1,m2,n3,n4),
+ + tempNC3(sC3,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory2.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_4
+ pJA=>JC_4
+
+ pIB=>IB3
+ pJB=>JB3
+
+ pIC=>IC_3
+ pJC=>JC_3
+
+ sA=sC4
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC4>1) then
+ pNA=>tempNC4(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC4
+ endif
+
+ if (sB3>1) then
+ pNB=>NB3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB3
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ k2=pJA(jp,2)
+ j=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k3=JB3(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC3
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC3(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC4)
+
+C third contraction
+ sC2=max(sC3,sB2)
+ rows=IC_2(ICrows_2)-1
+ allocate (w(m1,n2,n3,n4),
+ + x(min(sC2,maxload),m1,n2,n3,n4),
+ + tempNC2(sC2,rows),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory3.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_3
+ pJA=>JC_3
+
+ pIB=>IB2
+ pJB=>JB2
+
+ pIC=>IC_2
+ pJC=>JC_2
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC3>1) then
+ pNA=>tempNC3(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC3
+ endif
+
+ if (sB2>1) then
+ pNB=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB2
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ k1=pJA(jp,1)
+ j=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k2=JB2(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+C Choose among three options:
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+
+ end do
+ end do
+
+C assign the result in tempNC2
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ tempNC2(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC3)
+
+C fourth contraction
+ rows=IC_1(ICrows_1)-1
+ allocate (w(n1,n2,n3,n4),
+ + x(min(sC,maxload),n1,n2,n3,n4),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory4.')
+ endif
+
+ w=.false.
+ nz=1
+
+ pIA=>IC_2
+ pJA=>JC_2
+
+ pIB=>IB1
+ pJB=>JB1
+
+ pIC=>IC_1
+ pJC=>JC_1
+
+ do loadi=1,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (sC2>1) then
+ pNA=>tempNC2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNA=>tempNC2
+ endif
+
+ if (sB1>1) then
+ pNB=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB=>NB1
+ endif
+
+ do i=1,l
+ do jp=pIA(i),pIA(i+1)-1
+ j=pJA(jp,1)
+ k2=pJA(jp,2)
+ k3=pJA(jp,3)
+ k4=pJA(jp,4)
+ do kp=pIB(j),pIB(j+1)-1
+ k1=JB1(kp)
+C initialize x to zero
+ if (w(k1,k2,k3,k4)==.false.) then
+ w(k1,k2,k3,k4)=.true.
+ x(:,k1,k2,k3,k4)=0
+ endif
+
+ if (sC>1) then
+C Choose among three options and do not sum across rows
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(is,k1,k2,k3,k4)=x(is,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ else
+C Choose among three options and sum across rows.
+ if (sA==sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(is,kp)
+ end do
+ elseif (sA>sB) then
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(is,jp)*pNB(1,kp)
+ end do
+ else
+ !DEC$ simd
+ do is=1,load_
+ x(1,k1,k2,k3,k4)=x(1,k1,k2,k3,k4)+pNA(1,jp)*pNB(is,kp)
+ end do
+ endif
+ endif
+
+ end do
+ end do
+
+C assign the result in NC
+ do vp=pIC(i),pIC(i+1)-1
+ v1=pJC(vp,1)
+ v2=pJC(vp,2)
+ v3=pJC(vp,3)
+ v4=pJC(vp,4)
+ if (sC>1) then
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1,v2,v3,v4)
+ x(is,v1,v2,v3,v4)=0.0
+ end do
+ else
+ NC(1,vp)=NC(1,vp)+x(1,v1,v2,v3,v4)
+ x(1,v1,v2,v3,v4)=0.0
+ endif
+ end do
+
+ end do
+
+ end do
+
+ deallocate (w,x)
+ deallocate (tempNC2)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/do_mex.m b/105/replication_package/solution_methods/taylor_projection/MEX_files/do_mex.m
new file mode 100644
index 0000000000000000000000000000000000000000..cffd6feb448423255ba13286c2649c6f747d0004
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/do_mex.m
@@ -0,0 +1,8 @@
+folder_name='compiled_on_Windows10';
+
+mkdir(folder_name);
+
+for file = dir('*.F')'
+ mex('-largeArrayDims', file.name, '-outdir',folder_name)
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/multcol.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/multcol.F
new file mode 100644
index 0000000000000000000000000000000000000000..79751317e19f21028d15b5d0f588e2f6c27ad8be
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/multcol.F
@@ -0,0 +1,102 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [A] = multcol(mat,vec)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer mat,vec,A
+
+C Array information:
+ mwSize matM,matN
+ mwSize vecM,vecN
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '2 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ matM = mxGetM(prhs(1))
+ matN = mxGetN(prhs(1))
+
+ vecM = mxGetM(prhs(2))
+ vecN = mxGetN(prhs(2))
+
+C Create Fortran array from the input arguments.
+ mat = mxGetPr(prhs(1))
+ vec = mxGetPr(prhs(2))
+
+C Create matrix for the return arguments.
+ complexflag=0
+
+ plhs(1) = mxCreateDoubleMatrix(matM,matN,complexflag)
+ A = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(mat),%VAL(vec),%VAL(A),
+ + matM,matN,vecM,vecN)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(mat,vec,A,
+ + matM,matN,vecM,vecN)
+
+C Declarations
+ implicit none
+
+ mwSize matM,matN,vecM,vecN,i,j
+ real*8 mat(matM,matN),A(matM,matN),vec(vecM,vecN)
+
+ if ((vecM>1) .and. (vecN>1)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'second argument is not a vector.')
+ elseif ((vecM>1) .and. (matM.ne.vecM)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'incompatible dimensions.')
+ elseif ((vecN>1) .and. (matM.ne.vecN)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'incompatible dimensions.')
+ endif
+
+ if (vecN==1) then
+ do j=1,matN
+ !DEC$ simd
+ do i=1,matM
+ A(i,j)=mat(i,j)*vec(i,1)
+ end do
+ end do
+ else
+ do j=1,matN
+ !DEC$ simd
+ do i=1,matM
+ A(i,j)=mat(i,j)*vec(1,i)
+ end do
+ end do
+ endif
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/multrow.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/multrow.F
new file mode 100644
index 0000000000000000000000000000000000000000..4d6084975b7bc108e90b0297e2996c5bedd63201
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/multrow.F
@@ -0,0 +1,101 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [A] = multrow(mat,vec)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer mat,vec,A
+
+C Array information:
+ mwSize matM,matN
+ mwSize vecM,vecN
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '2 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 1 output required.')
+ endif
+
+C Get the size of the inputs array.
+
+ matM = mxGetM(prhs(1))
+ matN = mxGetN(prhs(1))
+
+ vecM = mxGetM(prhs(2))
+ vecN = mxGetN(prhs(2))
+
+C Create Fortran array from the input arguments.
+ mat = mxGetPr(prhs(1))
+ vec = mxGetPr(prhs(2))
+
+C Create matrix for the return arguments.
+ complexflag=0
+ plhs(1) = mxCreateDoubleMatrix(matM,matN,complexflag)
+ A = mxGetPr(plhs(1))
+
+
+C Call the computational routine.
+ call compute(%VAL(mat),%VAL(vec),%VAL(A),
+ + matM,matN,vecM,vecN)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(mat,vec,A,
+ + matM,matN,vecM,vecN)
+
+C Declarations
+ implicit none
+
+ mwSize matM,matN,vecM,vecN,i,j
+ real*8 mat(matM,matN),A(matM,matN),vec(vecM,vecN)
+
+ if ((vecM>1) .and. (vecN>1)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'second argument is not a vector.')
+ elseif ((vecM>1) .and. (matN.ne.vecM)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'incompatible dimensions.')
+ elseif ((vecN>1) .and. (matN.ne.vecN)) then
+ call mexErrMsgIdAndTxt ('MATLAB:multrow',
+ + 'incompatible dimensions.')
+ endif
+
+ if (vecN==1) then
+ do j=1,matN
+ !DEC$ simd
+ do i=1,matM
+ A(i,j)=mat(i,j)*vec(j,1)
+ end do
+ end do
+ else
+ do j=1,matN
+ !DEC$ simd
+ do i=1,matM
+ A(i,j)=mat(i,j)*vec(1,j)
+ end do
+ end do
+ endif
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/perm_rows.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/perm_rows.F
new file mode 100644
index 0000000000000000000000000000000000000000..d4782bd1aa6abfa0d82ec385ca655e59154628b2
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/perm_rows.F
@@ -0,0 +1,172 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC,JC,NC] = perm_rows(IA,JA,NA,l,perml)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,perml,IA,JA,NA
+ mwPointer IC,JC,NC
+
+C Array information:
+ mwSize IArows,JArows,JAcols,NArows,NAcols
+
+ mwSize sA,dims(2),ndims
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 5) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '5 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(1))
+ JArows = mxGetM(prhs(2))
+ NArows = mxGetM(prhs(3))
+
+ JAcols = mxGetN(prhs(2))
+ NAcols = mxGetN(prhs(3))
+
+C Create Fortran array from the input arguments.
+ IA = mxGetPr(prhs(1))
+ JA = mxGetPr(prhs(2))
+ NA = mxGetPr(prhs(3))
+ l = mxGetPr(prhs(4))
+ perml = mxGetPr(prhs(5))
+
+C Create return arguments.
+
+ classid = mxGetClassID(prhs(1))
+ complexflag = 0
+ ndims=1
+ plhs(1) = mxCreateNumericArray(ndims, IArows,
+ + classid,
+ + complexflag)
+
+ IC = mxGetPr(plhs(1))
+
+ classid = mxGetClassID(prhs(2))
+ ndims=2
+ dims(1)=JArows
+ dims(2)=JAcols
+ plhs(2) = mxCreateNumericArray(ndims, dims,
+ + classid,
+ + complexflag)
+
+ JC = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateDoubleMatrix(NArows,NAcols,complexflag)
+ NC = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ if (NArows==1) then
+ call compute1(%VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(l),%VAL(perml),
+ + %VAL(IC),%VAL(JC),%VAL(NC),
+ + IArows,JArows,JAcols,NArows,NAcols)
+ else
+ call compute2(%VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(l),%VAL(perml),
+ + %VAL(IC),%VAL(JC),%VAL(NC),
+ + IArows,JArows,JAcols,NArows,NAcols)
+ endif
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute1(IA,JA,NA,l,perml,
+ + IC,JC,NC,
+ + IArows,JArows,JAcols,NArows,NAcols)
+
+C Declarations
+ implicit none
+
+ mwSize IArows,JArows,JAcols,NArows,NAcols,l
+ mwSize IA(IArows),IC(IArows)
+ mwSize JA(JArows,JAcols),JC(JArows,JAcols)
+ real*8 NA(NAcols),NC(NAcols)
+
+ mwSize perml(l),i,j,k,startj,endj,si
+
+C create IC,JC,NC
+ IC(1)=1
+ do i=1,l
+ startj=IA(perml(i))
+ endj=IA(perml(i)+1)-1
+ IC(i+1)=IC(i)+endj-startj+1
+ !DEC$ simd
+ do j=startj,endj
+ NC(IC(i)+j-startj)=NA(j)
+ enddo
+ do k=1,JAcols
+ !DEC$ simd
+ do j=startj,endj
+ JC(IC(i)+j-startj,k)=JA(j,k)
+ enddo
+ enddo
+ enddo
+ return
+ end
+
+
+ subroutine compute2(IA,JA,NA,l,perml,
+ + IC,JC,NC,
+ + IArows,JArows,JAcols,NArows,NAcols)
+
+C Declarations
+ implicit none
+
+ mwSize IArows,JArows,JAcols,NArows,NAcols,l
+ mwSize IA(IArows),IC(IArows)
+ mwSize JA(JArows,JAcols),JC(JArows,JAcols)
+ real*8 NA(NArows,NAcols),NC(NArows,NAcols)
+
+ mwSize perml(l),i,j,k,startj,endj,si
+
+C create IC,JC,NC
+ IC(1)=1
+ do i=1,l
+ startj=IA(perml(i))
+ endj=IA(perml(i)+1)-1
+ IC(i+1)=IC(i)+endj-startj+1
+ do j=startj,endj
+ !DEC$ simd
+ do si=1,NArows
+ NC(si,IC(i)+j-startj)=NA(si,j)
+ enddo
+ enddo
+ do k=1,JAcols
+ !DEC$ simd
+ do j=startj,endj
+ JC(IC(i)+j-startj,k)=JA(j,k)
+ enddo
+ enddo
+ enddo
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/ptr2col_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/ptr2col_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..26d13eddc49455e633f5cde30b045474878a1fb4
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/ptr2col_mex.F
@@ -0,0 +1,91 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+
+C [ newcols ] = ptr2col_mex( ptr,n_vals )
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ mwPointer mxGetM, mxGetN
+ real*8 mxGetScalar
+
+ mwPointer ptr
+ mwPointer newcols
+
+ mwSize ptrM
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+ mwSize ndim
+ mwSize dims(1)
+ mwSize l1,l2
+ real*8 n_vals
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nInput',
+ + '2 inputs required.')
+ endif
+ if(nlhs .gt. 1) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nOutput',
+ + '1 output required.')
+ endif
+
+
+C Create Fortran array from the input arguments.
+
+ ptr = mxGetPr(prhs(1))
+
+ l1 = mxGetM(prhs(1))
+ l2 = mxGetN(prhs(1))-1
+
+C Create matrix for the return arguments.
+
+ n_vals=mxGetScalar(prhs(2))
+
+ complexflag = 0
+
+ classid = mxGetClassID(prhs(1))
+ ndim = 1
+ dims(1) = n_vals
+ plhs(1) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+ newcols = mxGetPr(plhs(1))
+
+C Call the computational routine.
+ call compute(%VAL(ptr),l1,l2,%VAL(newcols),n_vals)
+
+ return
+ end
+
+
+ subroutine compute(ptr,l1,l2,newcols,n_vals)
+ implicit none
+
+ real*8 n_vals
+ mwSize l1,l2
+ mwSize ptr(l1,l2+1),newcols(n_vals)
+
+ mwSize i1,i2,i
+ do i1=1,l1
+ do i2=1,l2
+ do i=ptr(i1,i2),ptr(i1,i2+1)-1
+ newcols(i)=i2
+ enddo
+ enddo
+ enddo
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/sortcol_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/sortcol_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..b57232d3a655cecf9f10a689e35c517e6e7736df
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/sortcol_mex.F
@@ -0,0 +1,175 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+
+C [ newcols,newvals ] = sortcol_mex( ptr,cols,vals,l,coldim,coli,colidim )
+C the function sorts columns by coli
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+ mwPointer mxGetPr
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+ mwPointer mxGetM, mxGetN
+
+ mwPointer ptr,cols,vals,l,coldim,coli
+ mwPointer newcols,newvals
+
+ mwSize ptrM,colsM,colsN,valsM,valsN,coldimM,coldimN
+ mwSize colidim
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+ mwSize ndim
+ mwSize dims(2)
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 7) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nInput',
+ + '7 inputs required.')
+ endif
+ if(nlhs .gt. 2) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:nOutput',
+ + '2 outputs required.')
+ endif
+
+
+C Create Fortran array from the input arguments.
+
+ ptr = mxGetPr(prhs(1))
+ cols = mxGetPr(prhs(2))
+ vals = mxGetPr(prhs(3))
+ l = mxGetPr(prhs(4))
+ coldim = mxGetPr(prhs(5))
+ coli = mxGetPr(prhs(6))
+
+ ptrM = mxGetM(prhs(1))
+
+ colsM = mxGetM(prhs(2))
+ colsN = mxGetN(prhs(2))
+
+ valsM = mxGetM(prhs(3))
+ valsN = mxGetN(prhs(3))
+
+ coldimM = mxGetM(prhs(5))
+ coldimN = mxGetN(prhs(5))
+ coldimN = coldimM*coldimN
+
+C Create matrix for the return arguments.
+
+ classid = mxGetClassID(prhs(2))
+ complexflag=0
+
+ ndim = 2
+ dims(1) = colsM
+ dims(2) = colsN
+ plhs(1) = mxCreateNumericArray(ndim, dims,
+ + classid,
+ + complexflag)
+
+ newcols = mxGetPr(plhs(1))
+
+ plhs(2) = mxCreateDoubleMatrix(valsM, valsN, complexflag)
+
+ newvals = mxGetPr(plhs(2))
+
+C Call the computational routine.
+ call compute(%VAL(ptr),%VAL(cols),%VAL(vals),
+ + %VAL(l),%VAL(coldim),%VAL(coli),
+ + ptrM,colsM,colsN,valsM,valsN,coldimN,
+ + %VAL(newcols),%VAL(newvals))
+
+ return
+ end
+
+ subroutine compute(ptr,cols,vals,l,coldim,coli,
+ + ptrM,colsM,colsN,valsM,valsN,coldimN,
+ + newcols,newvals)
+ implicit none
+
+ mwSize ptrM,colsM,colsN,valsM,valsN,coldimN
+ mwSize ptr(ptrM),coldim(coldimN)
+
+ mwSize l,coli,colidim
+ mwSize cols(colsM,colsN)
+
+ mwSize newcols(colsM,colsN)
+ real*8 vals(valsM,valsN),newvals(valsM,valsN)
+
+ mwSize i,n_vals,j,temploc1,temploc2,n_valsi
+
+ mwSize, allocatable :: countcol(:),z(:),loc(:),ind(:),tempptr(:)
+
+ integer AllocateStatus
+
+ colidim=coldim(coli)
+ n_vals=ptr(ptrM)-1
+
+ allocate (countcol(colidim),z(colidim+1),
+ + tempptr(colidim+1),loc(colidim),ind(n_vals),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory.')
+ endif
+ do i=1,l
+ n_valsi=ptr(i+1)-ptr(i)
+C count cols
+ countcol=0
+ do j=ptr(i),ptr(i+1)-1
+ countcol(cols(j,coli))=countcol(cols(j,coli))+1
+ end do
+
+C create ptr for the column dimension
+ z(1)=1
+ z(2:colidim+1)=countcol
+ call cumsum(tempptr,z,colidim+1)
+
+C create sort index
+ loc=tempptr(1:colidim)
+ do j=1,n_valsi
+ temploc1=ptr(i)+j-1
+ ind(j)=loc(cols(temploc1,coli))
+ loc(cols(temploc1,coli))=loc(cols(temploc1,coli))+1
+ end do
+
+C sort
+ do j=1,n_valsi
+ temploc1=ptr(i)+ind(j)-1
+ temploc2=ptr(i)+j-1
+ newvals(:,temploc1)=vals(:,temploc2)
+ newcols(temploc1,:)=cols(temploc2,:)
+ end do
+ end do
+
+ deallocate(countcol,z,
+ + tempptr,loc,ind,
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'cannot deallocate.')
+ endif
+
+ return
+ end
+
+ subroutine cumsum(cumx, x, n_x)
+ implicit none
+
+ mwSize i, n_x
+ mwSize cumx(n_x), x(n_x)
+
+ cumx(1)=x(1)
+ do i=2,n_x
+ cumx(i)=cumx(i-1)+x(i)
+ end do
+
+ return
+ end
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/takerows_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/takerows_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..fdb34bd97152cc27af9b08c47840c994667fc2bb
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/takerows_mex.F
@@ -0,0 +1,126 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [IC,JC,NC] = takerows_mex(IA,JA,NA,l,takel)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+ real*8 mxGetScalar
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,takel,IA,JA,NA
+ mwPointer IC,JC,NC
+
+C Array information:
+ mwSize IArows,JArows,JAcols,NArows,NAcols
+
+ mwSize sA,dims(2),ndims,n_takel
+
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 5) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '5 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IArows = mxGetM(prhs(1))
+ JArows = mxGetM(prhs(2))
+ NArows = mxGetM(prhs(3))
+
+ JAcols = mxGetN(prhs(2))
+ NAcols = mxGetN(prhs(3))
+
+ n_takel=mxGetM(prhs(5))*mxGetN(prhs(5))
+
+C Create Fortran array from the input arguments.
+ IA = mxGetPr(prhs(1))
+ JA = mxGetPr(prhs(2))
+ NA = mxGetPr(prhs(3))
+ l = mxGetPr(prhs(4))
+ takel = mxGetPr(prhs(5))
+
+C Create return arguments.
+
+ classid = mxGetClassID(prhs(1))
+ complexflag = 0
+ ndims=1
+ plhs(1) = mxCreateNumericArray(ndims, IArows,
+ + classid,
+ + complexflag)
+
+ IC = mxGetPr(plhs(1))
+
+ classid = mxGetClassID(prhs(2))
+ ndims=2
+ dims(1)=JArows
+ dims(2)=JAcols
+ plhs(2) = mxCreateNumericArray(ndims, dims,
+ + classid,
+ + complexflag)
+
+ JC = mxGetPr(plhs(2))
+
+ plhs(3) = mxCreateDoubleMatrix(NArows,NAcols,complexflag)
+ NC = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(IA),%VAL(JA),%VAL(NA),
+ + %VAL(l),%VAL(takel),
+ + %VAL(IC),%VAL(JC),%VAL(NC),
+ + IArows,JArows,JAcols,NArows,NAcols,n_takel)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(IA,JA,NA,l,takel,
+ + IC,JC,NC,
+ + IArows,JArows,JAcols,NArows,NAcols,n_takel)
+
+C Declarations
+ implicit none
+
+ mwSize IArows,JArows,JAcols,NArows,NAcols,n_takel
+ mwSize IA(IArows),IC(IArows)
+ mwSize JA(JArows,JAcols),JC(JArows,JAcols)
+ real*8 NA(NArows,NAcols),NC(NArows,NAcols)
+
+ mwSize l,takel(n_takel),i,j,k,nz,startc,endc
+
+C create IC,JC,NC
+ nz=0
+ k=0
+ IC(1)=1
+ do i=1,n_takel
+ k=k+1
+ j=takel(i)
+ IC(k+1)=IC(k)+IA(j+1)-IA(j)
+ JC(IC(k):IC(k+1)-1,:)=JA(IA(j):IA(j+1)-1,:)
+ NC(:,IC(k):IC(k+1)-1)=NA(:,IA(j):IA(j+1)-1)
+
+ enddo
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_2D_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_2D_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..667b38df83661ac2ae6ac2006b26755fd044734d
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_2D_mex.F
@@ -0,0 +1,320 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC,IC,JC] = tplus1_2D_mex(l1,l2,m1,...
+C IB1,JB1,NB1,IB2,JB2,NB2,
+C maxload)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l1,l2,m1
+ mwPointer IB1,JB1,IB2,JB2
+ mwPointer IC
+ mwPointer JC
+ mwPointer maxload
+ mwPointer NB1,NB2
+
+ mwPointer NC
+
+C Array information:
+ mwSize IB1rows, IB1cols, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize ICrows,ICcols
+ mwSize JCrows
+
+ mwSize s,sB1,sB2,ndim
+ mwSize dim(2)
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 10) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '10 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IB1rows = mxGetM(prhs(4))
+ IB1cols = mxGetN(prhs(4))
+ JB1rows = mxGetM(prhs(5))
+ IB2rows = mxGetM(prhs(7))
+ JB2rows = mxGetM(prhs(8))
+
+ ICrows=IB1rows
+ ICcols=IB1cols
+
+ JCrows=JB1rows+JB2rows ! temporary size, should be adjusted after calling the mex function.
+
+C Create Fortran array from the input arguments.
+ l1 = mxGetPr(prhs(1))
+ l2 = mxGetPr(prhs(2))
+ m1 = mxGetPr(prhs(3))
+ IB1 = mxGetPr(prhs(4))
+ JB1 = mxGetPr(prhs(5))
+ NB1 = mxGetPr(prhs(6))
+ IB2 = mxGetPr(prhs(7))
+ JB2 = mxGetPr(prhs(8))
+ NB2 = mxGetPr(prhs(9))
+ maxload = mxGetPr(prhs(10))
+
+C Get number of states
+ sB1 = mxGetM(prhs(6))
+ sB2 = mxGetM(prhs(9))
+
+ s=sB1
+
+C check compatibility of states
+ if (sB1.ne.sB2) then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C Create matrix for NC.
+ complexflag = 0
+
+ plhs(1) = mxCreateDoubleMatrix(s,JCrows,complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for IC and JC
+ classid = mxGetClassID(prhs(4))
+ ndim=2
+ dim(1)=ICrows
+ dim(2)=ICcols
+ plhs(2) = mxCreateNumericArray(ndim, dim,
+ + classid,
+ + complexflag)
+
+ IC = mxGetPr(plhs(2))
+
+ classid = mxGetClassID(prhs(5))
+ ndim=2
+ dim(1)=JCrows
+ dim(2)=1
+ plhs(3) = mxCreateNumericArray(ndim, dim,
+ + classid,
+ + complexflag)
+
+ JC = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(l1),%VAL(l2),%VAL(m1),
+ + %VAL(IB1),%VAL(JB1),%VAL(NB1),
+ + %VAL(IB2),%VAL(JB2),%VAL(NB2),
+ + %VAL(maxload),
+ + %VAL(NC),%VAL(IC),%VAL(JC),
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows,JCrows,
+ + s)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l1,l2,m1,
+ + IB1,JB1,NB1,IB2,JB2,NB2,
+ + maxload,
+ + NC,IC,JC,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows,JCrows,
+ + s)
+
+C Declarations
+ implicit none
+
+ mwSize l1,l2,m1,s
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize ICrows,ICcols
+ mwSize JCrows
+
+ mwSize maxload,n_vecload,loadi,load_
+ logical doind
+ real*8, target :: NB1(s,JB1rows)
+ real*8, target :: NB2(s,JB2rows)
+
+ real*8, pointer :: pNB1(:,:)
+ real*8, pointer :: pNB2(:,:)
+
+ real*8 NC(s,JCrows)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:)
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IB1(l1,l2+1)
+ mwSize, target :: JB1(JB1rows,1)
+ mwSize, target :: IB2(l1,l2+1)
+ mwSize, target :: JB2(JB2rows,1)
+
+ mwSize, target :: IC(l1,l2+1)
+ mwSize, target :: JC(JCrows,1)
+
+ mwSize i,i1,i2,jp,j,kp,k1,k2,vp,v1,v2
+ mwSize is,js,nz
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+C vecload
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C allocate
+ allocate (w(m1),
+ + x(min(s,maxload),m1),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ nz=1
+
+C run first time and calculate indices
+ loadi=1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i1=1,l1
+ w=0
+ do i2=1,l2
+ IC(i1,i2)=nz
+C run over rows of B1
+ do jp=IB1(i1,i2),IB1(i1,i2+1)-1
+ j=JB1(jp,1)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j)=pNB1(is,jp)
+ end do
+ JC(nz,1)=j
+ w(j)=i2
+ nz=nz+1
+ end do
+C run over rows of B2
+ do jp=IB2(i1,i2),IB2(i1,i2+1)-1
+ j=JB2(jp,1)
+ if (w(j)2) then
+ w=0
+ endif
+
+ do loadi=2,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i1=1,l1
+ do i2=1,l2
+C run over rows of B1
+ do jp=IB1(i1,i2),IB1(i1,i2+1)-1
+ j=JB1(jp,1)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j)=pNB1(is,jp)
+ end do
+ end do
+C run over rows of B2
+ do jp=IB2(i1,i2),IB2(i1,i2+1)-1
+ j=JB2(jp,1)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j)=x(is,j)+pNB2(is,jp)
+ end do
+ end do
+C assign result in NC
+ do vp=IC(i1,i2),IC(i1,i2+1)-1
+ v1=JC(vp,1)
+ !DEC$ simd
+ do is=1,load_
+ js=vecload(loadi)+is-1
+ NC(js,vp)=x(is,v1)
+ x(is,v1)=0.0
+ end do
+ end do
+ end do
+
+ end do
+ end do
+
+ deallocate (w,x)
+
+ return
+ end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_mex.F b/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_mex.F
new file mode 100644
index 0000000000000000000000000000000000000000..607d939b4dc1ab72f9c35e5074d7d2d9a6c48c94
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/MEX_files/tplus1_mex.F
@@ -0,0 +1,319 @@
+C � Copyright, Oren Levintal, June 13, 2016.
+
+#include "fintrf.h"
+C [NC,IC,JC] = tplus1_mex(l,m1,...
+C IB1,JB1,NB1,IB2,JB2,NB2,
+C maxload)
+ subroutine mexfunction(nlhs, plhs, nrhs, prhs)
+ implicit none
+
+C mexFunction arguments:
+ mwPointer plhs(*), prhs(*)
+ integer nlhs, nrhs
+
+C Function declarations:
+ mwPointer mxGetPr
+ mwPointer mxGetM, mxGetN
+ mwPointer mxCreateDoubleMatrix
+ mwPointer mxCreateNumericArray
+ integer*4 mxGetClassID
+
+C Arguments for mxCreateNumericArray
+ integer*4 classid
+ integer*4 complexflag
+
+C Pointers to input/output mxArrays:
+ mwPointer l,m1
+ mwPointer IB1,JB1,IB2,JB2
+ mwPointer IC
+ mwPointer JC
+ mwPointer maxload
+ mwPointer NB1,NB2
+
+ mwPointer NC
+
+C Array information:
+ mwSize IB1rows, JB1rows
+ mwSize IB2rows, JB2rows
+ mwSize ICrows
+ mwSize JCrows
+
+ mwSize s,sB1,sB2,ndim
+ mwSize dim(2)
+
+C-----------------------------------------------------------------------
+C Check for proper number of arguments.
+ if(nrhs .ne. 9) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction2:nInput',
+ + '9 inputs required.')
+ endif
+ if(nlhs .gt. 3) then
+ call mexErrMsgIdAndTxt ('MATLAB:contraction1:nOutput',
+ + 'Max 3 outputs required.')
+ endif
+
+C Get the size of the inputs array.
+
+ IB1rows = mxGetM(prhs(3))
+ JB1rows = mxGetM(prhs(4))
+ IB2rows = mxGetM(prhs(6))
+ JB2rows = mxGetM(prhs(7))
+
+ ICrows=IB1rows
+ JCrows=JB1rows+JB2rows ! temporary size, should be adjusted after calling the mex function.
+
+C Create Fortran array from the input arguments.
+ l = mxGetPr(prhs(1))
+ m1 = mxGetPr(prhs(2))
+ IB1 = mxGetPr(prhs(3))
+ JB1 = mxGetPr(prhs(4))
+ NB1 = mxGetPr(prhs(5))
+ IB2 = mxGetPr(prhs(6))
+ JB2 = mxGetPr(prhs(7))
+ NB2 = mxGetPr(prhs(8))
+ maxload = mxGetPr(prhs(9))
+
+C Get number of states
+ sB1 = mxGetM(prhs(5))
+ sB2 = mxGetM(prhs(8))
+
+ s=sB1
+
+C check compatibility of states
+ if (sB1.ne.sB2) then
+ call mexErrMsgIdAndTxt ('MATLAB:states',
+ + 'incompatible states.')
+ endif
+
+C Create matrix for NC.
+ complexflag = 0
+
+ plhs(1) = mxCreateDoubleMatrix(s,JCrows, complexflag)
+ NC = mxGetPr(plhs(1))
+
+C Create matrix for IC and JC
+ classid = mxGetClassID(prhs(3))
+ ndim=1
+ plhs(2) = mxCreateNumericArray(ndim, ICrows,
+ + classid,
+ + complexflag)
+
+ IC = mxGetPr(plhs(2))
+
+ classid = mxGetClassID(prhs(4))
+ ndim=2
+ dim(1)=JCrows
+ dim(2)=1
+ plhs(3) = mxCreateNumericArray(ndim, dim,
+ + classid,
+ + complexflag)
+
+ JC = mxGetPr(plhs(3))
+
+C Call the computational routine.
+ call compute(%VAL(l),%VAL(m1),
+ + %VAL(IB1),%VAL(JB1),%VAL(NB1),
+ + %VAL(IB2),%VAL(JB2),%VAL(NB2),
+ + %VAL(maxload),
+ + %VAL(NC),%VAL(IC),%VAL(JC),
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows,JCrows,
+ + s)
+
+ return
+ end
+
+C Computational subroutine
+ subroutine compute(l,m1,
+ + IB1,JB1,NB1,IB2,JB2,NB2,
+ + maxload,
+ + NC,IC,JC,
+ + IB1rows,JB1rows,IB2rows,JB2rows,
+ + ICrows,JCrows,
+ + s)
+
+C Declarations
+ implicit none
+
+ mwSize l,m1,s
+ mwSize IB1rows,JB1rows,IB2rows,JB2rows
+ mwSize ICrows
+ mwSize JCrows
+
+ mwSize maxload,n_vecload,loadi,load_
+ logical doind
+ real*8, target :: NB1(s,JB1rows)
+ real*8, target :: NB2(s,JB2rows)
+
+ real*8, pointer :: pNB1(:,:)
+ real*8, pointer :: pNB2(:,:)
+
+ real*8 NC(s,JCrows)
+
+ mwSize, allocatable :: vecload(:)
+
+ real*8, allocatable :: x(:,:)
+ mwSize, allocatable :: w(:)
+
+ mwSize, target :: IB1(IB1rows)
+ mwSize, target :: JB1(JB1rows,1)
+ mwSize, target :: IB2(IB2rows)
+ mwSize, target :: JB2(JB2rows,1)
+
+ mwSize, target :: IC(ICrows)
+ mwSize, target :: JC(JCrows,1)
+
+ mwSize i,jp,j,kp,k1,k2,vp,v1,v2
+ mwSize is,js,nz
+
+ mwSize jpstart, jpend
+ mwSize kpstart, kpend
+ mwSize vpstart, vpend
+
+ integer AllocateStatus
+
+C vecload
+ n_vecload=(s-1)/maxload+2
+
+ allocate (vecload(n_vecload),STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:compress:OutofMemory',
+ + 'Out of memory1.')
+ endif
+
+ vecload(1)=1
+ vecload(n_vecload)=s+1
+ do i=2,n_vecload-1
+ vecload(i)=vecload(i-1)+maxload
+ end do
+
+C allocate
+ allocate (w(m1),
+ + x(min(s,maxload),m1),
+ + STAT = AllocateStatus)
+ IF (AllocateStatus .ne. 0) then
+ call mexErrMsgIdAndTxt ('MATLAB:OutOfMemory',
+ + 'Out of memory.')
+ endif
+
+ w=0
+ nz=1
+
+C run first time and calculate indices
+ loadi=1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+ IC(i)=nz
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j=JB1(jp,1)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j)=pNB1(is,jp)
+ end do
+ JC(nz,1)=j
+ w(j)=i
+ nz=nz+1
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j=JB2(jp,1)
+ if (w(j)2) then
+ w=0
+ endif
+
+ do loadi=2,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j=JB1(jp,1)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j)=pNB1(is,jp)
+ end do
+ w(j)=i
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j=JB2(jp,1)
+ if (w(j)1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+ IC(i)=nz
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2)=pNB1(is,jp)
+ end do
+ JC(nz,1)=j1
+ JC(nz,2)=j2
+ w(j1,j2)=i
+ nz=nz+1
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ if (w(j1,j2)2) then
+ w=0
+ endif
+
+ do loadi=2,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2)=pNB1(is,jp)
+ end do
+ w(j1,j2)=i
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ if (w(j1,j2)1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+ IC(i)=nz
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ j3=JB1(jp,3)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2,j3)=pNB1(is,jp)
+ end do
+ JC(nz,1)=j1
+ JC(nz,2)=j2
+ JC(nz,3)=j3
+ w(j1,j2,j3)=i
+ nz=nz+1
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ j3=JB2(jp,3)
+ if (w(j1,j2,j3)2) then
+ w=0
+ endif
+
+ do loadi=2,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ j3=JB1(jp,3)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2,j3)=pNB1(is,jp)
+ end do
+ w(j1,j2,j3)=i
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ j3=JB2(jp,3)
+ if (w(j1,j2,j3)1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+ IC(i)=nz
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ j3=JB1(jp,3)
+ j4=JB1(jp,4)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2,j3,j4)=pNB1(is,jp)
+ end do
+ JC(nz,1)=j1
+ JC(nz,2)=j2
+ JC(nz,3)=j3
+ JC(nz,4)=j4
+ w(j1,j2,j3,j4)=i
+ nz=nz+1
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ j3=JB2(jp,3)
+ j4=JB2(jp,4)
+ if (w(j1,j2,j3,j4)2) then
+ w=0
+ endif
+
+ do loadi=2,n_vecload-1
+ load_=vecload(loadi+1)-vecload(loadi)
+
+ if (s>1) then
+ pNB1=>NB1(vecload(loadi):vecload(loadi+1)-1,:)
+ pNB2=>NB2(vecload(loadi):vecload(loadi+1)-1,:)
+ else
+ pNB1=>NB1
+ pNB2=>NB2
+ endif
+
+ do i=1,l
+C run over rows of B1
+ do jp=IB1(i),IB1(i+1)-1
+ j1=JB1(jp,1)
+ j2=JB1(jp,2)
+ j3=JB1(jp,3)
+ j4=JB1(jp,4)
+ !DEC$ simd
+ do is=1,load_
+ x(is,j1,j2,j3,j4)=pNB1(is,jp)
+ end do
+ w(j1,j2,j3,j4)=i
+ end do
+C run over rows of B2
+ do jp=IB2(i),IB2(i+1)-1
+ j1=JB2(jp,1)
+ j2=JB2(jp,2)
+ j3=JB2(jp,3)
+ j4=JB2(jp,4)
+ if (w(j1,j2,j3,j4)6
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B.tsize(1)
+ error('incompatible dimensions')
+end
+dosum=0;
+if nargin==6
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['sixth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==2
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==3
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=4
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==4
+ maxload=intarray(1);
+elseif nargin>=4
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+m=A.tsize(2);
+if length(A.tsize)~=3
+ error('columns must be 2D')
+end
+if A.tsize(3)~=m
+ error('columns are not symmetric')
+end
+n=B.tsize(2);
+if B.colsorted~=1
+ error('not sorted')
+end
+IA=A.ptr;
+JA=A.cols;
+IB=B.ptr;
+JB=B.cols;
+if type==0 % calculate A*kron(B,B)U without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU2vecI_mex( l,m,n,IA,JA,NA,IB,...
+ JB,NB,IC_1,IC_2,JCrows_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+1,2)];
+elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB);
+elseif type==2 % compute IC and JC
+ [IC_1,IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ [ varout1.JC_1,varout1.JC_2 ] = AkronBU2JC_mex( l,m,n,IA,JA,IB,JB,JCrows_1,JCrows_2,IC_2 );
+ % note: JC_1 has 3 columns. First column stores the location in the
+ % compressed matrix. Other columns store the location in a 2-D
+ % tensor.
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+elseif type==3 % compute A*kron(B,B)U with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU2vecI_mex( l,m,n,IA,JA,NA,IB,...
+ JB,NB,IC_1,IC_2,JCrows_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+1,2)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+elseif type==4 % compute A*kron(B,B)U with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2] = AkronBU2IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ [ JC_1,JC_2 ] = AkronBU2JC_mex( l,m,n,IA,JA,IB,JB,JCrows_1,JCrows_2,IC_2 );
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ end
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ varout1.vals = AkronBU2vec_mex( l,m,n,IA,JA,NA,IB,...
+ JB,NB,IC_1,JC_1,IC_2,JC_2,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1(:,1); % note that JC_1 stores 2 columns. First column is the compressed format, and other columns are the corresponding 2-D indices
+ varout1.tsize=[l,nchoosek(n+1,2)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+end
+
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ varout1.ptr2d=A.ptr2d;
+end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU3.m b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU3.m
new file mode 100644
index 0000000000000000000000000000000000000000..fb37f802f21be280b241ada31143f9b8a952d0b5
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU3.m
@@ -0,0 +1,191 @@
+function [varout1,varout2]=AkronBU3(A,B,varargin)
+%C=AkronBU3(A,B) calculates C=A*kron(B,B,B)*U3.
+%[C,ind]=AkronBU3(A,B,ind,1,maxload) calculates C using one precomputed
+%index ind. If ind=[] the function returns ind. The option maxload controls
+%the maximum number of flops performed in parallel by the simd. This is
+%relevant only if A or B represent sets of s tensors.
+%[C,ind]=AkronBU3(A,B,ind,2,maxload) calculates C using two precomputed
+%indices ind.
+%[C,ind]=AkronBU3(A,B,ind,1,maxload,'sum') sums across s if A
+%or B represent sets of s tensors. This option is useful for calculating
+%expected value of C.
+%[C,ind]=AkronBU3(A,B,ind,2,maxload,'sum') is similar but uses two
+%precomputed indices.
+%ind=AkronBU3(A,B,1) returns a structure ind with one field
+%to speed up calculation.
+%ind=AkronBU3(A,B,2) returns a structure ind with two fields. Speedup
+%is larger compared to one field, but requires more memory.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if nargin<2 || nargin>6
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B.tsize(1)
+ error('incompatible dimensions')
+end
+dosum=0;
+if nargin==6
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['eighth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==2
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==3
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=4
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==4
+ maxload=intarray(1);
+elseif nargin>=4
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+m=A.tsize(2);
+if length(A.tsize)~=4
+ error('columns must be 3D')
+end
+if A.tsize(3)~=m || A.tsize(4)~=m
+ error('columns are not symmetric')
+end
+n=B.tsize(2);
+if B.colsorted~=1
+ error('not sorted')
+end
+IA=A.ptr;
+JA=A.cols;
+IB=B.ptr;
+JB=B.cols;
+if type==0 % calculate A*kron(B,B,B)*U3 without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2,IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU3vecI_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,IC_2,IC_3,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+2,3)];
+elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2,varout1.IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB);
+elseif type==2 % compute IC and JC
+ [IC_1,IC_2,IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ [ varout1.JC_1,varout1.JC_2,varout1.JC_3 ] = AkronBU3JC_mex( l,m,n,IA,JA,IB,JB,...
+ JCrows_1,JCrows_2,JCrows_3,IC_2,IC_3 );
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+ varout1.IC_3=IC_3;
+elseif type==3 % compute A*kron(B,B,B)*U with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU3vecI_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,IC_2,IC_3,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+2,3)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+elseif type==4 % compute A*kron(B,B,B)*U with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3] = AkronBU3IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ [JC_1,JC_2,JC_3 ] = AkronBU3JC_mex( l,m,n,IA,JA,IB,JB,...
+ JCrows_1,JCrows_2,JCrows_3,IC_2,IC_3 );
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ JC_3=ind.JC_3;
+ end
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ varout1.vals = AkronBU3vec_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1(:,1); % recall that JC_1 contains the compressed index in the first column and the corresponding indices in the other columns.
+ varout1.tsize=[l,nchoosek(n+2,3)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+ varout2.JC_3=JC_3;
+end
+
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ varout1.ptr2d=A.ptr2d;
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4.m b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4.m
new file mode 100644
index 0000000000000000000000000000000000000000..b5f78bd82f2228f0cb597420f5dbbbe154b52d14
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4.m
@@ -0,0 +1,192 @@
+function [varout1,varout2]=AkronBU4(A,B,varargin)
+ %C=AkronBU4(A,B) calculates C=A*kron(B,B,B,B)*U.
+ %[C,ind]=AkronBU4(A,B,ind,1,maxload) calculates C using one precomputed
+ %index ind. If ind=[] the function returns ind. The option maxload controls
+ %the maximum number of flops performed in parallel by the simd. This is
+ %relevant only if A or B represent sets of s tensors.
+ %[C,ind]=AkronBU4(A,B,ind,2,maxload) calculates C using two precomputed
+ %indices ind.
+ %[C,ind]=AkronBU4(A,B,ind,1,maxload,'sum') sums across s if A
+ %or B represent sets of s tensors. This option is useful for calculating
+ %expected value of C.
+ %[C,ind]=AkronBU4(A,B,ind,2,maxload,'sum') is similar but uses two
+ %precomputed indices.
+ %ind=AkronBU4(A,B,1) returns a structure ind with one field
+ %to speed up calculation.
+ %ind=AkronBU4(A,B,2) returns a structure ind with two fields. Speedup
+ %is larger compared to one field, but requires more memory.
+
+ if nargin<2 || nargin>6
+ error('wrong number of input arguments')
+ end
+
+ if A.tsize(2)~=B.tsize(1)
+ error('incompatible dimensions')
+ end
+ dosum=0;
+ if nargin==6
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['sixth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+ end
+ if nargin==2
+ type=0; % index is not available
+ maxload=intarray(1);
+ end
+ if nargin==3
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ end
+ calculate_ind=0;
+ if nargin>=4
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+ end
+ if nargin==4
+ maxload=intarray(1);
+ elseif nargin>=4
+ maxload=intarray(varargin{3});
+ end
+
+ l=A.tsize(1);
+ m=A.tsize(2);
+ if length(A.tsize)~=5
+ error('columns must be 4D')
+ end
+ if A.tsize(3)~=m || A.tsize(4)~=m || A.tsize(5)~=m
+ error('columns are not symmetric')
+ end
+ n=B.tsize(2);
+ if B.colsorted~=1
+ error('not sorted')
+ end
+ IA=A.ptr;
+ JA=A.cols;
+ IB=B.ptr;
+ JB=B.cols;
+ IB=B.ptr;
+ if type==0 % calculate A*kron(B,B,B,B)*U without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU4vecI_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+3,4)];
+ elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2,varout1.IC_3,varout1.IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB);
+ elseif type==2 % compute IC and JC
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ JCrows_4=IC_4(end)-1;
+ [ varout1.JC_1,varout1.JC_2,varout1.JC_3,varout1.JC_4 ] = AkronBU4JC_mex( l,m,n,IA,JA,IB,JB,JCrows_1,JCrows_2,JCrows_3,JCrows_4,IC_2,IC_3,IC_4);
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+ varout1.IC_3=IC_3;
+ varout1.IC_4=IC_4;
+ elseif type==3 % compute A*kron(B,B,B,B)*U with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU4vecI_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+3,4)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+ elseif type==4 % compute A*kron(B4,B3,B2,B1) with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4IC_mex(l,m,n,IA,JA,IB,JB);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ JCrows_4=IC_4(end)-1;
+ [ JC_1,JC_2,JC_3,JC_4 ] = AkronBU4JC_mex( l,m,n,IA,JA,IB,JB,JCrows_1,JCrows_2,JCrows_3,JCrows_4,IC_2,IC_3,IC_4);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ JC_3=ind.JC_3;
+ JC_4=ind.JC_4;
+ end
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ varout1.vals = AkronBU4vec_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1(:,1);
+ varout1.tsize=[l,nchoosek(n+3,4)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+ varout2.JC_3=JC_3;
+ varout2.JC_4=JC_4;
+ end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4i.m b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4i.m
new file mode 100644
index 0000000000000000000000000000000000000000..bda7493c72581eb41957e94ae705f5595b6eec00
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/AkronBU4i.m
@@ -0,0 +1,139 @@
+function [varout1,varout2]=AkronBU4i(A,B,ind,n_ind,maxload,dosum,convertind,maxind)
+%calculate C=A*kron(B,B,B,B)*U, row by row. Like AkronBU4 but more memory
+%efficient.
+%[C,ind]=AkronBU4i(A,B,ind,n_ind,maxload,dosum,convertind,maxind).
+%convertind is a l-by-m matrix. Each row records the variables that have a
+%nonzero effect on A. maxind is the maximum number of such variables across
+%rows.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on January 20, 2017 (argin check for convertind was added)
+if A.tsize(2)~=B.tsize(1)
+ error('incompatible dimensions')
+end
+if size(convertind,1)~=A.tsize(1) || size(convertind,2)~=B.tsize(1)
+ error('wrong conversion index')
+end
+if strcmp(dosum,'sum')
+ dosum=1;
+elseif strcmp(dosum,'vec')
+ dosum=0;
+else
+ error(['sixth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+end
+
+maxload=intarray(min(1,maxload));
+maxind=intarray(maxind);
+convertind=intarray(convertind);
+
+if n_ind==1
+ type=3;
+elseif n_ind==2
+ type=4;
+else
+ error('number of precomputed indices should be 1 or 2')
+end
+
+calculate_ind=0;
+
+if isempty(ind)
+ calculate_ind=1;
+else
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if n_ind==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+end
+
+l=A.tsize(1);
+m=A.tsize(2);
+if length(A.tsize)~=5
+ error('columns must be 4D')
+end
+if A.tsize(3)~=m || A.tsize(4)~=m || A.tsize(5)~=m
+ error('columns are not symmetric')
+end
+n=B.tsize(2);
+if B.colsorted~=1
+ error('not sorted')
+end
+IA=A.ptr;
+JA=A.cols;
+IB=B.ptr;
+JB=B.cols;
+
+if type==3 % compute A*kron(B,B,B,B)*U with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4iIC_mex(l,m,n,IA,JA,IB,JB,convertind,maxind);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = AkronBU4ivecI_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+ maxload,dosum,convertind,maxind);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,nchoosek(n+3,4)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+elseif type==4 % compute A*kron(B4,B3,B2,B1) with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = AkronBU4iIC_mex(l,m,n,IA,JA,IB,JB,convertind,maxind);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ JCrows_4=IC_4(end)-1;
+ [ JC_1,JC_2,JC_3,JC_4 ] = AkronBU4iJC_mex( l,m,n,IA,JA,IB,JB,JCrows_1,JCrows_2,JCrows_3,JCrows_4,IC_2,IC_3,IC_4,convertind,maxind);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ JC_3=ind.JC_3;
+ JC_4=ind.JC_4;
+ end
+ NA=A.vals;
+ NB=B.vals;
+ if ~isreal(NA) || ~isreal(NB)
+ error('complex numbers not supported')
+ end
+ varout1.vals = AkronBU4ivec_mex(l,m,n,IA,JA,NA,...
+ IB,JB,NB,...
+ IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+ maxload,dosum,convertind,maxind);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1(:,1);
+ varout1.tsize=[l,nchoosek(n+3,4)];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+ varout2.JC_3=JC_3;
+ varout2.JC_4=JC_4;
+end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/changecols.m b/105/replication_package/solution_methods/taylor_projection/Tensors/changecols.m
new file mode 100644
index 0000000000000000000000000000000000000000..0dedf3ed6409b6c63b4663c9041374f93a20a285
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/changecols.m
@@ -0,0 +1,10 @@
+function [A]=changecols(A,newcols,coldim,coli)
+%Change the cols of tensor A
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+newcols=intarray(newcols);
+A.cols(:,coli)=newcols(A.cols(:,coli));
+A.tsize(coli+1)=intarray(coldim);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/changerows.m b/105/replication_package/solution_methods/taylor_projection/Tensors/changerows.m
new file mode 100644
index 0000000000000000000000000000000000000000..1c3e6ccd34b3a18d5b8dbad4c0936c35bd411f27
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/changerows.m
@@ -0,0 +1,15 @@
+function [A]=changerows(A,newrows,rowdim)
+%Change the rows of tensor A
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isfield(A,'ptr2d')
+ error('2D pointer not supported')
+end
+rowcount=zeros(rowdim,1);
+rowcount(newrows)=diff(A.ptr);
+A.ptr=intarray(cumsum([1;rowcount]));
+A.tsize(1)=intarray(rowdim);
+
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/col2ptr.m b/105/replication_package/solution_methods/taylor_projection/Tensors/col2ptr.m
new file mode 100644
index 0000000000000000000000000000000000000000..af87d8bf36e74c0247a709898a90fb1e24e67f60
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/col2ptr.m
@@ -0,0 +1,27 @@
+function [ R ] = col2ptr( ten,colptr )
+%A=col2ptr(A,j) converts the pointer of A into a 2D pointer.
+%A sparse tensor of size l,m1,m2,..,mk has a pointer for the row dimension
+%l. This function makes a pointer for l,mj, which is similar to permuting
+%and reshaping the tensor to size l*mj,m1,m2,..,mj-1,mj+1,..,mk.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(ten.ptr,2)>1
+ error('pointer must be 1D')
+end
+l=ten.tsize(1);
+coldim=ten.tsize(2:end);
+colptr=intarray(colptr);
+ptrcoldim=coldim(colptr)+1;
+
+[ newptr,newcols,newvals ] = col2ptr_mex( ten.ptr,ten.cols,ten.vals,l,coldim,colptr,ptrcoldim );
+
+R=sptensor;
+R.ptr=newptr;
+R.cols=newcols;
+R.vals=newvals;
+R.tsize=[l,coldim(colptr),coldim(1:colptr-1),coldim(colptr+1:end)];
+R.ptr2d=R.tsize(1:2);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/colsort.m b/105/replication_package/solution_methods/taylor_projection/Tensors/colsort.m
new file mode 100644
index 0000000000000000000000000000000000000000..2dc93e584ce9db5283e8ffb8c7f1328d30cbb3c0
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/colsort.m
@@ -0,0 +1,37 @@
+function [ A,index ] = colsort( ten,varargin )
+%sorts tensor columns
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(ten.ptr,2)>1
+ error('2D ptr not supported')
+end
+
+if nargin==2
+ index=varargin{1};
+elseif nargin==1
+ index=[];
+end
+
+
+if isempty(index) % sorting index is not available
+ if nargout==2 % regular sort with an index
+ [i,j]=tfind(ten);
+ [sortij,index]=sortrows([i,j]);
+ A=sptensor(sortij(:,1),sortij(:,2:end),ten.vals(:,index),ten.tsize(1),ten.tsize(2:end));
+ elseif nargout==1 % a mex sort without index
+ for coli=length(ten.tsize)-1:-1:1 % sort each col dimension
+ [ ten.cols,ten.vals ] = sortcol_mex( ten.ptr,ten.cols,ten.vals,ten.tsize(1),ten.tsize(2:end),intarray(coli),ten.tsize(coli+1) );
+ end
+ A=ten;
+ end
+else % sorting index is available
+ A=ten;
+ A.vals=ten.vals(:,index);
+ A.cols=ten.cols(index,:);
+end
+
+A.colsorted=1;
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/contraction1.m b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction1.m
new file mode 100644
index 0000000000000000000000000000000000000000..247e11ade0a491ad8621b8e1816ff307e9cf033f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction1.m
@@ -0,0 +1,206 @@
+function [varout1,varout2]=contraction1(A,B1,varargin)
+%C=contraction1(A,B1) calculates C=A*B1.
+%[C,ind]=contraction1(A,B1,ind,1,maxload) calculates C=A*B1 using one precomputed
+%index ind. If ind=[] the function returns ind. The option maxload controls
+%the maximum number of flops performed in parallel by the simd. This is
+%relevant only if A or B1 represent sets of s tensors.
+%[C,ind]=contraction1(A,B1,ind,2,maxload) calculates C=A*B1 using two precomputed
+%indices ind.
+%[C,ind]=contraction1(A,B1,ind,1,maxload,'sum') sums across s if A or B1
+%represent sets of s tensors. This option is useful for calculating
+%expected value of C.
+%[C,ind]=contraction1(A,B1,ind,2,maxload,'sum') is similar but uses two
+%precomputed indices.
+%ind=contraction1(A,B1,1) returns a structure ind with one field
+%to speed up calculation.
+%ind=contraction1(A,B1,2) returns a structure ind with two fields. Speedup
+%is larger compared to one field, but requires more memory.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if nargin<2 || nargin>6
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B1.tsize(1)
+ error('incompatible dimensions')
+end
+if size(A.ptr,2)>1
+ error('use ptr1d to convert A to 1D')
+end
+dosum=0;
+if nargin==6
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['sixth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==2
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==3
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=4
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==4
+ maxload=intarray(1);
+elseif nargin>=5
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+n1=B1.tsize(2);
+IA=A.ptr;
+JA1=A.cols;
+IB1=B1.ptr;
+JB1=B1.cols;
+
+ptr2D=0;
+if size(B1.ptr,2)>1
+ ptr2D=1;
+ n1=B1.tsize(3);
+end
+
+if type==0 % calculate A*B1 without precomputed index
+ varout1=sptensor;
+ [ IC_1 ] = contraction1IC_mex( l,n1,IA,JA1,IB1,JB1 );
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ if ~isreal(NA) || ~isreal(NB1)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC1_1] = contraction1vecI_mex( l,n1,IA,JA1,NA,IB1,JB1,NB1,IC_1,JCrows_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC1_1;
+ varout1.tsize=[l,n1];
+elseif type==1 % compute IC_1
+ if ptr2D==0
+ [ varout1.IC_1 ] = contraction1IC_mex( l,n1,IA,JA1,IB1,JB1 );
+ else
+ [ varout1.IC_1 ] = contraction1IC2D_mex( l,n1,IA,JA1,IB1,JB1 );
+ end
+elseif type==2 % compute IC_1 and JC_1
+ if ptr2D==0
+ [ IC_1 ] = contraction1IC_mex( l,n1,IA,JA1,IB1,JB1 );
+ JCrows_1=IC_1(end)-1;
+ [ JC_1 ] = contraction1JC_mex( l,n1,IA,JA1,IB1,JB1,JCrows_1 );
+ else
+ [ IC_1 ] = contraction1IC2D_mex( l,n1,IA,JA1,IB1,JB1 );
+ JCrows_1=IC_1(end)-1;
+ [ JC_1 ] = contraction1JC2D_mex( l,n1,IA,JA1,IB1,JB1,JCrows_1 );
+ end
+ varout1.IC_1=IC_1;
+ varout1.JC_1=JC_1;
+elseif type==3 % compute A*B1 with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ if ptr2D==0
+ [ IC_1 ] = contraction1IC_mex( l,n1,IA,JA1,IB1,JB1 );
+ else
+ [ IC_1 ] = contraction1IC2D_mex( l,n1,IA,JA1,IB1,JB1 );
+ end
+ else
+ IC_1=ind.IC_1;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ if ~isreal(NA) || ~isreal(NB1)
+ error('complex numbers not supported')
+ end
+ if ptr2D==0
+ [varout1.vals,JC_1] = contraction1vecI_mex( l,n1,IA,JA1,NA,IB1,JB1,NB1,IC_1,JCrows_1,maxload,dosum);
+ varout1.tsize=[l,n1];
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout2.IC_1=IC_1;
+ else
+ [varout1.vals,JC_1] = contraction1vecI2D_mex( l,n1,IA,JA1,NA,IB1,JB1,NB1,IC_1,JCrows_1,maxload,dosum);
+ varout1.tsize=intarray([l,B1.tsize(2),n1]);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.ptr2d=varout1.tsize(1:2);
+ varout2.IC_1=IC_1;
+ end
+elseif type==4 % compute A*B1 with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ if ptr2D==0
+ [ IC_1 ] = contraction1IC_mex( l,n1,IA,JA1,IB1,JB1 );
+ JCrows_1=IC_1(end)-1;
+ [ JC_1 ] = contraction1JC_mex( l,n1,IA,JA1,IB1,JB1,JCrows_1 );
+ else
+ [ IC_1 ] = contraction1IC2D_mex( l,n1,IA,JA1,IB1,JB1 );
+ JCrows_1=IC_1(end)-1;
+ [ JC_1 ] = contraction1JC2D_mex( l,n1,IA,JA1,IB1,JB1,JCrows_1 );
+ end
+ else
+ IC_1=ind.IC_1;
+ JC_1=ind.JC_1;
+ end
+ NA=A.vals;
+ NB1=B1.vals;
+ if ~isreal(NA) || ~isreal(NB1)
+ error('complex numbers not supported')
+ end
+ if ptr2D==0
+ varout1.vals = contraction1vec_mex( l,n1,IA,JA1,NA,IB1,JB1,NB1,IC_1,JC_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1];
+ varout2.IC_1=IC_1;
+ varout2.JC_1=JC_1;
+ else
+ [varout1.vals] = contraction1vec2D_mex( l,n1,IA,JA1,NA,IB1,JB1,NB1,IC_1,JC_1,maxload,dosum);
+ varout1.tsize=intarray([l,B1.tsize(2),n1]);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.ptr2d=varout1.tsize(1:2);
+ varout2.IC_1=IC_1;
+ varout2.JC_1=JC_1;
+ end
+end
+
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ if isfield(varout1,'ptr2d')
+ varout1.ptr2d=[A.ptr2d,varout1.ptr2d(2)];
+ else
+ varout1.ptr2d=[A.ptr2d];
+ end
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/contraction2.m b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction2.m
new file mode 100644
index 0000000000000000000000000000000000000000..23d9df8a6a6dfe27b50e044b3ca5aaeeb23b3a9e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction2.m
@@ -0,0 +1,172 @@
+function [varout1,varout2]=contraction2(A,B2,B1,varargin)
+%C=contraction2(A,B2,B1) calculates C=A*kron(B2,B1).
+%[C,ind]=contraction2(A,B2,B1,ind,1,maxload) calculates C using one precomputed
+%index ind. If ind=[] the function returns ind. The option maxload controls
+%the maximum number of flops performed in parallel by the simd. This is
+%relevant only if A or B1,B2 represent sets of s tensors.
+%[C,ind]=contraction2(A,B2,B1,ind,2,maxload) calculates C using two precomputed
+%indices ind.
+%[C,ind]=contraction2(A,B2,B1,ind,1,maxload,'sum') sums across s if A
+%or B1,B2 represent sets of s tensors. This option is useful for calculating
+%expected value of C.
+%[C,ind]=contraction2(A,B2,B1,ind,2,maxload,'sum') is similar but uses two
+%precomputed indices.
+%ind=contraction2(A,B2,B1,1) returns a structure ind with one field
+%to speed up calculation.
+%ind=contraction2(A,B2,B1,2) returns a structure ind with two fields. Speedup
+%is larger compared to one field, but requires more memory.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+varout2=[];
+if nargin<3 || nargin>7
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B1.tsize(1) || A.tsize(3)~=B2.tsize(1)
+ error('incompatible dimensions')
+end
+dosum=0;
+if nargin==7
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['seventh argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==3
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==4
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=5
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==5
+ maxload=intarray(1);
+elseif nargin>=5
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+m1=A.tsize(2);
+n1=B1.tsize(2);
+n2=B2.tsize(2);
+IA=A.ptr;
+JA=A.cols;
+IB1=B1.ptr;
+JB1=B1.cols;
+IB2=B2.ptr;
+JB2=B2.cols;
+if type==0 % calculate A*kron(B2,B1) without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction2vecI_mex( l,m1,n1,n2,IA,JA,NA,IB1,...
+ JB1,NB1,IB2,JB2,NB2,IC_1,IC_2,JCrows_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2];
+elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2);
+elseif type==2 % compute IC and JC
+ [IC_1,IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ [ varout1.JC_1,varout1.JC_2 ] = contraction2JC_mex( l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2,JCrows_1,JCrows_2,IC_2 );
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+elseif type==3 % compute A*kron(B2,B1) with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction2vecI_mex( l,m1,n1,n2,IA,JA,NA,IB1,...
+ JB1,NB1,IB2,JB2,NB2,IC_1,IC_2,JCrows_1,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+elseif type==4 % compute A*kron(B2,B1) with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2] = contraction2IC_mex(l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ [ JC_1,JC_2 ] = contraction2JC_mex( l,m1,n1,n2,IA,JA,IB1,JB1,IB2,JB2,JCrows_1,JCrows_2,IC_2 );
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ end
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2)
+ error('complex numbers not supported')
+ end
+ varout1.vals = contraction2vec_mex( l,m1,n1,n2,IA,JA,NA,IB1,...
+ JB1,NB1,IB2,JB2,NB2,IC_1,JC_1,IC_2,JC_2,maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+end
+
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ varout1.ptr2d=A.ptr2d;
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/contraction3.m b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction3.m
new file mode 100644
index 0000000000000000000000000000000000000000..ad4373811d37c7682b7b1cfcdb60d7d8655a667c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction3.m
@@ -0,0 +1,195 @@
+function [varout1,varout2]=contraction3(A,B3,B2,B1,varargin)
+%C=contraction3(A,B3,B2,B1) calculates C=A*kron(B3,B2,B1).
+%[C,ind]=contraction3(A,B3,B2,B1,ind,1,maxload) calculates C using one precomputed
+%index ind. If ind=[] the function returns ind. The option maxload controls
+%the maximum number of flops performed in parallel by the simd. This is
+%relevant only if A or B1,B2,B3 represent sets of s tensors.
+%[C,ind]=contraction3(A,B3,B2,B1,ind,2,maxload) calculates C using two precomputed
+%indices ind.
+%[C,ind]=contraction3(A,B3,B2,B1,ind,1,maxload,'sum') sums across s if A
+%or B1,B2 represent sets of s tensors. This option is useful for calculating
+%expected value of C.
+%[C,ind]=contraction3(A,B3,B2,B1,ind,2,maxload,'sum') is similar but uses two
+%precomputed indices.
+%ind=contraction3(A,B3,B2,B1,1) returns a structure ind with one field
+%to speed up calculation.
+%ind=contraction3(A,B3,B2,B1,2) returns a structure ind with two fields. Speedup
+%is larger compared to one field, but requires more memory.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+varout1=[]; varout2=[];
+
+if nargin<4 || nargin>8
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B1.tsize(1) || A.tsize(3)~=B2.tsize(1) || A.tsize(4)~=B3.tsize(1)
+ error('incompatible dimensions')
+end
+dosum=0;
+if nargin==8
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['eighth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==4
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==5
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=6
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==6
+ maxload=intarray(1);
+elseif nargin>=6
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+m1=A.tsize(2);
+m2=A.tsize(3);
+n1=B1.tsize(2);
+n2=B2.tsize(2);
+n3=B3.tsize(2);
+IA=A.ptr;
+JA=A.cols;
+IB1=B1.ptr;
+JB1=B1.cols;
+IB2=B2.ptr;
+JB2=B2.cols;
+IB3=B3.ptr;
+JB3=B3.cols;
+if type==0 % calculate A*kron(B3,B2,B1) without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2,IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction3vecI_mex(l,m1,m2,n1,n2,n3,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,...
+ IC_1,IC_2,IC_3,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3];
+elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2,varout1.IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3);
+elseif type==2 % compute IC and JC
+ [IC_1,IC_2,IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ [ varout1.JC_1,varout1.JC_2,varout1.JC_3 ] = contraction3JC_mex( l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,...
+ JCrows_1,JCrows_2,JCrows_3,IC_2,IC_3 );
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+ varout1.IC_3=IC_3;
+elseif type==3 % compute A*kron(B3,B2,B1) with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction3vecI_mex(l,m1,m2,n1,n2,n3,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,...
+ IC_1,IC_2,IC_3,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+elseif type==4 % compute A*kron(B3,B2,B1) with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3] = contraction3IC_mex(l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ [JC_1,JC_2,JC_3 ] = contraction3JC_mex( l,m1,m2,n1,n2,n3,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,...
+ JCrows_1,JCrows_2,JCrows_3,IC_2,IC_3 );
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ JC_3=ind.JC_3;
+ end
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3)
+ error('complex numbers not supported')
+ end
+ varout1.vals = contraction3vec_mex(l,m1,m2,n1,n2,n3,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,...
+ IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+ varout2.JC_3=JC_3;
+end
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ varout1.ptr2d=A.ptr2d;
+end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/contraction4.m b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction4.m
new file mode 100644
index 0000000000000000000000000000000000000000..20e3e555e33d4de6b86bf25d8639492963b3f521
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/contraction4.m
@@ -0,0 +1,205 @@
+function [varout1,varout2]=contraction4(A,B4,B3,B2,B1,varargin)
+%C=contraction4(A,B4,B3,B2,B1) calculates C=A*kron(B4,B3,B2,B1).
+%[C,ind]=contraction4(A,B4,B3,B2,B1,ind,1,maxload) calculates C using one precomputed
+%index ind. If ind=[] the function returns ind. The option maxload controls
+%the maximum number of flops performed in parallel by the simd. This is
+%relevant only if A or B1,B2,B3,B4 represent sets of s tensors.
+%[C,ind]=contraction4(A,B4,B3,B2,B1,ind,2,maxload) calculates C using two precomputed
+%indices ind.
+%[C,ind]=contraction4(A,B4,B3,B2,B1,ind,1,maxload,'sum') sums across s if A
+%or B1,B2 represent sets of s tensors. This option is useful for calculating
+%expected value of C.
+%[C,ind]=contraction4(A,B4,B3,B2,B1,ind,2,maxload,'sum') is similar but uses two
+%precomputed indices.
+%ind=contraction4(A,B4,B3,B2,B1,1) returns a structure ind with one field
+%to speed up calculation.
+%ind=contraction4(A,B4,B3,B2,B1,2) returns a structure ind with two fields. Speedup
+%is larger compared to one field, but requires more memory.
+
+if nargin<5 || nargin>9
+ error('wrong number of input arguments')
+end
+
+if A.tsize(2)~=B1.tsize(1) || A.tsize(3)~=B2.tsize(1) || A.tsize(4)~=B3.tsize(1)
+ error('incompatible dimensions')
+end
+dosum=0;
+if nargin==9
+ if strcmp(varargin{4},'sum')
+ dosum=1;
+ elseif ~strcmp(varargin{4},'vec')
+ error(['ninth argument must be charater ' '''' 'sum' '''' ' or ' '''' 'vec' ''''])
+ end
+end
+if nargin==5
+ type=0; % index is not available
+ maxload=intarray(1);
+end
+if nargin==6
+ if varargin{1}==1
+ type=1;
+ elseif varargin{1}==2
+ type=2;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+end
+calculate_ind=0;
+if nargin>=7
+ if varargin{2}==1
+ type=3;
+ elseif varargin{2}==2
+ type=4;
+ else
+ error('number of precomputed indices should be 1 or 2')
+ end
+ if isempty(varargin{1})
+ calculate_ind=1;
+ else
+ ind=varargin{1};
+ if ~isa(ind,'struct')
+ error('index variable incorrectly defined')
+ end
+ if ~isfield(ind,'IC_1')
+ error('index variable incorrectly defined')
+ end
+ if varargin{2}==2
+ if ~isfield(ind,'JC_1')
+ error('index variable incorrectly defined')
+ end
+ end
+ end
+end
+if nargin==7
+ maxload=intarray(1);
+elseif nargin>=7
+ maxload=intarray(varargin{3});
+end
+
+l=A.tsize(1);
+m1=A.tsize(2);
+m2=A.tsize(3);
+m3=A.tsize(4);
+n1=B1.tsize(2);
+n2=B2.tsize(2);
+n3=B3.tsize(2);
+n4=B4.tsize(2);
+IA=A.ptr;
+JA=A.cols;
+IB1=B1.ptr;
+JB1=B1.cols;
+IB2=B2.ptr;
+JB2=B2.cols;
+IB3=B3.ptr;
+JB3=B3.cols;
+IB4=B4.ptr;
+JB4=B4.cols;
+if type==0 % calculate A*kron(B4,B3,B2,B1) without precomputed index
+ varout1=sptensor;
+ [IC_1,IC_2,IC_3,IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4);
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ NB4=B4.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3) || ~isreal(NB4)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction4vecI_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,IB4,JB4,NB4,...
+ IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3,n4];
+elseif type==1 % compute IC
+ [varout1.IC_1,varout1.IC_2,varout1.IC_3,varout1.IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4);
+elseif type==2 % compute IC and JC
+ [IC_1,IC_2,IC_3,IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ JCrows_4=IC_4(end)-1;
+ [ varout1.JC_1,varout1.JC_2,varout1.JC_3,varout1.JC_4 ] = contraction4JC_mex( l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4,JCrows_1,JCrows_2,JCrows_3,JCrows_4,IC_2,IC_3,IC_4);
+ varout1.IC_1=IC_1;
+ varout1.IC_2=IC_2;
+ varout1.IC_3=IC_3;
+ varout1.IC_4=IC_4;
+elseif type==3 % compute A*kron(B4,B3,B2,B1) with one precomputed index IC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ end
+ JCrows_1=IC_1(end)-1;
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ NB4=B4.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3) || ~isreal(NB4)
+ error('complex numbers not supported')
+ end
+ [varout1.vals,JC_1] = contraction4vecI_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,IB4,JB4,NB4,...
+ IC_1,IC_2,IC_3,IC_4,JCrows_1,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3,n4];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+elseif type==4 % compute A*kron(B4,B3,B2,B1) with two precomputed indices IC,JC
+ varout1=sptensor;
+ if calculate_ind==1
+ [IC_1,IC_2,IC_3,IC_4] = contraction4IC_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4);
+ JCrows_1=IC_1(end)-1;
+ JCrows_2=IC_2(end)-1;
+ JCrows_3=IC_3(end)-1;
+ JCrows_4=IC_4(end)-1;
+ [ JC_1,JC_2,JC_3,JC_4 ] = contraction4JC_mex( l,m1,m2,m3,n1,n2,n3,n4,IA,JA,IB1,JB1,IB2,JB2,IB3,JB3,IB4,JB4,JCrows_1,JCrows_2,JCrows_3,JCrows_4,IC_2,IC_3,IC_4);
+ else
+ IC_1=ind.IC_1;
+ IC_2=ind.IC_2;
+ IC_3=ind.IC_3;
+ IC_4=ind.IC_4;
+ JC_1=ind.JC_1;
+ JC_2=ind.JC_2;
+ JC_3=ind.JC_3;
+ JC_4=ind.JC_4;
+ end
+ NA=A.vals;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ NB3=B3.vals;
+ NB4=B4.vals;
+ if ~isreal(NA) || ~isreal(NB1) || ~isreal(NB2) || ~isreal(NB3) || ~isreal(NB4)
+ error('complex numbers not supported')
+ end
+ varout1.vals = contraction4vec_mex(l,m1,m2,m3,n1,n2,n3,n4,IA,JA,NA,...
+ IB1,JB1,NB1,IB2,JB2,NB2,IB3,JB3,NB3,IB4,JB4,NB4,...
+ IC_1,JC_1,IC_2,JC_2,IC_3,JC_3,IC_4,JC_4,...
+ maxload,dosum);
+ varout1.ptr=IC_1;
+ varout1.cols=JC_1;
+ varout1.tsize=[l,n1,n2,n3,n4];
+ varout2.IC_1=IC_1;
+ varout2.IC_2=IC_2;
+ varout2.IC_3=IC_3;
+ varout2.IC_4=IC_4;
+ varout2.JC_1=JC_1;
+ varout2.JC_2=JC_2;
+ varout2.JC_3=JC_3;
+ varout2.JC_4=JC_4;
+end
+if isfield(A,'ptr2d') % if the pointer of A is 2D varout is also 2D
+ varout1.ptr2d=A.ptr2d;
+end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/extract.m b/105/replication_package/solution_methods/taylor_projection/Tensors/extract.m
new file mode 100644
index 0000000000000000000000000000000000000000..ddde7542f97e6725aac624816458641e1c2571b7
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/extract.m
@@ -0,0 +1,28 @@
+function [ A,ind ] = extract(B,extractrows,extractcols,compress,ind)
+%The function extract rows and columns from a tensor with symmetric column
+%and returns a new sparse tensor. If compress=1 the output is in compressed
+%form.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ [A,tempind1]=takerows(B,extractrows);
+ [A,tempind2]=takecols(A,extractcols);
+ if compress==1
+ [A,tempind3]=takeunique(A);
+ tempind2=tempind2(tempind3);
+ end
+ tempind=tempind1(tempind2);
+ ind.ptr=A.ptr;
+ ind.cols=A.cols;
+ ind.tsize=A.tsize;
+ ind.ind=tempind;
+else
+ A.vals=B.vals(:,ind.ind);
+ A.ptr=ind.ptr;
+ A.cols=ind.cols;
+ A.tsize=ind.tsize;
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/fold.m b/105/replication_package/solution_methods/taylor_projection/Tensors/fold.m
new file mode 100644
index 0000000000000000000000000000000000000000..2072f5ac852e2ff6bb255ae7d4ebbaec88f24093
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/fold.m
@@ -0,0 +1,48 @@
+function [R]=fold(A,varargin)
+% reshape a sparse matrix of dimensions m,n1*...*n4 to a tensor of
+% dimensions m,n1,...,n4
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if length(A.tsize)>2
+ A=unfold(A);
+end
+R=A;
+if nargin==3
+ n1=varargin{1};
+ n2=varargin{2};
+ [cols1,cols2]=ind2sub([n1,n2],A.cols);
+ R.cols=[cols1,cols2];
+ R.tsize=[A.tsize(1),n1,n2];
+elseif nargin==4
+ n1=varargin{1};
+ n2=varargin{2};
+ n3=varargin{3};
+ [cols1,cols2,cols3]=ind2sub([n1,n2,n3],A.cols);
+ R.cols=[cols1,cols2,cols3];
+ R.tsize=[A.tsize(1),n1,n2,n3];
+elseif nargin==5
+ n1=varargin{1};
+ n2=varargin{2};
+ n3=varargin{3};
+ n4=varargin{4};
+ [cols1,cols2,cols3,cols4]=ind2sub([n1,n2,n3,n4],A.cols);
+ R.cols=[cols1,cols2,cols3,cols4];
+ R.tsize=[A.tsize(1),n1,n2,n3,n4];
+elseif nargin==6
+ n1=varargin{1};
+ n2=varargin{2};
+ n3=varargin{3};
+ n4=varargin{4};
+ n5=varargin{5};
+ [cols1,cols2,cols3,cols4,cols5]=ind2sub([n1,n2,n3,n4,n5],A.cols);
+ R.cols=[cols1,cols2,cols3,cols4,cols5];
+ R.tsize=[A.tsize(1),n1,n2,n3,n4,n5];
+elseif nargin>6
+ error('tensor of rank higher than 6 not supported')
+end
+
+R.cols=intarray(R.cols);
+R.tsize=intarray(R.tsize);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/foldj.m b/105/replication_package/solution_methods/taylor_projection/Tensors/foldj.m
new file mode 100644
index 0000000000000000000000000000000000000000..41a959a5b917ca75f9d4b690c087f0de8f92622f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/foldj.m
@@ -0,0 +1,38 @@
+function [R]=foldj(A,j,dim)
+% [R]=foldj(A,j,dim) reshapes the j'th col dimension of a sparse tensor A
+% do new dimension dim.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+R=A;
+ndim=length(dim);
+dim=intarray(dim);
+if ndim==2
+ n1=dim(1);
+ n2=dim(2);
+ [cols1,cols2]=ind2sub([n1,n2],A.cols(:,j));
+ R.cols=[A.cols(:,1:j-1),cols1,cols2,A.cols(:,j+1:end)];
+ R.tsize=[A.tsize(1:j),n1,n2,A.tsize(j+2:end)];
+elseif ndim==3
+ n1=dim(1);
+ n2=dim(2);
+ n3=dim(3);
+ [cols1,cols2,cols3]=ind2sub([n1,n2,n3],A.cols(:,j));
+ R.cols=[A.cols(:,1:j-1),cols1,cols2,cols3,A.cols(:,j+1:end)];
+ R.tsize=[A.tsize(1:j),n1,n2,n3,A.tsize(j+2:end)];
+elseif ndim==4
+ n1=dim(1);
+ n2=dim(2);
+ n3=dim(3);
+ n4=dim(4);
+ [cols1,cols2,cols3,cols4]=ind2sub([n1,n2,n3,n4],A.cols(:,j));
+ R.cols=[A.cols(:,1:j-1),cols1,cols2,cols3,cols4,A.cols(:,j+1:end)];
+ R.tsize=[A.tsize(1:j),n1,n2,n3,n4,A.tsize(j+2:end)];
+elseif ndim>4
+ error('tensor of rank higher than 5 not supported')
+end
+
+R.cols=intarray(R.cols);
+R.tsize=intarray(R.tsize);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/intarray.m b/105/replication_package/solution_methods/taylor_projection/Tensors/intarray.m
new file mode 100644
index 0000000000000000000000000000000000000000..7b61c224edb43bcac9532cdfdd5e488d1318ccb6
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/intarray.m
@@ -0,0 +1,15 @@
+function [ y ] = intarray( x )
+%Convert to int32 or int64, depending on the operating system.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+archstr = computer('arch');
+if strcmp(archstr(end-1:end),'32')
+ y=int32(x);
+elseif strcmp(archstr(end-1:end),'64')
+ y=int64(x);
+else
+ error('cannot find if MATLAB runs on 32-bit or 64-bit operating system.')
+end
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/multscalar.m b/105/replication_package/solution_methods/taylor_projection/Tensors/multscalar.m
new file mode 100644
index 0000000000000000000000000000000000000000..b38a6160e8778dab6387fad40cbb784b5d5a3e06
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/multscalar.m
@@ -0,0 +1,9 @@
+function ten=multscalar(ten,n)
+% multiply sparse tensor ten by scalar n
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+ten.vals=ten.vals*n;
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/permutecols.m b/105/replication_package/solution_methods/taylor_projection/Tensors/permutecols.m
new file mode 100644
index 0000000000000000000000000000000000000000..779aff47fc3156b89cc0838894a0562861efb065
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/permutecols.m
@@ -0,0 +1,10 @@
+function ten=permutecols(ten,ind)
+% permute columns of a sparse sptensor
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+ind=ind(:)';
+ten.cols=ten.cols(:,ind);
+ten.tsize=ten.tsize([1,1+ind]);
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/permuterows.m b/105/replication_package/solution_methods/taylor_projection/Tensors/permuterows.m
new file mode 100644
index 0000000000000000000000000000000000000000..6df4e8d59e295821eae8e901a71e17fef575cf45
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/permuterows.m
@@ -0,0 +1,14 @@
+function [A]=permuterows(A,newrows)
+%Permute the rows of tensor A by newrows.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isfield(A,'ptr2d')
+ error('2D pointer not supported')
+end
+
+newrows=intarray(newrows);
+
+[A.ptr,A.cols,A.vals] = perm_rows(A.ptr,A.cols,A.vals,A.tsize(1),newrows);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/ptr1d.m b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr1d.m
new file mode 100644
index 0000000000000000000000000000000000000000..7fa4f9c59641ff5154bf19667adbfed9ceee04fc
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr1d.m
@@ -0,0 +1,14 @@
+function [ A ] = ptr1d( A )
+%convert the 2-D pointer to 1-D
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(A.ptr,2)>1
+ tempptr=A.ptr(:,1:end-1);
+ tempptr=tempptr';
+ A.ptr=[tempptr(:);A.ptr(end)];
+ A.tsize=[prod(A.tsize(1:2)),A.tsize(3:end)];
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2col.m b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2col.m
new file mode 100644
index 0000000000000000000000000000000000000000..8dcded14c0a3fa74d44db54803baffe80b7157f1
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2col.m
@@ -0,0 +1,21 @@
+function [ R ] = ptr2col( ten,coli )
+%A=ptr2col(A,j) converts a 2D pointer to 1D pointer.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if coli>length(ten.tsize)
+ error('column dimension too large')
+end
+
+l1=ten.ptr2d(1);
+l2=ten.ptr2d(2);
+[ newcol ] = ptr2col_mex( ten.ptr,ten.ptr(end)-1 );
+R=sptensor;
+R.vals=ten.vals;
+R.ptr=[ten.ptr(:,1);ten.ptr(end)];
+R.cols=[ten.cols(:,1:coli-1),newcol,ten.cols(:,coli:end)];
+R.tsize=[l1,ten.tsize(3:coli+1),l2,ten.tsize(coli+2:end)];
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2d.m b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2d.m
new file mode 100644
index 0000000000000000000000000000000000000000..0bcd1579b992b38d7ecc7754e0be57f0faa3ec5c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/ptr2d.m
@@ -0,0 +1,38 @@
+function [ A ] = ptr2d( A,l1,l2 )
+%Convert the pointer to 2-D. If the original pointer was obtained from a
+%2-D pointer then rows are assumed to be indexed l2,l1. Otherwis, rows
+%are assumed to be indexed l1,l2.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(A.ptr,2)==1
+ if isfield(A,'ptr2d')
+ if A.ptr2d(1)~=l1 || A.ptr2d(2)~=l2
+ error('dimensions of 2D pointer are wrong')
+ else
+ A=ptr2d_sub(A,l1,l2);
+ end
+ else % convert to 1,l1,l2 and move l1 to pointer
+ A=ptr2d_sub(A,1,l1*l2);
+ A.ptr2d=intarray([1,l1*l2]); % the size of the 2D pointer
+ A=ptr2col(A,1);
+ A=foldj(A,1,[l1,l2]);
+ A=col2ptr(A,1);
+ A=ptr1d(A);
+ A=rmfield(A,'ptr2d');
+ A=col2ptr(A,1);
+
+ end
+end
+
+end
+
+function A=ptr2d_sub(A,l1,l2)
+
+tempptr=zeros(l1,l2+1);
+tempptr(:,1:l2)=reshape(A.ptr(1:end-1),l2,l1)';
+tempptr(:,end)=[tempptr(2:end,1);A.ptr(end)];
+A.ptr=intarray(tempptr);
+A.tsize=intarray([l1,l2,A.tsize(2:end)]);
+
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/spmat2sptensor.m b/105/replication_package/solution_methods/taylor_projection/Tensors/spmat2sptensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..6bfc196877a755e7ced72a1ec96fab8ce9308d93
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/spmat2sptensor.m
@@ -0,0 +1,12 @@
+function [ A ] = spmat2sptensor( spmat )
+%convert sparse matrix to sparse tensor
+%can be improved by mexing (its basically a transpose)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% bug fixed on January 20, 2017 (a row vector produced an error)
+[i,j,vals]=find(spmat);
+[l,m]=size(spmat);
+A=sptensor(i(:),j(:),vals(:)',l,m);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor.m b/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..5df45ec69540da295d773ee220af1a733a4dbe71
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor.m
@@ -0,0 +1,157 @@
+function obj=sptensor(varargin)
+% sptensor constructs a sparse tensor.
+% T=sptensor(row,cols,vals,rowdim,colsdim) constructs a sparse tensor T.
+% The first index of nnz values is stored in vector row. The other indices
+% are stored in matrix cols, where size(cols,1)=length(row) and
+% size(cols,2) is the number of the other indices. Total number of indices
+% (tensor rank) is size(cols,2)+1. The nnz values are stored in vals, where
+% size(vals,2)=size(cols,1)=length(row). It is possible to store a set of s
+% tensors with the same sparse structure but different nnz values, by
+% storing the nnz values of these tensors as different rows in vals.
+% Namely, size(vals,1)=s.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if nargin==0 % empty tensor
+ obj.vals=[];
+ obj.ptr=[];
+ obj.cols=[];
+ obj.tsize=[];
+elseif nargin==1 % convert a matrix to a sparse tensor. if matrix is sparse better use spmat2sptensor
+ T=full(varargin{1});
+ if length(size(T))==2
+ vals=T';
+ obj.vals=vals(:)';
+ [m,n]=size(T);
+ obj.ptr=(1:n:m*n+1)';
+ obj.cols=repmat((1:n)',m,1);
+ obj.tsize=[m,n];
+ % convert integers to int32 or int64, depending on the
+ archstr = computer('arch');
+ if strcmp(archstr(end-1:end),'32')
+ sys=32;
+ elseif strcmp(archstr(end-1:end),'64')
+ sys=64;
+ else
+ error('cannot determine if MATLAB runs on 32-bit or 64-bit platform.')
+ end
+ if sys==32
+ obj.ptr=int32(obj.ptr);
+ obj.cols=int32(obj.cols);
+ obj.tsize=int32(obj.tsize);
+ elseif sys==64
+ obj.ptr=int64(obj.ptr);
+ obj.cols=int64(obj.cols);
+ obj.tsize=int64(obj.tsize);
+ end
+ else
+ error('full tensor not supported')
+ end
+elseif nargin==2 || nargin==3 % create a sparse tensor of zeros
+ rowdim=varargin{1};
+ colsdim=varargin{2};
+ if nargin==3
+ n_s=varargin{3};
+ else
+ n_s=1;
+ end
+
+ obj.vals=zeros(n_s,0);
+ obj.cols=zeros(0,length(colsdim));
+ obj.ptr=ones(rowdim+1,1);
+ obj.tsize=[rowdim,colsdim(:)'];
+
+ % convert integers to int32 or int64, depending on the
+ archstr = computer('arch');
+ if strcmp(archstr(end-1:end),'32')
+ sys=32;
+ elseif strcmp(archstr(end-1:end),'64')
+ sys=64;
+ else
+ error('cannot determine if MATLAB runs on 32-bit or 64-bit platform.')
+ end
+ if sys==32
+ obj.ptr=int32(obj.ptr);
+ obj.cols=int32(obj.cols);
+ obj.tsize=int32(obj.tsize);
+ elseif sys==64
+ obj.ptr=int64(obj.ptr);
+ obj.cols=int64(obj.cols);
+ obj.tsize=int64(obj.tsize);
+ end
+elseif nargin==5
+ row=varargin{1};
+ cols=varargin{2};
+ vals=varargin{3};
+ rowdim=varargin{4};
+ colsdim=varargin{5};
+ if size(row,1)~=1 && size(row,2)~=1
+ error('first argument must be a vector')
+ end
+ n_vals=size(vals,2);
+ if n_vals~=length(row)
+ error('length of row index must equal the number of nnz values')
+ end
+ if size(cols,1)~=n_vals
+ error('length of col indices must equal the number of nnz values')
+ end
+ if ~isa(vals,'double')
+ error('nnz values should be of class double')
+ end
+ % check indices for nonzero tensors
+ if n_vals>0
+ % check row index
+ if ~isequal(round(row),row)
+ error('Index into tensor must be an integer.')
+ end
+ if max(row)>rowdim
+ error('Index exceeds tensor dimensions')
+ end
+ if min(row)<1
+ error('Index into tensor must be positive.')
+ end
+ % check cols indices
+ if size(cols,2)~=length(colsdim)
+ error('incompatible column dimensions')
+ end
+ if ~isequal(round(cols),cols)
+ error('Index into tensor must be an integer.')
+ end
+ if max(cols(:))>colsdim
+ error('Index exceeds tensor dimensions')
+ end
+ if min(cols(:))<1
+ error('Index into tensor must be positive.')
+ end
+ end
+ % convert integers to int32 or int64, depending on the
+ archstr = computer('arch');
+ if strcmp(archstr(end-1:end),'32')
+ sys=32;
+ elseif strcmp(archstr(end-1:end),'64')
+ sys=64;
+ else
+ error('cannot determine if MATLAB runs on 32-bit or 64-bit platform.')
+ end
+ if sys==32
+ row=int32(row);
+ cols=int32(cols);
+ rowdim=int32(rowdim);
+ n_vals=int32(n_vals);
+ elseif sys==64
+ row=int64(row);
+ cols=int64(cols);
+ rowdim=int64(rowdim);
+ n_vals=int64(n_vals);
+ end
+ % store nnz values in CRS format
+% [ obj.vals,obj.ptr,obj.cols ] = compress( vals,row,cols,rowdim,n_vals );
+ [ obj.vals,obj.ptr,obj.cols ] = compress_mex( vals,row,cols,rowdim,n_vals );
+
+ obj.tsize=[rowdim,colsdim(:)'];
+else
+ error('wrong number of arguments')
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor2spmat.m b/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor2spmat.m
new file mode 100644
index 0000000000000000000000000000000000000000..20f60545bf4cfb0f7c59316ddb8cf084db9d5112
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/sptensor2spmat.m
@@ -0,0 +1,35 @@
+function [ A ] = sptensor2spmat( ten )
+%convert sparse tensor to sparse matrix
+%can be improved by mexing
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% extended to rank=5 on January 20, 2017
+
+if isfield(ten,'ptr2d') % 2D pointer
+ ten=ptr2d(ten,ten.ptr2d(1),ten.ptr2d(2));
+ ten=ptr2col(ten,1);
+end
+
+[i,j,vals]=tfind(ten);
+
+colsdim=ten.tsize(2:end);
+ncolsdim=length(colsdim);
+if ncolsdim==1
+ cols=j;
+elseif ncolsdim==2
+ cols=sub2ind(ten.tsize(2:end),j(:,1),j(:,2));
+elseif ncolsdim==3
+ cols=sub2ind(ten.tsize(2:end),j(:,1),j(:,2),j(:,3));
+elseif ncolsdim==4
+ cols=sub2ind(ten.tsize(2:end),j(:,1),j(:,2),j(:,3),j(:,4));
+elseif ncolsdim==5
+ cols=sub2ind(ten.tsize(2:end),j(:,1),j(:,2),j(:,3),j(:,4),j(:,5));
+else
+ error('tensor rank larger than 6')
+end
+
+ten.tsize=double(ten.tsize);
+A=sparse(double(i),double(cols),vals',ten.tsize(1),prod(ten.tsize(2:end)));
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/spteye.m b/105/replication_package/solution_methods/taylor_projection/Tensors/spteye.m
new file mode 100644
index 0000000000000000000000000000000000000000..6cade20cdb55655dea29f0d6188f4ef1c5726950
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/spteye.m
@@ -0,0 +1,21 @@
+function T=spteye(n,varargin)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if nargin==1
+ n_s=1;
+elseif nargin==2
+ n_s=varargin{1};
+else
+ error('wrong number of arguments')
+end
+% creates eye(T) as sptensor
+n=double(n);
+T.vals=ones(n_s,n);
+n=intarray(n);
+T.cols=(1:n)';
+T.ptr=(1:n+1)';
+T.tsize=[n,n];
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/takecols.m b/105/replication_package/solution_methods/taylor_projection/Tensors/takecols.m
new file mode 100644
index 0000000000000000000000000000000000000000..d706c836677c89b19cc8aed3ad59abf0bcb8d49c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/takecols.m
@@ -0,0 +1,34 @@
+function [ A,ind ] = takecols( ten,cols )
+%extract cols from a tensor class ten with symmetric columns.
+%improve by mex
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% bug corrected on Jan 11, 2018 for the cases of one or zero nonzero values in ten
+
+m=length(cols);
+temp=zeros(ten.tsize(2),1);
+temp(cols)=1:m;
+[i,j,vals]=tfind(ten);
+j=temp(j);
+
+n_vals=numel(i);
+if n_vals==1
+ j=j(:)';
+end
+
+if n_vals>0
+ prodj=prod(j,2);
+else
+ prodj=0;
+end
+
+if nnz(prodj)>0
+ A=sptensor(i(prodj~=0),j(prodj~=0,:),vals(:,prodj~=0),ten.tsize(1),repmat(m,1,length(ten.tsize)-1));
+else
+ A=sptensor(ten.tsize(1),repmat(m,1,length(ten.tsize)-1),size(ten.vals,1));
+end
+
+ind=find(prodj);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/takerows.m b/105/replication_package/solution_methods/taylor_projection/Tensors/takerows.m
new file mode 100644
index 0000000000000000000000000000000000000000..f20a3453b0d023dc00f0967668bef0e3a694dafc
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/takerows.m
@@ -0,0 +1,49 @@
+function [ A,ind ] = takerows( ten,rows )
+%extract rows from tensor ten.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% bug corrected on Jan 1, 2018 for the case of zero nonzero values in A
+% bug corrected on Jan 29, 2018 for the case of an empty tensor
+
+if ten.tsize(1)==0 && ~isempty(rows)
+ error('trying to extract rows from an empty tensor')
+elseif ten.tsize(1)==0 && isempty(rows)
+ if nargout==1
+ A=ten;
+ else
+ A=ten;
+ ind=[];
+ end
+else
+ if nargout==1 %mex version
+ A=sptensor;
+ IA=ten.ptr;
+ JA=ten.cols;
+ NA=ten.vals;
+ l=ten.tsize(1);
+ takel=intarray(rows);
+ [IC,JC,NC] = takerows_mex(IA,JA,NA,l,takel);
+ newl=length(takel);
+ A.ptr=IC(1:newl+1);
+ A.cols=JC(1:A.ptr(end)-1,:);
+ A.vals=NC(:,1:A.ptr(end)-1);
+ A.tsize=ten.tsize;
+ A.tsize(1)=newl;
+ else
+ l=length(rows);
+ temp=zeros(ten.tsize(1),1);
+ temp(rows)=1:l;
+ [i,j,vals]=tfind(ten);
+ i=temp(i);
+
+ if nnz(i)>0
+ A=sptensor(i(i~=0),j(i~=0,:),vals(:,i~=0),l,ten.tsize(2:end));
+ else
+ A=sptensor(l,ten.tsize(2:end),size(ten.vals,1));
+ end
+
+ ind=find(i);
+ end
+end
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/takeunique.m b/105/replication_package/solution_methods/taylor_projection/Tensors/takeunique.m
new file mode 100644
index 0000000000000000000000000000000000000000..03c9dbe3b0e28c7898667f772befaf834bb8fc00
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/takeunique.m
@@ -0,0 +1,21 @@
+function [ Ac,ind ] = takeunique( ten )
+%extract unique columns from a tensor with symmetric columns.
+%improve by mex
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+oldvals=ten.vals;
+ten.vals=ten.vals(1,:);
+[i,j,~]=tfind(ten);
+
+ij=[i,sort(j,2)]; % columns are sorted j1<=j2<=... below i use the function u2c which assumes j1>=j2>=.. so order of columns need to be reversed
+[uniqueij,ind]=unique(ij,'rows');
+
+Au=sptensor(uniqueij(:,1),uniqueij(:,end:-1:2),ind(:)',ten.tsize(1),ten.tsize(2:end)); % columns reversed
+
+Ac=u2c(Au);
+ind=Ac.vals(:);
+Ac.vals=oldvals(:,ind);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tfind.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tfind.m
new file mode 100644
index 0000000000000000000000000000000000000000..213bf2f3a6e86977327f83ad07f7eccaab691176
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tfind.m
@@ -0,0 +1,38 @@
+function [i,j,vals]=tfind(A)
+% similar to the function find for sparse matrices.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(A.vals)
+ i=zeros(0,1);
+ j=zeros(0,length(A.tsize)-1);
+else
+ if size(A.ptr,2)==1
+ x=zeros(size(A.cols,1)+1,1);
+ rows=1:A.tsize(1);
+ x(A.ptr(1:end-1))=rows;
+ x=x(1:end-1);
+ x(x>0)=[x(1);diff(x(x>0))];
+ x=cumsum(x);
+ i=x;
+ j=A.cols;
+ else
+%convert the 2-D pointer to 1-D
+ tempptr=A.ptr(:,1:end-1);
+ tempptr=tempptr';
+ tempptr=[tempptr(:);A.ptr(end)];
+ tempsize=[prod(A.tsize(1:2)),A.tsize(3:end)];
+ x=zeros(size(A.cols,1)+1,1);
+ rows=1:tempsize(1);
+ x(tempptr(1:end-1))=rows;
+ x=x(1:end-1);
+ x(x>0)=[x(1);diff(x(x>0))];
+ x=cumsum(x);
+ i=x;
+ [i2,i1]=ind2sub(A.tsize(2:-1:1),i);
+ i=i1;
+ j=[i2,A.cols];
+ end
+end
+vals=A.vals;
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tkron.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron.m
new file mode 100644
index 0000000000000000000000000000000000000000..8d91338d35b6420620f3bc3e8d69c9ffd75566db
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron.m
@@ -0,0 +1,30 @@
+function [varout1,varout2]=tkron(B2,B1,varargin)
+%C=tkron(B2,B1) calculates C=kron(B2,B1).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+sB1=size(B1.vals,1);
+sB2=size(B2.vals,1);
+
+if sB1==1
+ if sB2>1
+ B1.vals=repmat(B1.vals,sB2,1);
+ end
+elseif sB1>1
+ if sB2==1
+ B2.vals=repmat(B2.vals,sB1,1);
+ elseif sB2>1 && sB1~=sB2
+ error('incompatible states')
+ end
+end
+
+l1=B1.tsize(1);
+l2=B2.tsize(1);
+A=fold(spteye(l1*l2),l1,l2);
+if nargin>2
+ [varout1,varout2]=contraction2(A,B2,B1,varargin{:});
+elseif nargin==2
+ [varout1,varout2]=contraction2(A,B2,B1);
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3.m
new file mode 100644
index 0000000000000000000000000000000000000000..442eb75c81e30f5f223e5f3267c21b08422e0b08
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3.m
@@ -0,0 +1,48 @@
+function [varout1,varout2]=tkron3(B3,B2,B1,varargin)
+%C=tkron(B3,B2,B1) calculates C=kron(B3,B2,B1).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+sB1=size(B1.vals,1);
+sB2=size(B2.vals,1);
+sB3=size(B3.vals,1);
+
+if sB1==1
+ if sB2>1
+ B1.vals=repmat(B1.vals,sB2,1);
+ end
+elseif sB1>1
+ if sB2==1
+ B2.vals=repmat(B2.vals,sB1,1);
+ elseif sB2>1 && sB1~=sB2
+ error('incompatible states')
+ end
+end
+
+sB=max(sB1,sB2);
+
+if sB3==1
+ if sB>1
+ B3.vals=repmat(B3.vals,sB,1);
+ end
+elseif sB3>1
+ if sB==1
+ B2.vals=repmat(B2.vals,sB3,1);
+ B1.vals=repmat(B1.vals,sB3,1);
+ elseif sB>1 && sB3~=sB
+ error('incompatible states')
+ end
+end
+
+l1=B1.tsize(1);
+l2=B2.tsize(1);
+l3=B3.tsize(1);
+
+A=fold(spteye(l1*l2*l3),l1,l2,l3);
+if nargin>3
+ [varout1,varout2]=contraction3(A,B3,B2,B1,varargin{:});
+elseif nargin==3
+ [varout1,varout2]=contraction3(A,B3,B2,B1);
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d1.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d1.m
new file mode 100644
index 0000000000000000000000000000000000000000..a3ac422e42d6a2cb9014b91da656a855fc644f7a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d1.m
@@ -0,0 +1,52 @@
+function R=tkron3_d1(A,B,C,Ax,Bx,Cx)
+% Compute first derivative of kron(A,B,C) w.r.t x
+% A is m1-by-1
+% Ax is m1-by-n_x
+% B is m2-by-1
+% Bx is m2-by-n_x
+% C is m3-by-1
+% Cx is m3-by-n_x
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+m1=A.tsize(1);
+m2=B.tsize(1);
+m3=C.tsize(1);
+
+if m1~=prod(A.tsize)
+ error('A must be a vector')
+end
+if m2~=prod(B.tsize)
+ error('B must be a vector')
+end
+if m3~=prod(C.tsize)
+ error('C must be a vector')
+end
+
+if Ax.tsize(1)~=m1
+ error('Incompatible dimensions')
+end
+if Bx.tsize(1)~=m2
+ error('Incompatible dimensions')
+end
+if Cx.tsize(1)~=m3
+ error('Incompatible dimensions')
+end
+
+if Ax.tsize(2)~=Bx.tsize(2)
+ error('Incompatible dimensions')
+elseif Ax.tsize(2)~=Cx.tsize(2)
+ error('Incompatible dimensions')
+end
+
+term1=tkron3(Ax,B,C); %m3*m2*m1,n_x
+
+term2=tkron3(A,Bx,C); %m3*m2*m1,n_x
+
+term3=trkron3(A,B,Cx); %m3*m2*m1,n_x
+
+R=tplus(term1,term2);
+
+R=tplus(R,term3);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d2.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d2.m
new file mode 100644
index 0000000000000000000000000000000000000000..c3c6c65c77d701f37126f60f2c60e6c7928bd846
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_d2.m
@@ -0,0 +1,76 @@
+function R=tkron3_d2(A,B,C,Ax,Bx,Cx,Axx,Bxx,Cxx)
+% Compute first derivative of kron(A,B,C)
+% A is m1-by-1
+% Ax is m1-by-n_x
+% Axx is m1-by-n_x-by-n_x
+% B is m2-by-1
+% Bx is m2-by-n_x
+% Bxx is m2-by-n_x-by-n_x
+% C is m3-by-1
+% Cx is m3-by-n_x
+% Cxx is m3-by-n_x-by-n_x
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+m1=A.tsize(1);
+m2=B.tsize(1);
+m3=C.tsize(1);
+
+if m1~=prod(A.tsize)
+ error('A must be a vector')
+end
+if m2~=prod(B.tsize)
+ error('B must be a vector')
+end
+if m3~=prod(C.tsize)
+ error('C must be a vector')
+end
+
+if Ax.tsize(1)~=m1
+ error('Incompatible dimensions')
+end
+if Bx.tsize(1)~=m2
+ error('Incompatible dimensions')
+end
+if Cx.tsize(1)~=m3
+ error('Incompatible dimensions')
+end
+
+if Ax.tsize(2)~=Bx.tsize(2)
+ error('Incompatible dimensions')
+elseif Ax.tsize(2)~=Cx.tsize(2)
+ error('Incompatible dimensions')
+end
+
+Axx=ptr1d(col2ptr(Axx,1));
+Bxx=ptr1d(col2ptr(Bxx,1));
+Cxx=ptr1d(col2ptr(Cxx,1));
+
+
+term1=tkron3_d1(tvec(Ax),B,C,Axx,Bx,Cx); %m3*m2*m1*n_x,n_x
+
+term1=ptr2d(term1,m3*m2*m1,n_x);
+term1=ptr2col(term1,1); %m3*m2*m1,n_x,n_x
+
+
+term2=tkron3_d1(A,tvec(Bx),C,Ax,Bxx,Cx); %m3*m2*n_x*m1,n_x
+
+term2=ptr2d(term2,m3*m2,n_x*m1);
+term2=ptr2col(term2,1); %m3*m2,n_x*m1,n_x
+term2=fold(term2,n_x,m1,n_x);%m3*m2,n_x,m1,n_x
+term2=col2ptr(term2,2);
+term2=ptr1d(term2);%m3*m2*m1,n_x,n_x
+
+term3=trkron3_d1(A,B,Cx,Ax,Bx,Cxx); %m3*n_x*m2*m1,n_x
+
+term3=ptr2d(term3,m3,n_x*m2*m1);
+term3=ptr2col(term3,1); %m3,n_x*m2*m1,n_x
+term3=fold(term3,n_x,m2*m1,n_x);%m3,n_x,m2*m1,n_x
+term3=col2ptr(term3,2);
+term3=ptr1d(term3);%m3*m2*m1,n_x,n_x
+
+R=tplus(term1,term2);
+
+R=tplus(R,term3);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_x.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_x.m
new file mode 100644
index 0000000000000000000000000000000000000000..597dbb205753e66971cc9a162628475b7f77e163
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tkron3_x.m
@@ -0,0 +1,52 @@
+function R=tkron3_x(A,B,C,Ax,Bx,Cx)
+% Compute first derivative of kron(A,B,C) w.r.t x
+% A is m1-by-1
+% Ax is m1-by-n_x
+% B is m2-by-1
+% Bx is m2-by-n_x
+% C is m3-by-1
+% Cx is m3-by-n_x
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+m1=A.tsize(1);
+m2=B.tsize(1);
+m3=C.tsize(1);
+
+if m1~=prod(A.tsize)
+ error('A must be a vector')
+end
+if m2~=prod(B.tsize)
+ error('B must be a vector')
+end
+if m3~=prod(C.tsize)
+ error('C must be a vector')
+end
+
+if Ax.tsize(1)~=m1
+ error('Incompatible dimensions')
+end
+if Bx.tsize(1)~=m2
+ error('Incompatible dimensions')
+end
+if Cx.tsize(1)~=m3
+ error('Incompatible dimensions')
+end
+
+if Ax.tsize(2)~=Bx.tsize(2)
+ error('Incompatible dimensions')
+elseif Ax.tsize(2)~=Cx.tsize(2)
+ error('Incompatible dimensions')
+end
+
+term1=tkron3(Ax,B,C); %m3*m2*m1,n_x
+
+term2=tkron3(A,Bx,C); %m3*m2*m1,n_x
+
+term3=trkron3(A,B,Cx); %m3*m2*m1,n_x
+
+R=tplus(term1,term2);
+
+R=tplus(R,term3);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tplus.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tplus.m
new file mode 100644
index 0000000000000000000000000000000000000000..c26244f42a3f39b96d1730b268c468aa38b61e66
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tplus.m
@@ -0,0 +1,83 @@
+function [ A ] = tplus( B1,B2,varargin )
+%adds two tensors
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+sB1=size(B1.vals,1);
+sB2=size(B2.vals,1);
+
+if sB1==1
+ if sB2>1
+ B1.vals=repmat(B1.vals,sB2,1);
+ end
+elseif sB1>1
+ if sB2==1
+ B2.vals=repmat(B2.vals,sB1,1);
+ elseif sB2>1 && sB1~=sB2
+ error('incompatible states')
+ end
+end
+
+
+if size(B1.ptr,2)>1 % 2D pointers
+ if nargin==2
+ maxload=intarray(1);
+ elseif nargin==3
+ maxload=intarray(varargin{1});
+ end
+ [ A ] = tplus2d( B1,B2,maxload );
+else
+
+ rank1=length(B1.tsize);
+ rank2=length(B2.tsize);
+ if ~isequal(rank1,rank2)
+ error('incompatible dimensions')
+ end
+
+
+ A=sptensor;
+ A.tsize=B1.tsize;
+
+ l=B1.tsize(1);
+ m=B1.tsize(2:end);
+ IB1=B1.ptr;
+ IB2=B2.ptr;
+ JB1=B1.cols;
+ JB2=B2.cols;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ if ~isreal(NB1) || ~isreal(NB2)
+ error('complex numbers not supported')
+ end
+
+ if nargin==2
+ maxload=intarray(1);
+ elseif nargin==3
+ maxload=intarray(varargin{1});
+ end
+
+ if rank1==2
+ % A=tplus1(B1,B2);
+ [A.vals,A.ptr,A.cols] = tplus1_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+ A.vals=A.vals(:,1:A.ptr(end)-1);
+ A.cols=A.cols(1:A.ptr(end)-1,:);
+ elseif rank1==3
+ [A.vals,A.ptr,A.cols] = tplus2_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+ A.vals=A.vals(:,1:A.ptr(end)-1);
+ A.cols=A.cols(1:A.ptr(end)-1,:);
+ elseif rank1==4
+ [A.vals,A.ptr,A.cols] = tplus3_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+ A.vals=A.vals(:,1:A.ptr(end)-1);
+ A.cols=A.cols(1:A.ptr(end)-1,:);
+ elseif rank1==5
+ [A.vals,A.ptr,A.cols] = tplus4_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+ A.vals=A.vals(:,1:A.ptr(end)-1);
+ A.cols=A.cols(1:A.ptr(end)-1,:);
+ else
+ error('tensors of rank larger than 5 not supported')
+ end
+
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tplus2d.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tplus2d.m
new file mode 100644
index 0000000000000000000000000000000000000000..0bd770c5af43c00ce8871d58db4aefad065ef71c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tplus2d.m
@@ -0,0 +1,83 @@
+function [ A ] = tplus2d( B1,B2,varargin )
+%adds two tensors with two dimensional pointers
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(B1.ptr,2)==1
+ error('pointer should be 2-D')
+end
+rank1=length(B1.tsize);
+rank2=length(B2.tsize);
+if ~isequal(rank1,rank2)
+ error('incompatible dimensions')
+end
+
+
+A=sptensor;
+A.ptr2d=B1.ptr2d;
+A.tsize=B1.tsize;
+
+if nargin==2
+ maxload=intarray(1);
+elseif nargin==3
+ maxload=intarray(varargin{1});
+end
+
+if rank1==3
+ % A=tplus1(B1,B2);
+ l1=B1.tsize(1);
+ l2=B1.tsize(2);
+ m1=B1.tsize(3);
+ IB1=B1.ptr;
+ IB2=B2.ptr;
+ JB1=B1.cols;
+ JB2=B2.cols;
+ NB1=B1.vals;
+ NB2=B2.vals;
+ [A.vals,A.ptr,A.cols] = tplus1_2D_mex(l1,l2,m1,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+ A.vals=A.vals(:,1:A.ptr(end)-1);
+ A.cols=A.cols(1:A.ptr(end)-1,:);
+% A.ptr2d=1;
+% elseif rank1==3
+% l=B1.tsize(1);
+% m=B1.tsize(2:end);
+% IB1=B1.ptr;
+% IB2=B2.ptr;
+% JB1=B1.cols;
+% JB2=B2.cols;
+% NB1=B1.vals;
+% NB2=B2.vals;
+% [A.vals,A.ptr,A.cols] = tplus2_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+% A.vals=A.vals(:,1:A.ptr(end)-1);
+% A.cols=A.cols(1:A.ptr(end)-1,:);
+% elseif rank1==4
+% l=B1.tsize(1);
+% m=B1.tsize(2:end);
+% IB1=B1.ptr;
+% IB2=B2.ptr;
+% JB1=B1.cols;
+% JB2=B2.cols;
+% NB1=B1.vals;
+% NB2=B2.vals;
+% [A.vals,A.ptr,A.cols] = tplus3_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+% A.vals=A.vals(:,1:A.ptr(end)-1);
+% A.cols=A.cols(1:A.ptr(end)-1,:);
+% elseif rank1==5
+% l=B1.tsize(1);
+% m=B1.tsize(2:end);
+% IB1=B1.ptr;
+% IB2=B2.ptr;
+% JB1=B1.cols;
+% JB2=B2.cols;
+% NB1=B1.vals;
+% NB2=B2.vals;
+% [A.vals,A.ptr,A.cols] = tplus4_mex(l,m,IB1,JB1,NB1,IB2,JB2,NB2,maxload);
+% A.vals=A.vals(:,1:A.ptr(end)-1);
+% A.cols=A.cols(1:A.ptr(end)-1,:);
+else
+ error('tensors of rank larger than 3 not supported')
+end
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tscalar.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tscalar.m
new file mode 100644
index 0000000000000000000000000000000000000000..5a9dab520729132d7c48f739837311ec73c7bbda
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tscalar.m
@@ -0,0 +1,17 @@
+function [R]=tscalar(A)
+% returns a scalar tensor.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+A=tvec(A);
+
+[i,j,vals]=tfind(A);
+
+Rvals=zeros([A.tsize(1),size(A.vals,1)]);
+Rvals(i,:)=vals';
+
+R=sptensor(1);
+
+R.vals=Rvals(:);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/ttranspose.m b/105/replication_package/solution_methods/taylor_projection/Tensors/ttranspose.m
new file mode 100644
index 0000000000000000000000000000000000000000..600dd582e80bbbf74557c812725ee6fc330ed555
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/ttranspose.m
@@ -0,0 +1,22 @@
+function [ A ] = ttranspose( A )
+%transpose a 2D sparse tensor
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if length(A.tsize)>2
+ error('tensors or rank higher than 2 are not supported')
+end
+
+m=A.tsize(1);
+n=A.tsize(2);
+
+A.ptr2d=intarray([1,m]);
+A=ptr2d(A,1,m);
+A=ptr2col(A,1);
+A=col2ptr(A,2);
+A=ptr1d(A);
+
+A=rmfield(A,'ptr2d');
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/tvec.m b/105/replication_package/solution_methods/taylor_projection/Tensors/tvec.m
new file mode 100644
index 0000000000000000000000000000000000000000..0d36135d8fd71732da8fe9f649dad921a8ca8565
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/tvec.m
@@ -0,0 +1,16 @@
+function [R]=tvec(A)
+% vectorize a sparse tensor of dimensions m,n1,...,n4 to dimensions
+% m*n1*...*n4,1.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+A=unfold(A);
+
+A=ptr2d(A,1,A.tsize(1));
+A=ptr2col(A,1);
+A=fold(A,prod(A.tsize),1);
+A=col2ptr(A,1);
+A=ptr1d(A);
+R=rmfield(A,'ptr2d');
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/u2c.m b/105/replication_package/solution_methods/taylor_projection/Tensors/u2c.m
new file mode 100644
index 0000000000000000000000000000000000000000..e8ac1e8d2962d98908701b0c43ddbdb37c6a6c69
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/u2c.m
@@ -0,0 +1,28 @@
+function [ A ] = u2c( ten )
+%convert a tensor with symmetric column from unique form to compress form.
+%improve by mex
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+n=double(ten.tsize(2));
+k=double(length(ten.tsize)-1);
+
+n_unique=double(ten.ptr(end)-1);
+sortM=double(ten.cols(:,end:-1:1)); % the formula below assumes indices a1<=a2<=a3, so i have to change location of indices because i use the convention a3>=a2>=a1
+
+tempmat=repmat(n+k:-1:n+1,n_unique,1);
+loc=(repmat(prod(n+k-1:-1:n),n_unique,1)-prod(tempmat-repmat(sortM(:,1),1,k),2))/factorial(k)+1;
+
+for j=2:k-1
+ tempmat=repmat(n+k-j+1:-1:n+1,n_unique,1);
+ loc=loc+(prod(tempmat-repmat(sortM(:,j-1),1,k-j+1),2)-prod(tempmat-repmat(sortM(:,j),1,k-j+1),2))/factorial(k-j+1);
+end
+loc=loc+sortM(:,k)-sortM(:,k-1);
+
+A=ten;
+A.cols=intarray(loc);
+A.tsize=[ten.tsize(1),intarray(nchoosek(n+k-1,k))];
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/unfold.m b/105/replication_package/solution_methods/taylor_projection/Tensors/unfold.m
new file mode 100644
index 0000000000000000000000000000000000000000..ba5da36455c18731f9ad9cb046bc5e4f5559dc68
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/unfold.m
@@ -0,0 +1,40 @@
+function [R]=unfold(A)
+% unfold a sparse tensor of dimensions m,n1,...,n4 to a matrix of
+% dimensions m,n1*...*n4
+% the pointer can be 1D or 2D
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if size(A.ptr,2)==1 %1D pointer
+ rowdim=A.tsize(1);
+ coldim=A.tsize(2:end);
+ rank=length(A.tsize);
+
+else % 2D pointer
+ rowdim=A.tsize(1:2);
+ coldim=A.tsize(3:end);
+ rank=length(A.tsize)-1;
+end
+% check overflow on 32-bit system
+n=prod(int64(coldim));
+if intarray(n)==intarray(n-1)
+ error('integer overflow')
+end
+
+R=A;
+R.tsize=intarray([rowdim,n]);
+
+if rank==3
+ R.cols=sub2ind(coldim,A.cols(:,1),A.cols(:,2));
+elseif rank==4
+ R.cols=sub2ind(coldim,A.cols(:,1),A.cols(:,2),A.cols(:,3));
+elseif rank==5
+ R.cols=sub2ind(coldim,A.cols(:,1),A.cols(:,2),A.cols(:,3),A.cols(:,4));
+elseif rank==6
+ R.cols=sub2ind(coldim,A.cols(:,1),A.cols(:,2),A.cols(:,3),A.cols(:,4),A.cols(:,5));
+elseif rank>6
+ error('tensor of rank higher than 6 not supported')
+end
+R.cols=intarray(R.cols);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/uniquecols2ind.m b/105/replication_package/solution_methods/taylor_projection/Tensors/uniquecols2ind.m
new file mode 100644
index 0000000000000000000000000000000000000000..bf3758329590b5e2377b8577f23602c2278d9142
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/uniquecols2ind.m
@@ -0,0 +1,25 @@
+function [ loc ] = uniquecols2ind( cols,n )
+%convert unique columns to index (like u2c). Columns are assumed to satisfy
+%a1>=a2>=a3
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+[n_unique,k]=size(cols);
+
+if k>1
+ sortM=double(cols(:,end:-1:1)); % the formula below assumes indices a1<=a2<=a3, so i have to change location of indices because i use the convention a3>=a2>=a1
+
+ tempmat=repmat(n+k:-1:n+1,n_unique,1);
+ loc=(repmat(prod(n+k-1:-1:n),n_unique,1)-prod(tempmat-repmat(sortM(:,1),1,k),2))/factorial(k)+1;
+
+ for j=2:k-1
+ tempmat=repmat(n+k-j+1:-1:n+1,n_unique,1);
+ loc=loc+(prod(tempmat-repmat(sortM(:,j-1),1,k-j+1),2)-prod(tempmat-repmat(sortM(:,j),1,k-j+1),2))/factorial(k-j+1);
+ end
+ loc=loc+sortM(:,k)-sortM(:,k-1);
+else
+ loc=cols;
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/Tensors/vconcat.m b/105/replication_package/solution_methods/taylor_projection/Tensors/vconcat.m
new file mode 100644
index 0000000000000000000000000000000000000000..51da2450ed0e497b38231facf621815e4c8efc4a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/Tensors/vconcat.m
@@ -0,0 +1,21 @@
+function ten=vconcat(ten1,ten2)
+% vertical concatenation of two tensors of same column size.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if ~isequal(ten1.tsize(2:end),ten2.tsize(2:end))
+ error('incompatible dimensions')
+elseif size(ten1.vals,1)~=size(ten2.vals,1)
+ error('incompatible states')
+else
+ ten=sptensor;
+ ten.tsize=ten1.tsize;
+ ten.tsize(1)=ten1.tsize(1)+ten2.tsize(1);
+ ten.ptr=[ten1.ptr;ten2.ptr(2:end)+ten1.ptr(end)-1];
+ ten.cols=[ten1.cols;ten2.cols];
+ ten.vals=[ten1.vals,ten2.vals];
+end
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain0_theta_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain0_theta_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..ad85bae7ea0ea86fd969b41b7bad628b3360a4f1
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain0_theta_tensor.m
@@ -0,0 +1,9 @@
+function [ R,ind ] = chain0_theta_tensor( fv,vtheta,ind,n_ind,maxload,sum )
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+[R,ind]=contraction1(fv,vtheta,ind,n_ind,maxload,sum);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain1_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain1_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..afca203fa9de6903c1f8b42ff58f9bcdc05b3d20
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain1_tensor.m
@@ -0,0 +1,9 @@
+function [ R,ind ] = chain1_tensor(fv,vx,ind,n_ind,maxload,sum)
+%1st order chain rule.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+[R,ind]=contraction1(fv,vx,ind,n_ind,maxload,sum);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain1_theta_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain1_theta_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..e910b1721325f498729003969db0215e6077a133
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain1_theta_tensor.m
@@ -0,0 +1,28 @@
+function [ R,ind,term1,term2 ] = chain1_theta_tensor( fv,fvv,vx,vtheta,vxtheta,ind,n_ind,maxload,sum )
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(2,1);
+end
+
+n_f=fv.tsize(1);
+
+n_x=vx.tsize(2);
+n_theta=vtheta.tsize(2);
+n_s=max([size(fv.vals,1),size(vx.vals,1),size(vtheta.vals,1)]);
+
+if ~isempty(fvv.vals)
+ [term1,ind{1}]=contraction2(fvv,vx,vtheta,ind{1},n_ind,maxload,sum);
+ term1=permutecols(term1,[2,1]);
+else
+ term1=sptensor(n_f,[n_x,n_theta],n_s);
+end
+
+[term2,ind{2}]=contraction1(fv,vxtheta,ind{2},n_ind,maxload,sum);
+
+R=tplus(term1,fold(term2,n_x,n_theta),maxload);
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain2c_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain2c_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..2cb7d1deeae48a7b3e96b2673905940433622d73
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain2c_tensor.m
@@ -0,0 +1,23 @@
+function [ fxxc,ind ] = chain2c_tensor(fv,fvv,vx,vxxc,ind,n_ind,maxload,sum)
+%chain2c is compressed.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(2,1);
+end
+
+%fvv*kron(vx,vx)*U2
+[term1,ind{1}]=AkronBU2(fvv,vx,ind{1},n_ind,maxload,sum);
+
+%fv*vxxc
+[term2,ind{2}]=contraction1(fv,vxxc,ind{2},n_ind,maxload,sum);
+
+fxxc=tplus(term1,term2,maxload);
+
+if isfield(fv,'ptr2d')
+ fxxc.ptr2d=fv.ptr2d;
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain2c_theta_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain2c_theta_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..d227831ba4f400f166615c6d3e80514e4c9a89d2
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain2c_theta_tensor.m
@@ -0,0 +1,59 @@
+function [ R,ind] = chain2c_theta_tensor(fv,fvv,fvvv,vx,vxxc,vtheta,vxtheta,vxxctheta,M2,ind,n_ind,maxload,sum )
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(5,1);
+end
+
+n_f=fv.tsize(1);
+
+n_x=vx.tsize(2);
+n_theta=vtheta.tsize(2);
+unique2=nchoosek(n_x+1,2);
+n_s=max([size(fv.vals,1),size(vx.vals,1),size(vtheta.vals,1)]);
+
+
+if ~isempty(fvvv.vals)
+
+ [term1,ind{1}]=AkronB1U2B2(fvvv,vx,vtheta,ind{1},n_ind,maxload,sum);
+ term1=fold(term1,n_theta,unique2);
+
+ term1=col2ptr(term1,2);
+
+else
+ term1=sptensor(n_f,[unique2,n_theta],n_s);
+ term1=col2ptr(term1,1);
+end
+
+[term2,ind{2}]=contraction2(fvv,vx,vxtheta,ind{2},n_ind,maxload,sum);
+term2=foldj(term2,1,[n_x,n_theta]);
+
+term2=ptr1d(unfold(col2ptr(term2,2)));
+
+[term2,ind{3}]=contraction1(term2,M2,ind{3},n_ind,maxload,sum);
+term2=ptr2d(term2,n_f,n_theta);
+term2=ptr2col(term2,2); % tsize=[n_f*n_theta,unique2]
+term2=col2ptr(term2,1);
+
+
+sumterm=tplus(term1,term2,maxload);
+
+[term3,ind{4}]=contraction2(fvv,vxxc,vtheta,ind{4},n_ind,maxload,sum);
+
+term3=col2ptr(term3,2);
+sumterm=tplus(sumterm,term3,maxload);
+
+
+[term4,ind{5}]=contraction1(fv,vxxctheta,ind{5},n_ind,maxload,sum);
+term4=fold(term4,unique2,n_theta);
+term4=col2ptr(term4,1);
+
+
+
+R=tplus(sumterm,term4,maxload);
+
+R=ptr2col(R,1);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain3c_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain3c_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..0faa37cdc9a3415d42c489a18382e557e23165b6
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain3c_tensor.m
@@ -0,0 +1,30 @@
+function [ fxxxc,ind ] = chain3c_tensor(fv,fvv,fvvv,vx,vxxc,vxxxc,M2,ind,n_ind,maxload,sum)
+%chain3c is compressed.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(4,1);
+end
+
+%fvvv*kron(vx,vx,vx)*U3
+
+[term1,ind{1}]=AkronBU3(fvvv,vx,ind{1},n_ind,maxload,sum);
+
+[term2,ind{2}]=contraction2(fvv,vx,vxxc,ind{2},n_ind,maxload,sum);
+
+[term2,ind{3}]=contraction1(unfold(term2),M2,ind{3},n_ind,maxload,sum);
+
+sumterm=tplus(term1,term2,maxload); clear term1 term2
+
+[term3,ind{4}]=contraction1(fv,vxxxc,ind{4},n_ind,maxload,sum);
+
+fxxxc=tplus(sumterm,term3,maxload);
+
+if isfield(fv,'ptr2d')
+ fxxxc.ptr2d=fv.ptr2d;
+end
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain3c_theta_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain3c_theta_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..50af2df921d5be06262fbdd4ab205f402c0220e1
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain3c_theta_tensor.m
@@ -0,0 +1,138 @@
+function [ R ,ind] = chain3c_theta_tensor(fv,fvv,fvvv,fvvvv,...
+ vx,vxxc,vxxxc,vtheta,vxtheta,vxxctheta,vxxxctheta,...
+ M2,M3,M4,M5,ind,n_ind,maxload,sum )
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(15,1);
+end
+
+n_f=fv.tsize(1);
+n_v=fv.tsize(2);
+n_x=vx.tsize(2);
+n_theta=vtheta.tsize(2);
+unique2=nchoosek(n_x+1,2);
+unique3=nchoosek(n_x+2,3);
+
+n_s=max([size(fv.vals,1),size(vx.vals,1),size(vtheta.vals,1)]);
+
+if ~isempty(fvvvv.vals)
+ [term1,ind{1}]=AkronB1U3B2(fvvvv,vx,vtheta,ind{1},n_ind,maxload,sum);
+ term1=fold(term1,n_theta,unique3);
+ term1=col2ptr(term1,2);
+else
+ term1=sptensor(n_f,[unique3,n_theta],n_s);
+ term1=col2ptr(term1,1);
+end
+
+[term2,ind{2}]=AkronB1U2B2(fvvv,vx,vxtheta,ind{2},n_ind,maxload,sum);
+
+term2=fold(term2,n_x,n_theta,unique2);
+
+term2=ptr1d(unfold(col2ptr(term2,2)));
+
+[term2,ind{3}]=contraction1(term2,M2,ind{3},n_ind,maxload,sum);
+term2=ptr2d(term2,n_f,n_theta);% tsize=[n_f*n_theta,unique3]
+term2=ptr2col(term2,2);% tsize=[n_f,unique3,n_theta]
+term2=col2ptr(term2,1);% tsize=[n_f*unique3,n_theta]
+
+sumterm=tplus(term1,term2,maxload);
+
+
+fvvv=col2ptr(fvvv,1); %n_f*n_v,n_v,n_v
+fvvv=ptr1d(fvvv); %n_f*n_v,n_v,n_v
+[term3,ind{4}]=contraction2(fvvv,vx,vxxc,ind{4},n_ind,maxload,'vec'); %n_f*n_v,unique2,n_x
+term3=ptr2d(term3,n_f,n_v); %n_f*n_v,unique2,n_x
+term3=ptr2col(term3,1); %n_f,n_v,unique2,n_x
+
+term3=fold(term3,n_v,unique2*n_x);
+term3=col2ptr(term3,2);
+term3=ptr1d(term3);
+[term3,ind{12}]=contraction1(term3,vtheta,ind{12},n_ind,maxload,sum);
+term3=fold(ptr2col(ptr2d(term3,n_f,unique2*n_x),2),n_theta,unique2,n_x);
+
+term3=col2ptr(term3,1); %n_f*n_theta,unique2,n_x
+term3=ptr1d(unfold(term3)); %n_f*n_theta,unique2*n_x
+[term3,ind{5}]=contraction1(term3,M3,ind{5},n_ind,maxload,sum);
+term3=ptr2d(term3,n_f,n_theta); %n_f*n_theta,unique3
+term3=ptr2col(term3,2);%n_f,unique3,n_theta
+term3=col2ptr(term3,1);%n_f*unique3,n_theta
+
+sumterm=tplus(sumterm,term3,maxload);
+
+% term4
+
+rfvv=col2ptr(fvv,1); %n_f*n_v,n_v
+rfvv=ptr1d(rfvv); %n_f*n_v,n_v
+[term4,ind{6}]=contraction1(rfvv,vx,ind{6},n_ind,maxload,'vec'); %n_f*n_v,n_x
+term4=ptr2d(term4,n_f,n_v); %n_f*n_v,n_x
+term4=ptr2col(term4,1); %n_f,n_v,n_x
+
+term4=col2ptr(term4,2); %n_f*n_x,n_v
+term4=ptr1d(term4);
+[term4,ind{13}]=contraction1(term4,col2ptr(fold(vxxctheta,unique2,n_theta),1),ind{13},n_ind,maxload,sum);
+
+% this is special because term4 ptr has 3D
+term4.ptr2d=intarray([n_f*n_x,unique2]);
+term4=ptr2col(term4,1); %n_f*n_x,unique2,n_theta
+term4.ptr2d=intarray([n_f,n_x]);
+term4=ptr2d(term4,n_f,n_x);
+term4=ptr2col(term4,2); %n_f,unique2,n_x,n_theta
+term4=col2ptr(term4,3); %n_f*n_theta,unique2,n_x
+
+term4=ptr1d(unfold(term4)); %n_f*n_theta,unique2*n_x
+[term4,ind{7}]=contraction1(term4,M4,ind{7},n_ind,maxload,sum);
+term4=ptr2d(term4,n_f,n_theta); %n_f*n_theta,unique3
+term4=ptr2col(term4,2);%n_f,unique3,n_theta
+term4=col2ptr(term4,1);%n_f*unique3,n_theta
+
+sumterm=tplus(sumterm,term4,maxload);
+
+
+% term5
+
+[term5,ind{8}]=contraction1(rfvv,vxxc,ind{8},n_ind,maxload,'vec'); %n_f*n_v,unique2
+term5=ptr2d(term5,n_f,n_v); %n_f*n_v,unique2
+term5=ptr2col(term5,1); %n_f,n_v,unique2
+term5=col2ptr(term5,2); %n_f*unique2,n_v
+term5=ptr1d(term5);
+[term5,ind{14}]=contraction1(term5,col2ptr(fold(vxtheta,n_x,n_theta),1),ind{14},n_ind,maxload,sum);
+
+% this is special because term5 ptr has 3D
+term5.ptr2d=intarray([n_f*unique2,n_x]);
+term5=ptr2col(term5,1); %n_f*unique2,n_x,n_theta
+term5.ptr2d=intarray([n_f,unique2]);
+term5=ptr2d(term5,n_f,unique2);
+term5=ptr2col(term5,2); %n_f,n_x,unique2,n_theta
+term5=col2ptr(term5,3); %n_f*n_theta,n_x,unique2
+
+term5=ptr1d(unfold(term5)); %n_f*n_theta,n_x*unique2
+[term5,ind{9}]=contraction1(term5,M5,ind{9},n_ind,maxload,sum);
+term5=ptr2d(term5,n_f,n_theta); %n_f*n_theta,unique3
+term5=ptr2col(term5,2);%n_f,unique3,n_theta
+term5=col2ptr(term5,1);%n_f*unique3,n_theta
+
+sumterm=tplus(sumterm,term5,maxload);
+
+% term6
+
+[term6,ind{10}]=contraction1(rfvv,vxxxc,ind{10},n_ind,maxload,'vec'); %n_f*n_v,unique3
+term6=ptr2d(term6,n_f,n_v); %n_f*n_v,unique3
+term6=ptr2col(term6,1); %n_f,n_v,unique3
+term6=col2ptr(term6,2); %n_f*unique3,n_v
+term6=ptr1d(term6);
+[term6,ind{15}]=contraction1(term6,vtheta,ind{15},n_ind,maxload,sum);
+term6=ptr2d(term6,n_f,unique3); %n_f*unique3,n_theta
+
+sumterm=tplus(sumterm,term6,maxload);
+
+[term7,ind{11}]=contraction1(fv,col2ptr(fold(vxxxctheta,unique3,n_theta),1),ind{11},n_ind,maxload,sum);
+
+
+R=tplus(sumterm,term7,maxload);
+
+R=ptr2col(R,1);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain4c_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain4c_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..804ab99c26ee3ed298d1e77bfe163ae8a51a0988
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain4c_tensor.m
@@ -0,0 +1,53 @@
+function [ fxxxxc,ind ] = chain4c_tensor(fv,fvv,fvvv,fvvvv,vx,vxxc,vxxxc,vxxxxc,M2,M3,M4,ind,n_ind,maxload,sum,varargin)
+%chain4c is compressed.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if ~isempty(varargin)
+ convertind=varargin{1};
+ maxind=varargin{2};
+ doi=1;
+else
+ doi=0;
+end
+
+if isempty(ind)
+ ind=cell(8,1);
+end
+
+%fvvvv*kron(vx,vx,vx,vx)*U4
+if doi==0
+ [term1,ind{1}]=AkronBU4(fvvvv,vx,ind{1},n_ind,maxload,sum);
+else
+ [term1,ind{1}]=AkronBU4i(fvvvv,vx,ind{1},n_ind,maxload,sum,convertind,maxind);
+end
+
+
+%fvvv*kron(kron(vx,vx)*U,vxxc)*kron(W2,W2)*OMEGA2*U4
+[term2,ind{2}]=AkronB1U2B2(fvvv,vx,vxxc,ind{2},n_ind,maxload,sum);
+[term2,ind{3}]=contraction1(term2,M2,ind{3},n_ind,maxload,sum);
+
+
+sumterm=tplus(term1,term2); clear term1 term2
+
+%fvv*kron(vx,vxxxc)*kron(I,W3)*OMEGA3*U4
+[term3,ind{4}]=contraction2(fvv,vx,vxxxc,ind{4},n_ind,maxload,sum);
+[term3,ind{5}]=contraction1(unfold(term3),M3,ind{5},n_ind,maxload,sum);
+sumterm=tplus(sumterm,term3); clear term3
+
+%fvv*kron(vxxc,vxxc)*U*W*kron(W2,W2)*OMEGA4*U4
+[term4,ind{6}]=AkronBU2(fvv,vxxc,ind{6},n_ind,maxload,sum);
+
+[term4,ind{7}]=contraction1(unfold(term4),M4,ind{7},n_ind,maxload,sum);
+sumterm=tplus(sumterm,term4); clear term4
+
+[term5,ind{8}]=contraction1(fv,vxxxxc,ind{8},n_ind,maxload,sum);
+
+fxxxxc=tplus(sumterm,term5);
+
+if isfield(fv,'ptr2d')
+ fxxxxc.ptr2d=fv.ptr2d;
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain4c_theta_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain4c_theta_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..59433d16612c9ee0b2b929c6adb4888f85d0e0fe
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain4c_theta_tensor.m
@@ -0,0 +1,209 @@
+function [ R ,ind] = chain4c_theta_tensor(fv,fvv,fvvv,fvvvv,fvvvvv,...
+ vx,vxxc,vxxxc,vxxxxc,vtheta,vxtheta,vxxctheta,vxxxctheta,vxxxxctheta,...
+ M2,M3,M5,M6,M9,M10,ind,n_ind,maxload,sum )
+%
+% � Copyright, Oren Levintal, January 23, 2017.
+
+if isempty(ind)
+ ind=cell(21,1);
+end
+
+n_f=fv.tsize(1);
+n_v=fv.tsize(2);
+n_x=vx.tsize(2);
+n_theta=vtheta.tsize(2);
+unique2=nchoosek(n_x+1,2);
+unique3=nchoosek(n_x+2,3);
+unique4=nchoosek(n_x+3,4);
+
+n_s=max([size(fv.vals,1),size(vx.vals,1),size(vtheta.vals,1)]);
+
+vxtheta=unfold(vxtheta);
+vxxctheta=unfold(vxxctheta);
+vxxxctheta=unfold(vxxxctheta);
+vxxxxctheta=unfold(vxxxxctheta);
+
+%fvvvvv*kron(vtheta,kron(vx,vx,vx,vx)*U4)
+
+if ~isempty(fvvvvv.vals)
+ fv_vvvv=col2ptr(fvvvvv,1); %n_vn_f,n_v,n_v,n_v,n_v
+ fv_vvvv=ptr1d(fv_vvvv); %n_vn_f,n_v,n_v,n_v,n_v
+ [term1,ind{1}]=AkronBU4(fv_vvvv,vx,ind{1},n_ind,maxload,sum); % n_vn_f,unique4
+ term1.ptr2d=fv_vvvv.ptr2d;
+ term1=ptr2d(term1,n_f,n_v);
+ term1=ptr2col(term1,2); %n_f,unique4,n_v
+ term1=col2ptr(term1,1); %unique4 n_f,n_v
+ term1=ptr1d(term1);
+ [term1,ind{2}]=contraction1(term1,vtheta,ind{2},n_ind,maxload,sum); %unique4 n_f,n_theta
+ term1=ptr2d(term1,n_f,unique4);
+else
+ term1=sptensor(n_f,[unique4,n_theta],n_s);
+ term1=col2ptr(term1,1);
+end
+
+[term2,ind{3}]=AkronB1U3B2(fvvvv,vx,vxtheta,ind{3},n_ind,maxload,sum); %n_f,n_x,n_theta,unique3
+
+term2=fold(term2,n_x,n_theta,unique3);
+
+term2=ptr1d(unfold(col2ptr(term2,2))); %n_thetan_f,n_x,unique3
+
+
+[term2,ind{4}]=contraction1(term2,M2,ind{4},n_ind,maxload,sum);
+term2=ptr2d(term2,n_f,n_theta);% tsize=[n_f*n_theta,unique4]
+term2=ptr2col(term2,2);% tsize=[n_f,unique4,n_theta]
+term2=col2ptr(term2,1);% tsize=[n_f*unique4,n_theta]
+
+sumterm=tplus(term1,term2,maxload);
+
+
+clear term1 term2
+
+% term3
+
+fv_vvv=col2ptr(fvvvv,1); %n_f*n_v,n_v,n_v,n_v
+fv_vvv=ptr1d(fv_vvv); %n_f*n_v,n_v,n_v,n_v
+[term3,ind{5}]=AkronB1U2B2(fv_vvv,vx,vxxc,ind{5},n_ind,maxload,sum); %n_f*n_v,unique2,unique2
+term3.ptr2d=fv_vvv.ptr2d;
+term3=ptr2d(term3,n_f,n_v); %n_f*n_v,unique2*unique2
+term3=ptr2col(term3,1); %n_f,n_v,unique2*unique2
+
+term3=fold(term3,n_v,unique2*unique2);
+term3=col2ptr(term3,2);
+term3=ptr1d(term3);
+[term3,ind{6}]=contraction1(term3,vtheta,ind{6},n_ind,maxload,sum);
+term3=fold(ptr2col(ptr2d(term3,n_f,unique2*unique2),2),n_theta,unique2,unique2);
+
+term3=col2ptr(term3,1); %n_f*n_theta,unique2,unique2
+term3=ptr1d(unfold(term3)); %n_f*n_theta,unique2*unique2
+[term3,ind{7}]=contraction1(term3,M3,ind{7},n_ind,maxload,sum);
+term3=ptr2d(term3,n_f,n_theta); %n_f*n_theta,unique4
+term3=ptr2col(term3,2);%n_f,unique4,n_theta
+term3=col2ptr(term3,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term3,maxload);
+
+clear term3
+
+% term4
+
+[term4,ind{8}]=AkronB1U2B2(fvvv,vx,vxxctheta,ind{8},n_ind,maxload,sum); %n_f,unique2,n_theta,unique2
+term4=fold(term4,unique2,n_theta,unique2);
+term4=col2ptr(term4,2); %n_thetan_f,unique2,unique2
+term4=ptr1d(unfold(term4)); %n_thetan_f,unique2*unique2
+[term4,ind{9}]=contraction1(term4,M3,ind{9},n_ind,maxload,sum);
+term4=ptr2d(term4,n_f,n_theta); %n_f*n_theta,unique4
+term4=ptr2col(term4,2);%n_f,unique4,n_theta
+term4=col2ptr(term4,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term4,maxload);
+
+
+
+clear term4
+
+% term5
+
+[term5,ind{10}]=contraction3(fvvv,vx,vxtheta,vxxc,ind{10},n_ind,maxload,sum); %n_f,unique2,n_x,n_theta,n_x
+term5=fold(term5,unique2,n_x,n_theta,n_x);
+term5=col2ptr(term5,3); %n_thetan_f,unique2,n_x,n_x
+term5=ptr1d(unfold(term5)); %n_thetan_f,unique2*n_x*n_x
+[term5,ind{11}]=contraction1(term5,M5,ind{11},n_ind,maxload,sum);
+term5=ptr2d(term5,n_f,n_theta); %n_f*n_theta,unique4
+term5=ptr2col(term5,2);%n_f,unique4,n_theta
+term5=col2ptr(term5,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term5,maxload);
+
+
+clear term5
+
+% term6
+
+[term6,ind{12}]=contraction3(fvvv,vx,vxxxc,vtheta,ind{12},n_ind,maxload,sum); %n_f,n_theta,unique3,n_x
+term6=fold(term6,n_theta,unique3,n_x);
+term6=col2ptr(term6,1); %n_thetan_f,unique3,n_x
+
+
+% term7
+
+[term7,ind{13}]=contraction2(fvv,vx,vxxxctheta,ind{13},n_ind,maxload,sum); %n_f,unique3,n_theta,n_x
+term7=fold(term7,unique3,n_theta,n_x);
+term7=col2ptr(term7,2); %n_thetan_f,unique3,n_x
+
+term6_7_8=tplus(unfold(term6),unfold(term7),maxload);
+
+clear term6 term7
+
+[term8,ind{14}]=contraction2(fvv,vxtheta,vxxxc,ind{14},n_ind,maxload,sum); %n_f,unique3,n_x,n_theta
+term8=fold(term8,unique3,n_x,n_theta);
+term8=col2ptr(term8,3); %n_thetan_f,unique3,n_x
+
+term6_7_8=tplus(term6_7_8,unfold(term8),maxload); %n_thetan_f,unique3,n_x
+
+clear term8
+
+term6_7_8=unfold(term6_7_8); %n_thetan_f,unique3,n_x
+term6_7_8=ptr1d(term6_7_8);
+[term6_7_8,ind{15}]=contraction1(term6_7_8,M6,ind{15},n_ind,maxload,sum);
+term6_7_8=ptr2d(term6_7_8,n_f,n_theta); %n_f*n_theta,unique4
+term6_7_8=ptr2col(term6_7_8,2);%n_f,unique4,n_theta
+term6_7_8=col2ptr(term6_7_8,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term6_7_8,maxload);
+
+
+clear term6_7_8
+
+% term9
+unique2new=nchoosek(unique2+1,2);
+[term9,ind{16}]=AkronB1U2B2(fvvv,vxxc,vtheta,ind{16},n_ind,maxload,sum); %n_f,n_theta,unique2new
+term9=fold(term9,n_theta,unique2new);
+term9=col2ptr(term9,1); %n_thetan_f,unique2new
+term9=ptr1d(unfold(term9)); %n_thetan_f,unique2new
+[term9,ind{17}]=contraction1(term9,M9,ind{17},n_ind,maxload,sum);
+term9=ptr2d(term9,n_f,n_theta); %n_f*n_theta,unique4
+term9=ptr2col(term9,2);%n_f,unique4,n_theta
+term9=col2ptr(term9,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term9,maxload);
+
+clear term9
+
+% term10
+
+[term10,ind{18}]=contraction2(fvv,vxxc,vxxctheta,ind{18},n_ind,maxload,sum); %n_f,unique2,n_theta,unique2
+term10=fold(term10,unique2,n_theta,unique2);
+term10=col2ptr(term10,2); %n_thetan_f,unique2,unique2
+term10=ptr1d(unfold(term10)); %n_thetan_f,unique2*unique2
+[term10,ind{19}]=contraction1(term10,M10,ind{19},n_ind,maxload,sum);
+term10=ptr2d(term10,n_f,n_theta); %n_f*n_theta,unique4
+term10=ptr2col(term10,2);%n_f,unique4,n_theta
+term10=col2ptr(term10,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term10,maxload);
+
+
+clear term10
+
+% term11
+
+[term11,ind{20}]=contraction2(fvv,vtheta,vxxxxc,ind{20},n_ind,maxload,sum); % n_f,unique4,n_theta
+term11=col2ptr(term11,1);%n_f*unique4,n_theta
+
+sumterm=tplus(sumterm,term11,maxload);
+
+
+clear term11
+
+% term12
+
+[term12,ind{21}]=contraction1(fv,vxxxxctheta,ind{21},n_ind,maxload,sum); % n_f,unique4,n_theta
+term12=fold(term12,unique4,n_theta);
+term12=col2ptr(term12,1);%n_f*unique4,n_theta
+
+R=tplus(sumterm,term12,maxload);
+
+R=ptr2col(R,1);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chain5c_tensor.m b/105/replication_package/solution_methods/taylor_projection/chain5c_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..35a6df044e6c55a9895a2458140b3b317bc07f57
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chain5c_tensor.m
@@ -0,0 +1,189 @@
+function [ fxxxxxc,ind ] = chain5c_tensor(fv,fvv,fvvv,fvvvv,fvvvvv,vx,vxxc,vxxxc,vxxxxc,vxxxxxc...
+ ,M1,M2,M3,M4,M5,M6,ind,n_ind,maxload,sum,varargin)
+%chain5c is compressed.
+%
+% � Copyright, Oren Levintal, January 18, 2017.
+
+if ~isempty(varargin)
+ convertind=varargin{1};
+ maxind=varargin{2};
+ doi=1;
+else
+ doi=0;
+end
+
+if isempty(ind)
+ ind=cell(14,1);
+end
+
+n_f=fv.tsize(1);
+n_v=fv.tsize(2);
+n_x=vx.tsize(2);
+%fvvvvv*kron(vx,vx,vx,vx,vx)*U5
+
+%fvvvvv*kron(kron(vx,vx,vx,vx)U4W4,vx))*U5
+%fvvvvv*kron(kron(vx,vx,vx,vx)U4,vx))*kron(W4,I)*U5
+fv_vvvv=col2ptr(fvvvvv,1); %n_vn_f,n_v,n_v,n_v,n_v
+fv_vvvv=ptr1d(fv_vvvv); %n_vn_f,n_v,n_v,n_v,n_v
+if doi==0
+ [term1,ind{1}]=AkronBU4(fv_vvvv,vx,ind{1},n_ind,maxload,sum); %n_vn_f,unique4
+else
+ [term1,ind{1}]=AkronBU4i(fv_vvvv,vx,ind{1},n_ind,maxload,sum,reshape(repmat(convertind(:)',n_v,1),n_v*n_f,n_v),maxind); %n_vn_f,unique4
+end
+term1.ptr2d=fv_vvvv.ptr2d;
+term1=ptr2d(term1,n_f,n_v);
+term1=ptr2col(term1,2); %n_f,unique4,n_v
+term1=col2ptr(term1,1); %unique4 n_f,n_v
+term1=ptr1d(term1);
+[term1b,ind{2}]=contraction1(term1,vx,ind{2},n_ind,maxload,sum); %unique4 n_f,n_x
+term1b.ptr2d=term1.ptr2d;
+term1b=ptr2d(term1b,term1b.ptr2d(1),term1b.ptr2d(2));
+term1=ptr2col(term1b,2); % n_f,n_x,unique4
+clear term1b
+[term1,ind{3}]=contraction1(unfold(term1),M1,ind{3},n_ind,maxload,sum); %n_f,unique5
+
+ % test
+% fvvvvv1=fvvvvv;
+% fvvvvv1.vals=fvvvvv1.vals(1,:);
+% vx1=vx;
+% vx1.vals=vx1.vals(1,:);
+% sfvvvvv=sptensor2spmat(unfold(fvvvvv1));
+% svx=sptensor2spmat(vx1);
+% sfv_vvvv=reshape(sfvvvvv,n_f*n_v,[]);
+% n_x=vx.tsize(2);
+% [U4,W4]=create_UW(n_x,4);
+% temp1=sfv_vvvv*kron(kron(svx,svx),kron(svx,svx))*U4;
+% temp1=reshape(full(temp1),n_f,n_v,[]);
+% temp1=permute(temp1,[2,1,3]);
+% temp1=sparse(reshape(temp1,n_v*n_f,[])); %n_v,n_f,unique4
+%
+% temp1=reshape(temp1,n_v,[])'*svx; % n_f,unique4,n_x
+% unique4=nchoosek(n_x+3,4);
+% temp1=reshape(full(temp1),n_f,unique4,n_x);
+% temp1=permute(temp1,[1,3,2]);
+% temp1=sparse(reshape(temp1,n_f,unique4*n_x));
+% U5=create_UW(n_x,5);
+% term1_1=term1;
+% term1_1.vals=term1_1.vals(1,:);
+% temp1=sfvvvvv*kron(svx,kron(kron(svx,svx),kron(svx,svx)))*U5;
+% oren=sptensor2spmat(unfold(term1_1))-temp1;
+% max(abs(oren(:)))
+
+
+%fvvvv*kron(kron(vx,vx,vx)*U3,vxxc)*kron(W3,W2)*OMEGA5*U5
+[term2,ind{4}]=AkronB1U3B2(fvvvv,vx,vxxc,ind{4},n_ind,maxload,sum);
+[term2,ind{5}]=contraction1(term2,M2,ind{5},n_ind,maxload,sum);
+
+% test
+
+% fvvvv1=fvvvv;
+% fvvvv1.vals=fvvvv1.vals(1,:);
+% vx1=vx;
+% vx1.vals=vx1.vals(1,:);
+% vxxc1=vxxc;
+% vxxc1.vals=vxxc1.vals(1,:);
+% sfvvvv=sptensor2spmat(unfold(fvvvv1));
+% svx=sptensor2spmat(vx1);
+% svxxc=sptensor2spmat(vxxc1);
+%
+% n_x=vx.tsize(2);
+% [U2,W2]=create_UW(n_x,2);
+% [U5]=create_UW(n_x,5);
+%
+% OMEGA=create_OMEGA(n_x,5);
+% temp2=sfvvvv*kron(kron(svx,svx),kron(svx,svxxc*W2))*OMEGA.OMEGA5*U5;
+% temp2=sparse(temp2);
+% term2_1=term2;
+% term2_1.vals=term2_1.vals(1,:);
+% oren=sptensor2spmat(unfold(term2_1))-temp2;
+% max(abs(oren(:)))
+
+sumterm=tplus(term1,term2); clear term1 term2
+
+%fvvv*kron(kron(vx,vx)*U2,vxxxc)*kron(W2,W3)*OMEGA6*U5
+[term3,ind{6}]=AkronB1U2B2(fvvv,vx,vxxxc,ind{6},n_ind,maxload,sum);
+[term3,ind{7}]=contraction1(term3,M3,ind{7},n_ind,maxload,sum);
+
+% test
+
+% fvvv1=fvvv;
+% fvvv1.vals=fvvv1.vals(1,:);
+% vx1=vx;
+% vx1.vals=vx1.vals(1,:);
+% vxxxc1=vxxxc;
+% vxxxc1.vals=vxxxc1.vals(1,:);
+% sfvvv=sptensor2spmat(unfold(fvvv1));
+% svx=sptensor2spmat(vx1);
+% svxxxc=sptensor2spmat(vxxxc1);
+%
+% n_x=vx.tsize(2);
+% [U2,W2]=create_UW(n_x,2);
+% [U3,W3]=create_UW(n_x,3);
+% [U5]=create_UW(n_x,5);
+%
+% OMEGA=create_OMEGA(n_x,5);
+% temp3=sfvvv*kron(kron(svx,svx),svxxxc*W3)*OMEGA.OMEGA6*U5;
+% temp3=sparse(temp3);
+% term3_1=term3;
+% term3_1.vals=term3_1.vals(1,:);
+% oren=sptensor2spmat(unfold(term3_1))-temp3;
+% max(abs(oren(:)))
+
+sumterm=tplus(sumterm,term3); clear term3
+
+%fvvv*kron(vx,kron(vxxc*W2,vxxc*W2))*OMEGA7*U5
+%fvvv*kron(vx,kron(vxxc,vxxc))*kron(I,W2,W2)*OMEGA7*U5
+%fvvv*kron(vx,kron(vxxc,vxxc)UW)*kron(I,W2,W2)*OMEGA7*U5
+%fvvv*kron(vx,kron(vxxc,vxxc)U)*kron(I,W)*kron(I,W2,W2)*OMEGA7*U5
+[term4,ind{8}]=AkronB1U2B2(fvvv,vxxc,vx,ind{8},n_ind,maxload,sum);
+term4=permutecols(fold(term4,n_x,term4.tsize(2)/n_x),[2,1]);
+[term4,ind{9}]=contraction1(unfold(term4),M4,ind{9},n_ind,maxload,sum);
+
+% test
+
+% fvvv1=fvvv;
+% fvvv1.vals=fvvv1.vals(1,:);
+% vx1=vx;
+% vx1.vals=vx1.vals(1,:);
+% vxxc1=vxxc;
+% vxxc1.vals=vxxc1.vals(1,:);
+% sfvvv=sptensor2spmat(unfold(fvvv1));
+% svx=sptensor2spmat(vx1);
+% svxxc=sptensor2spmat(vxxc1);
+%
+% n_x=vx.tsize(2);
+% [U2,W2]=create_UW(n_x,2);
+% [U3,W3]=create_UW(n_x,3);
+% [U5]=create_UW(n_x,5);
+%
+% OMEGA=create_OMEGA(n_x,5);
+% temp4=sfvvv*kron(svx,kron(svxxc*W2,svxxc*W2))*OMEGA.OMEGA7*U5;
+% temp4=sparse(temp4);
+% term4_1=term4;
+% term4_1.vals=term4_1.vals(1,:);
+% oren=sptensor2spmat(unfold(term4_1))-temp4;
+% max(abs(oren(:)))
+
+sumterm=tplus(sumterm,term4); clear term4
+
+%fvv*kron(vx,vxxxxc)*kron(I,W4)*OMEGA8*U5
+[term5,ind{10}]=contraction2(fvv,vx,vxxxxc,ind{10},n_ind,maxload,sum);
+[term5,ind{11}]=contraction1(unfold(term5),M5,ind{11},n_ind,maxload,sum);
+sumterm=tplus(sumterm,term5); clear term5
+
+%fvv*kron(vxxc,vxxxc)*kron(W2,W3)*OMEGA9*U5
+[term6,ind{12}]=contraction2(fvv,vxxc,vxxxc,ind{12},n_ind,maxload,sum);
+[term6,ind{13}]=contraction1(unfold(term6),M6,ind{13},n_ind,maxload,sum);
+sumterm=tplus(sumterm,term6); clear term6
+
+%fv*vxxxxxc
+[term7,ind{14}]=contraction1(fv,vxxxxxc,ind{14},n_ind,maxload,sum);
+
+fxxxxxc=tplus(sumterm,term7);
+
+if isfield(fv,'ptr2d')
+ fxxxxxc.ptr2d=fv.ptr2d;
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/chainsM.m b/105/replication_package/solution_methods/taylor_projection/chainsM.m
new file mode 100644
index 0000000000000000000000000000000000000000..f7c36b83dccf84f59c31e50f7c2be3d38f9eae19
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/chainsM.m
@@ -0,0 +1,61 @@
+function [ M ] = chainsM( n,order,varargin )
+%calculate coefficient matrices for compressed chain rules.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+compress=1;
+if ~isempty(varargin)
+ compress=0;
+end
+
+if order==3
+ M=cell(2,1);
+ [~,W2]=create_UW(n,2);
+ [U3,~]=create_UW(n,3);
+ OMEGA=create_OMEGA(n,3);
+ M{2}=spmat2sptensor(kron(speye(n),W2)*OMEGA.OMEGA1*U3);
+elseif order==4
+ M=cell(4,1);
+ [~,W2]=create_UW(n,2);
+ [~,W3]=create_UW(n,3);
+ [U4,~]=create_UW(n,4);
+ OMEGA=create_OMEGA(n,4);
+ if compress==1
+ M{2}=spmat2sptensor(kron(W2,W2)*(OMEGA.OMEGA2*U4)); OMEGA=rmfield(OMEGA,'OMEGA2');
+ M{3}=spmat2sptensor(kron(speye(n),W3)*(OMEGA.OMEGA3*U4)); OMEGA=rmfield(OMEGA,'OMEGA3');
+ [~,tempW]=create_UW(nchoosek(n+1,2),2);
+ M{4}=spmat2sptensor(tempW*kron(W2,W2)*(OMEGA.OMEGA4*U4));
+ elseif compress==0
+ M{2}=spmat2sptensor(kron(W2,W2)*(OMEGA.OMEGA2)); OMEGA=rmfield(OMEGA,'OMEGA2');
+ M{3}=spmat2sptensor(kron(speye(n),W3)*(OMEGA.OMEGA3)); OMEGA=rmfield(OMEGA,'OMEGA3');
+ [~,tempW]=create_UW(nchoosek(n+1,2),2);
+ M{4}=spmat2sptensor(tempW*kron(W2,W2)*(OMEGA.OMEGA4));
+ end
+elseif order==5
+ M=cell(6,1);
+ [~,W2]=create_UW(n,2);
+ [~,W3]=create_UW(n,3);
+ [U4,W4]=create_UW(n,4);
+ [U5,W5]=create_UW(n,5);
+ OMEGA=create_OMEGA(n,5);
+ if compress==1
+ M{1}=spmat2sptensor(kron(W4,speye(n))*U5);
+ M{2}=spmat2sptensor(kron(W3,W2)*OMEGA.OMEGA5*U5); OMEGA=rmfield(OMEGA,'OMEGA5');
+ M{3}=spmat2sptensor(kron(W2,W3)*OMEGA.OMEGA6*U5); OMEGA=rmfield(OMEGA,'OMEGA6');
+ [~,tempW]=create_UW(nchoosek(n+1,2),2);
+ M{4}=spmat2sptensor(kron(speye(n),tempW)*kron(kron(speye(n),W2),W2)*OMEGA.OMEGA7*U5); OMEGA=rmfield(OMEGA,'OMEGA7');
+ M{5}=spmat2sptensor(kron(speye(n),W4)*OMEGA.OMEGA8*U5); OMEGA=rmfield(OMEGA,'OMEGA8');
+ M{6}=spmat2sptensor(kron(W2,W3)*OMEGA.OMEGA9*U5); OMEGA=rmfield(OMEGA,'OMEGA9');
+
+ % elseif compress==0
+% M{2}=spmat2sptensor(kron(W2,W2)*(OMEGA.OMEGA2)); OMEGA=rmfield(OMEGA,'OMEGA2');
+% M{3}=spmat2sptensor(kron(speye(n),W3)*(OMEGA.OMEGA3)); OMEGA=rmfield(OMEGA,'OMEGA3');
+% [~,tempW]=create_UW(nchoosek(n+1,2),2);
+% M{4}=spmat2sptensor(tempW*kron(W2,W2)*(OMEGA.OMEGA4));
+ end
+else
+ error('order is 3 or 4 or 5');
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/coeffs2derivs.m b/105/replication_package/solution_methods/taylor_projection/coeffs2derivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..a2f4001de44b3614448f5da77e6b2910fa45bc20
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/coeffs2derivs.m
@@ -0,0 +1,71 @@
+function [ derivs0,derivs1,derivs2,derivs3,derivs4,derivs5 ] = coeffs2derivs( coeffs,c0,x0,model )
+%The function transforms the vector of unique polynomial coefficients (coeffs) into
+%derivatives at x0.
+
+derivs0=[];
+derivs1=[];
+derivs2=[];
+derivs3=[];
+derivs4=[];
+derivs5=[];
+
+n_b=model.n_b;
+n_x=model.n_x;
+order=model.order(1);
+
+W=model.W;
+
+coeffs=reshape(coeffs,[],n_b);
+newc0=x0;
+GH0=coeffs(:,1);
+if order==1
+ GH1=coeffs(:,2:1+n_x);
+ [ GH0,GH1 ] = shiftpoly( newc0,c0,[],GH0,GH1 );
+ derivs0=GH0;
+ derivs1=GH1;
+elseif order==2
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ [ GH0,GH1,GH2 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2 );
+ derivs0=GH0;
+ derivs1=GH1;
+ derivs2=reshape(GH2*2,[],n_x,n_x);
+elseif order==3
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ GH3=coeffs(:,2+n_x+model.unique2:1+n_x+model.unique2+model.unique3)*W{3};
+ [ GH0,GH1,GH2,GH3 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3 );
+ derivs0=GH0;
+ derivs1=GH1;
+ derivs2=reshape(GH2*2,[],n_x,n_x);
+ derivs3=reshape(GH3*6,[],n_x,n_x,n_x);
+elseif order==4
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ GH3=coeffs(:,2+n_x+model.unique2:1+n_x+model.unique2+model.unique3)*W{3};
+ GH4=coeffs(:,2+n_x+model.unique2+model.unique3:1+n_x+model.unique2+model.unique3+model.unique4)*W{4};
+ [ GH0,GH1,GH2,GH3,GH4 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3,GH4 );
+ derivs0=GH0;
+ derivs1=GH1;
+ derivs2=reshape(GH2*2,[],n_x,n_x);
+ derivs3=reshape(GH3*6,[],n_x,n_x,n_x);
+ derivs4=reshape(GH4*24,[],n_x,n_x,n_x,n_x);
+elseif order==5
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,nchoosek(n_x+1,1)+(1:nchoosek(n_x+1,2)))*W{2};
+ GH3=coeffs(:,nchoosek(n_x+2,2)+(1:nchoosek(n_x+2,3)))*W{3};
+ GH4=coeffs(:,nchoosek(n_x+3,3)+(1:nchoosek(n_x+3,4)))*W{4};
+ GH5=coeffs(:,nchoosek(n_x+4,4)+(1:nchoosek(n_x+4,5)))*W{5};
+ [ GH0,GH1,GH2,GH3,GH4,GH5 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3,GH4,GH5 );
+ derivs0=GH0;
+ derivs1=GH1;
+ derivs2=reshape(GH2*2,[],n_x,n_x);
+ derivs3=reshape(GH3*6,[],n_x,n_x,n_x);
+ derivs4=reshape(GH4*24,[],n_x,n_x,n_x,n_x);
+ derivs5=reshape(GH5*120,[],n_x,n_x,n_x,n_x,n_x);
+else
+ error('order must not be larger than 5')
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/compderivs.m b/105/replication_package/solution_methods/taylor_projection/compderivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..16136099e082fe8daff30c56aff20573bbbbbfd2
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/compderivs.m
@@ -0,0 +1,157 @@
+function [derivs,uncomp]=compderivs(f,x,order)
+
+% [derivs,uncomp,U,W]=compderivs(f,x,order) differentiates f with respect to x
+% serveral times (given by order). The differentiation is done in
+% a compressed manner, by exploiting sparsity and symmetry of mixed derivatives.
+% The function returns two cell arrays. The first output contains the
+% nonzero unique derivatives up to the order defined by the user. The
+% second array contains matrices that uncompress the nonzero unique derivatives
+% into the full arrays of derivatives. U and W are compress/uncompress
+% matrices to unique elements.
+%
+% For details on the compressed differentiation routine see:
+% Levintal, Oren, "Fifth Order Perturbation Solution to DSGE Models".
+%
+% Input arguments:
+% f - a symbolic scalar.
+% x - a symbolic vector.
+% order - the maximum order of derivatives. For example, order=3 returns
+% the first, second and third derivatives.
+%
+% Output arguments:
+% derivs - a cell array of the nonzero unique derivatives. For example,
+% derivs{1} is a symbolic vector of the nonzero first derivatives, derivs{2} is a
+% symbolic vector of the nonzero unique second derivatives and so on.
+% uncomp - a cell array of sparse matrices that are used to uncompress the
+% compressed derivatives. For example, the full array of second order
+% derivatives is obtained by uncomp{2}*derivs{2}.
+%
+% Example: f=x1^3*x2^4, and x=[x1,x2], both are symbolic variables.
+% [derivs,uncomp]=compderivs(f,x,3) returns the first, second and third
+% compressed derivatives. The full array of third derivatives is obtained
+% by uncomp{3}*derivs{3}. This array can be reshaped into a 2-by-2-by-2
+% array by the reshape function.
+% The i,j,l element of this array is the third derivative of f
+% w.r.t xi, xj and xl.
+%
+% This code can be used freely for non commercial purposes.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+n_x=length(x);
+derivs=cell(order,1);
+uncomp=cell(order,1);
+
+if n_x==1
+ tempderiv=f;
+ for k=1:order
+ tempderiv=jacobian(tempderiv,x);
+ derivs{k}=tempderiv;
+ if logical(tempderiv==0)
+ uncomp{k}=sparse(0);
+ else
+ uncomp{k}=sparse(1);
+ end
+ end
+else
+ tempderiv=jacobian(f,x);
+ tempderiv=tempderiv(:);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ tempind=find(nnztempderiv);
+ countdf=sparse(tempind,ones(length(tempind),1),ones(length(tempind),1),numel(tempderiv),1); % counts nonzero derivatives.
+ N1=sparse(tempind,1:sum(countdf),ones(1,sum(countdf)),n_x,sum(countdf));
+ uncomp{1}=N1;
+ derivs{1}=tempderiv(countdf==1);
+
+ for k=2:order
+ tempderiv=jacobian(derivs{k-1}, x);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ [i,j]=find(nnztempderiv);
+
+ countdf_short=sparse(i,j,ones(length(i),1),size(tempderiv,1),size(tempderiv,2));
+ countdf=uncomp{k-1}*countdf_short;
+ countdf=countdf(:);
+ if nnz(countdf)>0
+ [U,W]=create_UW(n_x,k,countdf);
+ N=sparse(find(countdf),1:sum(countdf),ones(1,sum(countdf)),n_x^k,sum(countdf));
+ tempmat=[U'*(N'*kron(speye(n_x),uncomp{k-1}))];
+ [i,j]=find(tempmat');
+ tempderiv=tempderiv(i);
+ [colM,rowM]=find(N);
+ [rowW,colW]=find(W);
+ tempuncomp=sparse(size(N,1),size(W,1));
+ tempeye=speye(size(W,1));
+ tempuncomp(colM,:)=tempeye(rowW,:);
+ else
+ tempderiv=sym(0);
+ tempuncomp=sparse(n_x^k,1);
+ end
+ derivs{k}=tempderiv;
+ uncomp{k}=tempuncomp;
+ end
+end
+
+end
+
+function [U,W]=create_UW(n,k,varargin)
+% [U,W]=create_UW(n,k) creates two sparse matrices, U and W, that compress and
+% uncompress a symmetric array A with k dimensions and n^k elements.
+% A(:)'*U is a row vector that contains the unique elements of A,
+% and A(:)'=(A(:)'*U)*W.
+% [U,W]=create_UW(n,k,N) creates matrices U and W of a sparse symmetric
+% array A with k dimensions and n^k elements. N is a vector of size n^k,
+% where N(j)=1 if A(j)~=0 and zero otherwise. If B is a row
+% vector with the nonzero elements of the row vector A(:)', then B*U
+% is a row vector of the unique nonzero elements of A, and B=(B*U)*W.
+%
+% This code can be used freely for non commercial purposes, provided that
+% it is not altered.
+%
+% (c) Oren Levintal, December 20, 2013
+
+if isempty(varargin)
+% nonzero=ones(n^k,1);
+ I=[1:n^k];
+else
+ nonzero=varargin{1};
+ I=find(nonzero);
+end
+
+if isempty(I)
+ error('The symmetric array is all zero')
+end
+
+I=I(:);
+% nonzero(nonzero~=0)=1; nonzero=nonzero(:);
+sizeM='n';
+subind='I1';
+for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+end
+
+eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+eval(['M=[' subind '];']);
+
+M=sort(M,2); % sort columns
+[M,I]=sortrows(M); % sort rows
+if size(M,1)==1
+ DM=1;
+else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+end
+group=cumsum(DM);
+minI=accumarray(group,I,[],@min);
+newi=minI(group);
+
+unique=newi(DM>0); % index of unique nonzero elements
+
+n_unique=length(unique);
+
+U= sparse(unique,[1:n_unique]',ones(n_unique,1),length(I),n_unique);
+
+W= sparse(group,I,ones(length(I),1),n_unique,length(I));
+
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/compderivs_u.m b/105/replication_package/solution_methods/taylor_projection/compderivs_u.m
new file mode 100644
index 0000000000000000000000000000000000000000..b87d0c1bc8cbb13d80162c7e7d40d31d8a6321ba
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/compderivs_u.m
@@ -0,0 +1,126 @@
+function [derivs,uncomp]=compderivs_u(f,x,order)
+% This is like compderivs except that the uncompression matrix returns a
+% column vector of the full derivative matrix where non-unique derivatives
+% are zeroed.
+%
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% Changed on July 31, 2016 by Oren Levintal (corrected mistake for all zero
+% derivatives for the case n_x=1)
+n_x=length(x);
+derivs=cell(order,1);
+uncomp=cell(order,1);
+
+if n_x==1
+ tempderiv=f;
+ for k=1:order
+ tempderiv=jacobian(tempderiv,x);
+ derivs{k}=tempderiv;
+ if logical(tempderiv==0)
+ uncomp{k}=sparse(0);
+ else
+ uncomp{k}=sparse(1);
+ end
+ end
+else
+ tempderiv=jacobian(f,x);
+ tempderiv=tempderiv(:);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ tempind=find(nnztempderiv);
+ countdf=sparse(tempind,ones(length(tempind),1),ones(length(tempind),1),numel(tempderiv),1); % counts nonzero derivatives.
+ N1=sparse(tempind,1:sum(countdf),ones(1,sum(countdf)),n_x,sum(countdf));
+ uncomp{1}=N1;
+ derivs{1}=tempderiv(countdf==1);
+
+ for k=2:order
+ tempderiv=jacobian(derivs{k-1}, x);
+
+ nnztempderiv=1-logical(tempderiv==0);
+ [i,j]=find(nnztempderiv);
+
+ countdf_short=sparse(i,j,ones(length(i),1),size(tempderiv,1),size(tempderiv,2));
+ countdf=uncomp{k-1}*countdf_short;
+ countdf=countdf(:);
+ if nnz(countdf)>0
+ [U,W]=create_UW(n_x,k,countdf);
+ N=sparse(find(countdf),1:sum(countdf),ones(1,sum(countdf)),n_x^k,sum(countdf));
+ tempmat=[U'*(N'*kron(speye(n_x),uncomp{k-1}))];
+ [i,j]=find(tempmat');
+ tempderiv=tempderiv(i);
+ [colM,rowM]=find(N);
+ [rowW,colW]=find(W);
+ tempuncomp=sparse(size(N,1),size(W,1));
+ tempeye=speye(size(W,1));
+ tempuncomp(colM,:)=(U*U')*tempeye(rowW,:);
+ else
+ tempderiv=sym(0);
+ tempuncomp=sparse(n_x^k,1);
+ end
+ derivs{k}=tempderiv;
+ uncomp{k}=tempuncomp;
+ end
+end
+
+end
+
+function [U,W]=create_UW(n,k,varargin)
+% [U,W]=create_UW(n,k) creates two sparse matrices, U and W, that compress and
+% uncompress a symmetric array A with k dimensions and n^k elements.
+% A(:)'*U is a row vector that contains the unique elements of A,
+% and A(:)'=(A(:)'*U)*W.
+% [U,W]=create_UW(n,k,N) creates matrices U and W of a sparse symmetric
+% array A with k dimensions and n^k elements. N is a vector of size n^k,
+% where N(j)=1 if A(j)~=0 and zero otherwise. If B is a row
+% vector with the nonzero elements of the row vector A(:)', then B*U
+% is a row vector of the unique nonzero elements of A, and B=(B*U)*W.
+%
+% This code can be used freely for non commercial purposes, provided that
+% it is not altered.
+%
+% (c) Oren Levintal, December 20, 2013
+
+if isempty(varargin)
+% nonzero=ones(n^k,1);
+ I=[1:n^k];
+else
+ nonzero=varargin{1};
+ I=find(nonzero);
+end
+
+if isempty(I)
+ error('The symmetric array is all zero')
+end
+
+I=I(:);
+% nonzero(nonzero~=0)=1; nonzero=nonzero(:);
+sizeM='n';
+subind='I1';
+for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+end
+
+eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+eval(['M=[' subind '];']);
+
+M=sort(M,2); % sort columns
+[M,I]=sortrows(M); % sort rows
+if size(M,1)==1
+ DM=1;
+else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+end
+group=cumsum(DM);
+minI=accumarray(group,I,[],@min);
+newi=minI(group);
+
+unique=newi(DM>0); % index of unique nonzero elements
+
+n_unique=length(unique);
+
+U= sparse(unique,[1:n_unique]',ones(n_unique,1),length(I),n_unique);
+
+W= sparse(group,I,ones(length(I),1),n_unique,length(I));
+
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/convert_to_matrices.m b/105/replication_package/solution_methods/taylor_projection/convert_to_matrices.m
new file mode 100644
index 0000000000000000000000000000000000000000..19c5165e4c84aa0977ba6636954149c22f3db618
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/convert_to_matrices.m
@@ -0,0 +1,280 @@
+if ~isempty(model.prefrows)
+
+ if approx>=1
+ prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+ prefv=changecols(prefv,tempv,n_v,1);
+ prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ Phiv_vec=changecols(Phiv_vec,model.Phivars,n_v_tp,1);
+ Phiv_vec=changecols(Phiv_vec,tempv,n_v,1);
+
+ [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phiv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ fv=sparse(double([prei;stochi;Phii]),double([prej;stochj;Phij]),double([prevals(:);stochvals(:);Phivals(:)]),n_f,n_v);
+ end
+ if approx>=2
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+ prefvv=changecols(prefvv,tempv,n_v,1);
+ prefvv=changecols(prefvv,tempv,n_v,2);
+ prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,1);
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,2);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,1);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,2);
+
+ [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f*n_v^2,1);
+ end
+ if approx>=3
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+ prefvvv=changecols(prefvvv,tempv,n_v,1);
+ prefvvv=changecols(prefvvv,tempv,n_v,2);
+ prefvvv=changecols(prefvvv,tempv,n_v,3);
+ prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,1);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,2);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,3);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,1);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,2);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,3);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f*n_v^3,1);
+ end
+ if approx>=4
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+ prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,4);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,4);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvvv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f*n_v^4,1);
+ end
+else
+ if approx>=1
+% prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+% prefv=changecols(prefv,tempv,n_v,1);
+% prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ Phiv_vec=changecols(Phiv_vec,model.Phivars,n_v_tp,1);
+ Phiv_vec=changecols(Phiv_vec,tempv,n_v,1);
+
+% [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phiv_vec));
+ Phii=Phii+n_f-n_x2;
+
+% fv=sparse(double([prei;stochi]),double([prej;stochj]),double([prevals(:);stochvals(:)]),n_f,n_v);
+ fv=sparse(double([stochi;Phii]),double([stochj;Phij]),double([stochvals(:);Phivals(:)]),n_f,n_v);
+ end
+ if approx>=2
+% prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+% prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+% prefvv=changecols(prefvv,tempv,n_v,1);
+% prefvv=changecols(prefvv,tempv,n_v,2);
+% prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,1);
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,2);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,1);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,2);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f*n_v^2,1);
+ end
+ if approx>=3
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+% prefvvv=changecols(prefvvv,tempv,n_v,1);
+% prefvvv=changecols(prefvvv,tempv,n_v,2);
+% prefvvv=changecols(prefvvv,tempv,n_v,3);
+% prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,1);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,2);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,3);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,1);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,2);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,3);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f*n_v^3,1);
+ end
+ if approx>=4
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+% prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,4);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,4);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvvv_vec));
+ Phii=Phii+n_f-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f*n_v^4,1);
+ end
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/convert_to_matrices_i.m b/105/replication_package/solution_methods/taylor_projection/convert_to_matrices_i.m
new file mode 100644
index 0000000000000000000000000000000000000000..3db7a9a9723b00f9b6346d2aae155f9450d9e4ac
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/convert_to_matrices_i.m
@@ -0,0 +1,370 @@
+if ~isempty(model.prefrows)
+
+ if approx>=1
+ prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+ prefv=changecols(prefv,tempv,n_v,1);
+ prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ Phiv_vec=changecols(Phiv_vec,model.Phivars,n_v_tp,1);
+ Phiv_vec=changecols(Phiv_vec,tempv,n_v,1);
+
+ [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phiv_vec));
+
+ temp=repmat((0:n_s-1)*double(prefv.tsize(1)),numel(prei),1);
+ prei=repmat(prei,n_s,1)+temp(:);
+ prej=repmat(prej,n_s,1);
+ prevals=prevals';
+ prevals=prevals(:);
+
+ temp=repmat((0:n_s-1)*double(stochfv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivals=Phivals(1,:);
+
+ Phii=Phii+n_f_all-n_x2;
+
+ fv=sparse(double([prei;stochi;Phii]),double([prej;stochj;Phij]),double([prevals(:);stochvals(:);Phivals(:)]),n_f_all,n_v);
+ end
+ if approx>=2
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+ prefvv=changecols(prefvv,tempv,n_v,1);
+ prefvv=changecols(prefvv,tempv,n_v,2);
+ prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,1);
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,2);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,1);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,2);
+
+ [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivv_vec));
+
+ temp=repmat((0:n_s-1)*double(prefvv.tsize(1)),numel(prei),1);
+ prei=repmat(prei,n_s,1)+temp(:);
+ prej=repmat(prej,n_s,1);
+ prevals=prevals';
+ prevals=prevals(:);
+
+ temp=repmat((0:n_s-1)*double(stochfvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivals=Phivals(1,:);
+
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f_all*n_v^2,1);
+ end
+ if approx>=3
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+ prefvvv=changecols(prefvvv,tempv,n_v,1);
+ prefvvv=changecols(prefvvv,tempv,n_v,2);
+ prefvvv=changecols(prefvvv,tempv,n_v,3);
+ prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,1);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,2);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,3);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,1);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,2);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,3);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvv_vec));
+
+ temp=repmat((0:n_s-1)*double(prefvvv.tsize(1)),numel(prei),1);
+ prei=repmat(prei,n_s,1)+temp(:);
+ prej=repmat(prej,n_s,1);
+ prevals=prevals';
+ prevals=prevals(:);
+
+ temp=repmat((0:n_s-1)*double(stochfvvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivals=Phivals(1,:);
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f_all*n_v^3,1);
+ end
+ if approx>=4
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+ prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,4);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,4);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvvv_vec));
+ temp=repmat((0:n_s-1)*double(prefvvvv.tsize(1)),numel(prei),1);
+ prei=repmat(prei,n_s,1)+temp(:);
+ prej=repmat(prej,n_s,1);
+ prevals=prevals';
+ prevals=prevals(:);
+
+ temp=repmat((0:n_s-1)*double(stochfvvvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivals=Phivals(1,:);
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([prei;stochi;Phii]);
+ allj=double([prej;stochj;Phij]);
+ allvals=double([prevals(:);stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f_all*n_v^4,1);
+ end
+else
+ if approx>=1
+% prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+% prefv=changecols(prefv,tempv,n_v,1);
+% prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ Phiv_vec=changecols(Phiv_vec,model.Phivars,n_v_tp,1);
+ Phiv_vec=changecols(Phiv_vec,tempv,n_v,1);
+
+% [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+
+ temp=repmat((0:n_s-1)*double(stochfv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phiv_vec.vals=Phiv_vec.vals(1,:);
+
+ [Phii,Phij,Phivals]=tfind(unfold(Phiv_vec));
+ Phii=Phii+n_f_all-n_x2;
+
+% fv=sparse(double([prei;stochi]),double([prej;stochj]),double([prevals(:);stochvals(:)]),n_f,n_v);
+ fv=sparse(double([stochi;Phii]),double([stochj;Phij]),double([stochvals(:);Phivals(:)]),n_f_all,n_v);
+ end
+ if approx>=2
+% prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+% prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+% prefvv=changecols(prefvv,tempv,n_v,1);
+% prefvv=changecols(prefvv,tempv,n_v,2);
+% prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,1);
+ Phivv_vec=changecols(Phivv_vec,model.Phivars,n_v_tp,2);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,1);
+ Phivv_vec=changecols(Phivv_vec,tempv,n_v,2);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+
+ temp=repmat((0:n_s-1)*double(stochfvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivv_vec.vals=Phivv_vec.vals(1,:);
+
+ [Phii,Phij,Phivals]=tfind(unfold(Phivv_vec));
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f_all*n_v^2,1);
+ end
+ if approx>=3
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+% prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+% prefvvv=changecols(prefvvv,tempv,n_v,1);
+% prefvvv=changecols(prefvvv,tempv,n_v,2);
+% prefvvv=changecols(prefvvv,tempv,n_v,3);
+% prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,1);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,2);
+ Phivvv_vec=changecols(Phivvv_vec,model.Phivars,n_v_tp,3);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,1);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,2);
+ Phivvv_vec=changecols(Phivvv_vec,tempv,n_v,3);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+ temp=repmat((0:n_s-1)*double(stochfvvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivvv_vec.vals=Phivvv_vec.vals(1,:);
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvv_vec));
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f_all*n_v^3,1);
+ end
+ if approx>=4
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+% prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+% prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+% prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,model.Phivars,n_v_tp,4);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,1);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,2);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,3);
+ Phivvvv_vec=changecols(Phivvvv_vec,tempv,n_v,4);
+
+
+% [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+ temp=repmat((0:n_s-1)*double(stochfvvvv_vec.tsize(1)),numel(stochi),1);
+ stochi=repmat(stochi,n_s,1)+temp(:);
+ stochj=repmat(stochj,n_s,1);
+ stochvals=stochvals';
+ stochvals=stochvals(:);
+
+ Phivvvv_vec.vals=Phivvvv_vec.vals(1,:);
+
+ [Phii,Phij,Phivals]=tfind(unfold(Phivvvv_vec));
+ Phii=Phii+n_f_all-n_x2;
+
+ alli=double([stochi;Phii]);
+ allj=double([stochj;Phij]);
+ allvals=double([stochvals(:);Phivals(:)]);
+
+ newi=sub2ind([n_f_all,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f_all*n_v^4,1);
+ end
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_GAMMA.m b/105/replication_package/solution_methods/taylor_projection/create_GAMMA.m
new file mode 100644
index 0000000000000000000000000000000000000000..65022ab16a8ba242d5e72e16756ec4ab40fb1a80
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_GAMMA.m
@@ -0,0 +1,61 @@
+function [ GAMMA ] = create_GAMMA( n_x,n_theta,varargin )
+%The function creates sparse matrices GAMMA1, GAMMA2, ...
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if length(varargin)==1
+ order_vec=varargin{1}; % do only specified order
+else
+ order_vec=2:3; % do all orders
+end
+
+for order=order_vec
+
+ if order==2
+ ind=1:n_x*n_x;
+ M=reshape(ind,n_x,n_x);
+ Ix=speye(n_x*n_x);
+ GAMMA.GAMMA1=Ix(:,ipermute(M,[2,1]))+Ix(:,ipermute(M,[1,2]));
+ end
+
+ if order==3
+ ind=1:n_x^3;
+ M=reshape(ind,n_x,n_x,n_x);
+ Ix=speye(n_x^3);
+ GAMMA.GAMMA2=Ix(:,ipermute(M,[3,2,1]))+Ix(:,ipermute(M,[2,3,1]))+Ix(:,ipermute(M,[1,3,2]));
+
+ GAMMA.GAMMA3=Ix(:,ipermute(M,[2,3,1]))+Ix(:,ipermute(M,[1,3,2]))+Ix(:,ipermute(M,[1,2,3]));
+
+ GAMMA.GAMMA4=Ix(:,ipermute(M,[2,3,1]))+Ix(:,ipermute(M,[1,3,2]))+Ix(:,ipermute(M,[1,2,3]));
+
+ GAMMA.GAMMA5=Ix(:,ipermute(M,[ 2,3,1 ]))+Ix(:,ipermute(M,[ 1,3,2 ]))+Ix(:,ipermute(M,[ 1,2,3 ]));
+ end
+ if order==4
+ ind=1:n_x^4;
+ M=reshape(ind,n_x,n_x,n_x,n_x);
+ Ix=speye(n_x^4);
+ GAMMA.GAMMA16=Ix+Ix(:,ipermute(M,[4,3,5,6]-2))+Ix(:,ipermute(M,[5,3,4,6]-2))+Ix(:,ipermute(M,[6,3,4,5]-2));
+
+ GAMMA.GAMMA2=Ix+Ix(:,ipermute(M,[5,4,3,6]-2))+Ix(:,ipermute(M,[6,4,3,5]-2))+Ix(:,ipermute(M,[5,3,4,6]-2))+Ix(:,ipermute(M,[6,3,4,5]-2))+Ix(:,ipermute(M,[6,5,4,3]-2));
+
+ GAMMA.GAMMA17=Ix+Ix(:,ipermute(M,[3,4,6,5]-2));
+
+ GAMMA.GAMMA3=Ix+Ix(:,ipermute(M,[ 6 4 5 3]-2))+Ix(:,ipermute(M,[ 6 3 5 4]-2))+Ix(:,ipermute(M,[ 6 3 4 5]-2));
+
+ GAMMA.GAMMA4=Ix+Ix(:,ipermute(M,[5,4,3,6]-2))+Ix(:,ipermute(M,[5,3,4,6]-2));
+
+ GAMMA.GAMMA18=Ix+Ix(:,ipermute(M,[5,6,3,4]-2));
+
+
+% GAMMA.GAMMA3=1(:,ipermute(M,[2,3,1]))+Ix(:,ipermute(M,[1,3,2]))+Ix(:,ipermute(M,[1,2,3]));
+%
+% GAMMA.GAMMA4=Ix(:,ipermute(M,[2,3,1]))+Ix(:,ipermute(M,[1,3,2]))+Ix(:,ipermute(M,[1,2,3]));
+%
+% GAMMA.GAMMA5=Ix(:,ipermute(M,[ 2,3,1 ]))+Ix(:,ipermute(M,[ 1,3,2 ]))+Ix(:,ipermute(M,[ 1,2,3 ]));
+ end
+
+end
+
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/create_OMEGA.m b/105/replication_package/solution_methods/taylor_projection/create_OMEGA.m
new file mode 100644
index 0000000000000000000000000000000000000000..5d52e9f9310d08448e201238c59af2041fccb56c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_OMEGA.m
@@ -0,0 +1,53 @@
+function [ OMEGA ] = create_OMEGA( n_x,varargin )
+%The function creates sparse matrices OMEGA1,..,OMEGA9, that are used for
+%the high-order multivariate chain rules described in Levintal, Oren,
+%"Fifth Order Perturbation Solution to DSGE Models", 2014.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if length(varargin)==1
+ order=varargin{1}; % do only specified order
+else
+ order=0; % do orders 3,4,5
+end
+
+if order==3 || order==0
+ ind=[1:n_x^3];
+ M=reshape(ind,1,n_x,n_x,n_x);
+ Ix=speye(n_x^3);
+ OMEGA.OMEGA1=Ix(:,ipermute(M,[1,3,4,2]))+Ix(:,ipermute(M,[1,2,4,3]))+Ix(:,ipermute(M,[1,2,3,4]));
+end
+
+if order==4 || order==0
+ ind=[1:n_x^4];
+ M=reshape(ind,1,n_x,n_x,n_x,n_x);
+ Ix=speye(n_x^4);
+ OMEGA.OMEGA2=Ix(:,ipermute(M,[1,4,5,3,2]))+Ix(:,ipermute(M,[1,3,5,4,2]))+Ix(:,ipermute(M,[1,2,5,4,3]))...
+ +Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]));
+ OMEGA.OMEGA3=Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]))+Ix(:,ipermute(M,[1,2,3,4,5]));
+ OMEGA.OMEGA4=Ix(:,ipermute(M,[1,3,4,2,5]))+Ix(:,ipermute(M,[1,2,4,3,5]))+Ix(:,ipermute(M,[1,2,3,4,5]));
+end
+
+if order==5 || order==0
+ ind=[1:n_x^5];
+ M=reshape(ind,1,n_x,n_x,n_x,n_x,n_x);
+ Ix=speye(n_x^5);
+ OMEGA.OMEGA5=Ix(:,ipermute(M,[1,5,6,4,3,2]))+Ix(:,ipermute(M,[1,4,6,5,3,2]))+Ix(:,ipermute(M,[1,3,6,5,4,2]))+Ix(:,ipermute(M,[1,2,6,5,4,3]))...
+ +Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))...
+ +Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))+Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]));
+ OMEGA.OMEGA6=Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))+Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))...
+ +Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]))+Ix(:,ipermute(M,[1,3,4,5,6,2]))...
+ +Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]));
+ OMEGA.OMEGA7=Ix(:,ipermute(M,[1,4,5,3,6,2]))+Ix(:,ipermute(M,[1,3,5,4,6,2]))+Ix(:,ipermute(M,[1,2,5,4,6,3]))...
+ +Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))...
+ +Ix(:,ipermute(M,[1,4,5,2,6,3]))+Ix(:,ipermute(M,[1,3,5,2,6,4]))+Ix(:,ipermute(M,[1,2,5,3,6,4]))...
+ +Ix(:,ipermute(M,[1,3,4,2,6,5]))+Ix(:,ipermute(M,[1,2,4,3,6,5]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))...
+ +Ix(:,ipermute(M,[1,3,4,2,5,6]))+Ix(:,ipermute(M,[1,2,4,3,5,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
+ OMEGA.OMEGA8=Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
+ OMEGA.OMEGA9=Ix(:,ipermute(M,[1,3,4,5,2,6]))+Ix(:,ipermute(M,[1,2,4,5,3,6]))+Ix(:,ipermute(M,[1,2,3,5,4,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]))...
+ +Ix(:,ipermute(M,[1,3,4,6,2,5]))+Ix(:,ipermute(M,[1,2,4,6,3,5]))+Ix(:,ipermute(M,[1,2,3,6,4,5]))...
+ +Ix(:,ipermute(M,[1,2,5,6,3,4]))+Ix(:,ipermute(M,[1,3,5,6,2,4]))+Ix(:,ipermute(M,[1,4,5,6,2,3]));
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/create_OMEGA_x.m b/105/replication_package/solution_methods/taylor_projection/create_OMEGA_x.m
new file mode 100644
index 0000000000000000000000000000000000000000..467868e50ad9ddc14fd930528bce1bcd3b074574
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_OMEGA_x.m
@@ -0,0 +1,22 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+OMEGA_x=[];
+if approx>=3
+ tempOMEGA = create_OMEGA( n_x,3 );
+ OMEGA_x.OMEGA1=tempOMEGA.OMEGA1;
+end
+
+if approx>=4
+ tempOMEGA = create_OMEGA( n_x,4 );
+ OMEGA_x.OMEGA2=tempOMEGA.OMEGA2;
+ OMEGA_x.OMEGA3=tempOMEGA.OMEGA3;
+ OMEGA_x.OMEGA4=tempOMEGA.OMEGA4;
+end
+if approx>=5
+ tempOMEGA = create_OMEGA( n_x,5 );
+ OMEGA_x.OMEGA5=tempOMEGA.OMEGA5;
+ OMEGA_x.OMEGA6=tempOMEGA.OMEGA6;
+ OMEGA_x.OMEGA7=tempOMEGA.OMEGA7;
+ OMEGA_x.OMEGA8=tempOMEGA.OMEGA8;
+ OMEGA_x.OMEGA9=tempOMEGA.OMEGA9;
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_UW.m b/105/replication_package/solution_methods/taylor_projection/create_UW.m
new file mode 100644
index 0000000000000000000000000000000000000000..0560026cde9504572ee1e2a37619c85cea3f2563
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_UW.m
@@ -0,0 +1,59 @@
+function [U,W]=create_UW(n,k,varargin)
+% [U,W]=create_UW(n,k) creates two sparse matrices, U and W, that compress and
+% uncompress a symmetric array A with k dimensions and n^k elements.
+% A(:)'*U is a row vector that contains the unique elements of A,
+% and A(:)'=(A(:)'*U)*W.
+% [U,W]=create_UW(n,k,N) creates matrices U and W of a sparse symmetric
+% array A with k dimensions and n^k elements. N is a vector of size n^k,
+% where N(j)=1 if A(j)~=0 and zero otherwise. If B is a row
+% vector with the nonzero elements of the row vector A(:)', then B*U
+% is a row vector of the unique nonzero elements of A, and B=(B*U)*W.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(varargin)
+% nonzero=ones(n^k,1);
+ I=[1:n^k];
+else
+ nonzero=varargin{1};
+ I=find(nonzero);
+end
+
+if isempty(I)
+ error('The symmetric array is all zero')
+end
+
+I=I(:);
+% nonzero(nonzero~=0)=1; nonzero=nonzero(:);
+sizeM='n';
+subind='I1';
+for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+end
+
+eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+eval(['M=[' subind '];']);
+
+M=sort(M,2); % sort columns
+[M,I]=sortrows(M); % sort rows
+if size(M,1)==1
+ DM=1;
+else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+end
+group=cumsum(DM);
+minI=accumarray(group,I,[],@min);
+newi=minI(group);
+
+unique=newi(DM>0); % index of unique nonzero elements
+
+n_unique=length(unique);
+
+U= sparse(unique,[1:n_unique]',ones(n_unique,1),length(I),n_unique);
+
+W= sparse(group,I,ones(length(I),1),n_unique,length(I));
+
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/create_X.m b/105/replication_package/solution_methods/taylor_projection/create_X.m
new file mode 100644
index 0000000000000000000000000000000000000000..df1172f62163c91f578fafb07244cd8ce8a3b5c4
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_X.m
@@ -0,0 +1,52 @@
+function [X,Xx,Xxx,Xxxx,Xxxxx,Xxxxxx]=create_X(N,n_x,x,c0,W2,unique2,W3,unique3,W4,unique4)
+% compute the basis function and its derivatives
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% extended to 4th order on January 19, 2017.
+
+Xx=[];Xxx=[]; Xxxx=[]; Xxxxx=[]; Xxxxxx=[];
+if N==0
+ X=1;
+ Xx=sparse(1,n_x);
+elseif N>=1
+ x_c0=sparse(x-c0);
+ X=[1;x_c0];
+ Xx=[sparse(1,n_x);speye(n_x)];
+end
+if N==1
+ Xxx=sparse(1+n_x,n_x^2);
+elseif N>=2
+ tempx=reshape(reshape(W2,unique2*n_x,n_x)*x_c0,unique2,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+ Xx=[Xx;2*tempx];
+ Xxx=[sparse(1+n_x,n_x^2);2*W2];
+end
+if N==2
+ Xxxx=sparse(1+n_x+unique2,n_x^3);
+elseif N>=3
+ tempxx=reshape(reshape(W3,unique3*n_x^2,n_x)*x_c0,unique3,n_x^2);
+ tempx=reshape(reshape(tempxx,unique3*n_x,n_x)*x_c0,unique3,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+ Xx=[Xx;3*tempx];
+ Xxx=[Xxx;6*tempxx];
+ Xxxx=[sparse(1+n_x+unique2,n_x^3);6*W3];
+end
+if N==3
+ Xxxxx=sparse(1+n_x+unique2+unique3,n_x^4);
+elseif N>=4
+ tempxxx=reshape(reshape(W4,unique4*n_x^3,n_x)*x_c0,unique4,n_x^3);
+ tempxx=reshape(reshape(tempxxx,unique4*n_x^2,n_x)*x_c0,unique4,n_x^2);
+ tempx=reshape(reshape(tempxx,unique4*n_x,n_x)*x_c0,unique4,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+ Xx=[Xx;4*tempx];
+ Xxx=[Xxx;12*tempxx];
+ Xxxx=[Xxxx;24*tempxxx];
+ Xxxxx=[sparse(1+n_x+unique2+unique3,n_x^4);24*W4];
+end
+if N==4
+ Xxxxxx=sparse(1+n_x+unique2+unique3+unique4,n_x^5);
+end
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_X_no_derivs.m b/105/replication_package/solution_methods/taylor_projection/create_X_no_derivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..3df79da6c226da099cde0fa742f37c44c5204145
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_X_no_derivs.m
@@ -0,0 +1,28 @@
+function [X]=create_X_no_derivs(N,n_x,x,c0,W2,unique2,W3,unique3,W4,unique4)
+% compute the basis function and its derivatives
+%
+% � Copyright, Oren Levintal, April 25, 2017.
+
+
+x_c0=sparse(x-c0);
+X=[1;x_c0];
+if N>=2
+ tempx=reshape(reshape(W2,unique2*n_x,n_x)*x_c0,unique2,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+end
+if N>=3
+ tempxx=reshape(reshape(W3,unique3*n_x^2,n_x)*x_c0,unique3,n_x^2);
+ tempx=reshape(reshape(tempxx,unique3*n_x,n_x)*x_c0,unique3,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+end
+if N>=4
+ tempxxx=reshape(reshape(W4,unique4*n_x^3,n_x)*x_c0,unique4,n_x^3);
+ tempxx=reshape(reshape(tempxxx,unique4*n_x^2,n_x)*x_c0,unique4,n_x^2);
+ tempx=reshape(reshape(tempxx,unique4*n_x,n_x)*x_c0,unique4,n_x);
+ temp=tempx*x_c0;
+ X=[X;temp];
+end
+
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_X_tensor.m b/105/replication_package/solution_methods/taylor_projection/create_X_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..c82d72f01d99995c2bdd01e802b57985f6c32121
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_X_tensor.m
@@ -0,0 +1,65 @@
+function [X,Xx,Xxx,Xxxx,Xxxxx,Xxxxxx,ind]=create_X_tensor(N,x_c0,M2,M3,M3x,W2,W3,M4,M4x,M4xx,M4xxx,unique2,unique3,unique4,ind,n_ind,maxload,sum)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on January 23, 2017 - extended to 4th order
+if isempty(ind)
+ ind=cell(9,1);
+end
+n_x=x_c0.tsize(1);
+
+Xx=[];Xxx=[]; Xxxx=[]; Xxxxx=[]; Xxxxxx=[];
+n_s=size(x_c0.vals,1);
+temp=sptensor(1);
+temp.vals=repmat(temp.vals,n_s,1);
+X=temp;
+if N==0
+ Xx=sptensor(1,n_x,n_s);
+elseif N>=1
+ X=vconcat(X,x_c0);
+
+ Ix=spteye(n_x,n_s);
+ Xx=vconcat(sptensor(1,n_x,n_s),Ix);
+end
+if N==1
+ Xxx=sptensor(1+n_x,n_x^2,n_s);
+elseif N>=2
+ [temp,ind{1}]=contraction2(M2,x_c0,x_c0,ind{1},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+ twoW2=multscalar(W2,2);
+ twoW2.vals=repmat(twoW2.vals,n_s,1);
+ [tempx,ind{2}]=contraction2(twoW2,x_c0,Ix,ind{2},n_ind,maxload,sum);
+ Xx=vconcat(Xx,unfold(tempx));
+ Xxx=vconcat(sptensor(1+n_x,n_x^2,n_s),unfold(twoW2));
+end
+if N==2
+ Xxxx=sptensor(1+n_x+unique2,n_x^3,n_s);
+elseif N>=3
+ [temp,ind{3}]=contraction3(M3,x_c0,x_c0,x_c0,ind{3},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+ [tempx,ind{4}]=contraction3(M3x,x_c0,x_c0,Ix,ind{4},n_ind,maxload,sum);
+ Xx=vconcat(Xx,unfold(tempx));
+ Ix6=multscalar(Ix,6);
+ [tempxx,ind{5}]=contraction3(W3,x_c0,Ix,Ix6,ind{5},n_ind,maxload,sum);
+
+ Xxx=vconcat(Xxx,unfold(tempxx));
+ sixW3=multscalar(W3,6);
+ sixW3.vals=repmat(sixW3.vals,n_s,1);
+ Xxxx=vconcat(sptensor(1+n_x+unique2,n_x^3,n_s),unfold(sixW3));
+end
+if N==3
+ Xxxxx=sptensor(1+n_x+unique2+unique3,n_x^4,n_s);
+elseif N>=4
+ [temp,ind{6}]=contraction4(M4,x_c0,x_c0,x_c0,x_c0,ind{6},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+ [tempx,ind{7}]=contraction4(M4x,x_c0,x_c0,x_c0,Ix,ind{7},n_ind,maxload,sum);
+ Xx=vconcat(Xx,unfold(tempx));
+ [tempxx,ind{8}]=contraction4(M4xx,x_c0,x_c0,Ix,Ix,ind{8},n_ind,maxload,sum);
+ Xxx=vconcat(Xxx,unfold(tempxx));
+ [tempxxx,ind{9}]=contraction4(M4xxx,x_c0,Ix,Ix,Ix,ind{9},n_ind,maxload,sum);
+ Xxxx=vconcat(Xxxx,unfold(tempxxx));
+ M4xxx.vals=repmat(M4xxx.vals,n_s,1);
+ Xxxxx=vconcat(sptensor(1+n_x+unique2+unique3,n_x^4,n_s),unfold(M4xxx));
+end
+if N==4
+ Xxxxxx=sptensor(1+n_x+unique2+unique3+unique4,n_x^5,n_s);
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_X_tensor_no_derivs.m b/105/replication_package/solution_methods/taylor_projection/create_X_tensor_no_derivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..94f316bad34f375b1c76ae0ff77e6a2b908700cd
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_X_tensor_no_derivs.m
@@ -0,0 +1,32 @@
+function [X,ind]=create_X_tensor_no_derivs(N,x_c0,M2,M3,M4,ind,n_ind,maxload,sum)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(ind)
+ ind=cell(5,1);
+end
+n_x=x_c0.tsize(1);
+
+n_s=size(x_c0.vals,1);
+temp=sptensor(1);
+temp.vals=repmat(temp.vals,n_s,1);
+X=temp;
+
+if N>=1
+ X=vconcat(X,x_c0);
+end
+
+if N>=2
+ [temp,ind{1}]=contraction2(M2,x_c0,x_c0,ind{1},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+end
+
+if N>=3
+ [temp,ind{3}]=contraction3(M3,x_c0,x_c0,x_c0,ind{3},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+end
+
+if N>=4
+ [temp,ind{4}]=contraction4(M4,x_c0,x_c0,x_c0,x_c0,ind{4},n_ind,maxload,sum);
+ X=vconcat(X,unfold(temp));
+end
diff --git a/105/replication_package/solution_methods/taylor_projection/create_compression_matrices_nonzero2.m b/105/replication_package/solution_methods/taylor_projection/create_compression_matrices_nonzero2.m
new file mode 100644
index 0000000000000000000000000000000000000000..0cdec71d9d0d1c647fa4e6fb8066c48d52ed50b5
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/create_compression_matrices_nonzero2.m
@@ -0,0 +1,77 @@
+function [UW]=create_compression_matrices_nonzero2(approx,n_x)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if approx>=2
+ k=2;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x);
+ nonzero(end,1:end-1)=0;
+ nonzero(1:end-1,end)=0;
+ [U2,W2]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N2=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U2=N2*U2;
+ W2=W2*N2';
+end
+
+if approx>=3
+ k=3;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end)=0;
+ [U3,W3]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N3=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U3=N3*U3;
+ W3=W3*N3';
+end
+
+if approx>=4
+ k=4;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,end)=0;
+ [U4,W4]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N4=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U4=N4*U4;
+ W4=W4*N4';
+end
+
+if approx>=5
+ k=5;
+ nonzero=reshape(ones(1,n_x^k),n_x,n_x,n_x,n_x,n_x);
+ nonzero(end,1:end-1,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,end,1:end-1,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,end,1:end-1,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,end,1:end-1)=0;
+ nonzero(1:end-1,1:end-1,1:end-1,1:end-1,end)=0;
+ [U5,W5]=create_UW(n_x,k,nonzero(:));
+ nnz=find(nonzero);
+ N5=sparse(nnz,1:length(nnz),ones(1,length(nnz)),n_x^k,length(nnz));
+ U5=N5*U5;
+ W5=W5*N5';
+end
+
+if approx==1
+ UW=struct([]);
+elseif approx==2
+ UW.U2=U2; UW.W2=W2;
+elseif approx==3
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+elseif approx==4
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+ UW.U4=U4; UW.W4=W4;
+elseif approx==5
+ UW.U2=U2; UW.W2=W2;
+ UW.U3=U3; UW.W3=W3;
+ UW.U4=U4; UW.W4=W4;
+ UW.U5=U5; UW.W5=W5;
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/derivs2coeffs.m b/105/replication_package/solution_methods/taylor_projection/derivs2coeffs.m
new file mode 100644
index 0000000000000000000000000000000000000000..d0b549a13f8ea7bdf56edfcef48b7a9876f7a406
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/derivs2coeffs.m
@@ -0,0 +1,26 @@
+function [ coeffs ] = derivs2coeffs( model,G0,varargin )
+%The function converts derivatives into a column of unique Taylor
+%coefficients.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=length(varargin);
+coeffs=G0(:);
+n_y=length(coeffs);
+
+if order>=1
+ temp=reshape(varargin{1},n_y,[]);
+ n_x=size(temp,2);
+ coeffs=[coeffs,temp];
+end
+
+for k=2:order
+ U=model.U{k};
+ temp=reshape(varargin{k},n_y,[])*U/factorial(k);
+ coeffs=[coeffs,temp];
+end
+
+coeffs=coeffs(:);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/diff_fun.m b/105/replication_package/solution_methods/taylor_projection/diff_fun.m
new file mode 100644
index 0000000000000000000000000000000000000000..8a2e0b7e7a36f9efefa57d87fec057387c318241
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/diff_fun.m
@@ -0,0 +1,204 @@
+function model=diff_fun(f,x,symparams,order,varargin)
+
+% This file differentiates the symbolic function f w.r.t
+% the symbolic vector x up to order and returns data used to compute those
+% derivatives.
+%
+% � Copyright, Oren Levintal, September 8, 2017.
+
+model.n_params=numel(symparams);
+
+f=sym(f(:));
+
+x=sym(x(:));
+
+
+% SIZE VARIABLES
+n_f=length(f); n_x=length(x);
+v=x(:);
+n_v=length(v);
+
+if order>5
+ error('differentiation is allowed up to fifth order')
+end
+model.order=order;
+
+% fname
+
+if nargin>4
+ fname=varargin{3};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ fname='';
+end
+
+model.fname=fname;
+
+% DEFINE pi_ and u
+if isempty(varargin)
+ pi_=sym([]);
+ u=sym([]);
+elseif isempty(varargin{1})
+ warning('no substitutions assumed')
+ pi_=sym([]);
+ u=sym([]);
+else
+ pi_=varargin{1}; % pi_ is the function pi(v,u)
+ pi_=pi_(:);
+ u=varargin{2}; % auxiliary variables that are eventually substituted out
+ u=u(:);
+ if ~isequal(sort(u),unique(u))
+ error('substituted variables are not uniquely determined')
+ end
+end
+
+% check that all symbolic variables/parameters are defined
+actualsymvars=symvar([f;pi_]);
+for i=1:length(actualsymvars)
+ if isempty(v(v==actualsymvars(i))) && isempty(u(u==actualsymvars(i))) && isempty(symparams(symparams==actualsymvars(i)))
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+end
+
+n_u=length(u);
+model.n_u=n_u;
+tilf=f; % tilf(v,u) is a function of v and u
+n=find_n(pi_,u); % number of substitutions needed to eliminate u
+
+% Identify variables that affect u
+u_v=u; %u_v which is u as a function of v only u(v)
+uu=eye(n_u); % matrix to store which of u affect u
+uv=zeros(n_u,n_v);
+for k=1:n
+ u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+ uu=uu+logical(jacobian(u_v,u)~=0); % uu is a n_u-by-n_u matrix. the ij element is zero only if ui is independent of uj through all substitutions
+ uv=uv+logical(jacobian(u_v,v)~=0); % uv is a n_u-by-n_v matrix. the ij element is zero only if ui is independent of vj through all substitutions
+end
+
+fv=logical(logical(jacobian(tilf,v)~=0)+logical(jacobian(tilf,u)~=0)*uv~=0); % logical Jacobian of f w.r.t v
+fvars=find(sum(1-logical(fv==0),1));
+
+currentFolder=pwd;
+if ~exist([pwd '\fun_' fname], 'dir')
+ mkdir(['fun_' fname]);
+end
+
+cd(['fun_' fname])
+
+% Create an m file for u
+gen_fun_vec(u_v,symparams,v,'u','row');
+
+% build z and find the Jacobian of z
+z=[v;u];
+n_z=n_v+n_u;
+zz=[eye(n_v),zeros(n_v,n_u);uv,uu];
+for i=1:n_z
+ temp=zz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ zz(i,:)=temp;
+end
+zz=intarray(zz);
+model.maxzz=intarray(max(zz(:)));
+
+% build fv similar to zz
+fv=double(fv);
+for i=1:n_f
+ temp=fv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ fv(i,:)=temp;
+end
+model.fv=fv;
+
+tilfz=jacobian(tilf,z);
+
+% build tilfz
+tilfz=double(logical(tilfz~=0)); % only direct effects
+for i=1:n_f
+ temp=tilfz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilfz(i,:)=temp;
+end
+model.tilfz=tilfz;
+model.maxtilfz=intarray(max(tilfz(:)));
+
+% Create an m file for tilf
+tilfzvars=find(sum(1-logical(tilfz==0),1));
+model.tilfzvars=tilfzvars; % variables in z that affect tilf
+gen_fun_vec(tilf,symparams,z(tilfzvars),['tilf' fname],'row');
+
+% Differentiate PI and create m files
+
+PI=[v;pi_];
+
+[model.PI_ind_u]=getderivs_tensor(PI,z,order,symparams,'PI');
+
+fuvars=find(sum(uu(logical(sum(logical(jacobian(tilf,u)~=0),1)~=0),:),1));
+model.fuvars=fuvars;
+
+fzvars=[fvars,n_v+fuvars];
+model.n_fzvars=length(fzvars);
+
+[model.tilf_ind_u,model.pre_n]=gen_chainderivs_tensor(tilf,v,u,pi_,order,symparams,['tilf' fname]);
+
+% Store variables in struct model
+model.fvars=fvars;
+model.fzvars=fzvars;
+
+model.n_f=n_f;
+model.n_x=n_x;
+
+model.n_v=n_v;
+model.n_z=n_z;
+model.n_u=n_u;
+
+model.n_ind=1;
+
+% calculate some big matrices now
+
+if order>=3
+ save('tempfile')
+ n_fvars=length(fvars);
+ clearvars -except n_fvars
+
+ if n_fvars>0
+ [ tempM ] = chainsM( n_fvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.fvars_chain4c_M2=tempM{2};
+ model.fvars_chain4c_M3=tempM{3};
+ model.fvars_chain4c_M4=tempM{4};
+ clear tempM
+ delete('tempfile.mat')
+end
+
+if order>=4
+ save('tempfile')
+ n_fvars=length(fvars);
+ clearvars -except n_fvars
+
+ if n_fvars>0
+ [ tempM ] = chainsM( n_efvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.fvars_chain5c_M1=tempM{1};
+ model.fvars_chain5c_M2=tempM{2};
+ model.fvars_chain5c_M3=tempM{3};
+ model.fvars_chain5c_M4=tempM{4};
+ model.fvars_chain5c_M5=tempM{5};
+ model.fvars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+ delete('tempfile.mat')
+end
+
+rehash;
+
+
+cd(currentFolder)
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/diff_fun2.m b/105/replication_package/solution_methods/taylor_projection/diff_fun2.m
new file mode 100644
index 0000000000000000000000000000000000000000..f1725461595b2edfcffbec8f8bf2a1b859359e3e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/diff_fun2.m
@@ -0,0 +1,349 @@
+function model=diff_fun2(f,x,symparams,order,varargin)
+
+model.n_params=numel(symparams);
+
+f=sym(f(:));
+x=sym(x(:));
+
+% SIZE VARIABLES
+n_f=length(f); n_x=length(x);
+v=[x(:)];
+n_v=length(v);
+
+model.order=[order];
+
+% fname
+
+if nargin==7
+ fname=varargin{3};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ fname='new';
+end
+model.fname=fname;
+
+% DEFINE pi_ and u
+if isempty(varargin)
+ pi_=sym([]);
+ u=sym([]);
+elseif isempty(varargin{1})
+ warning('no substitutions assumed')
+ pi_=sym([]);
+ u=sym([]);
+else
+ pi_=varargin{1}; % pi_ is the function pi(v,u)
+ pi_=pi_(:);
+ u=varargin{2}; % auxiliary variables that are eventually substituted out
+ u=u(:);
+ if length(pi_)~=length(u)
+ error('wrong size of substituted variables or functions')
+ end
+ if ~isequal(sort(u),unique(u))
+ error('substituted variables are not uniquely determined')
+ end
+end
+
+% check that all symbolic variables/parameters are defined
+actualsymvars=symvar([f;pi_]);
+for i=1:length(actualsymvars)
+ if isempty(v(v==actualsymvars(i))) && isempty(u(u==actualsymvars(i))) && isempty(symparams(symparams==actualsymvars(i)))
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+end
+
+n_u=length(u);
+model.n_u=n_u;
+tilf=f; % tilf(v,u) is a function of v and u
+% [n,u_v]=find_n(pi_,u); % number of substitutions needed to eliminate u
+n=find_n_new(pi_,u);
+
+% Identify variables that affect u
+uu=eye(n_u); % matrix to store which of u affect u
+uv=zeros(n_u,n_v);
+
+piu0=double(logical(jacobian(pi_,u)~=0));
+piv0=double(logical(jacobian(pi_,v)~=0));
+piu=piu0;
+piv=piv0;
+
+for k=1:n
+ uu=uu+piu;
+ uv=uv+piv;
+ piv=piu*piv0;
+ piu=piu*piu0;
+end
+% uu_=uu;
+% uv_=uv;
+% % older version
+% u_v=u; %u_v which is u as a function of v only u(v)
+% uu=eye(n_u); % matrix to store which of u affect u
+% uv=zeros(n_u,n_v);
+% for k=1:n
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+% uu=uu+logical(jacobian(u_v,u)~=0); % uu is a n_u-by-n_u matrix. the ij element is zero only if ui is independent of uj through all substitutions
+% uv=uv+logical(jacobian(u_v,v)~=0); % uv is a n_u-by-n_v matrix. the ij element is zero only if ui is independent of vj through all substitutions
+% end
+
+% Identify stochasic and predetermined functions and variables
+% if n_x2>0
+% stochexog=find(sum(1-logical(eta(n_x1+1:end,:)==0),2)); % stochastic exogenous variables
+% else
+% stochexog=[];
+% end
+% preexog=1:n_x2;
+% preexog(stochexog)=[]; % predetermined exogenous variables
+%
+% stochvars=[1:n_y,2*n_y+n_x1+stochexog']; % all stochastic variables
+fv=ones(n_f,n_v);
+% fv=logical(logical(jacobian(tilf,v)~=0)+logical(jacobian(tilf,u)~=0)*uv~=0); % logical Jacobian of f w.r.t v
+
+% stochfrows=find(sum( 1-logical(fv(:,stochvars)==0),2)); % stochastic rows of f
+prefrows=1:n_f;
+% prefrows(stochfrows)=[]; % predetermined rows of f
+
+% variables that affect the predetermined and stochastic rows of f
+
+prefvars=find(sum(1-logical(fv(prefrows,:)==0),1));
+% stochfvars=find(sum(1-logical(fv(stochfrows,:)==0),1));
+
+
+currentFolder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+
+cd 'files'
+
+% generate a function that computes eta
+% gen_fun_vec(eta(:),[],symparams,'eta','row');
+
+
+% Create an m file for Phi and its derivatives w.r.t x
+% gen_fun_vec(Phi,symparams,x,'Phi','row');
+% if order>=1
+% model.Phi_indc=getderivs_c(Phi,x,max(order,pert_order),symparams,'Phi');
+% end
+
+% Create an m file for u
+% newuv=jacobian(u_v,v); % calculate uv again
+newuv=uv;
+% stochurows=find(sum( 1-logical(newuv(:,stochvars)==0),2)); % stochastic rows of u
+% model.stochurows=stochurows;
+preurows=1:n_u;
+% preurows(stochurows)=[]; % predetermined rows of u
+model.preurows=preurows;
+preuvars=find(sum( logical(newuv(preurows,:)~=0),1)); % variables of predetermined rows of u
+% stochuvars=find(sum( logical(newuv(stochurows,:)~=0),1)); % variables of stochastic rows of u
+gen_fun_vec_subs(u(preurows),symparams,v(preuvars),pi_,u,[fname 'u'],'row');
+% gen_fun_vec(u_v(stochurows),symparams,v(stochuvars),'stochu','row');
+model.preuvars=preuvars;
+% model.stochuvars=stochuvars;
+
+% build z and find the Jacobian of z
+z=[v;u];
+n_z=n_v+n_u;
+zz=[eye(n_v),zeros(n_v,n_u);uv,uu];
+for i=1:n_z
+ temp=zz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ zz(i,:)=temp;
+end
+zz=intarray(zz);
+model.maxzz=intarray(max(zz(:)));
+
+% build fv similar to zz
+fv=double(fv);
+for i=1:n_f
+ temp=fv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ fv(i,:)=temp;
+end
+model.fv=fv;
+
+tilfz=jacobian(tilf,z);
+
+% build tilfz
+tilfz=double(logical(tilfz~=0)); % only direct effects
+for i=1:n_f
+ temp=tilfz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilfz(i,:)=temp;
+end
+model.tilfz=tilfz;
+model.maxtilfz=intarray(max(tilfz(:)));
+
+% Create an m file for tilf
+pretilfzvars=find(sum(1-logical(tilfz(prefrows,:)==0),1));
+model.pretilfzvars=pretilfzvars; % variables in z that affect pretilf
+gen_fun_vec(tilf(prefrows),symparams,z(pretilfzvars),[fname 'f'],'row');
+
+% stochtilfzvars=find(sum(1-logical(tilfz(stochfrows,:)==0),1));
+% model.stochtilfzvars=stochtilfzvars; % variables in z that affect stochtilf
+% gen_fun_vec(tilf(stochfrows),symparams,z(stochtilfzvars),['stochtilf' fname],'row');
+
+% Differentiate PI and create m files
+
+PI=[v;pi_];
+prePI=PI;
+% prePI(n_v+stochurows)=0; % stochastic rows of PI are set to zero. Note: the first n_v rows include stochastic variables but their derivatives w.r.t are ones or zeros.
+% stochPI=PI;
+% stochPI([1:n_v,n_v+preurows])=0; % nonstochastic rows are set to zero. See the note above.
+
+[model.prePI_ind_u]=getderivs_tensor(prePI,z,order,symparams,[fname 'PI']);
+% [model.stochPI_ind_u]=getderivs_tensor(stochPI,z,max(order+1,pert_order),symparams,'stochPI');
+
+prefuvars=find(sum(uu(logical(sum(logical(jacobian(tilf(prefrows),u)~=0),1)~=0),:),1));
+% stochfuvars=find(sum(uu(logical(sum(logical(jacobian(tilf(stochfrows),u)~=0),1)~=0),:),1));
+model.prefuvars=prefuvars;
+% model.stochfuvars=stochfuvars;
+
+prefzvars=[prefvars,n_v+prefuvars];
+% stochfzvars=[stochfvars,n_v+stochfuvars];
+model.n_prefzvars=length(prefzvars);
+% model.n_stochfzvars=length(stochfzvars);
+
+% [model.stochtilf_ind_u,model.stoch_n]=gen_chainderivs_tensor(tilf(stochfrows),v(stochfvars),u(stochfuvars),pi_(stochfuvars),max(order+1,pert_order),symparams,['stochtilf' fname]);
+[model.pretilf_ind_u,model.pre_n]=gen_chainderivs_tensor(tilf(prefrows),v(prefvars),u(prefuvars),pi_(prefuvars),order,symparams,[fname 'tilf']);
+
+
+% Store variables in struct model
+model.prefrows=prefrows;
+% model.stochfrows=stochfrows;
+model.prefvars=prefvars;
+% model.stochfvars=stochfvars;
+% model.stochexog=stochexog;
+% model.preexog=preexog;
+% model.n_stochexog=length(stochexog);
+% model.n_preexog=length(preexog);
+% model.stochfzvars=stochfzvars;
+model.prefzvars=prefzvars;
+
+% model.n_theta=n_theta;
+% model.n_b=n_b;
+
+model.n_f=n_f;
+model.n_x=n_x;
+% model.n_y=n_y;
+% model.n_x1=n_x1;
+% model.n_x2=n_x2;
+
+model.n_v=n_v;
+model.n_z=n_z;
+model.n_u=n_u;
+
+model.n_ind=1;
+
+% model.U=cell(4,1);
+% model.W=cell(4,1);
+% for i=2:order+1
+% [model.U{i},model.W{i}]=create_UW(n_x,i);
+% end
+
+% model.stochzz=zz(model.stochfzvars,model.stochfzvars);
+model.prezz=zz(model.prefzvars,model.prefzvars);
+
+% model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+model.pretilfz=tilfz(model.prefrows,model.prefzvars);
+
+% calculate some big matrices now
+
+if order>=4
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+% save('tempfile')
+%
+%
+%
+% n_stochfvars=length(stochfvars);
+% clearvars -except n_stochfvars
+%
+% if n_stochfvars>0
+% [ tempM ] = chainsM( n_stochfvars,4 );
+% else
+% tempM=cell(4,1);
+% end
+% load('tempfile')
+% model.stochfvars_chain4c_M2=tempM{2};
+% model.stochfvars_chain4c_M3=tempM{3};
+% model.stochfvars_chain4c_M4=tempM{4};
+% clear tempM
+ delete('tempfile.mat')
+end
+
+if order>=5
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.prefvars_chain5c_M1=tempM{1};
+ model.prefvars_chain5c_M2=tempM{2};
+ model.prefvars_chain5c_M3=tempM{3};
+ model.prefvars_chain5c_M4=tempM{4};
+ model.prefvars_chain5c_M5=tempM{5};
+ model.prefvars_chain5c_M6=tempM{6};
+
+ clear tempM
+% save('tempfile')
+%
+%
+%
+% n_stochfvars=length(stochfvars);
+% clearvars -except n_stochfvars
+%
+% if n_stochfvars>0
+% [ tempM ] = chainsM( n_stochfvars,5 );
+% else
+% tempM=cell(6,1);
+% end
+% load('tempfile')
+% model.stochfvars_chain5c_M1=tempM{1};
+% model.stochfvars_chain5c_M2=tempM{2};
+% model.stochfvars_chain5c_M3=tempM{3};
+% model.stochfvars_chain5c_M4=tempM{4};
+% model.stochfvars_chain5c_M5=tempM{5};
+% model.stochfvars_chain5c_M6=tempM{6};
+%
+% clear tempM
+ delete('tempfile.mat')
+end
+
+% totindi=5+8;
+% totindi=totindi+(model.pre_n-1)*(1+3+4+6)+1+4+6+9;
+% totindi=totindi+3;
+% totindi=totindi+4;
+% totindi=totindi+2;
+% totindi=totindi+2;
+% totindi=totindi+1;
+% totindi=totindi+9;
+% totindi=totindi+8;
+% totindi=totindi+8+(model.stoch_n-1)*(1+3+4+6)+1+4+6+9;
+% totindi=totindi+2;
+% totindi=totindi+9;
+% totindi=totindi+7;
+%
+% model.totindi=totindi;
+
+rehash;
+
+
+cd(currentFolder)
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/disp_fun_vec.m b/105/replication_package/solution_methods/taylor_projection/disp_fun_vec.m
new file mode 100644
index 0000000000000000000000000000000000000000..ea03df6b4ca4d040da6886846aac3a1cba960697
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/disp_fun_vec.m
@@ -0,0 +1,49 @@
+function R=disp_fun_vec(fun_string,fun_sym,i,fid)
+%disp_fun breaks a function into several lines if the length of the function is
+%larger than 1000 characters.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+texp=char(fun_sym);
+
+texp=strrep(texp,'*','.*');
+texp=strrep(texp,'/','./');
+texp=strrep(texp,'^','.^');
+if length(texp)<1000
+ R=[fun_string '(' num2str(i) ',:)=' texp ';'];
+ fprintf(fid,'%s\n',R);
+ texp='';
+else
+ itexp=1000;
+ while strcmp(texp(itexp),'+')+strcmp(texp(itexp),'-')+strcmp(texp(itexp),'*')+strcmp(texp(itexp),'/')==0 && itexp1
+ error('only 1 regime is allowed')
+ end
+
+ msparams=msparams';
+
+ paramsvec=repmat(params(:)',model.n_regimes,1); % n_regimes*n_regimes,[]
+
+ s=repmat(regime,model.n_regimes,1);
+ sp=(1:model.n_regimes)';
+ paramsvec=[paramsvec,msparams(s,:),msparams(sp,:)]; %n_s,n_sp,n_params
+
+ paramsvec=[paramsvec,zeros(model.n_regimes,model.n_logicalparams)];
+
+ coeffs=reshape(full(coeffs),model.n_theta,model.n_regimes);
+ coeffsvec=coeffs(:,s)';
+ coeffspvec=coeffs(:,sp)';
+
+ x0vec=repmat(x0(:)',model.n_regimes,1);
+ c0vec=repmat(c0(:)',model.n_regimes,1);
+
+ nep=full(nep);
+ P=full(P);
+
+ [R0,g,h1,nPhi,nu_vec,model]=eval_model_vec(coeffsvec,x0vec,model,paramsvec,c0vec,nep,P,coeffspvec);
+
+ ny=reshape(g.vals,1,model.n_regimes,[]);
+ ny=ny(:,1,:);
+ g=squeeze(ny);
+
+ nx1=reshape(h1.vals,1,model.n_regimes,[]);
+ nx1=nx1(:,1,:);
+ h1=squeeze(nx1);
+
+ if model.hybrid==0
+ nPhi=reshape(nPhi,1,model.n_regimes,[]);
+ nPhi=nPhi(:,1,:);
+ nPhi=squeeze(nPhi);
+ else
+ nPhi=permute(reshape(nPhi,model.n_regimes,model.n_x2,n_nodes),[2,1,3]);
+% nPhi=nPhi(:,1,:);
+ nPhi=reshape(nPhi,model.n_x2,model.n_regimes,n_nodes);
+ end
+
+ n_nodes=length(P);
+ nu_vec=reshape(nu_vec,n_nodes,model.n_regimes,model.n_u); % n_nodes,sp,n_u
+ nu_vec=permute(nu_vec,[3,2,1]);
+ % sum across sp
+ R0=reshape(R0,1,model.n_regimes,[]);
+ R0=R0.*reshape(repmat(transition(regime,:),1,size(R0,3)),1,model.n_regimes,size(R0,3));
+
+ R0=reshape(sum(R0,2),1,[]);
+
+ R0=R0(:);
+
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/eval_modelMS_vec.m b/105/replication_package/solution_methods/taylor_projection/eval_modelMS_vec.m
new file mode 100644
index 0000000000000000000000000000000000000000..b2f9010b3de6e17801a383173de02c8598bdabe6
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/eval_modelMS_vec.m
@@ -0,0 +1,181 @@
+function [R0,g,h1,nPhi,nu_vec,model]=eval_modelMS_vec(coeffs,x0,model,params,msparams,transition,c0,nep,P,varargin)
+
+% INPUTS:
+% coeffs (n_s,n_endog*n_b*n_regimes,n_regimes)
+% x0 (n_s,n_x)
+% params (n_s,n_params)
+% msparams (n_msparams,n_regimes)
+
+% if size(coeffs,1)~=model.n_theta || size(coeffs,2)~=model.n_regimes
+% message=sprintf(['The first argument is wrong. The initial guess should be a ' num2str(model.n_theta) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of polynomial coefficients per regime is ' num2str(model.n_theta) ' and the number of regimes is ' num2str(model.n_regimes)'.']);
+% error(message);
+% end
+% x0=x0(:);
+% if length(x0)~=model.n_x
+% error(['The second argument is wrong. The approximation point should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+% end
+% if ~isstruct(model)
+% error('The third argument is wrong. It should be a structure generated by prepare_tpMS.')
+% elseif ~isfield(model,'n_x')
+% error('The third argument is wrong. It should be a structure generated by prepare_tpMS.')
+% end
+% params=params(:);
+% if length(params)~=model.n_params_no_ms
+% error(['The fourth argument is wrong. The number of model parameters should be ' num2str(model.n_params_no_ms) '.'])
+% end
+% if isempty(msparams)
+% msparams=zeros(0,model.n_regimes);
+% end
+% if size(msparams,1)~=model.n_msparams || size(msparams,2)~=model.n_regimes
+% error(sprintf(['The fifth argument is wrong. It should be a ' num2str(model.n_msparams) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of Markov switching parameters is ' num2str(model.n_msparams) ' and the number of regimes is ' num2str(model.n_regimes) '.']))
+% end
+% if size(transition,1)~=model.n_regimes || size(transition,2)~=model.n_regimes
+% error(['The sixth argument is wrong. The transition matrix should have ' num2str(model.n_regimes) ' rows and columns.'])
+% end
+% c0=c0(:);
+% if length(c0)~=model.n_x
+% error(['The seventh argument is wrong. The center of the approximating polynomial should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+% end
+% if size(nep,1)~=model.n_e
+% error(['The eighth argument is wrong. It should be a matrix with ' num2str(model.n_e) ' rows (=the number of shocks).'])
+% end
+% P=P(:);
+% if size(nep,2)~=length(P)
+% error('The eighth or ninth arguments are wrong. The number of columns in the eighth argument should be equal to the number of elements in the ninth argument.')
+% end
+
+% if isempty(varargin)
+
+if numel(x0)==model.n_x && numel(coeffs)==model.n_theta*model.n_regimes && numel(params)==model.n_params
+ n_s=1;
+else % x0,coeffs,params have a row dimension of 1 or n_s
+ temp=[size(x0,1),size(coeffs,1),size(params,1),size(c0,1)];
+ n_s=max(temp);
+ if min(temp)~=n_s
+ error('incompatible s dimension')
+ end
+end
+
+% if ~isequal(x0,c0)
+% error('x0 must be equal to c0')
+% end
+
+% msparams should have n_regimes columns
+
+if size(msparams,2)~=model.n_regimes
+ error('msparams should have n_regimes columns')
+end
+
+msparams=msparams'; %n_regimes,n_msparams
+
+paramsvec=reshape(repmat(params(:)',model.n_regimes^2,1),model.n_regimes^2*n_s,[]); % n_regimes*n_regimes,n_s*n_params
+
+[s,sp]=ndgrid([1:model.n_regimes],[1:model.n_regimes]);
+s=s(:);
+sp=sp(:);
+paramsvec=[paramsvec,repmat([msparams(s,:),msparams(sp,:)],n_s,1)];
+
+coeffs=reshape(full(coeffs),n_s*model.n_theta,model.n_regimes);
+coeffsvec=coeffs(:,s);
+coeffsvec=reshape(coeffsvec,n_s,model.n_theta,model.n_regimes^2);
+coeffsvec=permute(coeffsvec,[3,1,2]);
+coeffsvec=reshape(coeffsvec,model.n_regimes^2*n_s,[]);
+
+coeffspvec=coeffs(:,sp);
+coeffspvec=reshape(coeffspvec,n_s,model.n_theta,model.n_regimes^2);
+coeffspvec=permute(coeffspvec,[3,1,2]);
+coeffspvec=reshape(coeffspvec,model.n_regimes^2*n_s,[]);
+
+
+x0vec=repmat(x0(:)',model.n_regimes^2,1); %n_regimes^2,n_s*n_x
+x0vec=reshape(x0vec,model.n_regimes^2*n_s,[]); %n_regimes^2*n_s,n_x
+c0vec=repmat(c0(:)',model.n_regimes^2,1); %n_regimes^2,n_s*n_x
+c0vec=reshape(c0vec,model.n_regimes^2*n_s,[]); %n_regimes^2*n_s,n_x
+
+nep=full(nep);
+P=full(P);
+% row dimensions should be n_regimes*n_regimes*n_s
+
+ [R0,g,h1,nPhi,nu_vec,model]=eval_model_vec(coeffsvec,x0vec,model,paramsvec,c0vec,nep,P,coeffspvec);
+
+ ny=reshape(g.vals,model.n_regimes,model.n_regimes,n_s,[]);
+ ny=ny(:,1,:,:);
+ g=reshape(ny,model.n_regimes,n_s,model.n_y);
+ g=permute(g,[2,3,1]); %n_s,n_y,n_regimes
+
+ nx1=reshape(h1.vals,model.n_regimes,model.n_regimes,n_s,[]);
+ nx1=nx1(:,1,:,:);
+ h1=reshape(nx1,model.n_regimes,n_s,model.n_x1);
+ h1=permute(h1,[2,3,1]);
+
+ nPhi=reshape(nPhi,model.n_regimes,model.n_regimes,n_s,[]);
+ nPhi=nPhi(:,1,:,:);
+ nPhi=reshape(nPhi,model.n_regimes,n_s,model.n_x2);
+ nPhi=permute(nPhi,[2,3,1]);
+
+ n_nodes=length(P);
+ nu_vec=reshape(nu_vec,n_nodes,model.n_regimes,model.n_regimes,n_s,model.n_u); % n_nodes,s,sp,n_s,n_u
+ nu_vec=permute(nu_vec,[4,5,1,2,3]);
+
+ % sum across sp
+ R0=reshape(R0,model.n_regimes,model.n_regimes,[]);
+ R0=R0.*reshape(repmat(transition,1,size(R0,3)),model.n_regimes,model.n_regimes,size(R0,3));
+ R0=reshape(sum(R0,2),model.n_regimes,n_s,[]);
+ R0=permute(R0,[2,3,1]);
+ R0=reshape(R0,n_s,[]);
+
+% R0=R0(:);
+
+% else
+%
+% regime=varargin{1};
+% if numel(regime)>1
+% error('only 1 regime is allowed')
+% end
+%
+% msparams=msparams';
+%
+% paramsvec=repmat(params(:)',model.n_regimes,1); % n_regimes*n_regimes,[]
+%
+% s=repmat(regime,model.n_regimes,1);
+% sp=(1:model.n_regimes)';
+% paramsvec=[paramsvec,msparams(s,:),msparams(sp,:)]; %n_s,n_sp,n_params
+%
+% coeffs=reshape(full(coeffs),model.n_theta,model.n_regimes);
+% coeffsvec=coeffs(:,s)';
+% coeffspvec=coeffs(:,sp)';
+%
+% x0vec=repmat(x0(:)',model.n_regimes,1);
+% c0vec=repmat(c0(:)',model.n_regimes,1);
+%
+% nep=full(nep);
+% P=full(P);
+%
+% [R0,g,h1,nPhi,nu_vec,model]=eval_model_vec(coeffsvec,x0vec,model,paramsvec,c0vec,nep,P,coeffspvec);
+%
+% ny=reshape(g.vals,1,model.n_regimes,[]);
+% ny=ny(:,1,:);
+% g=squeeze(ny);
+%
+% nx1=reshape(h1.vals,1,model.n_regimes,[]);
+% nx1=nx1(:,1,:);
+% h1=squeeze(nx1);
+%
+% nPhi=reshape(nPhi,1,model.n_regimes,[]);
+% nPhi=nPhi(:,1,:);
+% nPhi=squeeze(nPhi);
+%
+% n_nodes=length(P);
+% nu_vec=reshape(nu_vec,n_nodes,model.n_regimes,model.n_u); % n_nodes,sp,n_u
+% nu_vec=permute(nu_vec,[3,2,1]);
+% % sum across sp
+% R0=reshape(R0,1,model.n_regimes,[]);
+% R0=R0.*reshape(repmat(transition(regime,:),1,size(R0,3)),1,model.n_regimes,size(R0,3));
+%
+% R0=reshape(sum(R0,2),1,[]);
+%
+% R0=R0(:);
+%
+% end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/eval_model_vec.m b/105/replication_package/solution_methods/taylor_projection/eval_model_vec.m
new file mode 100644
index 0000000000000000000000000000000000000000..83e2d9ebce9b967823d9bdc3245d8bbdc3dca586
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/eval_model_vec.m
@@ -0,0 +1,293 @@
+function [R0,g,h1,nPhi,nu_vec,model]=eval_model_vec(coeffs,x0,model,params,c0,nep,P,varargin)
+% The function evaluates the model residuals of tpvec.
+%
+% � Copyright, Oren Levintal, October 21, 2016.
+
+order=model.order(1);
+
+ms=0; % no Markov Switching
+if ~isempty(varargin)
+ coeffsp=varargin{1};
+ if ~isempty(coeffsp)
+ ms=1; % Markov Switching model
+ end
+end
+
+if numel(x0)==model.n_x && numel(coeffs)==model.n_theta && numel(params)==model.n_params
+ n_s=1;
+else % x0,coeffs,params have a row dimension of 1 or n_s
+ temp=[size(x0,1),size(coeffs,1),size(params,1),size(c0,1)];
+ n_s=max(temp);
+ if min(temp)~=n_s
+ error('incompatible s dimension')
+ end
+end
+
+% make sure all inputs are full
+coeffsvec=full(reshape(coeffs,n_s,model.n_theta));
+x0vec=full(reshape(x0,n_s,model.n_x));
+
+paramsvec=full(reshape(params,n_s,model.n_params));
+
+if model.hybrid==1 || model.hybrid==3
+ paramsvec=[zeros(n_s,model.n_e),paramsvec];
+end
+
+% eta=full(eta);
+if model.hybrid==0 || model.hybrid==1
+ etavec=eta_fun(paramsvec,[]);
+else
+ etavec=zeros(n_s,model.n_x*model.n_e);
+end
+etavec=reshape(full(etavec),n_s*model.n_x,[]);
+
+c0vec=full(reshape(c0,n_s,model.n_x));
+nep=full(nep);
+P=full(P);
+
+params=paramsvec;
+P=P(:);
+
+n_f=model.n_f; % no. of model conditions
+n_x=model.n_x; % no. of state variables
+n_y=model.n_y; % no. of control variables
+n_x2=model.n_x2; % no. of exogenous state variables
+n_x1=model.n_x1; % no. of endogenous state variabels
+n_v=model.n_v; % total no. of variables v=(yp,y,xp,x)
+n_theta=model.n_theta; % no. of Polynomial coefficients
+n_b=model.n_b; % no. of terms in the basis function
+n_nodes=size(nep,2); % no. nodes in the discrete shocks
+n_z=model.n_z; % no. of auxiliary variables
+n_e=model.n_e;
+
+n_prefrows=length(model.prefrows);
+n_stochfrows=length(model.stochfrows);
+
+n_params=model.n_params;
+
+if model.hybrid==1 || model.hybrid==3
+ n_params=n_params+n_e; % shocks are treated as parameters
+end
+
+coeffs=reshape(coeffsvec,n_s,[],n_b);
+
+% current state
+nx=x0vec;
+
+nx_c0_vec=x0vec-c0vec;
+nx_c0=sptensor(nx_c0_vec(1,:)'); % convert to 1D tensor
+nx_c0.vals=nx_c0_vec; % assign the correct values in vals.
+
+if ~isfield(model,'M2')
+ model.M2=[];
+ model.M3=[];
+ model.M3x=[];
+ model.TW2=[];
+ model.TW3=[];
+ model.M4=[];
+ model.M4x=[];
+ model.M4xx=[];
+ model.M4xxx=[];
+ if order>=2
+ model.M2=fold(spmat2sptensor(model.W{2}*model.W{2}'*model.U{2}'),n_x,n_x);
+ model.TW2=fold(spmat2sptensor(model.W{2}),n_x,n_x);
+ model.TW2U2=spmat2sptensor(model.W{2}*model.U{2});
+ end
+ if order>=3
+ model.M3=fold(spmat2sptensor(model.W{3}*model.W{3}'*model.U{3}'),n_x,n_x,n_x);
+ model.M3x=fold(spmat2sptensor(3*model.W{3}*kron(model.W{2}'*model.U{2}',speye(n_x))),n_x,n_x,n_x);
+ model.TW3=fold(spmat2sptensor(model.W{3}),n_x,n_x,n_x);
+ model.TW3U3=spmat2sptensor(model.W{3}*model.U{3});
+ end
+ if order>=4
+ model.M4=fold(spmat2sptensor(model.W{4}*model.W{4}'*model.U{4}'),n_x,n_x,n_x,n_x);
+ model.M4x=fold(spmat2sptensor(4*model.W{4}*kron(model.W{3}'*model.U{3}',speye(n_x))),n_x,n_x,n_x,n_x);
+ model.M4xx=fold(spmat2sptensor(12*model.W{4}*kron(model.W{2}'*model.U{2}',speye(n_x^2))),n_x,n_x,n_x,n_x);
+ model.M4xxx=fold(spmat2sptensor(24*model.W{4}),n_x,n_x,n_x,n_x);
+ end
+end
+
+[X_vecT]=create_X_tensor_no_derivs(order,nx_c0,...
+model.M2,model.M3,model.M4,[],model.n_ind,n_s,'vec');
+
+gh_coeffs=reshape(coeffs,n_s,(n_y+n_x1),n_b);
+% g_coeffs=reshape(gh_coeffs(:,1:n_y,:),n_s*n_y,n_b);
+
+gh_coeffsT=sptensor(ones(n_y+n_x1,n_b));
+tempvals=gh_coeffs; %n_s,n_y+n_x1,n_b
+tempvals=permute(tempvals,[1,3,2]); % n_s,n_b,n_y+n_x1
+tempvals=reshape(tempvals,n_s,n_b*(n_y+n_x1));
+gh_coeffsT.vals=tempvals;
+
+[gh1]=contraction1(gh_coeffsT,X_vecT,[],model.n_ind,n_s,'vec');
+
+g=takerows(gh1,1:n_y);
+h1=takerows(gh1,n_y+(1:n_x1));
+
+% control vars
+ny=g.vals;
+
+% expected values:
+
+% The residual function R is calculated in two steps. The first step
+% calculates the nonstochastic (predetermined) rows of f (pref). The second step calculates
+% the expected value of the stochastic rows of f (stochf).
+
+% Step 1. predetermined equations (pref)
+
+% preallocate
+h=zeros(n_s,n_x);
+
+% build h(x)
+
+h(:,1:n_x1)=h1.vals; % predetermined endogenous state vars
+
+if model.hybrid==0
+ nPhi=Phi_fun(nx,params);
+ h(:,n_x1+1:end)=nPhi; % expected value of exogenous state vars. shocks are added later
+end
+
+% next period state
+nxp=h;
+
+% evaluate residuals R0
+nv=[zeros(n_s,n_y),ny,nxp,nx]; % all variables with zeros for the stochastic vars.
+
+n_u=model.n_u;
+nu=zeros(n_s,n_u);
+npreu=preu_fun(nv(:,model.preuvars),params); % all predetermined u
+nu(:,model.preurows)=npreu;
+nz=[nv,nu];
+params(:,model.logical_params_loc)=double(logical(nz(:,model.logical_zvars)>=0));
+
+fname=['pretilf' model.fname '_fun'];
+pref=feval(fname,nz(:,model.pretilfzvars),params); % since i already have z, i use pretilf to evaluate f.
+
+preR0=pref;
+
+% Step 2. expected value of stochastic equations (stochf)
+
+% vectorized expressions
+%create stochy: index of future control variables that affect stochastic equations
+if isempty(model.stochfrows)
+ EstochR0=zeros(n_s,0);
+ nu_vec=reshape(repmat(nu(:)',n_nodes,1),n_nodes*n_s,[]);
+
+else
+ nx_vec=repmat(nx(:)',n_nodes,1); % n_nodes=the number of nodes of the discrete shocks.
+ nx_vec=reshape(nx_vec,n_nodes*n_s,[]);
+
+ % next period state
+ % next period state
+ if model.hybrid==0
+ nxp_vec=repmat(h(:),1,n_nodes)+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ elseif model.hybrid==1
+ h_vec=repmat(h(:),1,n_nodes); %n_s*n_x,n_nodes
+
+ params_vec=[repmat(nep',n_s,1),reshape(repmat(reshape(params(:,n_e+1:end),1,[]),n_nodes,1),n_nodes*n_s,[])]; %n_nodes*n_s,n_params
+ uname=['Phi' model.uname '_fun'];
+ tempvars=[nx,ny,nu(:,model.preurows)]; %n_s,n_x+n_y
+ tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+ Phi_vec=feval(uname,tempvars,params_vec); %n_s*n_nodes,n_x2
+ Phi_vec=permute(reshape(Phi_vec,n_s,n_nodes,n_x2),[1,3,2]); %n_s,n_x2,n_nodes
+ nPhi=Phi_vec;
+ h_vec=reshape(h_vec,n_s,n_x,n_nodes);
+ h_vec(:,n_x1+1:end,:)=Phi_vec; % expected value of exogenous state vars. shocks are added later
+ h_vec=reshape(h_vec,n_s*n_x,n_nodes);
+ nxp_vec=h_vec+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ elseif model.hybrid==3
+ h_vec=repmat(h(:),1,n_nodes); %n_s*n_x,n_nodes
+
+ params_vec=[repmat(nep',n_s,1),reshape(repmat(reshape(params(:,n_e+1:end),1,[]),n_nodes,1),n_nodes*n_s,[])]; %n_nodes*n_s,n_params
+ uname=['Phi' model.uname '_fun'];
+ tempvars=nz(:,model.Phizvars); %n_s,n_x+n_y
+ tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_nodes*n_s,n_x+n_y+n_preurows
+ Phi_vec=feval(uname,tempvars,params_vec); %n_nodes*n_s,n_x2
+ Phi_vec=permute(reshape(Phi_vec,n_nodes,n_s,n_x2),[2,3,1]); %n_s,n_x2,n_nodes
+ nPhi=Phi_vec;
+ h_vec=reshape(h_vec,n_s,n_x,n_nodes);
+ h_vec(:,n_x1+1:end,:)=Phi_vec;
+ h_vec=reshape(h_vec,n_s*n_x,n_nodes);
+ nxp_vec=h_vec+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ end
+
+ nxp_c0_vec=nxp_vec-reshape(repmat(c0vec,1,n_nodes),n_s*n_x,n_nodes);
+
+ nxp_vec_permuted=reshape(permute(reshape(nxp_vec,n_s,n_x,n_nodes),[3,1,2]),n_nodes*n_s,n_x);
+
+ tempxp=1:n_x;
+ tempxp=tempxp(:);
+ nxp_c0=sptensor(tempxp); % convert to 1D tensor
+ tempvals=reshape(nxp_c0_vec,n_s,n_x,n_nodes);
+ tempvals=permute(tempvals,[3,1,2]);
+ tempvals=reshape(tempvals,n_nodes*n_s,n_x);
+ nxp_c0.vals=tempvals; % assign the correct values in vals.
+
+
+[Xp_vecT]=create_X_tensor_no_derivs(order,nxp_c0,...
+ model.M2,model.M3,model.M4,[],model.n_ind,n_s*n_nodes,'vec');
+
+tempv=zeros(n_v,1);
+tempv(model.stochfvars)=model.stochfvars;
+tempv(n_y+1:end)=0;
+stochy=nonzeros(tempv);
+n_stochy=length(stochy);
+% stochg_coeffs=coeffs(:,stochy,:);
+if ms==0
+ stochg_coeffs=coeffs(:,stochy,:);
+else
+ coeffspvec=full(reshape(coeffsp,n_s,[],n_b));
+ stochg_coeffs=coeffspvec(:,stochy,:);
+end
+ stochg_coeffsT=sptensor(ones(n_stochy,n_b));
+ tempvals=stochg_coeffs; %n_s,n_stochy,n_b
+ tempvals=permute(tempvals,[1,3,2]); % n_s,n_b,n_stochy
+ tempvals=repmat(tempvals(:)',n_nodes,1); % n_nodes,n_s*n_b*n_stochy
+ tempvals=reshape(tempvals,n_nodes*n_s,n_b*n_stochy);
+ stochg_coeffsT.vals=tempvals;
+
+ [stochgp_vecT]=contraction1(stochg_coeffsT,Xp_vecT,[],model.n_ind,n_s*n_nodes,'vec');
+
+ gp_vec=changerows(stochgp_vecT,stochy,n_y);
+ temp=zeros(n_nodes*n_s,n_y);
+ temp(:,stochy)=gp_vec.vals;
+ gp_vec=temp; % n_nodes*n_s,n_y
+
+% control vars in t+1
+nyp_vec=gp_vec;
+
+% evaluate residuals R0
+ nv_vec=[nyp_vec,reshape(repmat(ny(:)',n_nodes,1),n_nodes*n_s,[]),nxp_vec_permuted,nx_vec];
+
+% nstochv_vec=nv_vec(stochfvars,:); % stochastic vars.
+
+ if model.hybrid==0
+ params_vec=reshape(repmat(params(:)',n_nodes,1),n_nodes*n_s,n_params);
+ end
+
+ nstochu_vec=stochu_fun(nv_vec(:,model.stochuvars),params_vec); % all stochastic u vars
+ nu_vec=reshape(repmat(nu(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ nu_vec(:,model.stochurows)=nstochu_vec;
+ nz_vec=[nv_vec,nu_vec];
+ params_vec(:,model.logical_params_loc)=double(logical(nz_vec(:,model.logical_zvars)>=0));
+
+ fname=['stochtilf' model.fname '_fun'];
+ stochf_vec=feval(fname,nz_vec(:,model.stochtilfzvars),params_vec);
+
+
+ EstochR0=P'*reshape(stochf_vec,n_nodes,[]); %expected value of stochR0
+ EstochR0=reshape(EstochR0,n_s,[]);
+end
+% tempT=sptensor(zeros(n_stochfrows,1));
+% tempT.vals=full(EstochR0);
+% EstochR0=tempT;
+
+ R0=zeros(n_s,n_f);
+R0(:,model.prefrows)=preR0;
+R0(:,model.stochfrows)=EstochR0;
+
+nu_vec=reshape(nu_vec,n_nodes,n_s,[]);
+model.coeffs=coeffs;
+model.nv=nv;
+
diff --git a/105/replication_package/solution_methods/taylor_projection/find_n.m b/105/replication_package/solution_methods/taylor_projection/find_n.m
new file mode 100644
index 0000000000000000000000000000000000000000..d7824be843e36089c31e4499f2234f39b68ace95
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/find_n.m
@@ -0,0 +1,24 @@
+function [n]=find_n(pi_,u)
+% Given u=pi_(v,u), how many compositions of type pi_(v,pi_(v,u)) are needed to get a
+% function of v only.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(pi_)
+ n=0;
+ subspi_=[];
+else
+ check=0;
+ subspi_=pi_;
+ n=0;
+ while check==0
+ n=n+1;
+ newsubspi_=subs(subspi_,u,pi_);
+% check=nnz(1-logical(jacobian(subspi_,u)==0));
+ check=isequal(newsubspi_,subspi_);
+ subspi_=newsubspi_;
+
+ end
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/find_n_new.m b/105/replication_package/solution_methods/taylor_projection/find_n_new.m
new file mode 100644
index 0000000000000000000000000000000000000000..4e1c501b9c2aadb70e2857325e6909aa394e1d56
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/find_n_new.m
@@ -0,0 +1,30 @@
+function [n,uu0]=find_n_new(pi_,u)
+% Given u=pi_(v,u), how many compositions of type pi_(v,pi_(v,u)) are needed to get a
+% function of v only.
+%
+% � Copyright, Oren Levintal, September 12, 2017.
+
+if isempty(pi_)
+ n=0;
+ uu0=zeros(0,0);
+else
+ n_u=length(u);
+ if length(pi_)~=n_u
+ error('wrong size of function')
+ end
+ pi_=pi_(:);
+ uu0=double(logical(jacobian(pi_,u)~=0));
+ if max(abs(real(eig(uu0))))>=1-2*eps
+ error('Auxiliary functions are not defined properly.')
+ end
+ n=1;
+ uu=uu0;
+ nuu=uu*uu0;
+ while ~isequal(logical(nuu),logical(uu))
+ n=n+1;
+ uu=nuu;
+ nuu=uu*uu0;
+ end
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/gen_chainderivs_tensor.m b/105/replication_package/solution_methods/taylor_projection/gen_chainderivs_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..dc83a01172ac3a73950f659c44af00280dfb496c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/gen_chainderivs_tensor.m
@@ -0,0 +1,20 @@
+function [index,n]=gen_chainderivs_tensor(tilf,v,u,pi_,order,symparams,fname)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if order>5
+ error('Differentiation order must not exceed 5')
+end
+
+n=find_n_new(pi_,u); % number of substitutions needed to eliminate u
+
+z=[v(:);u(:)];
+
+% Differentiate with chain rules
+
+[index]=getderivs_tensor(tilf,z,order,symparams,[fname '_tilf']);
+
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/gen_fun_vec.m b/105/replication_package/solution_methods/taylor_projection/gen_fun_vec.m
new file mode 100644
index 0000000000000000000000000000000000000000..8364c8d071340e40b69ee8687c99f655e6860ee0
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/gen_fun_vec.m
@@ -0,0 +1,61 @@
+function gen_fun_vec(f,symparams,v,fname,varargin)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+rowformat=0; % function returns a column vector (number of columns>1 in vectorized form)
+if ~isempty(varargin)
+ if strcmp(varargin{1},'row')
+ rowformat=1; % function returns a row vector (number of rows>1 in vectorized form)
+ end
+end
+
+f=f(:);
+if numel(f)>1
+ nnzf=1-logical(f==0);
+ index=find(nnzf);
+else
+ index=1;
+end
+fid = fopen([fname '_fun.m'], 'w');
+fprintf(fid,'%s\n', ['function function_f=' fname '_fun(variables_v,parameters)']);
+for i=1:length(symparams)
+ if strcmp(char(symparams(i)),'function_f') || strcmp(char(symparams(i)),'variables_v') || strcmp(char(symparams(i)),'parameters')
+ error([char(symparams(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ if rowformat==0
+ fprintf(fid,'%s\n', [char(symparams(i)) '=parameters(' num2str(i) ',:);']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', [char(symparams(i)) '=parameters(:,' num2str(i) ');']);
+ end
+end
+for i=1:length(v)
+ if strcmp(char(v(i)),'function_f') || strcmp(char(v(i)),'variables_v') || strcmp(char(v(i)),'parameters')
+ error([char(v(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ if rowformat==0
+ fprintf(fid,'%s\n', [char(v(i)) '=variables_v(' num2str(i) ',:);']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', [char(v(i)) '=variables_v(:,' num2str(i) ');']);
+ end
+end
+if isempty(f)
+ if rowformat==0
+ fprintf(fid,'%s\n', ['function_f=zeros(0,size(variables_v,2));']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', ['function_f=zeros(size(variables_v,1),0);']);
+ end
+else
+ if rowformat==0
+ fprintf(fid,'%s\n', ['function_f=zeros(' num2str(numel(f)) ',size(variables_v,2));']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', ['function_f=zeros(size(variables_v,1),' num2str(numel(f)) ');']);
+ end
+ for i=index(:)'
+ if rowformat==0
+ disp_fun_vec('function_f',f(i),i,fid);
+ elseif rowformat==1
+ disp_fun_vec_row('function_f',f(i),i,fid);
+ end
+ end
+end
+fclose(fid);
diff --git a/105/replication_package/solution_methods/taylor_projection/gen_fun_vec_subs.m b/105/replication_package/solution_methods/taylor_projection/gen_fun_vec_subs.m
new file mode 100644
index 0000000000000000000000000000000000000000..38ee5c35fc583ce488a3b4ac06fca614ead87c2f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/gen_fun_vec_subs.m
@@ -0,0 +1,137 @@
+function gen_fun_vec_subs(f,symparams,v,ufun,u,fname,varargin)
+%
+% � Copyright, Oren Levintal, September 11, 2017.
+
+rowformat=0; % function returns a column vector (number of columns>1 in vectorized form)
+if ~isempty(varargin)
+ if strcmp(varargin{1},'row')
+ rowformat=1; % function returns a row vector (number of rows>1 in vectorized form)
+ end
+end
+if nargin==8
+ uu0=varargin{2};
+end
+
+f=f(:);
+if numel(f)>1
+ nnzf=1-logical(f==0);
+ index=find(nnzf);
+else
+ index=1;
+end
+fid = fopen([fname '_fun.m'], 'w');
+fprintf(fid,'%s\n', ['function function_f=' fname '_fun(variables_v,parameters)']);
+for i=1:length(symparams)
+ if strcmp(char(symparams(i)),'function_f') || strcmp(char(symparams(i)),'variables_v') || strcmp(char(symparams(i)),'parameters')
+ error([char(symparams(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ if rowformat==0
+ fprintf(fid,'%s\n', [char(symparams(i)) '=parameters(' num2str(i) ',:);']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', [char(symparams(i)) '=parameters(:,' num2str(i) ');']);
+ end
+end
+for i=1:length(v)
+ if strcmp(char(v(i)),'function_f') || strcmp(char(v(i)),'variables_v') || strcmp(char(v(i)),'parameters')
+ error([char(v(i)) 'is reserved. Change variable/parameter name.']);
+ end
+ if rowformat==0
+ fprintf(fid,'%s\n', [char(v(i)) '=variables_v(' num2str(i) ',:);']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', [char(v(i)) '=variables_v(:,' num2str(i) ');']);
+ end
+end
+
+%%%%%%% substituted vars - version 1
+
+% subsu=ufun;
+% newsubsu=subs(subsu,u,ufun);
+%
+% n_u=length(u);
+% A=cell(n_u,1);
+% l=1;
+% uind=1:n_u;
+% while ~isequal(subsu,newsubsu)
+% for i=uind(logical(newsubsu==subsu))
+% texp=char(ufun(i));
+% texp=strrep(texp,'*','.*');
+% texp=strrep(texp,'/','./');
+% texp=strrep(texp,'^','.^');
+% A{l}=[char(u(i)) '=' texp ';'];l=l+1;
+% end
+% uind=uind(logical(newsubsu~=subsu));
+% subsu=newsubsu(logical(newsubsu~=subsu));
+% newsubsu=subs(subsu,u,ufun);
+% end
+% for i=uind
+% texp=char(ufun(i));
+% texp=strrep(texp,'*','.*');
+% texp=strrep(texp,'/','./');
+% texp=strrep(texp,'^','.^');
+% A{l}=[char(u(i)) '=' texp ';'];l=l+1;
+% end
+%
+% for i=1:l-1
+% fprintf(fid,'%s\n', A{i});
+% end
+
+%%%%%%% substituted vars - version 2
+
+if nargin~=8
+ uu0=double(logical(jacobian(ufun(:),u)~=0));
+end
+
+uu=uu0;
+
+n_u=length(u);
+A=cell(n_u,1);
+l=1;
+uind=1:n_u;
+while nnz(uu)~=0
+ for i=uind(logical(sum(uu,2)==0))
+ texp=char(ufun(i));
+ texp=strrep(texp,'*','.*');
+ texp=strrep(texp,'/','./');
+ texp=strrep(texp,'^','.^');
+ A{l}=[char(u(i)) '=' texp ';'];l=l+1;
+ end
+ uind=uind(logical(sum(uu,2)~=0));
+ uu=uu(logical(sum(uu,2)~=0),:);
+ uu=uu*uu0;
+end
+for i=uind
+ texp=char(ufun(i));
+ texp=strrep(texp,'*','.*');
+ texp=strrep(texp,'/','./');
+ texp=strrep(texp,'^','.^');
+ A{l}=[char(u(i)) '=' texp ';'];l=l+1;
+end
+
+for i=1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+%%%%%%%%%%%
+
+
+if isempty(f)
+ if rowformat==0
+ fprintf(fid,'%s\n', ['function_f=zeros(0,size(variables_v,2));']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', ['function_f=zeros(size(variables_v,1),0);']);
+ end
+else
+ if rowformat==0
+ fprintf(fid,'%s\n', ['function_f=zeros(' num2str(numel(f)) ',size(variables_v,2));']);
+ elseif rowformat==1
+ fprintf(fid,'%s\n', ['function_f=zeros(size(variables_v,1),' num2str(numel(f)) ');']);
+ end
+ for i=index(:)'
+ if rowformat==0
+ disp_fun_vec('function_f',f(i),i,fid);
+ elseif rowformat==1
+ disp_fun_vec_row('function_f',f(i),i,fid);
+ end
+ end
+end
+fclose(fid);
diff --git a/105/replication_package/solution_methods/taylor_projection/get_Phi_derivs.m b/105/replication_package/solution_methods/taylor_projection/get_Phi_derivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..1a3a7aca7721542077d61cfb40fbe52afd935267
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_Phi_derivs.m
@@ -0,0 +1,33 @@
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on November 28, 2016: the matrix nnzmat was wrong. Consequently,
+% uncompression of high-order derivatives was wrong. Now it's the right
+% matrix.
+params=params(:)';
+if approx>=1
+ nPhix=Phi_d_c1(nx(:)',params,model.Phi_indc);
+ nPhix.tsize=[n_x2,repmat(n_x,1,1)]; % change size to account for the perturbation parameter
+ nPhix=sptensor2spmat(unfold(nPhix));
+end
+if approx>=2
+ nPhixxc=Phi_d_c2(nx(:)',params,model.Phi_indc);
+ nnzmat=repmat(1:n_x_tp,n_x2,1);
+ [nPhixx,model.pertind{pertindi}]=uncompressderivs( nPhixxc,2,n_x_tp,nnzmat,model.pertind{pertindi} );
+ pertindi=pertindi+1;
+ nPhixx.tsize=[n_x2,repmat(n_x,1,2)]; % change size to account for the perturbation parameter
+ nPhixx=sptensor2spmat(unfold(nPhixx));
+end
+if approx>=3
+ nPhixxxc=Phi_d_c3(nx(:)',params,model.Phi_indc);
+ [nPhixxx,model.pertind{pertindi}]=uncompressderivs( nPhixxxc,3,n_x_tp,nnzmat,model.pertind{pertindi} );
+ pertindi=pertindi+1;
+ nPhixxx.tsize=[n_x2,repmat(n_x,1,3)]; % change size to account for the perturbation parameter
+ nPhixxx=sptensor2spmat(unfold(nPhixxx));
+end
+if approx>=4
+ nPhixxxxc=Phi_d_c4(nx(:)',params,model.Phi_indc);
+ [nPhixxxx,model.pertind{pertindi}]=uncompressderivs( nPhixxxxc,4,n_x_tp,nnzmat,model.pertind{pertindi} );
+ pertindi=pertindi+1;
+ nPhixxxx.tsize=[n_x2,repmat(n_x,1,4)]; % change size to account for the perturbation parameter
+ nPhixxxx=sptensor2spmat(unfold(nPhixxxx));
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/get_f_derivs.m b/105/replication_package/solution_methods/taylor_projection/get_f_derivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..805aaf4836553a6f9cbedb616d915f36770c00d7
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_f_derivs.m
@@ -0,0 +1,526 @@
+%%%%%%%%%%%%% code from tp to compute fv,fvv,fvvv,fvvvv, where v is the
+%%%%%%%%%%%%% vector of variables of the tp system (the pert system has a
+%%%%%%%%%%%%% larger v).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+nv=[zeros(n_y,1);nyss;nxss;nxss]'; % variables of tp
+
+n_u=model.n_u;
+nu=zeros(n_u,1)';
+npreu=preu_fun(nv(model.preuvars),params); % all predetermined u
+nu(model.preurows)=npreu;
+nz=[nv,nu]; % auxiliary variables
+params(:,model.logical_params_loc)=double(logical(nz(:,model.logical_zvars)>=0));
+
+pref=pretilf_fun(nz(model.pretilfzvars),params); % since i already have z, i use pretilf to evaluate f.
+
+% compute derivatives of prePI and pretilf w.r.t z (prePI=nonstochastic rows of PI, pretilf=nonstochastic rows of f)
+
+prePIz_full=prePI_d1(nz,params,model.prePI_ind_u);
+prefvars=model.prefvars;
+n_prefvars=length(prefvars);
+pretilfz=pretilf_tilf_d1([nv(prefvars),nu(model.prefuvars)],params,model.pretilf_ind_u);
+if approx>=2
+ prePIzz_full=prePI_d2(nz,params,model.prePI_ind_u);
+ pretilfzz=pretilf_tilf_d2([nv(prefvars),nu(model.prefuvars)],params,model.pretilf_ind_u);
+end
+if approx>=3
+ prePIzzz_full=prePI_d3(nz,params,model.prePI_ind_u);
+ pretilfzzz=pretilf_tilf_d3([nv(prefvars),nu(model.prefuvars)],params,model.pretilf_ind_u);
+end
+if approx>=4
+ prePIzzzz_full=prePI_d4(nz,params,model.prePI_ind_u);
+ pretilfzzzz=pretilf_tilf_d4([nv(prefvars),nu(model.prefuvars)],params,model.pretilf_ind_u);
+end
+
+% extract derivatives of prePI w.r.t v from prePIz, prePIzz, ...
+if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+end
+indi=5;
+
+if approx>=1
+ [prePIz,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefvars,0,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=2
+ [prePIzz,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=3
+ [prePIzzz,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain3c_M2')
+ [ tempM ] = chainsM( n_prefvars,3 );
+ model.prefvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if approx>=4
+ [prePIzzzz,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain4c_M2')
+ [ tempM ] = chainsM( n_prefvars,4 );
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+
+
+% Use high order chain rules to compute derivatives of prePI w.r.t v
+totindi=5+8;
+if approx==1
+ indi=totindi;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+elseif approx==2
+ indi=totindi+(model.pre_n-1)*(1)+1;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+elseif approx==3
+ indi=totindi+(model.pre_n-1)*(1+3)+1+4;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+elseif approx==4
+ indi=totindi+(model.pre_n-1)*(1+3+4)+1+4+6;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=chain4c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvvc,model.ind{indi}]=chain4c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvv,model.ind{indi} ] = uncompressderivs( prefvvvvc,4,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+end
+totindi=totindi+(model.pre_n-1)*(1+3+4+6)+1+4+6+9;
+
+%%%%%%%%%%%%% now stochastic equations
+n_nodes=1;
+nv_vec=[nyss;nyss;nxss;nxss]';
+stochfvars=model.stochfvars;
+n_stochfvars=length(stochfvars);
+nstochv_vec=nv_vec(:,stochfvars); % stochastic vars.
+
+nstochu_vec=stochu_fun(nv_vec(:,model.stochuvars),params); % all stochastic u vars
+nu_vec=repmat(nu,n_nodes,1);
+nu_vec(:,model.stochurows)=nstochu_vec;
+nz_vec=[nv_vec,nu_vec];
+params(model.logical_params_loc)=double(logical(nz_vec(model.logical_zvars)>=0));
+
+stochf_vec=stochtilf_fun(nz_vec(:,model.stochtilfzvars),params);
+
+% compute derivatives of stochPI and stochtilf w.r.t z
+
+stochPIz_vec=stochPI_d1(nz_vec,params,model.stochPI_ind_u);
+prePIz_full.vals=repmat(prePIz_full.vals,n_nodes,1);
+
+i1=tfind(prePIz_full);
+i2=tfind(stochPIz_vec);
+PIz_vec=sptensor([i1;i2],[prePIz_full.cols;stochPIz_vec.cols],[prePIz_full.vals,stochPIz_vec.vals],n_z,[n_z]);
+stochtilfz_vec=stochtilf_tilf_d1([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+
+if approx>=2
+ stochPIzz_vec=stochPI_d2(nz_vec,params,model.stochPI_ind_u);
+ prePIzz_full.vals=repmat(prePIzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzz_full);
+ i2=tfind(stochPIzz_vec);
+ PIzz_vec=sptensor([i1;i2],[prePIzz_full.cols;stochPIzz_vec.cols],[prePIzz_full.vals,stochPIzz_vec.vals],n_z,[n_z,n_z]);
+ stochtilfzz_vec=stochtilf_tilf_d2([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+end
+if approx>=3
+ stochPIzzz_vec=stochPI_d3(nz_vec,params,model.stochPI_ind_u);
+ prePIzzz_full.vals=repmat(prePIzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzz_full);
+ i2=tfind(stochPIzzz_vec);
+ PIzzz_vec=sptensor([i1;i2],[prePIzzz_full.cols;stochPIzzz_vec.cols],[prePIzzz_full.vals,stochPIzzz_vec.vals],n_z,[n_z,n_z,n_z]);
+ stochtilfzzz_vec=stochtilf_tilf_d3([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+end
+if approx>=4
+ stochPIzzzz_vec=stochPI_d4(nz_vec,params,model.stochPI_ind_u);
+ prePIzzzz_full.vals=repmat(prePIzzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzzz_full);
+ i2=tfind(stochPIzzzz_vec);
+ PIzzzz_vec=sptensor([i1;i2],[prePIzzzz_full.cols;stochPIzzzz_vec.cols],[prePIzzzz_full.vals,stochPIzzzz_vec.vals],n_z,[n_z,n_z,n_z,n_z]);
+ stochtilfzzzz_vec=stochtilf_tilf_d4([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+end
+
+% extract PIv,Pivv,... from PIz,PIzz,...
+
+totindi=totindi+3;
+totindi=totindi+4;
+totindi=totindi+2;
+totindi=totindi+2;
+totindi=totindi+1;
+totindi=totindi+9;
+
+
+indi=totindi;
+if approx>=1
+ [stochPIz_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfvars,0,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=2
+ [stochPIzz_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=3
+ [stochPIzzz_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain3c_M2')
+ [ tempM ] = chainsM( n_stochfvars,3 );
+ model.stochfvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if approx>=4
+ [stochPIzzzz_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain4c_M2')
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+
+totindi=totindi+8;
+
+% compute derivatives of stochf w.r.t v by high order chain rules
+
+if approx==1
+ indi=totindi;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+elseif approx==2
+ indi=totindi+(model.stoch_n-1)*(1)+1;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+elseif approx==3
+ indi=totindi+(model.stoch_n-1)*(1+3)+1+4;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+elseif approx==4
+ indi=totindi+(model.stoch_n-1)*(1+3+4)+1+4+6;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ [ stochfvvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvvc_vec,4,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvvc_vec
+
+end
+
+%%%%%%%%%%%%% convert to sparse matrices
+
+if approx>=1
+ prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+ prefv=changecols(prefv,tempv,n_v,1);
+ prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+
+ fv=sparse(double([prei;stochi]),double([prej;stochj]),double([prevals(:);stochvals(:)]),n_f,n_v);
+end
+if approx>=2
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+ prefvv=changecols(prefvv,tempv,n_v,1);
+ prefvv=changecols(prefvv,tempv,n_v,2);
+ prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f*n_v^2,1);
+end
+if approx>=3
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+ prefvvv=changecols(prefvvv,tempv,n_v,1);
+ prefvvv=changecols(prefvvv,tempv,n_v,2);
+ prefvvv=changecols(prefvvv,tempv,n_v,3);
+ prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f*n_v^3,1);
+end
+if approx>=4
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+ prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f*n_v^4,1);
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/get_f_derivs_fname.m b/105/replication_package/solution_methods/taylor_projection/get_f_derivs_fname.m
new file mode 100644
index 0000000000000000000000000000000000000000..e5e44cc220495ba6e56a62cff7d0e1130976ef7c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_f_derivs_fname.m
@@ -0,0 +1,686 @@
+%%%%%%%%%%%%% code from tp to compute fv,fvv,fvvv,fvvvv, where v is the
+%%%%%%%%%%%%% vector of variables of the tp system (the pert system has a
+%%%%%%%%%%%%% larger v).
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+nv=[zeros(model.n_y,1);nyss(:);nxss(:);nxss(:)]'; % variables of tp
+nv=repmat(nv,n_s,1);
+
+n_u=model.n_u;
+nu=zeros(n_s,n_u);
+npreu=preu_fun(nv(:,model.preuvars),params); % all predetermined u
+nu(:,model.preurows)=npreu;
+nz=[nv,nu];
+
+params(:,model.logical_params_loc)=double(logical(nz(:,model.logical_zvars)>=0));
+if isempty(model.prefrows)
+ % compute derivatives of prePI w.r.t z (prePI=nonstochastic rows of PI)
+
+ prePIz_full=prePI_d1(nz,params,model.prePI_ind_u);
+
+ if approx>=2
+ prePIzz_full=prePI_d2(nz,params,model.prePI_ind_u);
+ end
+ if approx>=3
+ prePIzzz_full=prePI_d3(nz,params,model.prePI_ind_u);
+ end
+ if approx>=4
+ prePIzzzz_full=prePI_d4(nz,params,model.prePI_ind_u);
+ end
+ if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+ end
+ totindi=5+8;
+ totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+else
+ fname=['pretilf' model.fname '_fun'];
+ pref=feval(fname,nz(:,model.pretilfzvars),params); % since i already have z, i use pretilf to evaluate f.
+
+ % compute derivatives of prePI and pretilf w.r.t z (prePI=nonstochastic rows of PI, pretilf=nonstochastic rows of f)
+
+ prePIz_full=prePI_d1(nz,params,model.prePI_ind_u);
+ prefvars=model.prefvars;
+ n_prefvars=length(prefvars);
+
+ fname=['pretilf' model.fname '_tilf_d1'];
+ pretilfz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ if approx>=2
+ prePIzz_full=prePI_d2(nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d2'];
+ pretilfzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+ if approx>=3
+ prePIzzz_full=prePI_d3(nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d3'];
+ pretilfzzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+ if approx>=4
+ prePIzzzz_full=prePI_d4(nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d4'];
+ pretilfzzzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+
+ % extract derivatives of prePI w.r.t v from prePIz, prePIzz, ...
+ if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+ end
+ indi=5;
+
+ if approx>=1
+ [prePIz,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefvars,0,model.ind{indi});
+ indi=indi+1;
+ end
+ if approx>=2
+ [prePIzz,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ end
+ if approx>=3
+ [prePIzzz,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain3c_M2')
+ [ tempM ] = chainsM( n_prefvars,3 );
+ model.prefvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+ end
+ if approx>=4
+ [prePIzzzz,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain4c_M2')
+ [ tempM ] = chainsM( n_prefvars,4 );
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+ end
+
+
+ % Use high order chain rules to compute derivatives of prePI w.r.t v
+ totindi=5+8;
+ if approx==1
+ indi=totindi;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ elseif approx==2
+ indi=totindi+model.count_pre_n*(1)+1;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ elseif approx==3
+ indi=totindi+model.count_pre_n*(1+3)+1+4;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ elseif approx==4
+ indi=totindi+model.count_pre_n*(1+3+4)+1+4+6;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=chain4c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvvc,model.ind{indi}]=chain4c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvv,model.ind{indi} ] = uncompressderivs( prefvvvvc,4,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+ end
+ totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+end
+
+%%%%%%%%%%%%% now stochastic equations
+n_nodes=1;
+nv_vec=repmat([nyss;nyss;nxss;nxss]',n_s,1);
+stochfvars=model.stochfvars;
+n_stochfvars=length(stochfvars);
+nstochv_vec=nv_vec(:,stochfvars); % stochastic vars.
+
+nstochu_vec=stochu_fun(nv_vec(:,model.stochuvars),params); % all stochastic u vars
+nu_vec=repmat(nu,n_nodes,1);
+nu_vec(:,model.stochurows)=nstochu_vec;
+nz_vec=[nv_vec,nu_vec];
+
+params(:,model.logical_params_loc)=double(logical(nz_vec(:,model.logical_zvars)>=0));
+
+% stochf_vec=stochtilf_fun(nz_vec(:,model.stochtilfzvars),params);
+fname=['stochtilf' model.fname '_fun'];
+stochf_vec=feval(fname,nz_vec(:,model.stochtilfzvars),params);
+
+% compute derivatives of stochPI and stochtilf w.r.t z
+
+stochPIz_vec=stochPI_d1(nz_vec,params,model.stochPI_ind_u);
+prePIz_full.vals=repmat(prePIz_full.vals,n_nodes,1);
+
+i1=tfind(prePIz_full);
+i2=tfind(stochPIz_vec);
+PIz_vec=sptensor([i1;i2],[prePIz_full.cols;stochPIz_vec.cols],[prePIz_full.vals,stochPIz_vec.vals],n_z,[n_z]);
+
+% stochtilfz_vec=stochtilf_tilf_d1([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+fname=['stochtilf' model.fname '_tilf_d1'];
+stochtilfz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+
+if approx>=2
+ stochPIzz_vec=stochPI_d2(nz_vec,params,model.stochPI_ind_u);
+ prePIzz_full.vals=repmat(prePIzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzz_full);
+ i2=tfind(stochPIzz_vec);
+ PIzz_vec=sptensor([i1;i2],[prePIzz_full.cols;stochPIzz_vec.cols],[prePIzz_full.vals,stochPIzz_vec.vals],n_z,[n_z,n_z]);
+% stochtilfzz_vec=stochtilf_tilf_d2([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+ fname=['stochtilf' model.fname '_tilf_d2'];
+ stochtilfzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+
+end
+if approx>=3
+ stochPIzzz_vec=stochPI_d3(nz_vec,params,model.stochPI_ind_u);
+ prePIzzz_full.vals=repmat(prePIzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzz_full);
+ i2=tfind(stochPIzzz_vec);
+ PIzzz_vec=sptensor([i1;i2],[prePIzzz_full.cols;stochPIzzz_vec.cols],[prePIzzz_full.vals,stochPIzzz_vec.vals],n_z,[n_z,n_z,n_z]);
+% stochtilfzzz_vec=stochtilf_tilf_d3([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+ fname=['stochtilf' model.fname '_tilf_d3'];
+ stochtilfzzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+end
+if approx>=4
+ stochPIzzzz_vec=stochPI_d4(nz_vec,params,model.stochPI_ind_u);
+ prePIzzzz_full.vals=repmat(prePIzzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzzz_full);
+ i2=tfind(stochPIzzzz_vec);
+ PIzzzz_vec=sptensor([i1;i2],[prePIzzzz_full.cols;stochPIzzzz_vec.cols],[prePIzzzz_full.vals,stochPIzzzz_vec.vals],n_z,[n_z,n_z,n_z,n_z]);
+% stochtilfzzzz_vec=stochtilf_tilf_d4([nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+ fname=['stochtilf' model.fname '_tilf_d4'];
+ stochtilfzzzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params,model.stochtilf_ind_u);
+end
+
+% extract PIv,Pivv,... from PIz,PIzz,...
+
+totindi=totindi+3;
+totindi=totindi+4;
+totindi=totindi+2;
+totindi=totindi+2;
+totindi=totindi+1;
+totindi=totindi+9;
+
+
+indi=totindi;
+if approx>=1
+ [stochPIz_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfvars,0,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=2
+ [stochPIzz_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+end
+if approx>=3
+ [stochPIzzz_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain3c_M2')
+ [ tempM ] = chainsM( n_stochfvars,3 );
+ model.stochfvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if approx>=4
+ [stochPIzzzz_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain4c_M2')
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+
+totindi=totindi+8;
+
+% compute derivatives of stochf w.r.t v by high order chain rules
+
+if approx==1
+ indi=totindi;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+elseif approx==2
+ indi=totindi+model.count_stoch_n*(1)+1;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+elseif approx==3
+ indi=totindi+model.count_stoch_n*(1+3)+1+4;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+elseif approx==4
+ indi=totindi+model.count_stoch_n*(1+3+4)+1+4+6;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ [ stochfvvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvvc_vec,4,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvvc_vec
+
+end
+
+%%%%%%%%%%%%% convert to sparse matrices
+if model.hybrid==0
+ if ~isempty(model.prefrows)
+
+ if approx>=1
+ prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+ prefv=changecols(prefv,tempv,n_v,1);
+ prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+
+ fv=sparse(double([prei;stochi]),double([prej;stochj]),double([prevals(:);stochvals(:)]),n_f,n_v);
+ end
+ if approx>=2
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+ prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+ prefvv=changecols(prefvv,tempv,n_v,1);
+ prefvv=changecols(prefvv,tempv,n_v,2);
+ prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f*n_v^2,1);
+ end
+ if approx>=3
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+ prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+ prefvvv=changecols(prefvvv,tempv,n_v,1);
+ prefvvv=changecols(prefvvv,tempv,n_v,2);
+ prefvvv=changecols(prefvvv,tempv,n_v,3);
+ prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f*n_v^3,1);
+ end
+ if approx>=4
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+ prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+ prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+ prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+
+ alli=double([prei;stochi]);
+ allj=double([prej;stochj]);
+ allvals=double([prevals(:);stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f*n_v^4,1);
+ end
+ else
+ if approx>=1
+ % prefv=changecols(prefv,model.prefvars,n_v_tp,1);
+ tempv=1:n_v;
+ tempv(2*n_y+n_x)=[];
+ tempv(end)=[];
+ % prefv=changecols(prefv,tempv,n_v,1);
+ % prefv=changerows(prefv,model.prefrows,n_f);
+
+ stochfv_vec=changecols(stochfv_vec,model.stochfvars,n_v_tp,1);
+ stochfv_vec=changecols(stochfv_vec,tempv,n_v,1);
+ stochfv_vec=changerows(stochfv_vec,model.stochfrows,n_f);
+
+ % [prei,prej,prevals]=tfind(unfold(prefv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfv_vec));
+
+ % fv=sparse(double([prei;stochi]),double([prej;stochj]),double([prevals(:);stochvals(:)]),n_f,n_v);
+ fv=sparse(double([stochi]),double([stochj]),double([stochvals(:)]),n_f,n_v);
+ end
+ if approx>=2
+ % prefvv=changecols(prefvv,model.prefvars,n_v_tp,1);
+ % prefvv=changecols(prefvv,model.prefvars,n_v_tp,2);
+ % prefvv=changecols(prefvv,tempv,n_v,1);
+ % prefvv=changecols(prefvv,tempv,n_v,2);
+ % prefvv=changerows(prefvv,model.prefrows,n_f);
+
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvv_vec=changecols(stochfvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,1);
+ stochfvv_vec=changecols(stochfvv_vec,tempv,n_v,2);
+ stochfvv_vec=changerows(stochfvv_vec,model.stochfrows,n_f);
+
+ % [prei,prej,prevals]=tfind(unfold(prefvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvv_vec));
+
+ % alli=double([prei;stochi]);
+ % allj=double([prej;stochj]);
+ % allvals=double([prevals(:);stochvals(:)]);
+ alli=double([stochi]);
+ allj=double([stochj]);
+ allvals=double([stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^2],alli,allj);
+ newj=ones(size(newi));
+
+ fvv=sparse(newi,newj,allvals,n_f*n_v^2,1);
+ end
+ if approx>=3
+ % prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,1);
+ % prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,2);
+ % prefvvv=changecols(prefvvv,model.prefvars,n_v_tp,3);
+ % prefvvv=changecols(prefvvv,tempv,n_v,1);
+ % prefvvv=changecols(prefvvv,tempv,n_v,2);
+ % prefvvv=changecols(prefvvv,tempv,n_v,3);
+ % prefvvv=changerows(prefvvv,model.prefrows,n_f);
+
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,1);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,2);
+ stochfvvv_vec=changecols(stochfvvv_vec,tempv,n_v,3);
+ stochfvvv_vec=changerows(stochfvvv_vec,model.stochfrows,n_f);
+
+ % [prei,prej,prevals]=tfind(unfold(prefvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvv_vec));
+
+ % alli=double([prei;stochi]);
+ % allj=double([prej;stochj]);
+ % allvals=double([prevals(:);stochvals(:)]);
+ alli=double([stochi]);
+ allj=double([stochj]);
+ allvals=double([stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^3],alli,allj);
+ newj=ones(size(newi));
+
+ fvvv=sparse(newi,newj,allvals,n_f*n_v^3,1);
+ end
+ if approx>=4
+ % prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,1);
+ % prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,2);
+ % prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,3);
+ % prefvvvv=changecols(prefvvvv,model.prefvars,n_v_tp,4);
+ % prefvvvv=changecols(prefvvvv,tempv,n_v,1);
+ % prefvvvv=changecols(prefvvvv,tempv,n_v,2);
+ % prefvvvv=changecols(prefvvvv,tempv,n_v,3);
+ % prefvvvv=changecols(prefvvvv,tempv,n_v,4);
+ % prefvvvv=changerows(prefvvvv,model.prefrows,n_f);
+
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,model.stochfvars,n_v_tp,4);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,1);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,2);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,3);
+ stochfvvvv_vec=changecols(stochfvvvv_vec,tempv,n_v,4);
+ stochfvvvv_vec=changerows(stochfvvvv_vec,model.stochfrows,n_f);
+
+ % [prei,prej,prevals]=tfind(unfold(prefvvvv));
+ [stochi,stochj,stochvals]=tfind(unfold(stochfvvvv_vec));
+
+ % alli=double([prei;stochi]);
+ % allj=double([prej;stochj]);
+ % allvals=double([prevals(:);stochvals(:)]);
+ alli=double([stochi]);
+ allj=double([stochj]);
+ allvals=double([stochvals(:)]);
+
+ newi=sub2ind([n_f,n_v^4],alli,allj);
+ newj=ones(size(newi));
+
+ fvvvv=sparse(newi,newj,allvals,n_f*n_v^4,1);
+ end
+ end
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_v.m b/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_v.m
new file mode 100644
index 0000000000000000000000000000000000000000..83d7e184f41f244be8a32d2255cab5b97a9c1a7f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_v.m
@@ -0,0 +1,289 @@
+% compute derivatives of Phi w.r.t v by high order chain rules.
+n_Phivars=length(model.Phivars);
+Phivars=model.Phivars;
+
+count_Phi_n=model.Phi_n-1;
+if count_Phi_n<0
+ count_Phi_n=0;
+end
+
+if ~isfield(model,'hind')
+ model.hind=cell(100+1+8+8+count_Phi_n*(1+3+4+6)+1+4+6+9,1);
+ model.hind4=cell(100+count_Phi_n,1);
+end
+
+
+hindi=1;
+hindi4=1;
+tothindi=1;
+
+% extract PhiPIv,PhiPivv,... from PIz,PIzz,...
+if order>=0
+ [PhiPIz_vec,model.hind{hindi}]=extract(PIz_vec,model.Phizvars,model.Phizvars,0,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIv_vec,model.hind{hindi}]=extract(PIz_vec,model.Phizvars,model.Phivars,0,model.hind{hindi});
+ hindi=hindi+1;
+ fname=['Phi' model.fname '_tilf_d1'];
+ Phiz_vec=feval(fname,[nv_vec(:,Phivars),nu_vec(:,model.Phiuvars)],params_vec,model.Phi_ind_u);
+end
+if order>=1
+ [PhiPIzz_vec,model.hind{hindi}]=extract(PIzz_vec,model.Phizvars,model.Phizvars,0,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=extract(PIzz_vec,model.Phizvars,model.Phivars,1,model.hind{hindi});
+ hindi=hindi+1;
+ fname=['Phi' model.fname '_tilf_d2'];
+ Phizz_vec=feval(fname,[nv_vec(:,Phivars),nu_vec(:,model.Phiuvars)],params_vec,model.Phi_ind_u);
+end
+if order>=2
+ [PhiPIzzz_vec,model.hind{hindi}]=extract(PIzzz_vec,model.Phizvars,model.Phizvars,0,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvvc_vec,model.hind{hindi}]=extract(PIzzz_vec,model.Phizvars,model.Phivars,1,model.hind{hindi});
+ hindi=hindi+1;
+ fname=['Phi' model.fname '_tilf_d3'];
+ Phizzz_vec=feval(fname,[nv_vec(:,Phivars),nu_vec(:,model.Phiuvars)],params_vec,model.Phi_ind_u);
+
+ if ~isfield(model,'Phivars_chain3c_M2')
+ [ tempM ] = chainsM( n_Phivars,3 );
+ model.Phivars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if order>=3
+ [PhiPIzzzz_vec,model.hind{hindi}]=extract(PIzzzz_vec,model.Phizvars,model.Phizvars,0,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvvvc_vec,model.hind{hindi}]=extract(PIzzzz_vec,model.Phizvars,model.Phivars,1,model.hind{hindi});
+ hindi=hindi+1;
+ fname=['Phi' model.fname '_tilf_d4'];
+ Phizzzz_vec=feval(fname,[nv_vec(:,Phivars),nu_vec(:,model.Phiuvars)],params_vec,model.Phi_ind_u);
+ if ~isfield(model,'Phivars_chain4c_M2')
+ [ tempM ] = chainsM( n_Phivars,4 );
+ model.Phivars_chain4c_M2=tempM{2};
+ model.Phivars_chain4c_M3=tempM{3};
+ model.Phivars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+if order>=4
+ [PhiPIzzzzz_vec,model.hind4{hindi4}]=extract(PIzzzzz_vec,model.Phizvars,model.Phizvars,0,model.hind4{hindi4});
+ hindi4=hindi4+1;
+ [PhiPIvvvvvc_vec,model.hind4{hindi4}]=extract(PIzzzzz_vec,model.Phizvars,model.Phivars,1,model.hind4{hindi4});
+ hindi4=hindi4+1;
+ fname=['Phi' model.fname '_tilf_d5'];
+ Phizzzzz_vec=feval(fname,[nv_vec(:,Phivars),nu_vec(:,model.Phiuvars)],params_vec,model.Phi_ind_u);
+end
+tothindi=tothindi+8;
+% hindi=tothindi;
+
+
+
+if order==0
+ hindi=tothindi;
+ for i=2:model.Phi_n
+ [PhiPIv_vec,model.hind{hindi}]=chain1_tensor(PhiPIz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ end
+ [Phiv_vec,model.hind{hindi}]=chain1_tensor(Phiz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+
+% stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+%
+% model.stochfv_vec=stochfv_vec;
+
+elseif order==1
+ hindi=tothindi+count_Phi_n*(1)+1;
+ for i=2:model.Phi_n
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=chain2c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIv_vec,model.hind{hindi}]=chain1_tensor(PhiPIz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ end
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+
+ [Phiv_vec,model.hind{hindi}]=chain1_tensor(Phiz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvc_vec,model.hind{hindi}]=chain2c_tensor(Phiz_vec,Phizz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+
+% stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+% stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+
+ [ Phivv_vec,model.hind{hindi} ] = uncompressderivs( Phivvc_vec,2,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvc_vec
+
+elseif order==2
+ hindi=tothindi+count_Phi_n*(1+3)+1+4;
+ for i=2:model.Phi_n
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvvc_vec,model.hind{hindi}]=chain3c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,model.Phivars_chain3c_M2,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=chain2c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIv_vec,model.hind{hindi}]=chain1_tensor(PhiPIz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ end
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+
+ [Phiv_vec,model.hind{hindi}]=chain1_tensor(Phiz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvc_vec,model.hind{hindi}]=chain2c_tensor(Phiz_vec,Phizz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvvc_vec,model.hind{hindi}]=chain3c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,...
+ model.Phivars_chain3c_M2,...
+ model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+
+% stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+% stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+% stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+
+ [ Phivv_vec,model.hind{hindi} ] = uncompressderivs( Phivvc_vec,2,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvc_vec
+
+ [ Phivvv_vec,model.hind{hindi} ] = uncompressderivs( Phivvvc_vec,3,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvvc_vec
+
+elseif order==3
+ hindi=tothindi+count_Phi_n*(1+3+4)+1+4+6;
+ for i=2:model.Phi_n
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=colsort(PhiPIvvc_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvvvc_vec,model.hind{hindi}]=chain4c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,PhiPIzzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,...
+ model.Phivars_chain4c_M2,model.Phivars_chain4c_M3,model.Phivars_chain4c_M4,...
+ model.hind{hindi},n_ind,maxload,'vec',model.Phizz,model.maxzz);
+ hindi=hindi+1;
+ [PhiPIvvvc_vec,model.hind{hindi}]=chain3c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,model.Phivars_chain3c_M2,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=chain2c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIv_vec,model.hind{hindi}]=chain1_tensor(PhiPIz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ end
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=colsort(PhiPIvvc_vec,model.hind{hindi});
+ hindi=hindi+1;
+
+ [Phiv_vec,model.hind{hindi}]=chain1_tensor(Phiz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvc_vec,model.hind{hindi}]=chain2c_tensor(Phiz_vec,Phizz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvvc_vec,model.hind{hindi}]=chain3c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,...
+ model.Phivars_chain3c_M2,...
+ model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+
+ [Phivvvvc_vec,model.hind{hindi}]=chain4c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,Phizzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,...
+ model.Phivars_chain4c_M2,model.Phivars_chain4c_M3,model.Phivars_chain4c_M4,...
+ model.hind{hindi},n_ind,maxload,'vec',model.tilPhiz,model.maxtilPhiz);
+ hindi=hindi+1;
+
+% stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+% stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+% stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+% stochfvvvvc_vec.vals=multcol(stochfvvvvc_vec.vals,Pvec);
+
+ [ Phivv_vec,model.hind{hindi} ] = uncompressderivs( Phivvc_vec,2,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvc_vec
+
+ [ Phivvv_vec,model.hind{hindi} ] = uncompressderivs( Phivvvc_vec,3,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvvc_vec
+
+ [ Phivvvv_vec,model.hind{hindi} ] = uncompressderivs( Phivvvvc_vec,4,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvvvc_vec
+
+elseif order==4
+ hindi=tothindi+count_Phi_n*(1+3+4)+1+4+6;
+ for i=2:model.Phi_n
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=colsort(PhiPIvvc_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvvvvc_vec,model.hind4{hindi4}]=chain5c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,PhiPIzzzz_vec,PhiPIzzzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,PhiPIvvvvvc_vec,...
+ model.Phivars_chain5c_M1,model.Phivars_chain5c_M2,model.Phivars_chain5c_M3,model.Phivars_chain5c_M4,model.Phivars_chain5c_M5,model.Phivars_chain5c_M6,...
+ model.hind4{hindi4},n_ind,maxload,'vec',model.Phizz,model.maxzz);
+ hindi4=hindi4+1;
+ [PhiPIvvvvc_vec,model.hind{hindi}]=chain4c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,PhiPIzzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,...
+ model.Phivars_chain4c_M2,model.Phivars_chain4c_M3,model.Phivars_chain4c_M4,...
+ model.hind{hindi},n_ind,maxload,'vec',model.Phizz,model.maxzz);
+ hindi=hindi+1;
+ [PhiPIvvvc_vec,model.hind{hindi}]=chain3c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,model.Phivars_chain3c_M2,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=chain2c_tensor(PhiPIz_vec,PhiPIzz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [PhiPIv_vec,model.hind{hindi}]=chain1_tensor(PhiPIz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ end
+ [PhiPIv_vec,model.hind{hindi}]=colsort(PhiPIv_vec,model.hind{hindi});
+ hindi=hindi+1;
+ [PhiPIvvc_vec,model.hind{hindi}]=colsort(PhiPIvvc_vec,model.hind{hindi});
+ hindi=hindi+1;
+
+ [Phiv_vec,model.hind{hindi}]=chain1_tensor(Phiz_vec,PhiPIv_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvc_vec,model.hind{hindi}]=chain2c_tensor(Phiz_vec,Phizz_vec,PhiPIv_vec,PhiPIvvc_vec,model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+ [Phivvvc_vec,model.hind{hindi}]=chain3c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,...
+ model.Phivars_chain3c_M2,...
+ model.hind{hindi},n_ind,maxload,'vec');
+ hindi=hindi+1;
+
+ [Phivvvvc_vec,model.hind{hindi}]=chain4c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,Phizzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,...
+ model.Phivars_chain4c_M2,model.Phivars_chain4c_M3,model.Phivars_chain4c_M4,...
+ model.hind{hindi},n_ind,maxload,'vec',model.tilPhiz,model.maxtilPhiz);
+ hindi=hindi+1;
+
+ [Phivvvvvc_vec,model.hind4{hindi4}]=chain5c_tensor(Phiz_vec,Phizz_vec,Phizzz_vec,Phizzzz_vec,Phizzzzz_vec,...
+ PhiPIv_vec,PhiPIvvc_vec,PhiPIvvvc_vec,PhiPIvvvvc_vec,PhiPIvvvvvc_vec,...
+ model.Phivars_chain5c_M1,model.Phivars_chain5c_M2,model.Phivars_chain5c_M3,model.Phivars_chain5c_M4,model.Phivars_chain5c_M5,model.Phivars_chain5c_M6,...
+ model.hind4{hindi4},n_ind,maxload,'vec',model.tilPhiz,model.maxtilPhiz);
+ hindi4=hindi4+1;
+
+% stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+% stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+% stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+% stochfvvvvc_vec.vals=multcol(stochfvvvvc_vec.vals,Pvec);
+% stochfvvvvvc_vec.vals=multcol(stochfvvvvvc_vec.vals,Pvec);
+
+ [ Phivv_vec,model.hind{hindi} ] = uncompressderivs( Phivvc_vec,2,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvc_vec
+
+ [ Phivvv_vec,model.hind{hindi} ] = uncompressderivs( Phivvvc_vec,3,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvvc_vec
+
+ [ Phivvvv_vec,model.hind{hindi} ] = uncompressderivs( Phivvvvc_vec,4,n_Phivars,model.Phiv(:,Phivars),model.hind{hindi} );
+ hindi=hindi+1;
+ clear Phivvvvc_vec
+
+ [ Phivvvvv_vec,model.hind4{hindi4} ] = uncompressderivs( Phivvvvvc_vec,5,n_Phivars,model.Phiv(:,Phivars),model.hind4{hindi4} );
+ hindi4=hindi4+1;
+ clear Phivvvvvc_vec
+
+end
+tothindi=tothindi+8+count_Phi_n*(1+3+4+6)+1+4+6+9;
+hindi=tothindi;
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_x_theta.m b/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_x_theta.m
new file mode 100644
index 0000000000000000000000000000000000000000..281ccbc2ed56bbb1e0915eda13b5785dbec44c90
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_hybridPhi_derivs_x_theta.m
@@ -0,0 +1,93 @@
+phiv_theta_vecT=takerows(v_theta,Phivars);
+phiv_theta_vecT.vals=reshape(repmat(phiv_theta_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+[ Phitheta,model.hind{hindi} ] = chain0_theta_tensor( Phiv_vec,phiv_theta_vecT,model.hind{hindi},n_ind,maxload,'vec' );
+hindi=hindi+1;
+
+if order>=1
+ phivxT=takerows(vx,Phivars);
+ phivxT.vals=reshape(repmat(phivxT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ phivx_theta_vecT=takerows(vx_theta,Phivars);
+ phivx_theta_vecT=unfold(phivx_theta_vecT);
+ phivx_theta_vecT.vals=reshape(repmat(phivx_theta_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ [ Phix,model.hind{hindi} ] = chain1_tensor( Phiv_vec,phivxT,model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+ [ Phixtheta,model.hind{hindi} ] = chain1_theta_tensor( Phiv_vec,Phivv_vec,...
+ phivxT,phiv_theta_vecT,phivx_theta_vecT,...
+ model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+end
+if order>=2
+ phivxxcT=takerows(vxxc,Phivars);
+ phivxxcT.vals=reshape(repmat(phivxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ phivxxc_theta_vecT=takerows(vxxc_theta,Phivars);
+ phivxxc_theta_vecT=unfold(phivxxc_theta_vecT);
+ phivxxc_theta_vecT.vals=reshape(repmat(phivxxc_theta_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ [phivxT,model.hind4{hindi4}]=colsort(phivxT,model.hind4{hindi4});
+ hindi4=hindi4+1;
+ [ Phixxc,model.hind{hindi} ] = chain2c_tensor( Phiv_vec,Phivv_vec,...
+ phivxT,phivxxcT,model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+ [ Phixxctheta,model.hind{hindi} ] = chain2c_theta_tensor( Phiv_vec,Phivv_vec,Phivvv_vec,...
+ phivxT,phivxxcT,...
+ phiv_theta_vecT,phivx_theta_vecT,phivxxc_theta_vecT,...
+ model.chain2c_theta_M2,...
+ model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+end
+if order>=3
+ phivxxxcT=takerows(vxxxc,Phivars);
+ phivxxxcT.vals=reshape(repmat(phivxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ phivxxxc_theta_vecT=takerows(vxxxc_theta,Phivars);
+ phivxxxc_theta_vecT=unfold(phivxxxc_theta_vecT);
+ phivxxxc_theta_vecT.vals=reshape(repmat(phivxxxc_theta_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ [ Phixxxc,model.hind{hindi} ] = chain3c_tensor( Phiv_vec,Phivv_vec,Phivvv_vec,...
+ phivxT,phivxxcT,phivxxxcT,...
+ model.x_chain3c_M2,...
+ model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+ [ Phixxxctheta,model.hind{hindi} ] = chain3c_theta_tensor( Phiv_vec,Phivv_vec,Phivvv_vec,Phivvvv_vec,...
+ phivxT,phivxxcT,phivxxxcT,...
+ phiv_theta_vecT,phivx_theta_vecT,phivxxc_theta_vecT,phivxxxc_theta_vecT,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.hind{hindi},n_ind,maxload,'vec' );
+ hindi=hindi+1;
+
+end
+if order>=4
+ phivxxxxcT=takerows(vxxxxc,Phivars);
+ phivxxxxcT.vals=reshape(repmat(phivxxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ phivxxxxc_theta_vecT=takerows(vxxxxc_theta,Phivars);
+ phivxxxxc_theta_vecT=unfold(phivxxxxc_theta_vecT);
+ phivxxxxc_theta_vecT.vals=reshape(repmat(phivxxxxc_theta_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ [phivxxcT,model.hind4{hindi4}]=colsort(phivxxcT,model.hind4{hindi4});
+ hindi4=hindi4+1;
+ [ Phixxxxc,model.hind4{hindi4} ] = chain4c_tensor( Phiv_vec,Phivv_vec,Phivvv_vec,Phivvvv_vec,...
+ phivxT,phivxxcT,phivxxxcT,phivxxxxcT,...
+ model.x_chain4c_M2,model.x_chain4c_M3,model.x_chain4c_M4,...
+ model.hind4{hindi4},n_ind,maxload,'vec' );
+ hindi4=hindi4+1;
+
+
+ [ Phixxxxctheta,model.hind4{hindi4} ] = chain4c_theta_tensor( Phiv_vec,Phivv_vec,Phivvv_vec,Phivvvv_vec,Phivvvvv_vec,...
+ phivxT,phivxxcT,phivxxxcT,phivxxxxcT,...
+ phiv_theta_vecT,phivx_theta_vecT,phivxxc_theta_vecT,phivxxxc_theta_vecT,phivxxxxc_theta_vecT,...
+ model.chain4c_theta_M2,model.chain4c_theta_M3,model.chain4c_theta_M5,model.chain4c_theta_M6,model.chain4c_theta_M9,model.chain4c_theta_M10,...
+ model.hind4{hindi4},n_ind,maxload,'vec' );
+ hindi4=hindi4+1;
+
+end
+tothindi=tothindi+7;
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/get_initial.m b/105/replication_package/solution_methods/taylor_projection/get_initial.m
new file mode 100644
index 0000000000000000000000000000000000000000..aa99d125b30e57feecb0eddc9aa114ceec6ec45a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_initial.m
@@ -0,0 +1,92 @@
+function [ stoch_pert,nonstoch_pert ] = get_initial(model,order,derivs,nyss,nxss )
+%This function transforms a pertrubation solution to an initial guess for Taylor
+%Projection. Two types of guess are available: stoch_pert includes
+%correction for volatility. nonstoch_pert does not include correction for
+%volatility.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=order(1);
+
+n_x=model.n_x;
+n_x1=model.n_x1;
+n_y=model.n_y;
+
+if order==1
+ [GH0,GH1]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)]);
+ stoch_pert=[GH0,GH1];
+ if nargout==2
+ [GH0,GH1]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)]);
+ nonstoch_pert=[GH0,GH1];
+ end
+elseif order==2
+ derivs.gxx=reshape(derivs.gxx,n_y,[]);
+ derivs.hxx=reshape(derivs.hxx(1:n_x1,:),n_x1,[]);
+ [GH0,GH1,GH2]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2);
+ [U2,~]=create_UW(n_x,2);
+ stoch_pert=[GH0,GH1,GH2*U2];
+ if nargout==2
+ [GH0,GH1,GH2]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2);
+ nonstoch_pert=[GH0,GH1,GH2*U2];
+ end
+elseif order==3
+ derivs.gxx=reshape(derivs.gxx,n_y,[]);
+ derivs.hxx=reshape(derivs.hxx(1:n_x1,:),n_x1,[]);
+ derivs.gxxx=reshape(derivs.gxxx,n_y,[]);
+ derivs.hxxx=reshape(derivs.hxxx(1:n_x1,:),n_x1,[]);
+ [GH0,GH1,GH2,GH3]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ stoch_pert=[GH0,GH1,GH2*U2,GH3*U3];
+ if nargout==2
+ [GH0,GH1,GH2,GH3]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3));
+ nonstoch_pert=[GH0,GH1,GH2*U2,GH3*U3];
+ end
+elseif order==4
+ derivs.gxx=reshape(derivs.gxx,n_y,[]);
+ derivs.hxx=reshape(derivs.hxx(1:n_x1,:),n_x1,[]);
+ derivs.gxxx=reshape(derivs.gxxx,n_y,[]);
+ derivs.hxxx=reshape(derivs.hxxx(1:n_x1,:),n_x1,[]);
+ derivs.gxxxx=reshape(derivs.gxxxx,n_y,[]);
+ derivs.hxxxx=reshape(derivs.hxxxx(1:n_x1,:),n_x1,[]);
+ [GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx;derivs.hxxxx(1:n_x1,:)]/factorial(4));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ [U4,~]=create_UW(n_x,4);
+ stoch_pert=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
+ if nargout==2
+ [GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx;derivs.hxxxx(1:n_x1,:)]/factorial(4));
+ nonstoch_pert=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
+ end
+elseif order==5
+ [GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx;derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx;derivs.hxxxxx(1:n_x1,:)]/factorial(5));
+ [U2,~]=create_UW(n_x,2);
+ [U3,~]=create_UW(n_x,3);
+ [U4,~]=create_UW(n_x,4);
+ [U5,~]=create_UW(n_x,5);
+ stoch_pert=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
+ if nargout==2
+ [GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx;derivs.hx(1:n_x1,:)],...
+ [derivs.gxx;derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx;derivs.hxxx(1:n_x1,:)]/factorial(3),...
+ [derivs.gxxxx;derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx;derivs.hxxxxx(1:n_x1,:)]/factorial(5));
+ nonstoch_pert=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
+ end
+end
+stoch_pert=stoch_pert(:);
+
+if nargout==2
+ nonstoch_pert=nonstoch_pert(:);
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/get_moments.m b/105/replication_package/solution_methods/taylor_projection/get_moments.m
new file mode 100644
index 0000000000000000000000000000000000000000..a047f7e86989553d0d032638ff9e85d791dd567c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_moments.m
@@ -0,0 +1,46 @@
+function M=get_moments(nep,P,order)
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=order(1);
+M2=0;M3=0;M4=0;M5=0;
+for i=1:length(P)
+ if order>=2
+ nep2=kron(nep(:,i),nep(:,i));
+ M2=M2+nep2*P(i);
+ end
+ if order>=3
+ nep3=kron(nep2,nep(:,i));
+ M3=M3+nep3*P(i);
+ end
+ if order>=4
+ nep4=kron(nep3,nep(:,i));
+ M4=M4+nep4*P(i);
+ end
+ if order>=5
+ nep5=kron(nep4,nep(:,i));
+ M5=M5+nep5*P(i);
+ end
+end
+
+if order==1
+ M.M1=sparse(size(nep,1),1);
+end
+if order>=2
+ M2(abs(M2)=3
+ M3(abs(M3)=4
+ M4(abs(M4)=5
+ M5(abs(M5)4
+ error('perturbation order cannot exceed 4')
+end
+
+params=[params(:);zeros(model.n_logicalparams,1)];
+
+if model.hybrid==0
+ eta=eta_fun(params(:)',[]);
+ eta=reshape(full(eta),model.n_x,[]);
+else
+ params=[zeros(1,model.n_e),params(:)'];
+ nv=[zeros(model.n_y,1);nyss(:);nxss(:);nxss(:)]'; % variables of tp
+ n_u=model.n_u;
+ nu=zeros(n_u,1)';
+ npreu=preu_fun(nv(model.preuvars),params); % all predetermined u
+ nu(model.preurows)=npreu;
+ nz=[nv,nu];
+ uname=['new_eta' model.uname '_fun'];
+ tempvars=nz(:,model.Phizvars); %n_s,n_x+n_y
+% tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+% tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+ eta=feval(uname,tempvars,params); %n_s*n_nodes,n_x2
+ eta=reshape(full(eta),model.n_x,[]);
+end
+
+tic
+n_f=model.n_f;
+
+n_y=model.n_y;
+n_x2=model.n_x2;
+n_x1=model.n_x1;
+n_z=model.n_z; % no. of auxiliary variables
+
+% note that pert system has one more state variable than tp system.
+n_x_tp=model.n_x;
+n_v_tp=model.n_v;
+n_x=model.n_x+1;
+n_v=model.n_v+2;
+
+if length(nyss)~=model.n_y
+ error('wrong size of steady state vector of control variables')
+elseif length(nxss)~=model.n_x
+ error('wrong size of steady state vector of state variables')
+end
+
+if isfield(model,'UW')
+ UW=model.UW; % IMPORTANT: THESE COMPRESSION MATRICES ASSUME A CERTAIN NONZERO PATTERN.
+else
+ UW=create_compression_matrices_nonzero2(approx,n_x); % compression matrices for the perturbation solution.
+ model.UW=UW;
+end
+
+if approx==2
+ W2=UW.W2; U2=UW.U2;
+elseif approx==3
+ W2=UW.W2; U2=UW.U2;
+ W3=UW.W3; U3=UW.U3;
+elseif approx==4
+ W2=UW.W2; U2=UW.U2;
+ W3=UW.W3; U3=UW.U3;
+ W4=UW.W4; U4=UW.U4;
+end
+
+if isfield(model,'OMEGA_x')
+ OMEGA_x=model.OMEGA_x;
+else
+ create_OMEGA_x;
+ model.OMEGA_x=OMEGA_x;
+end
+
+
+n_e=size(eta,2);
+eta=[eta;zeros(1,n_e)];
+
+nx=nxss;
+% nxss=[nxss(:);0]; % add steady state value of the perturbation variable.
+nxss=nxss(:);
+nyss=nyss(:);
+% nuss=eval_u([nyss;nyss;nxss;nxss],params);
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+if ~isfield(model,'maxload')
+ maxload=intarray(1);
+else
+ maxload=intarray(model.maxload);
+end
+if ~isfield(model,'pertind')
+ model.pertind=cell(model.totindi,1);
+end
+pertindi=1;
+
+% nPhi=Phi_fun(nx,params);
+if model.hybrid==0
+ get_Phi_derivs;
+end
+
+
+if isfield(model,'fname')
+ get_f_derivs_fname;
+else
+ get_f_derivs;
+end
+
+if model.hybrid==1 || model.hybrid==3
+ order=approx-1;
+ params_vec=params;
+ get_hybridPhi_derivs_v;
+ order=approx;
+ n_f=n_f+n_x2;
+ convert_to_matrices;
+ fv(n_y+n_x1+(1:n_x2),2*n_y+n_x1+(1:n_x2))=-eye(n_x2);
+ if approx>=1
+ nPhix=zeros(0,n_x);
+ end
+ if approx>=2
+ nPhixx=zeros(0,n_x^2);
+ end
+ if approx>=3
+ nPhixxx=zeros(0,n_x^3);
+ end
+ if approx>=4
+ nPhixxxx=zeros(0,n_x^4);
+ end
+ n_x2=0;
+ n_x1=n_x1+n_x2;
+end
+% numu_derivs=evalu_derivs(params,nxss,nyss,approx);
+% call_evalf_derivs;
+%
+% sym2script_fv;
+
+
+
+
+%%%%%%%%%%%%%
+fyp=fv(:,1:n_y); fy=fv(:,n_y+1:2*n_y); fxp=fv(:,2*n_y+1:2*n_y+n_x); fx=fv(:,2*n_y+n_x+1:end);
+
+% First Order
+
+% use the function gx_hx of Schmitt-Grohe and Uribe (2004) to solve the
+% first order solution
+
+% tic
+if isfield(model,'stake')
+ stake=model.stake;
+else
+ stake=1;
+end
+[gx,hx,exitflag]=gx_hx(full([fy;zeros(n_x2,n_y)]),full([fx(:,1:end-1);nPhix(:,1:end-1)]),full([fyp;zeros(n_x2,n_y)]),full([fxp(:,1:end-1);[zeros(n_x2,n_x1),-eye(n_x2)]]),stake);
+
+gx=[gx,zeros(n_y,1)];
+hx=[hx;zeros(1,n_x-1)];
+hx=[hx,zeros(n_x,1)];
+hx(end,end)=1;
+% replace relevant rows of hx with nPhix which is more numerically accurate
+hx(n_x1+1:n_x1+n_x2,:)=nPhix;
+
+% disp(['1st order completed in ' num2str(toc,'%15.2f') ' seconds'])
+
+hx=sparse(hx);
+gx=sparse(gx);
+
+% Second Order
+if approx>=2
+% tic
+ M2=M.M2;
+ eta2_M2=reshape([eta*reshape(M2,n_e,n_e)]',n_e,n_x);
+ eta2_M2=reshape([eta*eta2_M2]',n_x^2,1);
+
+% sym2script_fvv;
+
+ unique=nchoosek(n_x+2-1,2);
+ unique=unique-nchoosek(n_x-1+1-1,1);
+
+ Vx0=[gx*hx;gx;hx;speye(n_x)];
+ Vx1=[gx;sparse(n_y,n_x);speye(n_x,n_x);sparse(n_x,n_x)];
+
+ Ezeta2=[ sparse(n_x^2,n_x^2-1) , eta2_M2 ];
+
+ A=innerkron(n_f,n_v,fvv,Vx0,Vx0)+innerkron(n_f,n_v,fvv,Vx1,Vx1)*Ezeta2;
+
+ fy_fxp_fypgx=[fv(:,n_y+1:2*n_y) fv(:,2*n_y+1:2*n_y+n_x)+fv(:,1:n_y)*gx];
+
+ G=fy_fxp_fypgx(:,1:n_f);
+ H=fy_fxp_fypgx(:,n_f+1:n_f+n_x2);
+
+ D=sparse(n_f,n_f);
+ D(:,1:n_y)=fv(:,1:n_y);
+
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixx);
+ end
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2=logical(choosex2==1);
+ tempeye=speye(n_x^2);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ hx_hat=hx(1:end-1,1:end-1);
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,2 );
+ time=toc;
+ else
+ G=full(G);
+ D=full(D);
+ hx_hat=full(hx_hat);
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-CZ) );
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^2);
+ X(:,choosex2)=full(Xtemp);
+ gxx_hat=Xtemp(1:n_y,:);
+ hat_eta2_M2=eta2_M2(choosex2,:);
+ %Block 2: ss
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2=logical(choosex2==1);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ tic
+ Xtemp=-(D+G)\(CZ+(fyp*gxx_hat)*hat_eta2_M2);
+ time=toc;
+
+ acc=norm(full(CZ+(fyp*gxx_hat)*hat_eta2_M2+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex2)=full(Xtemp); clear Xtemp
+ else
+ if n_x2==0
+ CU2=A*U2;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ CU2=A*U2+H*(nPhixx*U2);
+ end
+ W2BU2=(innerkron(unique,n_x,W2,hx,hx)+W2*Ezeta2)*U2;
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ CU2Z=CU2*Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(full(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U2,2));
+ X(:,choosex2U)=full(Xtemp); clear Xtemp ZTW2BU2Z
+ %Block 2
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ W2BU2Z=W2BU2*Z;
+ CU2Z=CU2*Z+D*X*W2BU2Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z);
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex2U)=full(Xtemp); clear Xtemp W2BU2Z ZTW2BU2Z
+ X=X*W2;
+ end
+ gxx=X(1:n_y,:);
+ hxx=[X(n_y+1:end,:);nPhixx;zeros(1,n_x^2)];
+end
+
+% Third Order
+if approx>=3
+ Vxx0=[chain2(gx,gxx,hx,hxx);gxx;hxx;sparse(n_x,n_x^2)];
+ Vxx1=[gxx;sparse(n_y+2*n_x,n_x^2)];
+
+ M3=M.M3(:);
+
+ eta3_M3=reshape([eta*reshape(M3,n_e,n_e^2)]',n_e,n_e*n_x);
+ eta3_M3=reshape([eta*eta3_M3]',n_e,n_x^2);
+ eta3_M3=reshape([eta*eta3_M3]',n_x^3,1);
+
+ Ezeta3=[ sparse(n_x^3,n_x^3-1) , eta3_M3 ];
+ Ix=speye(n_x);
+ Ix_Ezeta2=kron(Ix,Ezeta2);
+
+ unique=nchoosek(n_x+3-1,3);
+ unique=unique-nchoosek(n_x-1+2-1,2);
+ A_third_order; % create matrix A of a third order solution
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxx);
+ end
+ %Block 1:xxx
+ choosex3=kron(spx,kron(spx,spx));
+ choosex3=logical(choosex3==1);
+ tempeye=speye(n_x^3);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,3 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 3,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,3)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^3);
+ X(:,choosex3)=full(Xtemp);
+ gxxx_hat=Xtemp(1:n_y,:);
+ hat_eta3_M3=eta3_M3(choosex3,:);
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxx_hat,n_f*(n_x-1),(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f,n_x-1)*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ %Block 2:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=(fyp*gxxx_hat)*hat_eta3_M3;
+ cons=CZ+term2;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices, because the
+ % compression matrices assume i1>=i2>=i3, while block xss has
+ % i11e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U3,2));
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=choosex3+kron(kron(sps,spx),sps);
+ choosex3=choosex3+kron(kron(spx,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 3:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z W3BU3
+ X=X*W3;
+ end
+
+ gxxx=X(1:n_y,:);
+ hxxx=[X(n_y+1:end,:);nPhixxx;zeros(1,n_x^3)];
+end
+
+% Fourth Order
+if approx>=4
+ Vxxx0=[chain3(gx,gxx,gxxx,hx,hxx,hxxx,OMEGA_x.OMEGA1);gxxx;hxxx;sparse(n_x,n_x^3)];
+ Vxxx1=[gxxx;sparse(n_y+2*n_x,n_x^3)];
+
+ M4=M.M4(:);
+
+ eta4_M4=reshape([eta*reshape(M4,n_e,n_e^3)]',n_e,n_e^2*n_x);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_e*n_x^2);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_x^3);
+ eta4_M4=reshape([eta*eta4_M4]',n_x^4,1);
+
+ Ezeta4=[ sparse(n_x^4,n_x^4-1) , eta4_M4 ];
+ Ix_Ezeta3=kron(Ix,Ezeta3);
+ Ix2=speye(n_x^2);
+ Ix2_Ezeta2=kron(Ix2,Ezeta2);
+
+ hx2=kron(hx,hx);
+ hx_Ezeta2_hx=kron(kron(hx,Ezeta2),hx);
+ hx_Ezeta3=kron(hx,Ezeta3);
+ hx2_Ezeta2=kron(hx2,Ezeta2);
+
+ unique=nchoosek(n_x+4-1,4);
+ unique=unique-nchoosek(n_x-1+3-1,3);
+
+ clear result R
+
+ A_fourth_order; % create matrix A of a fourth order solution
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxxx);
+ end
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ tempeye=speye(n_x^4);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,4 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 4,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,4)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^4);
+ X(:,choosex4)=full(Xtemp);
+ gxxxx_hat=Xtemp(1:n_y,:);
+ hat_eta4_M4=eta4_M4(choosex4,:);
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1)^2,(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f*(n_x-1),(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)*n_f,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^2,n_f);
+ term2=term2';
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,2 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ gxxss_hat=Xtemp(1:n_y,:);
+ %Block 2:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1),(n_x-1)^3)*hat_eta3_M3;
+ term2=reshape(term2',n_f,(n_x-1))*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ %Block 2:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=(6*fyp*gxxss_hat)*hat_eta2_M2;
+ term3=(fyp*gxxxx_hat)*hat_eta4_M4;
+ cons=CZ+term2+term3;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices.
+ X=reshape(permute(reshape(X,[],n_x,n_x,n_x,n_x),[1,5,4,3,2]),[],n_x^4)*U4*W4;
+ else
+ if n_x2==0
+ CU4=A*U4;
+ else
+ CU4=A*U4+H*(nPhixxxx*U4);
+ end
+ kron_hx_hx=kron(hx,hx);
+ WBU_fourth_order; % create the matrix W4BU4
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4U=logical(U4'*choosex4~=0);
+ tempeye=speye(size(U4,2));
+ Z=tempeye(:,choosex4U);
+ CU4Z=CU4*Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U4,2));
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(spx,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,spx),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 3:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 4:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ X=X*W4;
+ end
+
+ gxxxx=X(1:n_y,:);
+ hxxxx=[X(n_y+1:end,:);nPhixxxx;zeros(1,n_x^4)];
+end
+
+
+
+clear derivs
+derivs.gx=full(gx);
+derivs.hx=full(hx(1:end-1,:));
+derivs.gxx=sparse(n_y,n_x^2);
+derivs.hxx=sparse(n_x-1,n_x^2);
+derivs.gxxx=sparse(n_y,n_x^3);
+derivs.hxxx=sparse(n_x-1,n_x^3);
+
+if approx>=2
+ derivs.gxx=reshape(full(gxx),n_y,n_x,n_x);
+ derivs.hxx=reshape(full(hxx(1:end-1,:)),n_x-1,n_x,n_x);
+end
+if approx>=3
+ derivs.gxxx=reshape(full(gxxx),n_y,n_x,n_x,n_x);
+ derivs.hxxx=reshape(full(hxxx(1:end-1,:)),n_x-1,n_x,n_x,n_x);
+end
+if approx>=4
+ derivs.gxxxx=reshape(full(gxxxx),n_y,n_x,n_x,n_x,n_x);
+ derivs.hxxxx=reshape(full(hxxxx(1:end-1,:)),n_x-1,n_x,n_x,n_x,n_x);
+end
+
+[ stoch_pert, nonstoch_pert ] = get_initial( model,model.order(1),derivs,nyss,nxss );
+
+stoch_pert=repmat(stoch_pert(:),1,model.n_regimes); % construct a matrix with n_regimes columns for the initial guess.
+nonstoch_pert=repmat(nonstoch_pert(:),1,model.n_regimes); % construct a matrix with n_regimes columns for the initial guess.
+
+
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/get_pertMS.m b/105/replication_package/solution_methods/taylor_projection/get_pertMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..f43568c3a658f1fd0e0589679f0ce3616787c5d4
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_pertMS.m
@@ -0,0 +1,7 @@
+function [derivs,stoch_pert,nonstoch_pert,model]=get_pertMS(model,params,msparams_ss,M,nxss,nyss,algo)
+%Get a standard perturbation solution for fixed parameters.
+
+[derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,[params(:);msparams_ss(:);msparams_ss(:)],M,nxss,nyss,algo);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/get_perti.m b/105/replication_package/solution_methods/taylor_projection/get_perti.m
new file mode 100644
index 0000000000000000000000000000000000000000..0eced85c3fdbe1c8b06c44374192a03d2495d9aa
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/get_perti.m
@@ -0,0 +1,776 @@
+function [derivs,stoch_pert,nonstoch_pert,model]=get_perti(model,params,paramsi,M,nxss,nyss,algo,varargin)
+%get_pert(model,params,M,eta,nxss,nyss,algo)
+%This function solves the model with perturbation up to fourth
+%order.
+%Input variables:
+%model: a structure that is generated automatically by the function
+%prepare_model.m
+%params: a vector of all parameter values ordered in the same order of symparams.
+%M: a structure that contains all the cross moments of the shocks. The fields of
+%this structure should be M2,M3,M4.
+%eta: The matrix eta as defined in Schmitt-Grohe and Uribe (2004).
+%nxss,nyss: steady state values of x and y
+%algo: algorithm type. 'dlyap' for dlyap or 'vectorize' for vectorization.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+if isempty(M)
+ M=gaussian_moments(1);
+end
+
+if size(paramsi,1)~=model.n_paramsi
+ error('wrong size of varying parameters')
+end
+
+n_s=size(paramsi,2);
+
+params=[repmat(params(:)',n_s,1),paramsi'];
+
+
+if nargin==8
+ msparams_ss=varargin{1};
+ params=[params,repmar([msparams_ss(:);msparams_ss(:)]',n_s,1)];
+end
+
+if strcmpi(algo,'gensylv')
+ kamenik_type=2;
+ algo='Kamenik';
+elseif ~strcmpi(algo,'dlyap') && ~strcmpi(algo,'vectorize')
+ error('wrong algorithm')
+end
+
+approx=model.order(2);
+
+if approx>4
+ error('perturbation order cannot exceed 4')
+end
+
+params=[params,zeros(n_s,model.n_logicalparams)];
+
+if model.hybrid==0
+ error('model must be hybrid')
+% eta=eta_fun(params(:)',[]);
+% eta=reshape(full(eta),model.n_x,[]);
+else
+ params=[zeros(n_s,model.n_e),params];
+ nv=[zeros(model.n_y,1);nyss(:);nxss(:);nxss(:)]'; % variables of tp
+ nv=repmat(nv,n_s,1);
+ n_u=model.n_u;
+ nu=zeros(n_s,n_u);
+ npreu=preu_fun(nv(:,model.preuvars),params); % all predetermined u
+ nu(:,model.preurows)=npreu;
+ nz=[nv,nu];
+ uname=['new_eta' model.uname '_fun'];
+ tempvars=nz(:,model.Phizvars); %n_s,n_x+n_y
+% tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+% tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+ eta=feval(uname,tempvars,params); %n_s*n_nodes,n_x2
+ eta=reshape(full(eta(1,:)),model.n_x,[]);
+ warning('I assume that law of motion of state variables is independent of varying parameters; otherwise, Blanchard-Khan method not applicable.');
+end
+
+tic
+n_f=model.n_f;
+
+n_y=model.n_y;
+n_x2=model.n_x2;
+n_x1=model.n_x1;
+n_z=model.n_z; % no. of auxiliary variables
+
+% note that pert system has one more state variable than tp system.
+n_x_tp=model.n_x;
+n_v_tp=model.n_v;
+n_x=model.n_x+1;
+n_v=model.n_v+2;
+
+if isfield(model,'UW')
+ UW=model.UW; % IMPORTANT: THESE COMPRESSION MATRICES ASSUME A CERTAIN NONZERO PATTERN.
+else
+ UW=create_compression_matrices_nonzero2(approx,n_x); % compression matrices for the perturbation solution.
+ model.UW=UW;
+end
+
+if approx==2
+ W2=UW.W2; U2=UW.U2;
+elseif approx==3
+ W2=UW.W2; U2=UW.U2;
+ W3=UW.W3; U3=UW.U3;
+elseif approx==4
+ W2=UW.W2; U2=UW.U2;
+ W3=UW.W3; U3=UW.U3;
+ W4=UW.W4; U4=UW.U4;
+end
+
+if isfield(model,'OMEGA_x')
+ OMEGA_x=model.OMEGA_x;
+else
+ create_OMEGA_x;
+ model.OMEGA_x=OMEGA_x;
+end
+
+
+n_e=size(eta,2);
+eta=[eta;zeros(1,n_e)];
+
+nx=nxss;
+% nxss=[nxss(:);0]; % add steady state value of the perturbation variable.
+nxss=nxss(:);
+nyss=nyss(:);
+% nuss=eval_u([nyss;nyss;nxss;nxss],params);
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+if ~isfield(model,'maxload')
+ maxload=intarray(1);
+else
+ maxload=intarray(model.maxload);
+end
+if ~isfield(model,'pertind')
+ model.pertind=cell(model.totindi,1);
+end
+pertindi=1;
+
+% nPhi=Phi_fun(nx,params);
+if model.hybrid==0
+ get_Phi_derivs;
+end
+
+
+if isfield(model,'fname')
+ get_f_derivs_fname;
+else
+ get_f_derivs;
+end
+
+if model.hybrid==1 || model.hybrid==3
+ order=approx-1;
+ params_vec=params;
+ get_hybridPhi_derivs_v;
+ order=approx;
+
+ n_f_all=n_y+n_x1+n_x2;
+ convert_to_matrices_i;
+ n_f=n_f_all;
+ fv(n_y+n_x1+(1:n_x2),2*n_y+n_x1+(1:n_x2))=-eye(n_x2);
+ if approx>=1
+ nPhix=zeros(0,n_x);
+ end
+ if approx>=2
+ nPhixx=zeros(0,n_x^2);
+ end
+ if approx>=3
+ nPhixxx=zeros(0,n_x^3);
+ end
+ if approx>=4
+ nPhixxxx=zeros(0,n_x^4);
+ end
+ n_x2=0;
+ n_x1=n_x1+n_x2;
+end
+% numu_derivs=evalu_derivs(params,nxss,nyss,approx);
+% call_evalf_derivs;
+%
+% sym2script_fv;
+
+
+
+
+%%%%%%%%%%%%%
+fyp=fv(:,1:n_y); fy=fv(:,n_y+1:2*n_y); fxp=fv(:,2*n_y+1:2*n_y+n_x); fx=fv(:,2*n_y+n_x+1:end);
+
+% First Order
+
+% use the function gx_hx of Schmitt-Grohe and Uribe (2004) to solve the
+% first order solution
+
+% tic
+[gx,hx,exitflag]=gx_hx(full([fy;zeros(n_x2,n_y)]),full([fx(:,1:end-1);nPhix(:,1:end-1)]),full([fyp;zeros(n_x2,n_y)]),full([fxp(:,1:end-1);[zeros(n_x2,n_x1),-eye(n_x2)]]));
+
+gx=[gx,zeros(n_y,1)];
+hx=[hx;zeros(1,n_x-1)];
+hx=[hx,zeros(n_x,1)];
+hx(end,end)=1;
+% replace relevant rows of hx with nPhix which is more numerically accurate
+hx(n_x1+1:n_x1+n_x2,:)=nPhix;
+
+% disp(['1st order completed in ' num2str(toc,'%15.2f') ' seconds'])
+
+hx=sparse(hx);
+gx=sparse(gx);
+
+% Second Order
+if approx>=2
+% tic
+ M2=M.M2;
+ eta2_M2=reshape([eta*reshape(M2,n_e,n_e)]',n_e,n_x);
+ eta2_M2=reshape([eta*eta2_M2]',n_x^2,1);
+
+% sym2script_fvv;
+
+ unique=nchoosek(n_x+2-1,2);
+ unique=unique-nchoosek(n_x-1+1-1,1);
+
+ Vx0=[gx*hx;gx;hx;speye(n_x)];
+ Vx1=[gx;sparse(n_y,n_x);speye(n_x,n_x);sparse(n_x,n_x)];
+
+ Ezeta2=[ sparse(n_x^2,n_x^2-1) , eta2_M2 ];
+
+ A=innerkron(n_f,n_v,fvv,Vx0,Vx0)+innerkron(n_f,n_v,fvv,Vx1,Vx1)*Ezeta2;
+
+ fy_fxp_fypgx=[fv(:,n_y+1:2*n_y) fv(:,2*n_y+1:2*n_y+n_x)+fv(:,1:n_y)*gx];
+
+ G=fy_fxp_fypgx(:,1:n_f);
+ H=fy_fxp_fypgx(:,n_f+1:n_f+n_x2);
+
+ D=sparse(n_f,n_f);
+ D(:,1:n_y)=fv(:,1:n_y);
+
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixx);
+ end
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2=logical(choosex2==1);
+ tempeye=speye(n_x^2);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ hx_hat=hx(1:end-1,1:end-1);
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,2 );
+ time=toc;
+ else
+ G=full(G);
+ D=full(D);
+ hx_hat=full(hx_hat);
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-CZ) );
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^2);
+ X(:,choosex2)=full(Xtemp);
+ gxx_hat=Xtemp(1:n_y,:);
+ hat_eta2_M2=eta2_M2(choosex2,:);
+ %Block 2: ss
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2=logical(choosex2==1);
+ Z=tempeye(:,choosex2);
+ CZ=C*Z;
+ tic
+ Xtemp=-(D+G)\(CZ+(fyp*gxx_hat)*hat_eta2_M2);
+ time=toc;
+
+ acc=norm(full(CZ+(fyp*gxx_hat)*hat_eta2_M2+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex2)=full(Xtemp); clear Xtemp
+ else
+ if n_x2==0
+ CU2=A*U2;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ CU2=A*U2+H*(nPhixx*U2);
+ end
+ W2BU2=(innerkron(unique,n_x,W2,hx,hx)+W2*Ezeta2)*U2;
+ %Block 1: xx
+ spx=sparse([ones(n_x-1,1);0]);
+ choosex2=kron(spx,spx);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ CU2Z=CU2*Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(full(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z));
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U2,2));
+ X(:,choosex2U)=full(Xtemp); clear Xtemp ZTW2BU2Z
+ %Block 2
+ sps=sparse([zeros(n_x-1,1);1]);
+ choosex2=kron(sps,sps);
+ choosex2U=logical(U2'*choosex2==1);
+ tempeye=speye(size(U2,2));
+ Z=tempeye(:,choosex2U);
+ W2BU2Z=W2BU2*Z;
+ CU2Z=CU2*Z+D*X*W2BU2Z;
+ ZTW2BU2Z=Z'*W2BU2*Z;
+ if strcmpi(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW2BU2Z',D)+kron(speye(size(Z,2)),G))\CU2Z(:),n_f,size(Z,2));
+ elseif strcmpi(algo,'dlyap')
+ Xtemp=dlyap(ZTW2BU2Z',(-G\D)',(-G\CU2Z)');
+ Xtemp=Xtemp';
+ elseif strcmpi(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW2BU2Z'),full((G\D)'),full((-G\CU2Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW2BU2Z+CU2Z);
+ if acc>1e-8
+ warning(['Second order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex2U)=full(Xtemp); clear Xtemp W2BU2Z ZTW2BU2Z
+ X=X*W2;
+ end
+ gxx=X(1:n_y,:);
+ hxx=[X(n_y+1:end,:);nPhixx;zeros(1,n_x^2)];
+end
+
+% Third Order
+if approx>=3
+ Vxx0=[chain2(gx,gxx,hx,hxx);gxx;hxx;sparse(n_x,n_x^2)];
+ Vxx1=[gxx;sparse(n_y+2*n_x,n_x^2)];
+
+ M3=M.M3(:);
+
+ eta3_M3=reshape([eta*reshape(M3,n_e,n_e^2)]',n_e,n_e*n_x);
+ eta3_M3=reshape([eta*eta3_M3]',n_e,n_x^2);
+ eta3_M3=reshape([eta*eta3_M3]',n_x^3,1);
+
+ Ezeta3=[ sparse(n_x^3,n_x^3-1) , eta3_M3 ];
+ Ix=speye(n_x);
+ Ix_Ezeta2=kron(Ix,Ezeta2);
+
+ unique=nchoosek(n_x+3-1,3);
+ unique=unique-nchoosek(n_x-1+2-1,2);
+ A_third_order; % create matrix A of a third order solution
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxx);
+ end
+ %Block 1:xxx
+ choosex3=kron(spx,kron(spx,spx));
+ choosex3=logical(choosex3==1);
+ tempeye=speye(n_x^3);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,3 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 3,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,3)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^3);
+ X(:,choosex3)=full(Xtemp);
+ gxxx_hat=Xtemp(1:n_y,:);
+ hat_eta3_M3=eta3_M3(choosex3,:);
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxx_hat,n_f*(n_x-1),(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f,n_x-1)*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ %Block 2:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3=logical(choosex3==1);
+ Z=tempeye(:,choosex3);
+ CZ=C*Z;
+ term2=(fyp*gxxx_hat)*hat_eta3_M3;
+ cons=CZ+term2;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex3)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices, because the
+ % compression matrices assume i1>=i2>=i3, while block xss has
+ % i11e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U3,2));
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 2:xss
+ choosex3=kron(kron(sps,sps),spx);
+ choosex3=choosex3+kron(kron(sps,spx),sps);
+ choosex3=choosex3+kron(kron(spx,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z
+ %Block 3:sss
+ choosex3=kron(kron(sps,sps),sps);
+ choosex3U=logical(U3'*choosex3~=0);
+ Z=tempeye(:,choosex3U);
+ W3BU3Z=W3BU3*Z;
+ CU3Z=CU3*Z+D*X*W3BU3Z;
+ ZTW3BU3Z=Z'*W3BU3*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW3BU3Z',D)+kron(speye(size(Z,2)),G))\CU3Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW3BU3Z',(-G\D)',(-G\CU3Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW3BU3Z'),full((G\D)'),full((-G\CU3Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW3BU3Z+CU3Z);
+ if acc>1e-8
+ warning(['Third order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex3U)=full(Xtemp); clear Xtemp ZTW3BU3Z W3BU3
+ X=X*W3;
+ end
+
+ gxxx=X(1:n_y,:);
+ hxxx=[X(n_y+1:end,:);nPhixxx;zeros(1,n_x^3)];
+end
+
+% Fourth Order
+if approx>=4
+ Vxxx0=[chain3(gx,gxx,gxxx,hx,hxx,hxxx,OMEGA_x.OMEGA1);gxxx;hxxx;sparse(n_x,n_x^3)];
+ Vxxx1=[gxxx;sparse(n_y+2*n_x,n_x^3)];
+
+ M4=M.M4(:);
+
+ eta4_M4=reshape([eta*reshape(M4,n_e,n_e^3)]',n_e,n_e^2*n_x);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_e*n_x^2);
+ eta4_M4=reshape([eta*eta4_M4]',n_e,n_x^3);
+ eta4_M4=reshape([eta*eta4_M4]',n_x^4,1);
+
+ Ezeta4=[ sparse(n_x^4,n_x^4-1) , eta4_M4 ];
+ Ix_Ezeta3=kron(Ix,Ezeta3);
+ Ix2=speye(n_x^2);
+ Ix2_Ezeta2=kron(Ix2,Ezeta2);
+
+ hx2=kron(hx,hx);
+ hx_Ezeta2_hx=kron(kron(hx,Ezeta2),hx);
+ hx_Ezeta3=kron(hx,Ezeta3);
+ hx2_Ezeta2=kron(hx2,Ezeta2);
+
+ unique=nchoosek(n_x+4-1,4);
+ unique=unique-nchoosek(n_x-1+3-1,3);
+
+ clear result R
+
+ A_fourth_order; % create matrix A of a fourth order solution
+
+ if strcmp(algo,'Kamenik')
+ if n_x2==0
+ C=A;
+ else % do not solve exogenous state variables (see appendix A.6 in the paper). H is the last block of G.
+ C=A+H*(nPhixxxx);
+ end
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ tempeye=speye(n_x^4);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-CZ,4 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 4,G,D,hx_hat,full(-CZ));
+ time=toc;
+ end
+ acc=norm(full(CZ+AkronkC(D*Xtemp,hx_hat,4)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,n_x^4);
+ X(:,choosex4)=full(Xtemp);
+ gxxxx_hat=Xtemp(1:n_y,:);
+ hat_eta4_M4=eta4_M4(choosex4,:);
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1)^2,(n_x-1)^2)*hat_eta2_M2;
+ term2=reshape(term2',n_f*(n_x-1),(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)*n_f,(n_x-1))*hx_hat;
+ term2=reshape(term2',(n_x-1)^2,n_f);
+ term2=term2';
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,2 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 2,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,2)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ gxxss_hat=Xtemp(1:n_y,:);
+ %Block 2:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=reshape(fyp*gxxxx_hat,n_f*(n_x-1),(n_x-1)^3)*hat_eta3_M3;
+ term2=reshape(term2',n_f,(n_x-1))*hx_hat;
+ cons=CZ+term2;
+ if kamenik_type==1
+ tic
+ Xtemp=kamenik( G,D,hx_hat,-cons,1 );
+ time=toc;
+ else
+ tic
+ [~,Xtemp]=gensylv( 1,G,D,hx_hat,full(-cons));
+ time=toc;
+ end
+ acc=norm(full(cons+AkronkC(D*Xtemp,hx_hat,1)+G*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp);
+ %Block 2:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4=logical(choosex4==1);
+ Z=tempeye(:,choosex4);
+ CZ=C*Z;
+ term2=(6*fyp*gxxss_hat)*hat_eta2_M2;
+ term3=(fyp*gxxxx_hat)*hat_eta4_M4;
+ cons=CZ+term2+term3;
+ tic
+ Xtemp=-(D+G)\cons;
+ time=toc;
+ acc=norm(full(cons+(D+G)*Xtemp));
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ Xtemp=reshape(Xtemp,n_f,size(Z,2));
+ X(:,choosex4)=full(Xtemp); clear Xtemp
+ % add symmetric entries, but first permute the indices.
+ X=reshape(permute(reshape(X,[],n_x,n_x,n_x,n_x),[1,5,4,3,2]),[],n_x^4)*U4*W4;
+ else
+ if n_x2==0
+ CU4=A*U4;
+ else
+ CU4=A*U4+H*(nPhixxxx*U4);
+ end
+ kron_hx_hx=kron(hx,hx);
+ WBU_fourth_order; % create the matrix W4BU4
+ %Block 1:xxxx
+ choosex4=kron(kron(spx,spx),kron(spx,spx));
+ choosex4U=logical(U4'*choosex4~=0);
+ tempeye=speye(size(U4,2));
+ Z=tempeye(:,choosex4U);
+ CU4Z=CU4*Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X=zeros(n_f,size(U4,2));
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 2:xxss
+ choosex4=kron(kron(sps,sps),kron(spx,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,spx),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(spx,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(spx,spx),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 3:xsss
+ choosex4=kron(kron(sps,sps),kron(sps,spx));
+ choosex4=choosex4+kron(kron(sps,sps),kron(spx,sps));
+ choosex4=choosex4+kron(kron(sps,spx),kron(sps,sps));
+ choosex4=choosex4+kron(kron(spx,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ %Block 4:ssss
+ choosex4=kron(kron(sps,sps),kron(sps,sps));
+ choosex4U=logical(U4'*choosex4~=0);
+ Z=tempeye(:,choosex4U);
+ W4BU4Z=W4BU4*Z;
+ CU4Z=CU4*Z+D*X*W4BU4Z;
+ ZTW4BU4Z=Z'*W4BU4*Z;
+ if strcmp(algo,'vectorize')
+ Xtemp=reshape(-(kron(ZTW4BU4Z',D)+kron(speye(size(Z,2)),G))\CU4Z(:),n_f,size(Z,2));
+ elseif strcmp(algo,'dlyap')
+ Xtemp=dlyap(ZTW4BU4Z',(-G\D)',(-G\CU4Z)');
+ Xtemp=Xtemp';
+ elseif strcmp(algo,'slicot')
+ Xtemp=HessSchur(full(ZTW4BU4Z'),full((G\D)'),full((-G\CU4Z)'));
+ Xtemp=Xtemp';
+ end
+ acc=norm(G*Xtemp+D*Xtemp*ZTW4BU4Z+CU4Z);
+ if acc>1e-8
+ warning(['Fourth order derivatives may be inaccurate, norm(error)=' num2str(acc) '. Try a different solver.'])
+ end
+ X(:,choosex4U)=full(Xtemp); clear Xtemp ZTW4BU4Z
+ X=X*W4;
+ end
+
+ gxxxx=X(1:n_y,:);
+ hxxxx=[X(n_y+1:end,:);nPhixxxx;zeros(1,n_x^4)];
+end
+
+
+
+clear derivs
+derivs.gx=full(gx);
+derivs.hx=full(hx(1:end-1,:));
+derivs.gxx=sparse(n_y,n_x^2);
+derivs.hxx=sparse(n_x-1,n_x^2);
+derivs.gxxx=sparse(n_y,n_x^3);
+derivs.hxxx=sparse(n_x-1,n_x^3);
+
+if approx>=2
+ derivs.gxx=reshape(full(gxx),n_y,n_x,n_x);
+ derivs.hxx=reshape(full(hxx(1:end-1,:)),n_x-1,n_x,n_x);
+end
+if approx>=3
+ derivs.gxxx=reshape(full(gxxx),n_y,n_x,n_x,n_x);
+ derivs.hxxx=reshape(full(hxxx(1:end-1,:)),n_x-1,n_x,n_x,n_x);
+end
+if approx>=4
+ derivs.gxxxx=reshape(full(gxxxx),n_y,n_x,n_x,n_x,n_x);
+ derivs.hxxxx=reshape(full(hxxxx(1:end-1,:)),n_x-1,n_x,n_x,n_x,n_x);
+end
+
+[ stoch_pert, nonstoch_pert ] = get_initial( model,model.order(1),derivs,nyss,nxss );
+
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/getderivs_c.m b/105/replication_package/solution_methods/taylor_projection/getderivs_c.m
new file mode 100644
index 0000000000000000000000000000000000000000..43fc65fa12b9d5bb8107ad1fa4eb4ea56603f4ea
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/getderivs_c.m
@@ -0,0 +1,102 @@
+function [index]=getderivs_c(f,v,order,symparams,fname)
+%This function is like getderivs, but only unique nonzero derivatives are
+%returned.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% Changed on July 31, 2016 by Oren Levintal: conversion of relevant indices
+% to full indices was wrong for the case of only one nonzero derivative.
+
+if order<1
+ error('order must be at least 1')
+end
+
+f=f(:);
+v=v(:);
+
+n_f=length(f);
+n_v=length(v);
+
+uncomp=cell(n_f,order);
+derivs=cell(n_f,order);
+% differentiate rows of f separately w.r.t to relevant variables ONLY
+relevant_v=logical(jacobian(f(:),v)~=0);
+for frow=1:n_f
+% disp(['Differentiating row no. ' num2str(frow) ' of ' fname ' ...'])
+ [derivs(frow,:),uncomp(frow,:)]=compderivs_u(f(frow),v(relevant_v(frow,:)),order);
+end
+
+% transform uncompression matrices into indices, and create totalloc.
+% totalloc(frow,k) stores the total number of nonzero unique k-order derivatives of f(frow).
+index=[];
+totalloc=zeros(n_f,order);
+for k=1:order
+ for frow=1:n_f
+ [index.loc{frow,k},index.nnz{frow,k}]=find(uncomp{frow,k});
+ totalloc(frow,k)=length(index.loc{frow,k});
+ if isempty(index.loc{frow,k})
+ index.loc{frow,k}=0;
+ end
+ end
+end
+
+% create matlab functions to calculate the derivatives
+for k=1:order
+ fun_name=[fname '_d_c' num2str(k)];
+ fid = fopen([fun_name '.m'], 'w');
+ fprintf(fid,'%s\n', ['function derivs=' fun_name '(vars,params,index)']);
+ fprintf(fid,'%s\n', 'n_s=size(vars,1);');
+ for i=1:length(v)
+ fprintf(fid,'%s\n', [char(v(i)) '=vars(:,' num2str(i) ');']);
+ end
+ for i=1:length(symparams)
+ fprintf(fid,'%s\n', [char(symparams(i)) '=params(:,' num2str(i) ');']);
+ end
+ fprintf(fid,'%s\n', ['full_rows=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_cols=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_vals=zeros(n_s,' num2str(sum(totalloc(:,k))) ');']);
+ fprintf(fid,'%s\n', ['svec=1:n_s;']);
+ for frow=1:n_f
+ if totalloc(frow,k)>0
+ tempderiv=derivs{frow,k};
+ fprintf(fid,'%s\n', ['compressed_deriv=zeros(n_s,' num2str(length(tempderiv)) ');']);
+ for i=1:length(tempderiv)
+ disp_fun_row('compressed_deriv',tempderiv(i),i,fid);
+ end
+ fprintf(fid,'%s\n', ['uncompressed_deriv=compressed_deriv(:,index.nnz{' num2str(frow) ',' num2str(k) '});']);
+ tempstart=sum(totalloc(1:frow-1,k));
+ tempend=sum(totalloc(1:frow,k));
+ fprintf(fid,'%s\n', ['full_vals(:,' num2str(tempstart+1) ':' num2str(tempend) ')=uncompressed_deriv;']);
+
+ % transform columns to n-dimensions
+ tempcols='tempcol1';
+ n_relevant_v=sum(relevant_v(frow,:));
+ tempdim=num2str(n_relevant_v);
+ for tempk=2:k
+ tempcols=[tempcols ',tempcol' num2str(tempk)];
+ tempdim=[tempdim ',' num2str(n_relevant_v)];
+ end
+ eval(['[' tempcols ']=ind2sub([' tempdim '],index.loc{' num2str(frow) ',' num2str(k) '});']);
+ tempcols=eval(['[' tempcols ']']);
+ % each row of f was differentiated w.r.t relevant variables.
+ % now, translate dimensions to the full vector of variables.
+ tempv=1:n_v;
+ takev=tempv(relevant_v(frow,:));
+
+ tempcols=takev(tempcols);
+ if k==1
+ tempcols=tempcols(:);
+ end
+
+ % find location in compressed matrix
+ uniqueind=uniquecols2ind(tempcols,n_v);
+ % return to index
+ index.loc{frow,k}=uniqueind;
+ fprintf(fid,'%s\n', ['full_cols(' num2str(tempstart+1) ':' num2str(tempend) ',:)=index.loc{' num2str(frow) ',' num2str(k) '};']);
+ fprintf(fid,'%s\n', ['full_rows(' num2str(tempstart+1) ':' num2str(tempend) ')=' num2str(frow) ';']);
+ end
+ end
+ fprintf(fid,'%s\n', ['derivs=sptensor(full_rows,full_cols,full_vals,' num2str(n_f) ',' num2str(nchoosek(n_v+k-1,k)) ');']);
+ fclose(fid);
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/getderivs_tensor.m b/105/replication_package/solution_methods/taylor_projection/getderivs_tensor.m
new file mode 100644
index 0000000000000000000000000000000000000000..f07c64686021501c4a218c57483a70aa7f9d2996
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/getderivs_tensor.m
@@ -0,0 +1,97 @@
+function [index]=getderivs_tensor(f,v,order,symparams,fname)
+%This function differentiates f w.r.t v up to order, and generates
+%vectorized functions that calculate these derivatives. The derivatives are
+%stored in a sparse tensor of dimensions n_f,n_v,..,n_v, where n_f
+%is the size of f and n_v is the size of v.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+if order<1
+ error('order must be at least 1')
+end
+
+f=f(:);
+v=v(:);
+
+n_f=length(f);
+n_v=length(v);
+
+uncomp=cell(n_f,order);
+derivs=cell(n_f,order);
+
+% differentiate rows of f separately w.r.t to relevant variables ONLY
+relevant_v=logical(jacobian(f(:),v)~=0);
+for frow=1:n_f
+ [derivs(frow,:),uncomp(frow,:)]=compderivs(f(frow),v(relevant_v(frow,:)),order);
+end
+
+% transform uncompression matrices into indices, and create totalloc.
+% totalloc(frow,k) stores the total number of nonzero k-order derivatives of f(frow), including all (nonzero) mixed derivatives.
+index=[];
+totalloc=zeros(n_f,order);
+for k=1:order
+ for frow=1:n_f
+ [index.loc{frow,k},index.nnz{frow,k}]=find(uncomp{frow,k});
+ totalloc(frow,k)=length(index.loc{frow,k});
+ if isempty(index.loc{frow,k})
+ index.loc{frow,k}=0;
+ end
+ end
+end
+
+% create matlab functions to calculate the derivatives
+for k=1:order
+ fun_name=[fname '_d' num2str(k)];
+ fid = fopen([fun_name '.m'], 'w');
+ fprintf(fid,'%s\n', ['function derivs=' fun_name '(vars,params,index)']);
+ fprintf(fid,'%s\n', 'n_s=size(vars,1);');
+ for i=1:length(v)
+ fprintf(fid,'%s\n', [char(v(i)) '=vars(:,' num2str(i) ');']);
+ end
+ for i=1:length(symparams)
+ fprintf(fid,'%s\n', [char(symparams(i)) '=params(:,' num2str(i) ');']);
+ end
+ fprintf(fid,'%s\n', ['full_rows=zeros(' num2str(sum(totalloc(:,k))) ',1);']);
+ fprintf(fid,'%s\n', ['full_cols=zeros(' num2str(sum(totalloc(:,k))) ',' num2str(k) ');']);
+ fprintf(fid,'%s\n', ['full_vals=zeros(n_s,' num2str(sum(totalloc(:,k))) ');']);
+
+ for frow=1:n_f
+ if totalloc(frow,k)>0
+ tempderiv=derivs{frow,k};
+ fprintf(fid,'%s\n', ['compressed_deriv=zeros(n_s,' num2str(length(tempderiv)) ');']);
+ for i=1:length(tempderiv)
+ disp_fun_row('compressed_deriv',tempderiv(i),i,fid);
+ end
+ fprintf(fid,'%s\n', ['uncompressed_deriv=compressed_deriv(:,index.nnz{' num2str(frow) ',' num2str(k) '});']);
+ tempstart=sum(totalloc(1:frow-1,k));
+ tempend=sum(totalloc(1:frow,k));
+ fprintf(fid,'%s\n', ['full_vals(:,' num2str(tempstart+1) ':' num2str(tempend) ')=uncompressed_deriv;']);
+
+ % transform columns to n-dimensions
+ tempcols='tempcol1';
+ n_relevant_v=sum(relevant_v(frow,:));
+ tempdim=num2str(n_relevant_v);
+ for tempk=2:k
+ tempcols=[tempcols ',tempcol' num2str(tempk)];
+ tempdim=[tempdim ',' num2str(n_relevant_v)];
+ end
+ eval(['[' tempcols ']=ind2sub([' tempdim '],index.loc{' num2str(frow) ',' num2str(k) '});']);
+ tempcols=eval(['[' tempcols ']']);
+ % each row of f was differentiated w.r.t relevant variables.
+ % now, translate dimensions to the full vector of variables.
+ tempv=1:n_v;
+ takev=tempv(relevant_v(frow,:));
+ tempcols=takev(tempcols);
+ % return to index
+ index.loc{frow,k}=tempcols;
+ fprintf(fid,'%s\n', ['full_cols(' num2str(tempstart+1) ':' num2str(tempend) ',:)=index.loc{' num2str(frow) ',' num2str(k) '};']);
+
+ fprintf(fid,'%s\n', ['full_rows(' num2str(tempstart+1) ':' num2str(tempend) ')=' num2str(frow) ';']);
+ end
+ end
+ fprintf(fid,'%s\n', ['derivs=sptensor(full_rows,full_cols,full_vals,' num2str(n_f) ',repmat(' num2str(n_v) ',1,' num2str(k) '));']);
+ fclose(fid);
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residual.m b/105/replication_package/solution_methods/taylor_projection/make_residual.m
new file mode 100644
index 0000000000000000000000000000000000000000..26830f78dfe9e35960346efc0aae75a9e38a039f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residual.m
@@ -0,0 +1,370 @@
+function make_residual(f,Phi,yp,y,xp,x,symparams,eta,order,varargin)
+% The function creates a Matlab file that computes the residual function.
+
+if nargin==9
+ ufun=[];
+ u=[];
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==12
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==13
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type=varargin{4};
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==14
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type='normal';
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+elseif nargin==15
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type=varargin{4};
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+else
+ error('wrong number of input arguments')
+end
+
+% search for reserved names
+
+allnames=[yp(:);y(:);xp(:);x(:);symparams(:);u(:)];
+reserved_names={'coeffs','x','params','c0','nodes','weights','n_y','n_x1',...
+ 'n_f','X','n_b','endogenous_vars','y','expected_endogenous_states',...
+ 'expected_exogenous_states','h_fun','eta_matrix','Resid','i','xp','Xp','yp','f'};
+
+reserved='';
+
+
+for i=1:length(reserved_names)
+ if nnz(logical(allnames==sym(reserved_names{i})))~=0
+ reserved=[reserved, ' \n ', reserved_names{i}];
+ end
+end
+
+if ~isempty(reserved)
+ error_message=['The following names are reserved and should be changed:', reserved];
+ error('ErrorTests:convertTest',error_message)
+end
+
+% Lenght of vectors
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=size(Phi,1); n_x1=n_x-n_x2;
+n_e=size(eta,2); n_u=length(u);
+% n_subs=find_n_new(ufun,u);
+
+n_subs=1;
+if ~isempty(u)
+ uu=sparse(uu0);
+ while nnz(uu)>0
+ n_subs=n_subs+1;
+ uu=uu*uu0;
+ end
+end
+order=order(1);
+n_b=nchoosek(n_x+order,order);
+
+% make a basis function
+
+A=cell(1000+n_b+n_x,1);
+l=1;
+
+A{l}='function X=make_basis(x,c0)'; l=l+1;
+
+A{l}='% The function computes the basis function at x'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% compute x-c0'; l=l+1;
+
+x_c=sym(zeros(n_x,1));
+for i=1:n_x
+ A{l}=['x' num2str(i) '=x(' num2str(i) ')-c0(' num2str(i) ');']; l=l+1;
+ x_c(i)=sym(['x' num2str(i)]);
+end
+
+A{l}=''; l=l+1;
+A{l}='% create the basis function X'; l=l+1;
+
+
+kronx=x_c;
+symX=sym(1);
+if order>=1
+ symX=[sym(1);kronx];
+end
+for i=2:order
+ kronx=kron(x_c,kronx);
+ [~,W]=create_UW(n_x,i);
+ symX=[symX;W*kronx];
+end
+
+A{l}=['X=zeros(' num2str(length(symX)) ',1);']; l=l+1;
+
+for i=1:length(symX)
+ A{l}=['X(' num2str(i) ')=' char(symX(i)) ';'];
+ l=l+1;
+end
+
+% Write cell A into txt
+
+fid = fopen(['make_basis.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+%%%%%%%%%%%%%%%%%%%%
+
+if strcmp(type,'normal')
+ A=cell(1000+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function Resid=residual(coeffs,x,params,c0,nodes,weights)'; l=l+1;
+elseif strcmp(type,'MS')
+ A=cell(1100+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function RMS=residual(coeffs,x,params,msparams,transition,c0,nodes,weights)'; l=l+1;
+
+ A{l}='% The function computes the residual function of a model with Markov-switching parameters'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='n_regimes=size(transition,1);'; l=l+1;
+ A{l}=['n_f=' num2str(length(f)) ';']; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='% compute residual function for all current regimes'; l=l+1;
+ A{l}='RMS=zeros(n_f,n_regimes);'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='for i=1:n_regimes'; l=l+1;
+ A{l}=' for j=1:n_regimes'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % all model parameters given current regime i and future regime j'; l=l+1;
+ A{l}=' all_params=[params(:);msparams(:,i);msparams(:,j)];'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}=' % model conditions given current regime i and future regime j'; l=l+1;
+ A{l}=' R=residual_sub(coeffs(:,i),coeffs(:,j),x,all_params,c0,nodes,weights);'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % weight by transition probabilities'; l=l+1;
+ A{l}=' RMS(:,i)=RMS(:,i)+R*transition(i,j);'; l=l+1;
+ A{l}=' end'; l=l+1;
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='function Resid=residual_sub(coeffs,coeffsp,x,params,c0,nodes,weights)'; l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% parameters'; l=l+1;
+
+for i=1:length(symparams)
+ A{l}=[char(symparams(i)) '=params(' num2str(i) ');']; l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% number of control variables'; l=l+1;
+A{l}=['n_y=' num2str(n_y) ';']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% number of endogenous state variables'; l=l+1;
+A{l}=['n_x1=' num2str(n_x1) ';']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% number of all endogenous variables (controls and states)'; l=l+1;
+A{l}=['n_f=n_y+n_x1;']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% state variables'; l=l+1;
+
+for i=1:n_x
+ A{l}=[char(x(i)) '=x(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% basis function at the current state x'; l=l+1;
+
+A{l}='X=make_basis(x,c0);'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% size of basis function'; l=l+1;
+
+A{l}='n_b=size(X,1);'; l=l+1;
+
+
+
+A{l}='coeffs=reshape(coeffs,n_f,n_b);'; l=l+1;
+
+
+A{l}='endogenous_vars=coeffs*X;'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% control variables y'; l=l+1;
+
+A{l}=['y=endogenous_vars(1:n_y);']; l=l+1;
+
+for i=1:n_y
+ A{l}=[char(y(i)) '=y(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% expected value of future state variables'; l=l+1;
+
+A{l}=['expected_endogenous_states=endogenous_vars(n_y+1:end);']; l=l+1;
+
+A{l}=['expected_exogenous_states=zeros(' num2str(n_x2) ',1);']; l=l+1;
+
+for i=1:n_x2
+ A{l}=['expected_exogenous_states(' num2str(i) ')=' char(Phi(i)) ';'];l=l+1;
+end
+
+A{l}=['h_fun=[expected_endogenous_states;expected_exogenous_states];']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% eta matrix'; l=l+1;
+
+A{l}=['eta_matrix=zeros(' num2str(n_x) ',' num2str(n_e) ');']; l=l+1;
+
+for i=1:n_x
+ for j=1:n_e
+ if eta(i,j)~=0
+ A{l}=['eta_matrix(' num2str(i) ',' num2str(j) ')=' char(eta(i,j)) ';'];l=l+1;
+ end
+ end
+end
+
+
+
+A{l}=''; l=l+1;
+A{l}='% compute the residual function'; l=l+1;
+
+A{l}='Resid=zeros(n_f,1);'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% use quadrature nodes and weights to approximate expectations'; l=l+1;
+
+A{l}='for i=1:length(weights)'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=' % future state variables for node i'; l=l+1;
+
+A{l}=' xp=h_fun+eta_matrix*nodes(:,i);'; l=l+1;
+
+for i=1:n_x
+ A{l}=[' ' char(xp(i)) '=xp(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}=' % basis function at the future state xp'; l=l+1;
+
+A{l}=' Xp=make_basis(xp,c0);'; l=l+1;
+
+if strcmp(type,'normal')
+ A{l}=' yp=coeffs(1:n_y,:)*Xp;'; l=l+1;
+elseif strcmp(type,'MS')
+ A{l}=' coeffsp=reshape(coeffsp,n_f,n_b);'; l=l+1;
+ A{l}=' yp=coeffsp(1:n_y,:)*Xp;'; l=l+1;
+end
+
+for i=1:n_y
+ A{l}=[' ' char(yp(i)) '=yp(' num2str(i) ');'];l=l+1;
+end
+
+if ~isempty(u)
+ A{l}=''; l=l+1;
+ A{l}=' % auxiliary variables'; l=l+1;
+
+ % v=[yp(:);y(:);xp(:);x(:)];
+
+
+ % subsu=ufun;
+ % newsubsu=subs(subsu,u,ufun);
+ %
+ % uind=1:n_u;
+ % while ~isequal(subsu,newsubsu)
+ % for i=uind(logical(newsubsu==subsu))
+ % A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ % end
+ % uind=uind(logical(newsubsu~=subsu));
+ % subsu=newsubsu(logical(newsubsu~=subsu));
+ % newsubsu=subs(subsu,u,ufun);
+ % end
+ % for i=uind
+ % A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ % end
+
+ % version 2
+
+ % if nargin~=8
+% uu0=double(logical(jacobian(ufun(:),u)~=0));
+ % end
+
+
+ uu=uu0;
+
+ n_u=length(u);
+ uind=1:n_u;
+ while nnz(uu)~=0
+ for i=uind(logical(sum(uu,2)==0))
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+ uind=uind(logical(sum(uu,2)~=0));
+ uu=uu(logical(sum(uu,2)~=0),:);
+ uu=uu*uu0;
+ end
+ for i=uind
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+end
+
+%%%%%%%%%%
+
+if ~isempty(logicalparams)
+ A{l}=''; l=l+1;
+ for i=1:length(logicalparams)
+ A{l}=[' ' char(logicalparams(i)) '=double(logical(' char(logicalvars(i)) '>=0));'];l=l+1;
+ end
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % compute function f'];l=l+1;
+
+A{l}=[' f=zeros(n_f,1);'];l=l+1;
+for i=1:n_f
+ A{l}=[' f(' num2str(i) ')=' char(f(i)) ';'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % multiply by weight i and add to Resid'];l=l+1;
+
+A{l}=[' Resid=Resid+f*weights(i);'];l=l+1;
+
+A{l}='end'; l=l+1;
+A{l}=''; l=l+1;
+A{l}='end'; l=l+1;
+
+
+% Write cell A into txt
+
+fid = fopen(['residual.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+rehash;
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residual2.m b/105/replication_package/solution_methods/taylor_projection/make_residual2.m
new file mode 100644
index 0000000000000000000000000000000000000000..2b6882836c854ef2c87bd7d28746fea6bfdeb730
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residual2.m
@@ -0,0 +1,377 @@
+function make_residual2(f,Phi,yp,y,xp,x,shocks,symparams,eta,order,varargin)
+% The function creates a Matlab file that computes the residual function.
+
+nargs=1;
+
+if nargin==nargs+9
+ ufun=[];
+ u=[];
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+12
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+13
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type=varargin{4};
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+14
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type='normal';
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+elseif nargin==nargs+15
+ ufun=varargin{1};
+ u=varargin{2};
+ uu0=varargin{3};
+ type=varargin{4};
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+else
+ error('wrong number of input arguments')
+end
+
+% search for reserved names
+
+allnames=[yp(:);y(:);xp(:);x(:);symparams(:);u(:);shocks(:)];
+reserved_names={'coeffs','x','params','c0','nodes','weights','n_y','n_x1',...
+ 'n_f','X','n_b','n_nodes','endogenous_vars','y','expected_endogenous_states',...
+ 'expected_exogenous_states','h_fun','eta_matrix','Resid','i','xp','Xp','yp','f'};
+
+reserved='';
+
+
+for i=1:length(reserved_names)
+ if nnz(logical(allnames==sym(reserved_names{i})))~=0
+ reserved=[reserved, ' \n ', reserved_names{i}];
+ end
+end
+
+if ~isempty(reserved)
+ error_message=['The following names are reserved and should be changed:', reserved];
+ error('ErrorTests:convertTest',error_message)
+end
+
+% Lenght of vectors
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=size(Phi,1); n_x1=n_x-n_x2;
+n_e=size(eta,2); n_u=length(u);
+% n_subs=find_n_new(ufun,u);
+
+n_subs=1;
+if ~isempty(u)
+ uu=sparse(uu0);
+ while nnz(uu)>0
+ n_subs=n_subs+1;
+ uu=uu*uu0;
+ end
+end
+order=order(1);
+n_b=nchoosek(n_x+order,order);
+
+% make a basis function
+
+A=cell(1000+n_b+n_x,1);
+l=1;
+
+A{l}='function X=make_basis(x,c0)'; l=l+1;
+
+A{l}='% The function computes the basis function at x'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% compute x-c0'; l=l+1;
+
+x_c=sym(zeros(n_x,1));
+for i=1:n_x
+ A{l}=['x' num2str(i) '=x(' num2str(i) ')-c0(' num2str(i) ');']; l=l+1;
+ x_c(i)=sym(['x' num2str(i)]);
+end
+
+A{l}=''; l=l+1;
+A{l}='% create the basis function X'; l=l+1;
+
+
+kronx=x_c;
+symX=sym(1);
+if order>=1
+ symX=[sym(1);kronx];
+end
+for i=2:order
+ kronx=kron(x_c,kronx);
+ [~,W]=create_UW(n_x,i);
+ symX=[symX;W*kronx];
+end
+
+A{l}=['X=zeros(' num2str(length(symX)) ',1);']; l=l+1;
+
+for i=1:length(symX)
+ A{l}=['X(' num2str(i) ')=' char(symX(i)) ';'];
+ l=l+1;
+end
+
+% Write cell A into txt
+
+fid = fopen(['make_basis.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+%%%%%%%%%%%%%%%%%%%%
+
+if strcmp(type,'normal')
+ A=cell(1000+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function [Resid,y,tilh_fun,Phi_fun]=residual(coeffs,x,params,c0,nodes,weights)'; l=l+1;
+elseif strcmp(type,'MS')
+ A=cell(1100+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function [RMS,yMS,tilh_funMS,Phi_funMS]=residual(coeffs,x,params,msparams,transition,c0,nodes,weights)'; l=l+1;
+
+ A{l}='% The function computes the residual function of a model with Markov-switching parameters'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='n_regimes=size(transition,1);'; l=l+1;
+ A{l}=['n_f=' num2str(length(f)) ';']; l=l+1;
+ A{l}=['n_y=' num2str(length(y)) ';']; l=l+1;
+ A{l}=['n_x1=' num2str(n_x1) ';']; l=l+1;
+ A{l}=['n_x2=' num2str(n_x2) ';']; l=l+1;
+ A{l}=['n_nodes=length(weights);']; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='% compute residual function for all current regimes'; l=l+1;
+ A{l}='RMS=zeros(n_f,n_regimes);'; l=l+1;
+ A{l}='yMS=zeros(n_y,n_regimes);'; l=l+1;
+ A{l}='tilh_funMS=zeros(n_x1,n_regimes);'; l=l+1;
+ A{l}='Phi_funMS=zeros(n_x2,n_nodes,n_regimes,n_regimes);'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='for i=1:n_regimes'; l=l+1;
+ A{l}=' for j=1:n_regimes'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % all model parameters given current regime i and future regime j'; l=l+1;
+ A{l}=' all_params=[params(:);msparams(:,i);msparams(:,j)];'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}=' % model conditions given current regime i and future regime j'; l=l+1;
+ A{l}=' [R,y,tilh_fun,Phi_fun]=residual_sub(coeffs(:,i),coeffs(:,j),x,all_params,c0,nodes,weights);'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % weight by transition probabilities'; l=l+1;
+ A{l}=' RMS(:,i)=RMS(:,i)+R*transition(i,j);'; l=l+1;
+ A{l}=' Phi_funMS(:,:,i,j)=Phi_fun;'; l=l+1;
+ A{l}=' end'; l=l+1;
+ A{l}=' yMS(:,i)=y;'; l=l+1;
+ A{l}=' tilh_funMS(:,i)=reshape(tilh_fun,n_x1,1);'; l=l+1;
+
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='function [Resid,y,tilh_fun,Phi_fun]=residual_sub(coeffs,coeffsp,x,params,c0,nodes,weights)'; l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% parameters'; l=l+1;
+
+for i=1:length(symparams)
+ A{l}=[char(symparams(i)) '=params(' num2str(i) ');']; l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% number of control variables'; l=l+1;
+A{l}=['n_y=' num2str(n_y) ';']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% number of endogenous state variables'; l=l+1;
+A{l}=['n_x1=' num2str(n_x1) ';']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% number of all endogenous variables (controls and states)'; l=l+1;
+A{l}=['n_f=n_y+n_x1;']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% state variables'; l=l+1;
+
+for i=1:n_x
+ A{l}=[char(x(i)) '=x(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% basis function at the current state x'; l=l+1;
+
+A{l}='X=make_basis(x,c0);'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% size of basis function'; l=l+1;
+
+A{l}='n_b=size(X,1);'; l=l+1;
+
+
+
+A{l}='coeffs=reshape(coeffs,n_f,n_b);'; l=l+1;
+
+
+A{l}='endogenous_vars=coeffs*X;'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% control variables y'; l=l+1;
+
+A{l}=['y=endogenous_vars(1:n_y);']; l=l+1;
+
+for i=1:n_y
+ A{l}=[char(y(i)) '=y(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}='% future state variables'; l=l+1;
+
+if n_x1>0
+ A{l}=['tilh_fun=endogenous_vars(n_y+1:end);']; l=l+1;
+else
+ A{l}=['tilh_fun=zeros(0,1);']; l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}=['n_nodes=length(weights);']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=['Phi_fun=zeros(' num2str(n_x2) ',n_nodes);']; l=l+1;
+
+
+
+% A{l}=['h_fun=[expected_endogenous_states;expected_exogenous_states];']; l=l+1;
+% A{l}=['tilh_fun=future_endogenous_states;']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% eta matrix'; l=l+1;
+
+A{l}=['eta_matrix=zeros(' num2str(n_x) ',' num2str(n_e) ');']; l=l+1;
+
+for i=1:n_x
+ for j=1:n_e
+ if eta(i,j)~=0
+ A{l}=['eta_matrix(' num2str(i) ',' num2str(j) ')=' char(eta(i,j)) ';'];l=l+1;
+ end
+ end
+end
+
+
+
+A{l}=''; l=l+1;
+A{l}='% compute the residual function'; l=l+1;
+
+A{l}='Resid=zeros(n_f,1);'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% use quadrature nodes and weights to approximate expectations'; l=l+1;
+
+A{l}='for i=1:length(weights)'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=' % future state variables for node i'; l=l+1;
+
+for j=1:length(shocks)
+ A{l}=[' ' char(shocks(j)) '=nodes(' num2str(j) ',i);'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+
+subsPhi=subsf(Phi,u,ufun);
+for i=1:n_x2
+ A{l}=[' Phi_fun(' num2str(i) ',i)=' char(subsPhi(i)) ';'];l=l+1;
+end
+
+A{l}=' xp=[tilh_fun;Phi_fun(:,i)]+eta_matrix*nodes(:,i);'; l=l+1;
+
+for i=1:n_x
+ A{l}=[' ' char(xp(i)) '=xp(' num2str(i) ');'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=' % basis function at the future state xp'; l=l+1;
+
+A{l}=' Xp=make_basis(xp,c0);'; l=l+1;
+
+if strcmp(type,'normal')
+ A{l}=' yp=coeffs(1:n_y,:)*Xp;'; l=l+1;
+elseif strcmp(type,'MS')
+ A{l}=' coeffsp=reshape(coeffsp,n_f,n_b);'; l=l+1;
+ A{l}=' yp=coeffsp(1:n_y,:)*Xp;'; l=l+1;
+end
+
+for i=1:n_y
+ A{l}=[' ' char(yp(i)) '=yp(' num2str(i) ');'];l=l+1;
+end
+
+if ~isempty(u)
+ A{l}=''; l=l+1;
+ A{l}=' % auxiliary variables'; l=l+1;
+
+ uu=uu0;
+
+ n_u=length(u);
+ uind=1:n_u;
+ while nnz(uu)~=0
+ for i=uind(logical(sum(uu,2)==0))
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+ uind=uind(logical(sum(uu,2)~=0));
+ uu=uu(logical(sum(uu,2)~=0),:);
+ uu=uu*uu0;
+ end
+ for i=uind
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+end
+
+%%%%%%%%%%
+
+if ~isempty(logicalparams)
+ A{l}=''; l=l+1;
+ for i=1:length(logicalparams)
+ A{l}=[' ' char(logicalparams(i)) '=double(logical(' char(logicalvars(i)) '>=0));'];l=l+1;
+ end
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % compute function f'];l=l+1;
+
+A{l}=[' f=zeros(n_f,1);'];l=l+1;
+for i=1:n_f
+ A{l}=[' f(' num2str(i) ')=' char(f(i)) ';'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % multiply by weight i and add to Resid'];l=l+1;
+
+A{l}=[' Resid=Resid+f*weights(i);'];l=l+1;
+
+A{l}='end'; l=l+1;
+A{l}=''; l=l+1;
+A{l}='end'; l=l+1;
+
+
+% Write cell A into txt
+
+fid = fopen(['residual.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+rehash;
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residual3.m b/105/replication_package/solution_methods/taylor_projection/make_residual3.m
new file mode 100644
index 0000000000000000000000000000000000000000..0a3861de417406ed7a278c38ef46732cd8942d6a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residual3.m
@@ -0,0 +1,565 @@
+function make_residual3(f,Phi,yp,y,xp,x,shocks,symparams,order,varargin)
+% The function creates a Matlab file that computes the residual function.
+
+nargs=0;
+
+if nargin==nargs+9
+ ufun=[];
+ u=[];
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+12
+ ufun=varargin{1};
+ u=varargin{2};
+ model=varargin{3};
+ type='normal';
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+13
+ ufun=varargin{1};
+ u=varargin{2};
+ model=varargin{3};
+ type=varargin{4};
+ logicalparams=[];
+ logicalvars=[];
+elseif nargin==nargs+14
+ ufun=varargin{1};
+ u=varargin{2};
+ model=varargin{3};
+ type='normal';
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+elseif nargin==nargs+15
+ ufun=varargin{1};
+ u=varargin{2};
+ model=varargin{3};
+ type=varargin{4};
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+else
+ error('wrong number of input arguments')
+end
+
+uu0=model.piu0;
+tilPhiu=model.tilPhiu*model.uu; % this is a matrix for all auxiliary variables that affect Phi (through all substitutions)
+
+
+
+% search for reserved names
+
+allnames=[yp(:);y(:);xp(:);x(:);symparams(:);u(:);shocks(:)];
+reserved_names={'coeffs','coeffsp','state','future_state','control','future_control','regime','future_regime','params','msparams','regimes','n_regimes',...
+ 'shock','center','nodes','n_nodes','weights','Basis','n_nodes','endogenous_vars','transition',...
+ 'R_fun','g_fun','Phi_fun','aux_fun','i','j','f_fun',...
+ 'R_funMS','g_funMS','Phi_funMS','aux_funMS'};
+
+reserved='';
+
+
+for i=1:length(reserved_names)
+ if nnz(logical(allnames==sym(reserved_names{i})))~=0
+ reserved=[reserved, ' \n ', reserved_names{i}];
+ end
+end
+
+if ~isempty(reserved)
+ error_message=['The following names are reserved and should be changed:', reserved];
+ error('ErrorTests:convertTest',error_message)
+end
+
+% Length of vectors
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=size(Phi,1); n_x1=n_x-n_x2;
+n_e=length(shocks); n_u=length(u);
+% n_subs=find_n_new(ufun,u);
+
+n_subs=1;
+if ~isempty(u)
+ uu=sparse(uu0);
+ while nnz(uu)>0
+ n_subs=n_subs+1;
+ uu=uu*uu0;
+ end
+end
+order=order(1);
+n_b=nchoosek(n_x+order,order);
+
+% make a basis function
+
+A=cell(1000+n_b+n_x,1);
+l=1;
+
+A{l}='function X=make_basis(x,c0)'; l=l+1;
+
+A{l}='% The function computes the basis function at x'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% compute x-c0'; l=l+1;
+
+x_c=sym(zeros(n_x,1));
+for i=1:n_x
+ A{l}=['x' num2str(i) '=x(' num2str(i) ')-c0(' num2str(i) ');']; l=l+1;
+ x_c(i)=sym(['x' num2str(i)]);
+end
+
+A{l}=''; l=l+1;
+A{l}='% create the basis function X'; l=l+1;
+
+
+kronx=x_c;
+symX=sym(1);
+if order>=1
+ symX=[sym(1);kronx];
+end
+for i=2:order
+ kronx=kron(x_c,kronx);
+ [~,W]=create_UW(n_x,i);
+ symX=[symX;W*kronx];
+end
+
+A{l}=['X=zeros(' num2str(length(symX)) ',1);']; l=l+1;
+
+for i=1:length(symX)
+ A{l}=['X(' num2str(i) ')=' char(symX(i)) ';'];
+ l=l+1;
+end
+
+% Write cell A into txt
+
+fid = fopen(['make_basis.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+%%%%%%%%%%%%%%%%%%%%
+
+if strcmp(type,'normal')
+ A=cell(1000+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function [R_fun,g_fun,Phi_fun,aux_fun]=residual(coeffs,state,params,center,nodes,weights)'; l=l+1;
+ A{l}='% The function computes the residual function for a model with iid shocks'; l=l+1;
+elseif strcmp(type,'MS')
+ A=cell(1100+length(symparams)+2*n_x+2*n_y+n_subs*n_u+n_f,1);
+ l=1;
+ A{l}='function [R_funMS,g_funMS,Phi_funMS,aux_funMS]=residual(coeffs,state,params,msparams,transition,center,nodes,weights,varargin)'; l=l+1;
+
+ A{l}='% The function computes the residual function for a model with iid shocks and Markov shocks'; l=l+1;
+
+ A{l}=''; l=l+1;
+
+ A{l}='if nargin==8'; l=l+1;
+ A{l}=[' regimes=1:' num2str(model.n_regimes) ';']; l=l+1;
+ A{l}='else'; l=l+1;
+ A{l}=[' regimes=varargin{1};']; l=l+1;
+ A{l}='end'; l=l+1;
+ A{l}='n_regimes=length(regimes);'; l=l+1;
+ A{l}=''; l=l+1;
+% A{l}=['n_f=' num2str(length(f)) ';']; l=l+1;
+% A{l}=['n_y=' num2str(length(y)) ';']; l=l+1;
+% % A{l}=['n_x1=' num2str(n_x1) ';']; l=l+1;
+% A{l}=['n_x=' num2str(n_x2) ';']; l=l+1;
+ A{l}=['n_nodes=length(weights);']; l=l+1;
+% A{l}='n_regimes=size(transition,1);'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}=['coeffs=reshape(coeffs,' num2str(model.n_y*model.n_b) ',' num2str(model.n_regimes) ');']; l=l+1;
+ A{l}=['msparams=reshape(msparams,' num2str(model.n_msparams) ',' num2str(model.n_regimes) ');']; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='% preallocate variables'; l=l+1;
+ A{l}=['R_funMS=zeros(' num2str(model.n_f) ',n_regimes);']; l=l+1;
+ A{l}=['g_funMS=zeros(' num2str(model.n_y) ',n_regimes);']; l=l+1;
+% A{l}='h_funMS=zeros(n_x1,n_regimes);'; l=l+1;
+ A{l}=['Phi_funMS=zeros(' num2str(model.n_x) ',n_nodes,n_regimes,' num2str(model.n_regimes) ');']; l=l+1;
+ A{l}=['aux_funMS=zeros(' num2str(n_u) ',n_nodes,n_regimes,' num2str(model.n_regimes) ');']; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}='loc=0;'; l=l+1;
+ A{l}=['for i=regimes']; l=l+1;
+ A{l}=[' loc=loc+1;']; l=l+1;
+ A{l}=[' for j=1:' num2str(model.n_regimes)]; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % all model parameters given current regime i and future regime j'; l=l+1;
+ A{l}=' all_params=[params(:);msparams(:,i);msparams(:,j)];'; l=l+1;
+
+ A{l}=''; l=l+1;
+ A{l}=' % model conditions given current regime i and future regime j'; l=l+1;
+ A{l}=' [R_fun,g_fun,Phi_fun,aux_fun]=residual_sub(coeffs,state,i,j,all_params,center,nodes,weights);'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=' % weight by transition probabilities'; l=l+1;
+ A{l}=' R_funMS(:,loc)=R_funMS(:,loc)+R_fun*transition(i,j);'; l=l+1;
+ A{l}=' Phi_funMS(:,:,loc,j)=Phi_fun;'; l=l+1;
+ A{l}=' aux_funMS(:,:,loc,j)=aux_fun;'; l=l+1;
+ A{l}=' end'; l=l+1;
+ A{l}=' g_funMS(:,loc)=g_fun;'; l=l+1;
+% A{l}=' h_funMS(:,i)=reshape(h_fun,n_x1,1);'; l=l+1;
+
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='end'; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}=''; l=l+1;
+ A{l}='function [R_fun,g_fun,Phi_fun,aux_fun]=residual_sub(coeffs,state,regime,future_regime,params,center,nodes,weights)'; l=l+1;
+end
+
+l1=l;
+A{l}=''; l=l+1;
+A{l}='% parameters'; l=l+1;
+
+for i=1:length(symparams)
+ A{l}=[char(symparams(i)) '=params(' num2str(i) ');']; l=l+1;
+end
+l2=l;
+
+% A{l}=''; l=l+1;
+% A{l}='% number of control variables'; l=l+1;
+% A{l}=['n_y=' num2str(n_y) ';']; l=l+1;
+
+% A{l}=''; l=l+1;
+% A{l}='% number of predetermined state variables'; l=l+1;
+% A{l}=['n_x1=' num2str(n_x1) ';']; l=l+1;
+%
+% A{l}=''; l=l+1;
+% A{l}='% number of endogenous variables'; l=l+1;
+% A{l}=['n_endog=n_y+n_x1;']; l=l+1;
+
+A{l}=''; l=l+1;
+l3=l;
+
+A{l}='% state variables'; l=l+1;
+
+for i=1:n_x
+ A{l}=[char(x(i)) '=state(' num2str(i) ');'];l=l+1;
+end
+l4=l;
+
+% A{l}='% basis function at the current state'; l=l+1;
+%
+% A{l}='Basis=make_basis(state,c0);'; l=l+1;
+%
+% A{l}=''; l=l+1;
+% A{l}='% size of basis function'; l=l+1;
+%
+% A{l}='n_b=size(Basis,1);'; l=l+1;
+
+
+% A{l}=''; l=l+1;
+
+% A{l}=['coeffs=reshape(coeffs,' num2str(model.n_y) ',' num2str(model.n_b) ');']; l=l+1;
+% if strcmp(type,'MS')
+% A{l}='coeffsp=reshape(coeffsp,n_y,n_b);'; l=l+1;
+% end
+
+% A{l}='endogenous_vars=coeffs*X;'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% the function g(x)'; l=l+1;
+if strcmp(type,'normal')
+ A{l}=['g_fun=evalg(state,coeffs,center);']; l=l+1;
+else
+ A{l}=['g_fun=evalg(state,regime,coeffs,center);']; l=l+1;
+end
+
+l5=l;
+A{l}=''; l=l+1;
+A{l}='% control variables'; l=l+1;
+
+
+for i=1:n_y
+ A{l}=[char(y(i)) '=g_fun(' num2str(i) ');'];l=l+1;
+end
+l6=l;
+%%%%%
+
+
+
+%%%%%
+
+A{l}=''; l=l+1;
+A{l}=['if isempty(weights) || isempty(nodes)']; l=l+1;
+A{l}=[' weights=1;']; l=l+1;
+A{l}=[' nodes=0;']; l=l+1;
+A{l}=['end']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=['n_nodes=length(weights);']; l=l+1;
+% A{l}=['n_f=' num2str(length(f)) ';']; l=l+1;
+
+
+
+% A{l}=['h_fun=[expected_endogenous_states;expected_exogenous_states];']; l=l+1;
+% A{l}=['h_fun=future_endogenous_states;']; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}='% preallocate variables'; l=l+1;
+A{l}=['f_fun=zeros(' num2str(model.n_f) ',1);'];l=l+1;
+A{l}=['R_fun=zeros(' num2str(model.n_f) ',1);']; l=l+1;
+A{l}=['Phi_fun=zeros(' num2str(n_x2) ',n_nodes);']; l=l+1;
+A{l}=['aux_fun=zeros(' num2str(n_u) ',n_nodes);']; l=l+1;
+
+
+A{l}=''; l=l+1;
+A{l}='% approximate expectations by quadrature nodes and weights'; l=l+1;
+
+A{l}='for i=1:n_nodes'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=' % realization of shocks at node i'; l=l+1;
+
+for j=1:length(shocks)
+ A{l}=[' ' char(shocks(j)) '=nodes(' num2str(j) ',i);'];l=l+1;
+end
+
+if isempty(u)
+ A{l}=''; l=l+1;
+ for i=1:n_x2
+ A{l}=[' Phi_fun(' num2str(i) ',i)=' char(Phi(i)) ';'];l=l+1;
+ end
+else
+ l7=l;
+ A{l}=''; l=l+1;
+
+
+ n_u=length(u);
+ uind=1:n_u;
+
+ uu=uu0;
+ newuind=uind;
+ Phiuind=find(logical(sum(tilPhiu,1)~=0));
+ while nnz(uu(Phiuind,:))~=0
+
+ for i=Phiuind(logical(sum(uu(Phiuind,:),2)==0))
+ if l==l7+1
+ A{l}=' % auxiliary variables'; l=l+1;
+ end
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ newuind(i)=0;
+ end
+ Phiuind=Phiuind(logical(sum(uu(Phiuind,:),2)~=0));
+ uu=uu*uu0;
+ end
+ for i=Phiuind
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ newuind(i)=0;
+ end
+ l8=l;
+ A{l}=''; l=l+1;
+ A{l}=' % function Phi'; l=l+1;
+
+ for i=1:n_x2
+ A{l}=[' Phi_fun(' num2str(i) ',i)=' char(Phi(i)) ';'];l=l+1;
+ end
+
+% A{l}=''; l=l+1;
+% A{l}=' % store auxiliary variables'; l=l+1;
+% for i=1:length(u)
+% A{l}=[' auxvars(' num2str(i) ',i)=' char(u(i)) ';'];l=l+1;
+% end
+end
+
+A{l}=''; l=l+1;
+A{l}=' % future state variables'; l=l+1;
+
+A{l}=' future_state=Phi_fun(:,i);'; l=l+1;
+
+% A{l}=''; l=l+1;
+for i=1:n_x
+ A{l}=[' ' char(xp(i)) '=future_state(' num2str(i) ');'];l=l+1;
+end
+
+% A{l}=''; l=l+1;
+% A{l}=' % basis function at the future state xp'; l=l+1;
+%
+% A{l}=' Xp=make_basis(xp,c0);'; l=l+1;
+
+A{l}=''; l=l+1;
+A{l}=' % control variables at the future state'; l=l+1;
+
+if strcmp(type,'normal')
+ A{l}=' future_control=evalg(future_state,coeffs,center);'; l=l+1;
+elseif strcmp(type,'MS')
+ A{l}=' future_control=evalg(future_state,future_regime,coeffs,center);'; l=l+1;
+end
+
+for i=1:n_y
+ A{l}=[' ' char(yp(i)) '=future_control(' num2str(i) ');'];l=l+1;
+end
+
+if ~isempty(u) && nnz(newuind)>0
+ A{l}=''; l=l+1;
+ A{l}=' % auxiliary variables'; l=l+1;
+
+
+ uu=uu0;
+
+ uind=nonzeros(newuind);
+ uind=uind(:)';
+ uu=uu(uind,:);
+ while nnz(uu)~=0
+ for i=uind(logical(sum(uu,2)==0))
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+ uind=uind(logical(sum(uu,2)~=0));
+ uu=uu(logical(sum(uu,2)~=0),:);
+ uu=uu*uu0;
+ end
+ for i=uind
+ A{l}=[' ' char(u(i)) '=' char(ufun(i)) ';'];l=l+1;
+ end
+
+ A{l}=''; l=l+1;
+ A{l}=' % store auxiliary variables'; l=l+1;
+ for i=1:n_u
+ A{l}=[' aux_fun(' num2str(i) ',i)=' char(u(i)) ';'];l=l+1;
+ end
+
+end
+
+%%%%%%%%%%
+
+if ~isempty(logicalparams)
+ A{l}=''; l=l+1;
+ A{l}=[' % logical parameters'];l=l+1;
+ for i=1:length(logicalparams)
+ A{l}=[' ' char(logicalparams(i)) '=double(logical(' char(logicalvars(i)) '>0));'];l=l+1;
+ end
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % compute function f'];l=l+1;
+
+for i=1:n_f
+ A{l}=[' f_fun(' num2str(i) ')=' char(f(i)) ';'];l=l+1;
+end
+
+A{l}=''; l=l+1;
+A{l}=[' % multiply by weight i and add to R_fun'];l=l+1;
+
+A{l}=[' R_fun=R_fun+f_fun*weights(i);'];l=l+1;
+
+A{l}='end'; l=l+1;
+A{l}=''; l=l+1;
+A{l}='end'; l=l+1;
+
+
+% Write cell A into txt
+
+fid = fopen(['residual.m'], 'w');
+for i = 1:l-1
+ fprintf(fid,'%s\n', A{i});
+end
+
+fclose(fid);
+
+
+% Write evalg
+
+fid = fopen(['evalg.m'], 'w');
+
+if strcmp(type,'normal')
+ fprintf(fid,'%s\n', 'function g_fun=evalg(x,coeffs,c0)');
+ fprintf(fid,'%s\n', '% The function computes the function g(x), where x is the state vector');
+else
+ fprintf(fid,'%s\n', 'function g_fun=evalg(x,s,coeffs,c0)');
+ fprintf(fid,'%s\n', '% The function computes the function g(x,s), where x is the state vector and s is the regime');
+end
+
+fprintf(fid,'%s\n', '');
+
+fprintf(fid,'%s\n', ['Basis=make_basis(x,c0);']);
+fprintf(fid,'%s\n', '');
+if strcmp(type,'MS')
+ fprintf(fid,'%s\n', ['coeffs=reshape(coeffs,' num2str(model.n_y*model.n_b) ',' num2str(model.n_regimes) ');']);
+ fprintf(fid,'%s\n', ['coeffs=coeffs(:,s);']);
+end
+fprintf(fid,'%s\n', ['coeffs=reshape(coeffs,' num2str(model.n_y) ',' num2str(model.n_b) ');']);
+fprintf(fid,'%s\n', '');
+fprintf(fid,'%s\n', ['g_fun=coeffs*Basis;']);
+fprintf(fid,'%s\n', '');
+
+fprintf(fid,'%s\n', ['end']);
+
+
+fclose(fid);
+
+
+% Write evalPhi
+
+fid = fopen(['evalPhi.m'], 'w');
+
+if strcmp(type,'normal')
+ fprintf(fid,'%s\n', 'function Phi_fun=evalPhi(state,control,shock,params)');
+ fprintf(fid,'%s\n', '% The function computes the function Phi(x,y,epsp), where x is the state vector,');
+ fprintf(fid,'%s\n', '% y is the control vector given by y=g(x), and epsp is the realization of the shocks next period.');
+else
+ fprintf(fid,'%s\n', 'function Phi_fun=evalPhi(state,control,shock,future_regime,regime,params,msparams)');
+ fprintf(fid,'%s\n', '% The function computes the function Phi(x,y,epsp,chi(sp),chi(s)), where x is the state vector,');
+ fprintf(fid,'%s\n', '% y is the control vector given by y=g(x,s), chi(s) is the value of the Markov shocks at the current regime s,');
+ fprintf(fid,'%s\n', '% chi(sp) is the value of the Markov shocks at the future regime sp, and epsp is the realization of the shocks next period.');
+end
+
+% parameters
+if strcmp(type,'MS')
+ fprintf(fid,'%s\n', '');
+ temp='params=[params(:);msparams(:,regime);msparams(:,future_regime)];';
+ fprintf(fid,'%s\n', temp);
+end
+
+for i = l1:l2
+ fprintf(fid,'%s\n', A{i});
+end
+
+
+% state variables
+for i = l3:l4
+ fprintf(fid,'%s\n', A{i});
+end
+
+% control variables
+temp=['% control variables'];
+fprintf(fid,'%s\n', temp);
+
+for j=1:model.n_y
+ temp=[char(y(j)) '=control(' num2str(j) ');'];
+ fprintf(fid,'%s\n', temp);
+end
+fprintf(fid,'%s\n', '');
+
+temp=['% shocks'];
+fprintf(fid,'%s\n', temp);
+
+% shocks
+for j=1:length(shocks)
+ temp=[char(shocks(j)) '=shock(' num2str(j) ');'];
+ fprintf(fid,'%s\n', temp);
+end
+fprintf(fid,'%s\n', '');
+
+temp=['% function Phi'];
+fprintf(fid,'%s\n', temp);
+
+if ~isempty(u)
+ for i = l7:l8
+ fprintf(fid,'%s\n', A{i}(4:end));
+ end
+end
+
+temp=['Phi_fun=zeros(' num2str(model.n_x2) ',1);'];
+fprintf(fid,'%s\n', temp);
+
+for i=1:n_x2
+ temp=['Phi_fun(' num2str(i) ')=' char(Phi(i)) ';'];
+ fprintf(fid,'%s\n', temp);
+end
+
+fprintf(fid,'%s\n', '');
+
+fprintf(fid,'%s\n', ['end']);
+
+
+fclose(fid);
+
+rehash;
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residualMS.m b/105/replication_package/solution_methods/taylor_projection/make_residualMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..4deb8a0f3ea3ec8f8170434a9d4714602fb8d5a4
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residualMS.m
@@ -0,0 +1,12 @@
+function make_residualMS(f,Phi,yp,y,xp,x,chip,chi,symparams,eta,order,ufun,u,uu0,logicalparams,logicalvars)
+% make_residualMS(f,Phi,yp,y,xp,x,symparams_msp,symparams_ms,symparams,eta,order,auxfuns,auxvars,model.uu0,logicalparams,logicalvars);
+% The function creates a Matlab file that computes the residual function for
+% a model with Markov-switching parameters.
+
+all_symparams=[symparams(:);chi(:);chip(:)];
+
+make_residual(f,Phi,yp,y,xp,x,all_symparams,eta,order,ufun,u,uu0,'MS',logicalparams,logicalvars);
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residualMS2.m b/105/replication_package/solution_methods/taylor_projection/make_residualMS2.m
new file mode 100644
index 0000000000000000000000000000000000000000..1b69d10a32109800d34dae349f7c3254a91f9ee0
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residualMS2.m
@@ -0,0 +1,12 @@
+function make_residualMS2(f,Phi,yp,y,xp,x,shocks,chip,chi,symparams,eta,order,ufun,u,uu0,logicalparams,logicalvars)
+% make_residualMS(f,Phi,yp,y,xp,x,symparams_msp,symparams_ms,symparams,eta,order,auxfuns,auxvars,model.uu0,logicalparams,logicalvars);
+% The function creates a Matlab file that computes the residual function for
+% a model with Markov-switching parameters.
+
+all_symparams=[symparams(:);chi(:);chip(:)];
+
+make_residual2(f,Phi,yp,y,xp,x,shocks,all_symparams,eta,order,ufun,u,uu0,'MS',logicalparams,logicalvars);
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/make_residualMS3.m b/105/replication_package/solution_methods/taylor_projection/make_residualMS3.m
new file mode 100644
index 0000000000000000000000000000000000000000..ca13884e6c3a2e9779cddc919c0e82e10aff52e1
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/make_residualMS3.m
@@ -0,0 +1,12 @@
+function make_residualMS3(f,Phi,yp,y,xp,x,shocks,chip,chi,symparams,order,ufun,u,uu0,logicalparams,logicalvars)
+% make_residualMS(f,Phi,yp,y,xp,x,symparams_msp,symparams_ms,symparams,eta,order,auxfuns,auxvars,model.uu0,logicalparams,logicalvars);
+% The function creates a Matlab file that computes the residual function for
+% a model with Markov-switching parameters.
+
+all_symparams=[symparams(:);chi(:);chip(:)];
+
+make_residual3(f,Phi,yp,y,xp,x,shocks,all_symparams,order,ufun,u,uu0,'MS',logicalparams,logicalvars);
+
+
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/model.mat b/105/replication_package/solution_methods/taylor_projection/model.mat
new file mode 100644
index 0000000000000000000000000000000000000000..75f32963ea598a163421ccc81cadd9b8ad20f8bb
Binary files /dev/null and b/105/replication_package/solution_methods/taylor_projection/model.mat differ
diff --git a/105/replication_package/solution_methods/taylor_projection/nnz_UW.m b/105/replication_package/solution_methods/taylor_projection/nnz_UW.m
new file mode 100644
index 0000000000000000000000000000000000000000..0139484e32efcac9fe45f52bdae979361312bb7d
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/nnz_UW.m
@@ -0,0 +1,98 @@
+function [varout1,varout2]=nnz_UW(n,k,nonzero,varargin)
+% [U,W]=nnz_UW(n,k,nonzero) creates compression matrices that compress a
+% symmetric row vector A, where A(i)~=0 iff nonzero(i)~=0.
+% [loc,ind]=nnz_UW(n,k,nonzero,'ind') returns two indices. loc(i) is the
+% location in the compressed matrix of elemnt ind(i) in the uncompressed
+% matrix.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% bug fixed on Sep 9, 2017 (the case nonzero==0 was not addressed properly)
+
+if ~isempty(varargin)
+ if strcmp(varargin{1},'sparse')
+ dosparse=1;
+ elseif strcmp(varargin{1},'ind')
+ dosparse=0;
+ else
+ error('allowed options are sparse or ind')
+ end
+else
+ dosparse=1;
+end
+
+I=find(nonzero);
+
+if isempty(I)
+ if dosparse==1
+ U=sparse(n^k,nchoosek(n+k-1,k));
+ W=sparse(nchoosek(n+k-1,k),n^k);
+ varout1=U;
+ varout2=W;
+ else
+ varout1=[];
+ varout2=[];
+ end
+else
+ I=I(:);
+ origI=I;
+ sizeM='n';
+ subind='I1';
+ for i=2:k
+ sizeM=[sizeM ' n'];
+ subind=[subind ',I' num2str(i) ];
+ end
+
+ eval(['[' subind ']=ind2sub([' sizeM '],I);']); % I is a linear index of all nonzero elements.
+ eval(['M=[' subind '];']);
+
+ sortM=sort(M,2); % sort columns
+ [M,I]=sortrows(sortM); % sort rows
+ if size(M,1)==1
+ DM=1;
+ else
+ DM=[1;(sum(abs(diff(M)),2)~=0)];
+ end
+ group=cumsum(DM);
+ minI=accumarray(group,I,[],@min);
+ newi=minI(group);
+
+ unique=newi(DM>0); % index of unique nonzero elements
+
+ n_unique=length(unique);
+
+ if k>1
+ sortM=sortM(unique,:);
+ tempmat=repmat(n+k:-1:n+1,n_unique,1);
+ loc=(repmat(prod(n+k-1:-1:n),n_unique,1)-prod(tempmat-repmat(sortM(:,1),1,k),2))/factorial(k)+1;
+
+ for j=2:k-1
+ tempmat=repmat(n+k-j+1:-1:n+1,n_unique,1);
+ loc=loc+(prod(tempmat-repmat(sortM(:,j-1),1,k-j+1),2)-prod(tempmat-repmat(sortM(:,j),1,k-j+1),2))/factorial(k-j+1);
+ end
+ loc=loc+sortM(:,k)-sortM(:,k-1);
+ if dosparse==1
+ U= sparse(origI(unique),loc,ones(n_unique,1),n^k,nchoosek(n+k-1,k));
+ origI=origI(I); % sort the original index
+ W= sparse(loc(group),origI,ones(length(origI),1),nchoosek(n+k-1,k),n^k);
+ varout1=U;
+ varout2=W;
+ else
+ varout1=loc;
+ varout2=origI(unique);
+ end
+ elseif k==1
+ if dosparse==1
+ U=sparse(origI,origI,ones(length(origI),1),n,n);
+ W=U;
+ varout1=U;
+ varout2=W;
+ else
+ varout1=origI;
+ varout2=origI;
+ end
+ end
+end
+
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/precompute.m b/105/replication_package/solution_methods/taylor_projection/precompute.m
new file mode 100644
index 0000000000000000000000000000000000000000..fcc47ef5fd3bfa466b05c87a363d22d4473f1994
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/precompute.m
@@ -0,0 +1,106 @@
+function [ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta,gxxxxc_theta,hxxxxc_theta,model ] = precompute(x0,c0,model,order )
+%This function precomputese expressions that are independent of coeffs.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+x0=full(x0);
+c0=full(c0);
+
+if ~isequal(x0,c0)
+ error('x0 is not equal to c0')
+end
+
+n_x=model.n_x;
+n_x2=model.n_x2;
+n_y=model.n_y;
+n_f=model.n_x1+model.n_y; % n_f here is the number of endogenous variables, which might be different than the number of equations in HA models
+n_theta=model.n_theta;
+U=model.U;
+W=model.W;
+
+if ~isfield(model,'unique2')
+ model.unique2=[];
+end
+if ~isfield(model,'unique3')
+ model.unique3=[];
+end
+if ~isfield(model,'unique4')
+ model.unique4=[];
+end
+
+[X,Xx,Xxx,Xxxx,Xxxxx]=create_X(order,n_x,x0,c0,W{2},model.unique2,W{3},model.unique3,W{4},model.unique4);
+X=spmat2sptensor(X); Xxxc=[];Xxxxc=[]; Xxxxxc=[];
+
+if order>=1
+ Xx=spmat2sptensor(Xx);
+end
+if order>=2
+ Xxxc=Xxx*U{2};
+ Xxxc=spmat2sptensor(Xxxc);
+end
+if order>=3
+ Xxxxc=Xxxx*U{3};
+ Xxxxc=spmat2sptensor(Xxxxc);
+end
+if order>=4
+ Xxxxxc=Xxxxx*U{4};
+ Xxxxxc=spmat2sptensor(Xxxxxc);
+end
+
+if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+end
+indi=1;
+
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+
+hx_theta=[]; hxxc_theta=[]; hxxxc_theta=[]; hxxxxc_theta=[];
+gx_theta=[]; gxxc_theta=[]; gxxxc_theta=[]; gxxxxc_theta=[];
+
+IfT=spteye(n_f); % this is the identity matrix
+
+[gh_theta,model.ind{indi}]=tkron(ttranspose(X),IfT,model.ind{indi},n_ind);
+indi=indi+1;
+gh_theta=unfold(gh_theta);
+g_theta=takerows(gh_theta,1:n_y);
+h_theta=vconcat(takerows(gh_theta,n_y+1:n_f),sptensor(n_x2,n_theta));
+
+if order>=1
+ [ghx_theta,model.ind{indi}]=tkron(ttranspose(Xx),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghx_theta=ptr2col(ptr2d(unfold(ghx_theta),n_f,n_x),1); %n_y,n_x,n_theta
+ gx_theta=takerows(ghx_theta,1:n_y);
+ hx_theta=vconcat(takerows(ghx_theta,n_y+1:n_f),sptensor(n_x2,[n_x,n_theta]));
+end
+
+if order>=2
+ [ghxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxc_theta=ptr2col(ptr2d(unfold(ghxxc_theta),n_f,model.unique2),1); %n_y,unique2,n_theta
+ gxxc_theta=takerows(ghxxc_theta,1:n_y);
+ hxxc_theta=vconcat(takerows(ghxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique2,n_theta]));
+end
+
+if order>=3
+ [ghxxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxxc_theta=ptr2col(ptr2d(unfold(ghxxxc_theta),n_f,model.unique3),1); %n_y,unique3,n_theta
+ gxxxc_theta=takerows(ghxxxc_theta,1:n_y);
+ hxxxc_theta=vconcat(takerows(ghxxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique3,n_theta]));
+end
+
+if order>=4
+% [ghxxxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxxxc),IfT,model.ind{indi},n_ind);
+ [ghxxxxc_theta]=tkron(ttranspose(Xxxxxc),IfT);
+% indi=indi+1;
+ ghxxxxc_theta=ptr2col(ptr2d(unfold(ghxxxxc_theta),n_f,model.unique4),1); %n_y,unique4,n_theta
+ gxxxxc_theta=takerows(ghxxxxc_theta,1:n_y);
+ hxxxxc_theta=vconcat(takerows(ghxxxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique4,n_theta]));
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/precompute_no_shift.m b/105/replication_package/solution_methods/taylor_projection/precompute_no_shift.m
new file mode 100644
index 0000000000000000000000000000000000000000..0a4134a0a212133965b8979c5cf9d45e6346bc9c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/precompute_no_shift.m
@@ -0,0 +1,89 @@
+function [ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta,model ] = precompute_no_shift(x0,c0,model,order )
+%This function precomputese expressions that are independent of coeffs.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+x0=full(x0);
+c0=full(c0);
+
+% if ~isequal(x0,c0)
+% error('x0 is not equal to c0')
+% end
+
+n_x=model.n_x;
+n_x2=model.n_x2;
+n_y=model.n_y;
+n_f=model.n_f;
+n_theta=model.n_theta;
+U=model.U;
+W=model.W;
+
+if ~isfield(model,'unique2')
+ model.unique2=[];
+end
+if ~isfield(model,'unique3')
+ model.unique3=[];
+end
+
+[X,Xx,Xxx,Xxxx]=create_X(order,n_x,x0,c0,W{2},model.unique2,W{3},model.unique3);
+X=spmat2sptensor(X); Xxxc=[];Xxxxc=[];
+
+if order>=1
+ Xx=spmat2sptensor(Xx);
+end
+if order>=2
+ Xxxc=Xxx*U{2};
+ Xxxc=spmat2sptensor(Xxxc);
+end
+if order>=3
+ Xxxxc=Xxxx*U{3};
+ Xxxxc=spmat2sptensor(Xxxxc);
+end
+
+if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+end
+indi=1;
+
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+
+hx_theta=[]; hxxc_theta=[]; hxxxc_theta=[];
+gx_theta=[]; gxxc_theta=[]; gxxxc_theta=[];
+
+IfT=spteye(n_f);
+[gh_theta,model.ind{indi}]=tkron(ttranspose(X),IfT,model.ind{indi},n_ind);
+indi=indi+1;
+gh_theta=unfold(gh_theta);
+g_theta=takerows(gh_theta,1:n_y);
+h_theta=vconcat(takerows(gh_theta,n_y+1:n_f),sptensor(n_x2,n_theta));
+
+if order>=1
+ [ghx_theta,model.ind{indi}]=tkron(ttranspose(Xx),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghx_theta=ptr2col(ptr2d(unfold(ghx_theta),n_f,n_x),1); %n_y,n_x,n_theta
+ gx_theta=takerows(ghx_theta,1:n_y);
+ hx_theta=vconcat(takerows(ghx_theta,n_y+1:n_f),sptensor(n_x2,[n_x,n_theta]));
+end
+
+if order>=2
+ [ghxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxc_theta=ptr2col(ptr2d(unfold(ghxxc_theta),n_f,model.unique2),1); %n_y,unique2,n_theta
+ gxxc_theta=takerows(ghxxc_theta,1:n_y);
+ hxxc_theta=vconcat(takerows(ghxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique2,n_theta]));
+end
+
+if order>=3
+ [ghxxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxxc_theta=ptr2col(ptr2d(unfold(ghxxxc_theta),n_f,model.unique3),1); %n_y,unique3,n_theta
+ gxxxc_theta=takerows(ghxxxc_theta,1:n_y);
+ hxxxc_theta=vconcat(takerows(ghxxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique3,n_theta]));
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/precomputevec.m b/105/replication_package/solution_methods/taylor_projection/precomputevec.m
new file mode 100644
index 0000000000000000000000000000000000000000..d16d89e137623e410cf6311aa7d45e3c699f01d2
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/precomputevec.m
@@ -0,0 +1,116 @@
+function [ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta,model ] = precomputevec(x0vec,c0vec,model,order )
+%This function precomputese expressions that are independent of coeffs.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+x0vec=full(x0vec);
+c0vec=full(c0vec);
+
+if ~isequal(x0vec,c0vec)
+ error('x0 is not equal to c0')
+end
+
+n_x=model.n_x;
+n_x2=model.n_x2;
+n_y=model.n_y;
+n_f=model.n_x1+model.n_y; % n_f here is the number of endogenous varaibles, which might be different than the number of equations in HA models
+n_theta=model.n_theta;
+U=model.U;
+W=model.W;
+
+if ~isfield(model,'unique2')
+ model.unique2=[];
+end
+if ~isfield(model,'unique3')
+ model.unique3=[];
+end
+
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+
+indi=1;
+
+if ~isfield(model,'M2')
+ model.M2=[];
+ model.M3=[];
+ model.M3x=[];
+ model.TW2=[];
+ model.TW3=[];
+ if order>=2
+ model.M2=fold(spmat2sptensor(model.W{2}*model.W{2}'*model.U{2}'),n_x,n_x);
+ model.TW2=fold(spmat2sptensor(model.W{2}),n_x,n_x);
+ model.TW2U2=spmat2sptensor(model.W{2}*model.U{2});
+ end
+ if order>=3
+ model.M3=fold(spmat2sptensor(model.W{3}*model.W{3}'*model.U{3}'),n_x,n_x,n_x);
+ model.M3x=fold(spmat2sptensor(3*model.W{3}*kron(model.W{2}'*model.U{2}',speye(n_x))),n_x,n_x,n_x);
+ model.TW3=fold(spmat2sptensor(model.W{3}),n_x,n_x,n_x);
+ model.TW3U3=spmat2sptensor(model.W{3}*model.U{3});
+ end
+end
+
+[X,Xx,Xxx,Xxxx,model.ind{indi}]=create_X_tensor(order,nxp_c0,...
+ model.M2,model.M3,model.M3x,model.TW2,model.TW3,unique2,unique3,model.ind{indi},n_ind,maxload,'vec');
+indi=indi+1;
+
+[X,Xx,Xxx,Xxxx]=create_X(order,n_x,x0,c0,W{2},model.unique2,W{3},model.unique3);
+X=spmat2sptensor(X); Xxxc=[];Xxxxc=[];
+
+if order>=1
+ Xx=spmat2sptensor(Xx);
+end
+if order>=2
+ Xxxc=Xxx*U{2};
+ Xxxc=spmat2sptensor(Xxxc);
+end
+if order>=3
+ Xxxxc=Xxxx*U{3};
+ Xxxxc=spmat2sptensor(Xxxxc);
+end
+
+if ~isfield(model,'ind')
+ model.ind=cell(model.totindi,1);
+end
+indi=1;
+
+
+
+hx_theta=[]; hxxc_theta=[]; hxxxc_theta=[];
+gx_theta=[]; gxxc_theta=[]; gxxxc_theta=[];
+
+IfT=spteye(n_f);
+[gh_theta,model.ind{indi}]=tkron(ttranspose(X),IfT,model.ind{indi},n_ind);
+indi=indi+1;
+gh_theta=unfold(gh_theta);
+g_theta=takerows(gh_theta,1:n_y);
+h_theta=vconcat(takerows(gh_theta,n_y+1:n_f),sptensor(n_x2,n_theta));
+
+if order>=1
+ [ghx_theta,model.ind{indi}]=tkron(ttranspose(Xx),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghx_theta=ptr2col(ptr2d(unfold(ghx_theta),n_f,n_x),1); %n_y,n_x,n_theta
+ gx_theta=takerows(ghx_theta,1:n_y);
+ hx_theta=vconcat(takerows(ghx_theta,n_y+1:n_f),sptensor(n_x2,[n_x,n_theta]));
+end
+
+if order>=2
+ [ghxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxc_theta=ptr2col(ptr2d(unfold(ghxxc_theta),n_f,model.unique2),1); %n_y,unique2,n_theta
+ gxxc_theta=takerows(ghxxc_theta,1:n_y);
+ hxxc_theta=vconcat(takerows(ghxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique2,n_theta]));
+end
+
+if order>=3
+ [ghxxxc_theta,model.ind{indi}]=tkron(ttranspose(Xxxxc),IfT,model.ind{indi},n_ind);
+ indi=indi+1;
+ ghxxxc_theta=ptr2col(ptr2d(unfold(ghxxxc_theta),n_f,model.unique3),1); %n_y,unique3,n_theta
+ gxxxc_theta=takerows(ghxxxc_theta,1:n_y);
+ hxxxc_theta=vconcat(takerows(ghxxxc_theta,n_y+1:n_f),sptensor(n_x2,[model.unique3,n_theta]));
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tp.m b/105/replication_package/solution_methods/taylor_projection/prepare_tp.m
new file mode 100644
index 0000000000000000000000000000000000000000..e508a89dc36a851f662ef7fb5ee588c9319b6f45
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tp.m
@@ -0,0 +1,150 @@
+function model=prepare_tp(f,Phi,yp,y,xp,x,shocks,varargin)
+% function model=prepare_tp(f,Phi,yp,y,xp,x,shocks,symparams,order)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the law of motion of state varialbes.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% shocks = symbolic shocks.
+% symparams = symbolic vector of the model parameters.
+% order = order of the approximiating Polynomials. Can be 1, 2, 3 or 4.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, March 19, 2017.
+% changed on April 19, 2018
+
+disp('Taylor Projection:')
+
+n_regimes=1;
+chi=[];
+chip=[];
+auxfuns=[];
+auxvars=[];
+logicalparams=[];
+logicalvars=[];
+
+nargs=9;
+
+if nargin==nargs
+ symparams=varargin{1};
+ order=varargin{2};
+elseif nargin==nargs+2
+ symparams=varargin{1};
+ order=varargin{2};
+ auxfuns=varargin{3};
+ auxvars=varargin{4};
+elseif nargin==nargs+4
+ symparams=varargin{1};
+ order=varargin{2};
+ auxfuns=varargin{3};
+ auxvars=varargin{4};
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+elseif nargin==nargs+3
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+elseif nargin==nargs+5
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+ auxfuns=varargin{6};
+ auxvars=varargin{7};
+elseif nargin==nargs+7
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+ auxfuns=varargin{6};
+ auxvars=varargin{7};
+ logicalparams=varargin{8};
+ logicalvars=varargin{9};
+else
+ error('wrong number of input arguments')
+end
+
+f=f(:);
+Phi=Phi(:);
+yp=yp(:);
+y=y(:);
+xp=xp(:);
+x=x(:);
+shocks=shocks(:);
+chip=chip(:);
+chi=chi(:);
+symparams=symparams(:);
+auxfuns=auxfuns(:);
+auxvars=auxvars(:);
+logicalparams=logicalparams(:);
+logicalvars=logicalvars(:);
+
+if length(yp)~=length(y)
+ error('current and future control variables must have the same number of elements')
+end
+if length(xp)~=length(x)
+ error('current and future state variables must have the same number of elements')
+end
+if length(chip)~=length(chi)
+ error('current and future Markov-switching parameters must have the same number of elements')
+end
+if length(auxvars)~=length(auxfuns)
+ error('auxiliary functions and variables must have the same number of elements')
+end
+if length(logicalparams)~=length(logicalvars)
+ error('logical parameters and their arguments must have the same number of elements')
+end
+
+
+
+symparams_ms=chi;
+symparams_msp=chip;
+
+fname='ms';
+nocheck=0;
+uname='';
+
+Phi=sym(Phi);
+if isempty(shocks)
+ shocks=sym('unused_shock__');
+ eta=sym(zeros(length(x),1));
+else
+ eta=sym(zeros(length(x),length(shocks)));
+end
+
+model=prepare_tpMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,eta,...
+ n_regimes,order,auxfuns,auxvars,fname,nocheck,uname,logicalparams,logicalvars);
+model.pde=0;
+
+fprintf('writing residual function to file...')
+home_folder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+cd('files')
+if isempty(chi)
+ make_residual3(f,Phi,yp,y,xp,x,shocks,symparams,order,auxfuns,auxvars,model,logicalparams,logicalvars);
+else
+ make_residualMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,order,auxfuns,auxvars,model,logicalparams,logicalvars);
+end
+cd(home_folder);
+fprintf('done\n')
+
+model.hybrid=3;
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tp3.m b/105/replication_package/solution_methods/taylor_projection/prepare_tp3.m
new file mode 100644
index 0000000000000000000000000000000000000000..ca0b09e9f736f49f92654049e31c403c1f2ffc3b
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tp3.m
@@ -0,0 +1,122 @@
+function model=prepare_tp3(f,Phi,yp,y,xp,x,shocks,varargin)
+% function model=prepare_tp(f,Phi,yp,y,xp,x,symparams,eta,order,varargin)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the lower block of h(x). This is the evolution law
+% of the exogenoust state variables, or any other state variables with a
+% known policy function.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% symparams = symbolic vector of the model parameters.
+% eta = the matrix eta as in Schmitt-Grohe and Uribe (2004).
+% order = order of the approximiating Polynomials. Can be 1, 2 or 3.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, March 19, 2017.
+
+disp('Taylor Projection:')
+
+n_regimes=1;
+chi=[];
+chip=[];
+auxfuns=[];
+auxvars=[];
+logicalparams=[];
+logicalvars=[];
+
+% if isempty(shocks)
+% error('shocks are empty')
+% end
+nargs=9;
+
+if nargin==nargs
+ symparams=varargin{1};
+ order=varargin{2};
+elseif nargin==nargs+2
+ symparams=varargin{1};
+ order=varargin{2};
+ auxfuns=varargin{3};
+ auxvars=varargin{4};
+elseif nargin==nargs+4
+ symparams=varargin{1};
+ order=varargin{2};
+ auxfuns=varargin{3};
+ auxvars=varargin{4};
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+elseif nargin==nargs+3
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+elseif nargin==nargs+5
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+ auxfuns=varargin{6};
+ auxvars=varargin{7};
+elseif nargin==nargs+7
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ order=varargin{4};
+ n_regimes=varargin{5};
+ auxfuns=varargin{6};
+ auxvars=varargin{7};
+ logicalparams=varargin{8};
+ logicalvars=varargin{9};
+else
+ error('wrong number of input arguments')
+end
+
+symparams_ms=chi;
+symparams_msp=chip;
+
+fname='ms';
+nocheck=0;
+uname='';
+
+Phi=sym(Phi);
+if isempty(shocks)
+ shocks=sym('unused_shock');
+ eta=sym(zeros(length(x),1));
+else
+ eta=sym(zeros(length(x),length(shocks)));
+end
+
+
+
+model=prepare_tpMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,eta,...
+ n_regimes,order,auxfuns,auxvars,fname,nocheck,uname,logicalparams,logicalvars);
+
+fprintf('writing residual function to file...')
+home_folder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+cd('files')
+if isempty(chi)
+ make_residual3(f,Phi,yp,y,xp,x,shocks,symparams,order,auxfuns,auxvars,model.uu0,logicalparams,logicalvars);
+else
+ make_residualMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,order,auxfuns,auxvars,model.uu0,logicalparams,logicalvars);
+end
+cd(home_folder);
+fprintf('done\n')
+
+model.hybrid=3;
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tp3i.m b/105/replication_package/solution_methods/taylor_projection/prepare_tp3i.m
new file mode 100644
index 0000000000000000000000000000000000000000..fb2a1d4dd34087448034fd19fec794a551dca498
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tp3i.m
@@ -0,0 +1,135 @@
+function model=prepare_tp3i(f,Phi,yp,y,xp,x,shocks,varargin)
+% function model=prepare_tp(f,Phi,yp,y,xp,x,symparams,eta,order,varargin)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the lower block of h(x). This is the evolution law
+% of the exogenoust state variables, or any other state variables with a
+% known policy function.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% symparams = symbolic vector of the model parameters.
+% eta = the matrix eta as in Schmitt-Grohe and Uribe (2004).
+% order = order of the approximiating Polynomials. Can be 1, 2 or 3.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, March 19, 2017.
+
+disp('Taylor Projection:')
+
+n_regimes=1;
+chi=[];
+chip=[];
+auxfuns=[];
+auxvars=[];
+logicalparams=[];
+logicalvars=[];
+
+% if isempty(shocks)
+% error('shocks are empty')
+% end
+nargs=10;
+
+if nargin==nargs
+ symparams=varargin{1};
+ symparamsi=varargin{2};
+ order=varargin{3};
+elseif nargin==nargs+2
+ symparams=varargin{1};
+ symparamsi=varargin{2};
+ order=varargin{3};
+ auxfuns=varargin{4};
+ auxvars=varargin{5};
+elseif nargin==nargs+4
+ symparams=varargin{1};
+ symparamsi=varargin{2};
+ order=varargin{3};
+ auxfuns=varargin{4};
+ auxvars=varargin{5};
+ logicalparams=varargin{6};
+ logicalvars=varargin{7};
+elseif nargin==nargs+3
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ symparamsi=varargin{4};
+ order=varargin{5};
+ n_regimes=varargin{6};
+elseif nargin==nargs+5
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ symparamsi=varargin{4};
+ order=varargin{5};
+ n_regimes=varargin{6};
+ auxfuns=varargin{7};
+ auxvars=varargin{8};
+elseif nargin==nargs+7
+ chip=varargin{1};
+ chi=varargin{2};
+ symparams=varargin{3};
+ symparamsi=varargin{4};
+ order=varargin{5};
+ n_regimes=varargin{6};
+ auxfuns=varargin{7};
+ auxvars=varargin{8};
+ logicalparams=varargin{9};
+ logicalvars=varargin{10};
+else
+ error('wrong number of input arguments')
+end
+
+n_paramsi=numel(symparamsi);
+symparams=[symparams(:);symparamsi(:)];
+
+symparams_ms=chi;
+symparams_msp=chip;
+
+fname='ms';
+nocheck=1;
+uname='';
+
+Phi=sym(Phi);
+if isempty(shocks)
+ shocks=sym('unused_shock');
+ eta=sym(zeros(length(x),1));
+else
+ eta=sym(zeros(length(x),length(shocks)));
+end
+
+
+
+model=prepare_tpMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,eta,...
+ n_regimes,order,auxfuns,auxvars,fname,nocheck,uname,logicalparams,logicalvars);
+
+fprintf('writing residual function to file...')
+home_folder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+cd('files')
+if isempty(chi)
+ make_residual3(f,Phi,yp,y,xp,x,shocks,symparams,order,auxfuns,auxvars,model,logicalparams,logicalvars);
+else
+ make_residualMS3(f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,order,auxfuns,auxvars,model,logicalparams,logicalvars);
+end
+cd(home_folder);
+fprintf('done\n')
+
+model.hybrid=3;
+
+model.n_paramsi=n_paramsi;
+
+model.pde=0;
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpMS.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..7792398d4beb4d578c4e5186738b91b99984cb56
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS.m
@@ -0,0 +1,56 @@
+function [ model ] = prepare_tpMS( f,Phi,yp,y,xp,x,symparams_msp,symparams_ms,symparams,eta,n_regimes,order,auxfuns,auxvars,varargin )
+
+
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+
+fname='ms';
+nocheck=0;
+uname='';
+logicalparams=[];
+logicalvars=[];
+
+if ~isempty(varargin)
+ fname=varargin{1};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+ if length(varargin)>1
+ nocheck=varargin{2};
+ end
+ if length(varargin)>2
+ uname=varargin{3};
+ end
+ if length(varargin)>3
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+ end
+end
+
+if nocheck==0
+ fprintf('preprocessing (this may take a while)...')
+end
+
+if n_f~=n_y+n_x1 && nocheck==0
+ error('number of model conditions should be equal to the number of endogenous variables')
+end
+
+if numel(symparams_msp)~=numel(symparams_ms)
+ error('wrong size of future and current Markov switching parameters')
+end
+
+new_symparams=[symparams(:);symparams_ms(:);symparams_msp(:)];
+
+model=prepare_tpvec(f,Phi,yp,y,xp,x,new_symparams,eta,order,auxfuns,auxvars,fname,uname,logicalparams,logicalvars);
+model.n_regimes=n_regimes;
+
+model.n_msparams=numel(symparams_ms);
+model.n_params_no_ms=numel(symparams)+length(logicalparams);
+
+model.steady_state=0;
+
+if nocheck==0
+ fprintf('done\n')
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpMS2.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS2.m
new file mode 100644
index 0000000000000000000000000000000000000000..dede6595d389f394ef654c82110820dc39b14886
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS2.m
@@ -0,0 +1,57 @@
+function [ model ] = prepare_tpMS2( f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,...
+ eta,n_regimes,order,auxfuns,auxvars,varargin )
+
+
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+
+fname='ms';
+nocheck=0;
+uname='';
+logicalparams=[];
+logicalvars=[];
+
+if ~isempty(varargin)
+ fname=varargin{1};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+ if length(varargin)>1
+ nocheck=varargin{2};
+ end
+ if length(varargin)>2
+ uname=varargin{3};
+ end
+ if length(varargin)>3
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+ end
+end
+
+if nocheck==0
+ fprintf('preprocessing (this may take a while)...')
+end
+
+if n_f~=n_y+n_x1 && nocheck==0
+ error('number of model conditions should be equal to the number of endogenous variables')
+end
+
+if numel(symparams_msp)~=numel(symparams_ms)
+ error('wrong size of future and current Markov switching parameters')
+end
+
+new_symparams=[symparams(:);symparams_ms(:);symparams_msp(:)];
+
+model=prepare_tpvec2(f,Phi,yp,y,xp,x,shocks,new_symparams,eta,order,auxfuns,auxvars,fname,uname,logicalparams,logicalvars);
+model.n_regimes=n_regimes;
+
+model.n_msparams=numel(symparams_ms);
+model.n_params_no_ms=numel(symparams)+length(logicalparams);
+
+model.steady_state=0;
+
+if nocheck==0
+ fprintf('done\n')
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpMS3.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS3.m
new file mode 100644
index 0000000000000000000000000000000000000000..1b26a2c59d68c39c95f82b57e1073c7023d35407
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpMS3.m
@@ -0,0 +1,54 @@
+function [ model ] = prepare_tpMS3( f,Phi,yp,y,xp,x,shocks,symparams_msp,symparams_ms,symparams,...
+ eta,n_regimes,order,auxfuns,auxvars,varargin )
+
+
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+
+fname='ms';
+nocheck=0;
+uname='';
+logicalparams=[];
+logicalvars=[];
+
+if ~isempty(varargin)
+ fname=varargin{1};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+ if length(varargin)>1
+ nocheck=varargin{2};
+ end
+ if length(varargin)>2
+ uname=varargin{3};
+ end
+ if length(varargin)>3
+ logicalparams=varargin{4};
+ logicalvars=varargin{5};
+ end
+end
+
+fprintf('preprocessing (this may take a while)...')
+
+if n_f~=n_y && nocheck==0
+ error('number of model conditions should be equal to the number of endogenous variables')
+end
+
+if numel(symparams_msp)~=numel(symparams_ms)
+ error('wrong size of future and current Markov switching parameters')
+end
+
+new_symparams=[symparams(:);symparams_ms(:);symparams_msp(:)];
+
+model=prepare_tpvec3(f,Phi,yp,y,xp,x,shocks,new_symparams,eta,order,auxfuns,auxvars,fname,uname,logicalparams,logicalvars);
+
+model.n_regimes=n_regimes;
+
+model.n_msparams=numel(symparams_ms);
+model.n_params_no_ms=numel(symparams)+length(logicalparams);
+
+model.steady_state=0;
+
+fprintf('done\n')
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpvec.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec.m
new file mode 100644
index 0000000000000000000000000000000000000000..ba9f5ea76e7e4d0efa195d177028e6f6e64135e9
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec.m
@@ -0,0 +1,533 @@
+function model=prepare_tpvec(f,Phi,yp,y,xp,x,symparams,eta,order,varargin)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the lower block of h(x). This is the evolution law
+% of the exogenoust state variables, or any other state variables with a
+% known policy function.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% symparams = symbolic vector of the model parameters.
+% eta = the matrix eta as in Schmitt-Grohe and Uribe (2004).
+% order = order of the approximiating Polynomials. Can be 1, 2 or 3.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on March 19, 2017 - the function is vectorized and extended to
+% fourth order.
+
+
+
+model.n_e=size(eta,2);
+
+f=sym(f(:));
+Phi=sym(Phi(:));
+eta=sym(eta);
+
+x=sym(x(:));
+xp=sym(xp(:));
+y=sym(y(:));
+yp=sym(yp(:));
+
+if length(x)~=length(xp)
+ error('wrong size of current or future state variables')
+end
+if length(y)~=length(yp)
+ error('wrong size of current or future control variables')
+end
+
+
+% SIZE VARIABLES
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+v=[yp(:); y(:); xp(:); x(:)];
+n_v=length(v);
+
+if size(eta,1)~=n_x
+ error('wrong number of rows for matrix eta')
+end
+if nnz(eta(1:n_x1,:))~=0
+ error('the first n_x1 rows of eta should be zero')
+end
+
+% if n_f>n_y+n_x1
+% error('number of model conditions exceeds the number of endogenous variables');
+% elseif n_f4
+ error('perturbation order cannot exceed 4');
+ end
+ order=order(1);
+else
+ pert_order=order;
+end
+model.order=[order,pert_order];
+
+n_b=1;
+for k=1:order
+ n_b=n_b+nchoosek(n_x+k-1,k); % number of parameters in the basis function
+end
+
+n_theta=n_b*(n_y+n_x1); % total number of parameters to be solved
+
+% if order>=2
+ model.unique2=nchoosek(n_x+1,2);
+% end
+% if order>=3
+ model.unique3=nchoosek(n_x+2,3);
+% end
+% if order>=4
+ model.unique4=nchoosek(n_x+3,4);
+% end
+
+% fname
+
+if nargin>11
+ fname=varargin{3};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ fname='';
+end
+if nargin>12
+ uname=varargin{4};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ uname='';
+end
+model.fname=fname;
+model.uname=uname;
+
+if nargin>13
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+ if length(logicalparams)~=length(logicalvars)
+ error('wrong size of logical parameters or variables')
+ end
+else
+ logicalparams=sym([]);
+ logicalvars=sym([]);
+end
+
+% DEFINE pi_ and u
+if isempty(varargin)
+ pi_=sym([]);
+ u=sym([]);
+elseif isempty(varargin{1})
+ warning('no substitutions assumed')
+ pi_=sym([]);
+ u=sym([]);
+else
+ pi_=varargin{1}; % pi_ is the function pi(v,u)
+ pi_=pi_(:);
+ u=varargin{2}; % auxiliary variables that are eventually substituted out
+ u=u(:);
+ if length(pi_)~=length(u)
+ error('wrong size of substituted variables or functions')
+ end
+ if ~isequal(sort(u),sort(unique(u)))
+ error('substituted variables are not uniquely determined')
+ end
+end
+
+% check that auxiliary functions do not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(pi_)
+ if ~isequal(pi_,subs(pi_,logicalparams,sym(zeros(size(logicalparams)))))
+ error('auxiliary variables must not depend on logical parameters')
+ end
+end
+
+% check that Phi function does not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(Phi)
+ if ~isequal(Phi,subs(Phi,logicalparams,sym(zeros(size(logicalparams)))))
+ error('function Phi must not depend on logical parameters')
+ end
+end
+
+% check that all symbolic variables/parameters are defined
+
+actualsymvars=symvar([f;pi_;eta(:);Phi(:)]);
+definedvars=[v(:);u(:);symparams(:);logicalparams(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+
+n_definedvars=length(definedvars);
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+% check that logical variables are defined
+actualsymvars=unique(logicalvars);
+definedvars=[v(:);u(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+n_definedvars=length(definedvars);
+
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+
+% for i=1:length(logicalvars)
+% if isempty(v(v==logicalvars(i))) && isempty(u(u==logicalvars(i)))
+% error([char(logicalvars(i)) ' is not defined'])
+% end
+% end
+
+symparams=[symparams(:);logicalparams(:)];
+model.n_params=numel(symparams);
+model.logical_params_loc=model.n_params-length(logicalparams)+1:model.n_params;
+model.n_logicalparams=length(logicalparams);
+
+n_u=length(u);
+model.n_u=n_u;
+tilf=f; % tilf(v,u) is a function of v and u
+% n=find_n(pi_,u); % number of substitutions needed to eliminate u
+[n,piu0]=find_n_new(pi_,u);
+model.uu0=piu0;
+
+% Identify variables that affect u
+u_v=u; %u_v which is u as a function of v only u(v)
+uu=eye(n_u); % matrix to store which of u affect u
+uv=zeros(n_u,n_v);
+
+% piu0=double(logical(jacobian(pi_,u)~=0));
+piv0=double(logical(jacobian(pi_,v)~=0));
+piu=piu0;
+piv=piv0;
+
+for k=1:n
+ uu=uu+piu;
+ uv=uv+piv;
+ piv=piu*piv0;
+ piu=piu*piu0;
+ u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+end
+
+% for k=1:n
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+% uu=uu+logical(jacobian(u_v,u)~=0); % uu is a n_u-by-n_u matrix. the ij element is zero only if ui is independent of uj through all substitutions
+% uv=uv+logical(jacobian(u_v,v)~=0); % uv is a n_u-by-n_v matrix. the ij element is zero only if ui is independent of vj through all substitutions
+% end
+
+% Identify stochasic and predetermined functions and variables
+if n_x2>0
+ stochexog=find(sum(1-logical(eta(n_x1+1:end,:)==0),2)); % stochastic exogenous variables
+else
+ stochexog=[];
+end
+preexog=1:n_x2;
+preexog(stochexog)=[]; % predetermined exogenous variables
+
+stochvars=[1:n_y,2*n_y+n_x1+stochexog']; % all stochastic variables
+
+tilfv=double(logical(jacobian(tilf,v)~=0));
+tilfu=double(logical(jacobian(tilf,u)~=0));
+fv=double(logical(tilfv+tilfu*uv~=0)); % logical Jacobian of f w.r.t v
+
+stochfrows=find(sum( 1-logical(fv(:,stochvars)==0),2)); % stochastic rows of f
+prefrows=1:n_f;
+prefrows(stochfrows)=[]; % predetermined rows of f
+
+% variables that affect the predetermined and stochastic rows of f
+
+prefvars=find(sum(1-logical(fv(prefrows,:)==0),1));
+stochfvars=find(sum(1-logical(fv(stochfrows,:)==0),1));
+
+
+currentFolder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+
+cd 'files'
+
+% generate a function that computes eta
+gen_fun_vec(eta(:),[],symparams,['eta' uname],'row');
+
+
+% Create an m file for Phi and its derivatives w.r.t x
+gen_fun_vec(Phi,symparams,x,['Phi' uname],'row');
+if order>=1
+ model.Phi_indc=getderivs_c(Phi,x,max(order,pert_order),symparams,'Phi');
+end
+
+% Create an m file for u
+% newuv=jacobian(u_v,v); % calculate uv again
+newuv=uv;
+stochurows=find(sum( 1-logical(newuv(:,stochvars)==0),2)); % stochastic rows of u
+model.stochurows=stochurows;
+preurows=1:n_u;
+preurows(stochurows)=[]; % predetermined rows of u
+model.preurows=preurows;
+preuvars=find(sum( logical(newuv(preurows,:)~=0),1)); % variables of predetermined rows of u
+stochuvars=find(sum( logical(newuv(stochurows,:)~=0),1)); % variables of stochastic rows of u
+
+% gen_fun_vec(u_v(preurows),symparams,v(preuvars),['preu' uname],'row');
+% gen_fun_vec(u_v(stochurows),symparams,v(stochuvars),['stochu' uname],'row');
+preurows_allsubs=logical(sum(uu(preurows,:),1));
+gen_fun_vec_subs(u(preurows),symparams,v(preuvars),pi_(preurows_allsubs),u(preurows_allsubs),['preu' uname],'row',piu0(preurows_allsubs,preurows_allsubs));
+
+stochurows_allsubs=logical(sum(uu(stochurows,:),1));
+gen_fun_vec_subs(u(stochurows),symparams,v(stochuvars),pi_(stochurows_allsubs),u(stochurows_allsubs),['stochu' uname],'row',piu0(stochurows_allsubs,stochurows_allsubs));
+
+model.preuvars=preuvars;
+model.stochuvars=stochuvars;
+
+% build z and find the Jacobian of z
+z=[v;u];
+
+% locate the logical variables in z
+
+logical_zvars=zeros(length(logicalvars),1);
+for i=1:length(logical_zvars)
+ logical_zvars(i)=find(logical(z==logicalvars(i)));
+end
+model.logical_zvars=logical_zvars;
+
+n_z=n_v+n_u;
+zz=[eye(n_v),zeros(n_v,n_u);uv,uu];
+for i=1:n_z
+ temp=zz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ zz(i,:)=temp;
+end
+zz=intarray(zz);
+model.maxzz=intarray(max(zz(:)));
+
+% build fv similar to zz
+fv=double(fv);
+for i=1:n_f
+ temp=fv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ fv(i,:)=temp;
+end
+model.fv=fv;
+
+% tilfz=jacobian(tilf,z);
+tilfz=[tilfv,tilfu];
+
+% build tilfz
+% tilfz=double(logical(tilfz~=0)); % only direct effects
+for i=1:n_f
+ temp=tilfz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilfz(i,:)=temp;
+end
+model.tilfz=tilfz;
+model.maxtilfz=intarray(max(tilfz(:)));
+
+% Create an m file for tilf
+pretilfzvars=find(sum(1-logical(tilfz(prefrows,:)==0),1));
+model.pretilfzvars=pretilfzvars; % variables in z that affect pretilf
+gen_fun_vec(tilf(prefrows),symparams,z(pretilfzvars),['pretilf' fname],'row');
+
+stochtilfzvars=find(sum(1-logical(tilfz(stochfrows,:)==0),1));
+model.stochtilfzvars=stochtilfzvars; % variables in z that affect stochtilf
+gen_fun_vec(tilf(stochfrows),symparams,z(stochtilfzvars),['stochtilf' fname],'row');
+
+% Differentiate PI and create m files
+
+PI=[v;pi_];
+prePI=PI;
+prePI(n_v+stochurows)=0; % stochastic rows of PI are set to zero. Note: the first n_v rows include stochastic variables but their derivatives w.r.t are ones or zeros.
+stochPI=PI;
+stochPI([1:n_v,n_v+preurows])=0; % nonstochastic rows are set to zero. See the note above.
+
+[model.prePI_ind_u]=getderivs_tensor(prePI,z,max(order+1,pert_order),symparams,['prePI' uname]);
+[model.stochPI_ind_u]=getderivs_tensor(stochPI,z,max(order+1,pert_order),symparams,['stochPI' uname]);
+
+prefuvars=find(sum(uu(logical(sum(logical(tilfu(prefrows,:)~=0),1)~=0),:),1));
+stochfuvars=find(sum(uu(logical(sum(logical(tilfu(stochfrows,:)~=0),1)~=0),:),1));
+model.prefuvars=prefuvars;
+model.stochfuvars=stochfuvars;
+
+prefzvars=[prefvars,n_v+prefuvars];
+stochfzvars=[stochfvars,n_v+stochfuvars];
+model.n_prefzvars=length(prefzvars);
+model.n_stochfzvars=length(stochfzvars);
+
+[model.stochtilf_ind_u,model.stoch_n]=gen_chainderivs_tensor(tilf(stochfrows),v(stochfvars),u(stochfuvars),pi_(stochfuvars),max(order+1,pert_order),symparams,['stochtilf' fname]);
+[model.pretilf_ind_u,model.pre_n]=gen_chainderivs_tensor(tilf(prefrows),v(prefvars),u(prefuvars),pi_(prefuvars),max(order+1,pert_order),symparams,['pretilf' fname]);
+
+
+% Store variables in struct model
+model.prefrows=prefrows;
+model.stochfrows=stochfrows;
+model.prefvars=prefvars;
+model.stochfvars=stochfvars;
+model.stochexog=stochexog;
+model.preexog=preexog;
+model.n_stochexog=length(stochexog);
+model.n_preexog=length(preexog);
+model.stochfzvars=stochfzvars;
+model.prefzvars=prefzvars;
+
+model.n_theta=n_theta;
+model.n_b=n_b;
+
+model.n_f=n_f;
+model.n_x=n_x;
+model.n_y=n_y;
+model.n_x1=n_x1;
+model.n_x2=n_x2;
+
+model.n_v=n_v;
+model.n_z=n_z;
+model.n_u=n_u;
+
+model.n_ind=1;
+
+model.U=cell(4,1);
+model.W=cell(4,1);
+for i=2:order+1
+ [model.U{i},model.W{i}]=create_UW(n_x,i);
+end
+
+model.stochzz=zz(model.stochfzvars,model.stochfzvars);
+model.prezz=zz(model.prefzvars,model.prefzvars);
+
+model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+model.pretilfz=tilfz(model.prefrows,model.prefzvars);
+
+% calculate some big matrices now
+
+if order>=3
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+ save('tempfile')
+
+
+
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+ delete('tempfile.mat')
+end
+
+if order>=4
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.prefvars_chain5c_M1=tempM{1};
+ model.prefvars_chain5c_M2=tempM{2};
+ model.prefvars_chain5c_M3=tempM{3};
+ model.prefvars_chain5c_M4=tempM{4};
+ model.prefvars_chain5c_M5=tempM{5};
+ model.prefvars_chain5c_M6=tempM{6};
+
+ clear tempM
+ save('tempfile')
+
+
+
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain5c_M1=tempM{1};
+ model.stochfvars_chain5c_M2=tempM{2};
+ model.stochfvars_chain5c_M3=tempM{3};
+ model.stochfvars_chain5c_M4=tempM{4};
+ model.stochfvars_chain5c_M5=tempM{5};
+ model.stochfvars_chain5c_M6=tempM{6};
+
+ clear tempM
+ delete('tempfile.mat')
+end
+
+totindi=5+8;
+totindi=totindi+(model.pre_n-1)*(1+3+4+6)+1+4+6+9;
+totindi=totindi+3;
+totindi=totindi+4;
+totindi=totindi+2;
+totindi=totindi+2;
+totindi=totindi+1;
+totindi=totindi+9;
+totindi=totindi+8;
+totindi=totindi+8+(model.stoch_n-1)*(1+3+4+6)+1+4+6+9;
+totindi=totindi+2;
+totindi=totindi+9;
+totindi=totindi+7;
+
+model.totindi=totindi;
+
+model.count_pre_n=0;
+model.count_stoch_n=0;
+
+rehash;
+
+
+cd(currentFolder)
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpvec2.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec2.m
new file mode 100644
index 0000000000000000000000000000000000000000..7f3afd4e2779ee536f69ecb5196b19da407f7c9a
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec2.m
@@ -0,0 +1,661 @@
+function model=prepare_tpvec2(f,Phi,yp,y,xp,x,shocks,symparams,eta,order,varargin)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the lower block of h(x). This is the evolution law
+% of the exogenoust state variables, or any other state variables with a
+% known policy function.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% symparams = symbolic vector of the model parameters.
+% eta = the matrix eta as in Schmitt-Grohe and Uribe (2004).
+% order = order of the approximiating Polynomials. Can be 1, 2 or 3.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on March 19, 2017 - the function is vectorized and extended to
+% fourth order.
+
+
+
+model.n_e=size(eta,2);
+
+f=sym(f(:));
+Phi=sym(Phi(:));
+eta=sym(eta);
+
+x=sym(x(:));
+xp=sym(xp(:));
+y=sym(y(:));
+yp=sym(yp(:));
+shocks=sym(shocks(:));
+
+if length(x)~=length(xp)
+ error('wrong size of current or future state variables')
+end
+if length(y)~=length(yp)
+ error('wrong size of current or future control variables')
+end
+
+
+% SIZE VARIABLES
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+v=[yp(:); y(:); xp(:); x(:)];
+n_v=length(v);
+
+if size(eta,1)~=n_x
+ error('wrong number of rows for matrix eta')
+elseif size(eta,2)~=numel(shocks)
+ error('wrong number of columns for matrix eta')
+end
+if nnz(eta(1:n_x1,:))~=0
+ error('the first n_x1 rows of eta should be zero')
+end
+
+% if n_f>n_y+n_x1
+% error('number of model conditions exceeds the number of endogenous variables');
+% elseif n_f4
+ error('perturbation order cannot exceed 4');
+ end
+ order=order(1);
+else
+ pert_order=order;
+end
+model.order=[order,pert_order];
+
+n_b=0;
+for k=0:order
+ n_b=n_b+nchoosek(n_x+k-1,k); % number of parameters in the basis function
+end
+
+n_theta=n_b*(n_y+n_x1); % total number of parameters to be solved
+
+if order>=2
+ model.unique2=nchoosek(n_x+1,2);
+end
+if order>=3
+ model.unique3=nchoosek(n_x+2,3);
+end
+if order>=4
+ model.unique4=nchoosek(n_x+3,4);
+end
+
+% fname
+nargs=11;
+
+if nargin>nargs
+ fname=varargin{3};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ fname='';
+end
+if nargin>nargs+1
+ uname=varargin{4};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ uname='';
+end
+model.fname=fname;
+model.uname=uname;
+
+if nargin>nargs+2
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+ if length(logicalparams)~=length(logicalvars)
+ error('wrong size of logical parameters or variables')
+ end
+else
+ logicalparams=sym([]);
+ logicalvars=sym([]);
+end
+
+
+% DEFINE pi_ and u
+if isempty(varargin)
+ pi_=sym([]);
+ u=sym([]);
+elseif isempty(varargin{1})
+ warning('no substitutions assumed')
+ pi_=sym([]);
+ u=sym([]);
+else
+ pi_=varargin{1}; % pi_ is the function pi(v,u)
+ pi_=pi_(:);
+ u=varargin{2}; % auxiliary variables that are eventually substituted out
+ u=u(:);
+ if length(pi_)~=length(u)
+ error('wrong size of substituted variables or functions')
+ end
+ if ~isequal(sort(u),sort(unique(u)))
+ error('substituted variables are not uniquely determined')
+ end
+end
+
+% check that auxiliary functions do not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(pi_)
+ if ~isequal(pi_,subs(pi_,logicalparams,sym(zeros(size(logicalparams)))))
+ error('auxiliary variables must not depend on logical parameters')
+ end
+end
+
+% check that Phi function does not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(Phi)
+ if ~isequal(Phi,subs(Phi,logicalparams,sym(zeros(size(logicalparams)))))
+ error('function Phi must not depend on logical parameters')
+ end
+end
+
+%%%% NEED TO ADD MORE CHECKS ON PHI - must be independent of yp and xp
+%%%% directly and through all substitutions and must be independent of
+%%%% stochastic auxiliary vars.
+
+% check that all symbolic variables/parameters are defined
+
+actualsymvars=symvar([f;pi_;eta(:);Phi(:)]);
+definedvars=[v(:);u(:);symparams(:);logicalparams(:);shocks(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+
+n_definedvars=length(definedvars);
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+% check that logical variables are defined
+actualsymvars=unique(logicalvars);
+definedvars=[v(:);u(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+n_definedvars=length(definedvars);
+
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+% substitute x2p in f and create an auxiliary variable
+
+x2p=Phi+eta(n_x1+1:end,:)*shocks;
+n_u=length(u);
+u=[u(:);sym(zeros(n_x2,1))];
+
+for i=1:n_x2
+ u(n_u+i)=sym([char(xp(n_x1+i)),'_aux']);
+end
+
+f=subs(f,xp(n_x1+1:end),u(n_u+1:end));
+warning('i am substituting x2p into auxiliary functions - need to check that it is correct')
+pi_=subs(pi_,xp(n_x1+1:end),u(n_u+1:end));
+
+
+pi_=[pi_(:);x2p(:)];
+
+model.f=f;
+model.auxvars=u;
+model.auxfuns=pi_;
+
+new_eta=eta;
+new_eta(n_x1+1:end,:)=jacobian(x2p,shocks);
+
+%%%%%%%%%%%%%%
+symparams=[symparams(:);logicalparams(:)];
+model.n_params=numel(symparams);
+model.logical_params_loc=model.n_params+model.n_e-length(logicalparams)+(1:length(logicalparams));
+model.n_logicalparams=length(logicalparams);
+
+% add shocks to symparams
+symparams=[shocks(:);symparams(:)];
+
+n_u=length(u);
+model.n_u=n_u;
+tilf=f; % tilf(v,u) is a function of v and u
+% n=find_n(pi_,u); % number of substitutions needed to eliminate u
+[n,piu0]=find_n_new(pi_,u);
+model.uu0=piu0(1:end-n_x2,1:end-n_x2);
+
+% Identify variables that affect u
+% u_v=u; %u_v which is u as a function of v only u(v)
+uu=eye(n_u); % matrix to store which of u affect u
+uv=zeros(n_u,n_v);
+
+% piu0=double(logical(jacobian(pi_,u)~=0));
+piv0=double(logical(jacobian(pi_,v)~=0));
+piu=piu0;
+piv=piv0;
+
+
+for k=1:n
+ uu=uu+piu;
+ uv=uv+piv;
+ piv=piu*piv0;
+ piu=piu*piu0;
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+end
+
+pishocks0=double(sum(logical(jacobian(pi_,shocks)~=0),2));
+ushocks=uu*pishocks0;
+% for k=1:n
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+% uu=uu+logical(jacobian(u_v,u)~=0); % uu is a n_u-by-n_u matrix. the ij element is zero only if ui is independent of uj through all substitutions
+% uv=uv+logical(jacobian(u_v,v)~=0); % uv is a n_u-by-n_v matrix. the ij element is zero only if ui is independent of vj through all substitutions
+% end
+
+% Identify stochasic and predetermined functions and variables
+warning('need to define all exog vars as stochastic')
+if n_x2>0
+ stochexog=find(sum(1-logical(new_eta(n_x1+1:end,:)==0),2)); % stochastic exogenous variables
+else
+ stochexog=[];
+end
+preexog=1:n_x2;
+preexog(stochexog)=[]; % predetermined exogenous variables
+
+stochvars=[1:n_y,2*n_y+n_x1+stochexog']; % all stochastic variables
+
+tilfv=double(logical(jacobian(tilf,v)~=0));
+tilfu=double(logical(jacobian(tilf,u)~=0));
+tilfshocks=sum(double(logical(jacobian(tilf,shocks)~=0)),2);
+
+fv=double(logical(tilfv+tilfu*uv~=0)); % logical Jacobian of f w.r.t v
+fshocks=double(logical(tilfshocks+tilfu*ushocks~=0)); % logical Jacobian of f w.r.t shocks
+
+tilPhiv=double(logical(jacobian(Phi,v)~=0));
+tilPhiu=double(logical(jacobian(Phi,u)~=0));
+Phiv=double(logical(tilPhiv+tilPhiu*uv~=0)); % logical Jacobian of Phi w.r.t v
+
+
+tempind=sum( 1-logical(fv(:,stochvars)==0),2)+fshocks;
+
+
+stochfrows=find(tempind); % stochastic rows of f
+prefrows=1:n_f;
+
+
+prefrows(stochfrows)=[]; % predetermined rows of f
+
+% variables that affect the predetermined and stochastic rows of f
+
+prefvars=find(sum(1-logical(fv(prefrows,:)==0),1));
+stochfvars=find(sum(1-logical(fv(stochfrows,:)==0),1));
+
+Phivars=find(sum(1-logical(Phiv==0),1));
+
+currentFolder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+
+cd 'files'
+
+% generate a function that computes eta
+gen_fun_vec(eta(:),[],symparams,['eta' uname],'row');
+
+
+% if order>=1
+% model.Phi_indc=getderivs_c(Phi,x,max(order,pert_order),symparams,'Phi');
+% end
+
+% Create an m file for u
+% newuv=jacobian(u_v,v); % calculate uv again
+newuv=uv;
+tempind=sum( 1-logical(newuv(:,stochvars)==0),2)+ushocks; % logical index of stochastic auxiliary variables
+% tempind(end-n_x2+1:end)=stochexog; % add the stochastic exogenous variables to the stochastic auxiliary variables
+stochurows=find(tempind); % stochastic rows of u
+model.stochurows=stochurows;
+preurows=1:n_u;
+preurows(stochurows)=[]; % predetermined rows of u
+model.preurows=preurows;
+preuvars=find(sum( logical(newuv(preurows,:)~=0),1)); % variables of predetermined rows of u
+stochuvars=find(sum( logical(newuv(stochurows,:)~=0),1)); % variables of stochastic rows of u
+
+% gen_fun_vec(u_v(preurows),symparams,v(preuvars),['preu' uname],'row');
+% gen_fun_vec(u_v(stochurows),symparams,v(stochuvars),['stochu' uname],'row');
+preurows_allsubs=logical(sum(uu(preurows,:),1));
+gen_fun_vec_subs(u(preurows),symparams,v(preuvars),pi_(preurows_allsubs),u(preurows_allsubs),['preu' uname],'row',piu0(preurows_allsubs,preurows_allsubs));
+
+stochurows_allsubs=logical(sum(uu(stochurows,:),1));
+gen_fun_vec_subs(u(stochurows),symparams,v(stochuvars),pi_(stochurows_allsubs),u(stochurows_allsubs),['stochu' uname],'row',piu0(stochurows_allsubs,stochurows_allsubs));
+
+model.preuvars=preuvars;
+model.stochuvars=stochuvars;
+
+% Create an m file for Phi and its derivatives w.r.t x
+gen_fun_vec(Phi,symparams,[x(:);y(:);u(preurows)],['Phi' uname],'row');
+
+gen_fun_vec(new_eta,symparams,[x(:);y(:);u(preurows)],['new_eta' uname],'row');
+
+% build z and find the Jacobian of z
+z=[v;u];
+
+% locate the logical variables in z
+
+logical_zvars=zeros(length(logicalvars),1);
+for i=1:length(logical_zvars)
+ logical_zvars(i)=find(logical(z==logicalvars(i)));
+end
+model.logical_zvars=logical_zvars;
+
+n_z=n_v+n_u;
+zz=[eye(n_v),zeros(n_v,n_u);uv,uu];
+for i=1:n_z
+ temp=zz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ zz(i,:)=temp;
+end
+zz=intarray(zz);
+model.maxzz=intarray(max(zz(:)));
+
+% build fv similar to zz
+fv=double(fv);
+for i=1:n_f
+ temp=fv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ fv(i,:)=temp;
+end
+model.fv=fv;
+
+% build Phiv similar to zz
+Phiv=double(Phiv);
+for i=1:n_x2
+ temp=Phiv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ Phiv(i,:)=temp;
+end
+model.Phiv=Phiv;
+
+% tilfz=jacobian(tilf,z);
+tilfz=[tilfv,tilfu];
+
+% build tilfz
+% tilfz=double(logical(tilfz~=0)); % only direct effects
+for i=1:n_f
+ temp=tilfz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilfz(i,:)=temp;
+end
+model.tilfz=tilfz;
+model.maxtilfz=intarray(max(tilfz(:)));
+
+% build tilPhiz
+tilPhiz=[tilPhiv,tilPhiu];
+for i=1:n_x2
+ temp=tilPhiz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilPhiz(i,:)=temp;
+end
+% model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+
+% Create an m file for tilf
+pretilfzvars=find(sum(1-logical(tilfz(prefrows,:)==0),1));
+model.pretilfzvars=pretilfzvars; % variables in z that affect pretilf
+gen_fun_vec(tilf(prefrows),symparams,z(pretilfzvars),['pretilf' fname],'row');
+
+stochtilfzvars=find(sum(1-logical(tilfz(stochfrows,:)==0),1));
+model.stochtilfzvars=stochtilfzvars; % variables in z that affect stochtilf
+gen_fun_vec(tilf(stochfrows),symparams,z(stochtilfzvars),['stochtilf' fname],'row');
+
+% Differentiate PI and create m files
+
+PI=[v;pi_];
+prePI=PI;
+prePI(n_v+stochurows)=0; % stochastic rows of PI are set to zero. Note: the first n_v rows include stochastic variables but their derivatives w.r.t are ones or zeros.
+stochPI=PI;
+stochPI([1:n_v,n_v+preurows])=0; % nonstochastic rows are set to zero. See the note above.
+
+[model.prePI_ind_u]=getderivs_tensor(prePI,z,max(order+1,pert_order),symparams,['prePI' uname]);
+[model.stochPI_ind_u]=getderivs_tensor(stochPI,z,max(order+1,pert_order),symparams,['stochPI' uname]);
+
+prefuvars=find(sum(uu(logical(sum(logical(tilfu(prefrows,:)~=0),1)~=0),:),1));
+stochfuvars=find(sum(uu(logical(sum(logical(tilfu(stochfrows,:)~=0),1)~=0),:),1));
+
+Phiuvars=find(sum(uu(logical(sum(logical(tilPhiu~=0),1)~=0),:),1));
+
+model.prefuvars=prefuvars;
+model.stochfuvars=stochfuvars;
+model.Phiuvars=Phiuvars;
+
+prefzvars=[prefvars,n_v+prefuvars];
+stochfzvars=[stochfvars,n_v+stochfuvars];
+
+Phizvars=[Phivars,n_v+Phiuvars];
+
+model.n_prefzvars=length(prefzvars);
+model.n_stochfzvars=length(stochfzvars);
+model.n_Phizvars=length(Phizvars);
+
+[model.stochtilf_ind_u,model.stoch_n]=gen_chainderivs_tensor(tilf(stochfrows),v(stochfvars),u(stochfuvars),pi_(stochfuvars),max(order+1,pert_order),symparams,['stochtilf' fname]);
+[model.pretilf_ind_u,model.pre_n]=gen_chainderivs_tensor(tilf(prefrows),v(prefvars),u(prefuvars),pi_(prefuvars),max(order+1,pert_order),symparams,['pretilf' fname]);
+
+[model.Phi_ind_u,model.Phi_n]=gen_chainderivs_tensor(Phi,v(Phivars),u(Phiuvars),pi_(Phiuvars),max(order+1,pert_order),symparams,['Phi' fname]);
+
+% Store variables in struct model
+model.prefrows=prefrows;
+model.stochfrows=stochfrows;
+model.prefvars=prefvars;
+model.stochfvars=stochfvars;
+model.stochexog=stochexog;
+model.preexog=preexog;
+model.n_stochexog=length(stochexog);
+model.n_preexog=length(preexog);
+model.stochfzvars=stochfzvars;
+model.prefzvars=prefzvars;
+model.Phizvars=Phizvars;
+model.Phivars=Phivars;
+
+model.n_theta=n_theta;
+model.n_b=n_b;
+
+model.n_f=n_f;
+model.n_x=n_x;
+model.n_y=n_y;
+model.n_x1=n_x1;
+model.n_x2=n_x2;
+
+model.n_v=n_v;
+model.n_z=n_z;
+model.n_u=n_u;
+
+model.n_ind=1;
+
+model.U=cell(4,1);
+model.W=cell(4,1);
+for i=2:order+1
+ [model.U{i},model.W{i}]=create_UW(n_x,i);
+end
+
+model.stochzz=zz(model.stochfzvars,model.stochfzvars);
+model.prezz=zz(model.prefzvars,model.prefzvars);
+
+model.Phizz=zz(model.Phizvars,model.Phizvars);
+
+model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+model.pretilfz=tilfz(model.prefrows,model.prefzvars);
+
+model.tilPhiz=tilPhiz(:,Phizvars);
+model.maxtilPhiz=intarray(max(tilPhiz(:)));
+
+% calculate some big matrices now
+
+if order>=3
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+
+ save('tempfile')
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+
+ save('tempfile')
+ n_Phivars=length(Phivars);
+ clearvars -except n_Phivars
+
+ if n_Phivars>0
+ [ tempM ] = chainsM( n_Phivars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.Phivars_chain4c_M2=tempM{2};
+ model.Phivars_chain4c_M3=tempM{3};
+ model.Phivars_chain4c_M4=tempM{4};
+ clear tempM
+
+
+ delete('tempfile.mat')
+end
+
+if order>=4
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.prefvars_chain5c_M1=tempM{1};
+ model.prefvars_chain5c_M2=tempM{2};
+ model.prefvars_chain5c_M3=tempM{3};
+ model.prefvars_chain5c_M4=tempM{4};
+ model.prefvars_chain5c_M5=tempM{5};
+ model.prefvars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+ save('tempfile')
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain5c_M1=tempM{1};
+ model.stochfvars_chain5c_M2=tempM{2};
+ model.stochfvars_chain5c_M3=tempM{3};
+ model.stochfvars_chain5c_M4=tempM{4};
+ model.stochfvars_chain5c_M5=tempM{5};
+ model.stochfvars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+ save('tempfile')
+ n_Phivars=length(Phivars);
+ clearvars -except n_Phivars
+
+ if n_Phivars>0
+ [ tempM ] = chainsM( n_Phivars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.Phivars_chain5c_M1=tempM{1};
+ model.Phivars_chain5c_M2=tempM{2};
+ model.Phivars_chain5c_M3=tempM{3};
+ model.Phivars_chain5c_M4=tempM{4};
+ model.Phivars_chain5c_M5=tempM{5};
+ model.Phivars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+
+ delete('tempfile.mat')
+end
+
+model.count_pre_n=model.pre_n-1;
+if model.count_pre_n<0
+ model.count_pre_n=0;
+end
+
+model.count_stoch_n=model.stoch_n-1;
+if model.count_stoch_n<0
+ model.count_stoch_n=0;
+end
+
+totindi=5+8;
+totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+totindi=totindi+3;
+totindi=totindi+4;
+totindi=totindi+2;
+totindi=totindi+2;
+totindi=totindi+1;
+totindi=totindi+9;
+totindi=totindi+8;
+totindi=totindi+8+model.count_stoch_n*(1+3+4+6)+1+4+6+9;
+totindi=totindi+2;
+totindi=totindi+9;
+totindi=totindi+7;
+
+model.totindi=totindi;
+
+rehash;
+
+
+cd(currentFolder)
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/prepare_tpvec3.m b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec3.m
new file mode 100644
index 0000000000000000000000000000000000000000..05dd84e88797ecca16b11c910a7e4c8fe69f7cc5
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/prepare_tpvec3.m
@@ -0,0 +1,702 @@
+function model=prepare_tpvec3(f,Phi,yp,y,xp,x,shocks,symparams,eta,order,varargin)
+
+% This file prepares codes and data that are used later to compute the
+% nonlinear system of Taylor projection and the Jacobian.
+% Input args:
+% f = symbolic vector of the model conditions (Ef=0)
+% Phi = symbolic vector of the lower block of h(x). This is the evolution law
+% of the exogenoust state variables, or any other state variables with a
+% known policy function.
+% yp,y,xp,x = symbolic vectors of the control and state varaibles for
+% current (y,x) and future (yp,xp) periods.
+% symparams = symbolic vector of the model parameters.
+% eta = the matrix eta as in Schmitt-Grohe and Uribe (2004).
+% order = order of the approximiating Polynomials. Can be 1, 2 or 3.
+% Optional arguments:
+% subsfuns,subsvars = subsvars (the second optional argument) is a symbolic
+% vector of auxiliary variables that are eventually substituted out.
+% subsfuns (the first optional argument) is a symbolic vector of the
+% expressions of subsvars (see example in the documentation). Use
+% subsfuns and subsvars to speed up differentiation.
+% Output arg:
+% model = a structure variable with data, that is used to compute the
+% system.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on March 19, 2017 - the function is vectorized and extended to
+% fourth order.
+
+
+
+model.n_e=size(eta,2);
+
+f=sym(f(:));
+Phi=sym(Phi(:));
+eta=sym(eta);
+
+x=sym(x(:));
+xp=sym(xp(:));
+y=sym(y(:));
+yp=sym(yp(:));
+shocks=sym(shocks(:));
+
+
+
+if length(x)~=length(xp)
+ error('wrong size of current or future state variables')
+end
+if length(x)~=length(Phi)
+ error('wrong size of law of motion of state variables')
+end
+if length(y)~=length(yp)
+ error('wrong size of current or future control variables')
+end
+
+% SIZE VARIABLES
+n_f=length(f); n_x=length(x); n_y=length(y); n_x2=length(Phi); n_x1=n_x-n_x2;
+v=[yp(:); y(:); xp(:); x(:)];
+n_v=length(v);
+
+if size(eta,1)~=n_x
+ error('wrong number of rows for matrix eta')
+end
+if nnz(eta(1:n_x1,:))~=0
+ error('the first n_x1 rows of eta should be zero')
+end
+
+% if order is a vector of length 2, the first element is the order of
+% Taylor projection and the second is the order of perturbation.
+if length(order)==2
+ pert_order=order(2);
+ if pert_order>4
+ error('perturbation order cannot exceed 4');
+ end
+ order=order(1);
+else
+ pert_order=order;
+end
+model.order=[order,pert_order];
+
+n_b=1;
+for k=1:order
+ n_b=n_b+nchoosek(n_x+k-1,k); % number of parameters in the basis function
+end
+
+n_theta=n_b*(n_y+n_x1); % total number of parameters to be solved
+
+% if order>=2
+ model.unique2=nchoosek(n_x+1,2);
+% end
+% if order>=3
+ model.unique3=nchoosek(n_x+2,3);
+% end
+% if order>=4
+ model.unique4=nchoosek(n_x+3,4);
+% end
+
+% fname
+nargs=11;
+
+if nargin>nargs
+ fname=varargin{3};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ fname='';
+end
+if nargin>nargs+1
+ uname=varargin{4};
+ if ~ischar(fname)
+ error('function name must be a string')
+ end
+else
+ uname='';
+end
+model.fname=fname;
+model.uname=uname;
+
+if nargin>nargs+2
+ logicalparams=varargin{5};
+ logicalvars=varargin{6};
+ if length(logicalparams)~=length(logicalvars)
+ error('wrong size of logical parameters or variables')
+ end
+else
+ logicalparams=sym([]);
+ logicalvars=sym([]);
+end
+
+
+% DEFINE pi_ and u
+if isempty(varargin)
+ pi_=sym([]);
+ u=sym([]);
+elseif isempty(varargin{1})
+% warning('no substitutions assumed')
+ pi_=sym([]);
+ u=sym([]);
+else
+ pi_=varargin{1}; % pi_ is the function pi(v,u)
+ pi_=pi_(:);
+ u=varargin{2}; % auxiliary variables that are eventually substituted out
+ u=u(:);
+ if length(pi_)~=length(u)
+ error('wrong size of substituted variables or functions')
+ end
+ if ~isequal(sort(u),sort(unique(u)))
+ error('substituted variables are not uniquely determined')
+ end
+end
+
+% check that auxiliary functions do not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(pi_)
+ if ~isequal(pi_,subs(pi_,logicalparams,sym(zeros(size(logicalparams)))))
+ error('auxiliary variables must not depend on logical parameters')
+ end
+end
+
+% check that Phi function does not depend on logical parameters
+if ~isempty(logicalparams) && ~isempty(Phi)
+ if ~isequal(Phi,subs(Phi,logicalparams,sym(zeros(size(logicalparams)))))
+ error('function Phi must not depend on logical parameters')
+ end
+end
+
+%%%% NEED TO ADD MORE CHECKS ON PHI - must be independent of yp and xp
+%%%% directly and through all substitutions - done below
+% and must be independent of
+%%%% stochastic auxiliary vars - i removed this restriction - to evaluate
+%%%% the function i substitute auxvars out, and to compute derivatives i do
+%%%% it after i have all stochastic auxiliary variables.
+subsPhi=subsf(Phi,u,pi_);
+% subsPhi=Phi;
+
+%%%%%%%%%% search for reserved names
+
+allnames=[v(:);u(:);symparams(:);logicalparams(:);shocks(:)];
+reserved_names={'coeffs','coeffsp','state','future_state','control','future_control','regime','future_regime','params','msparams','regimes','n_regimes',...
+ 'shock','center','nodes','n_nodes','weights','Basis','n_nodes','endogenous_vars','transition',...
+ 'R_fun','g_fun','Phi_fun','aux_fun','i','j','f_fun',...
+ 'R_funMS','g_funMS','Phi_funMS','aux_funMS','Amat'};
+
+reserved='';
+
+for i=1:length(reserved_names)
+ if nnz(logical(allnames==sym(reserved_names{i})))~=0
+ reserved=[reserved, ' \n ', reserved_names{i}];
+ end
+end
+
+if ~isempty(reserved)
+ error_message=['The following names are reserved and should be changed:', reserved];
+ error('ErrorTests:convertTest',error_message)
+end
+
+%%%%%%%%%%%
+
+% check that all symbolic variables/parameters are defined
+
+actualsymvars=symvar([f;pi_;eta(:);Phi(:)]);
+definedvars=[v(:);u(:);symparams(:);logicalparams(:);shocks(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+
+n_definedvars=length(definedvars);
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+% check that logical variables are defined
+actualsymvars=unique(logicalvars);
+definedvars=[v(:);u(:)];
+actualsymvars=sort(actualsymvars(:));
+definedvars=sort(definedvars);
+n_definedvars=length(definedvars);
+
+j=0;
+for i=1:length(actualsymvars)
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ while ~isequal(actualsymvars(i),definedvars(j))
+ j=j+1;
+ if j>n_definedvars
+ error([char(actualsymvars(i)) ' is not defined'])
+ end
+ end
+end
+
+% substitute x2p in f and create an auxiliary variable
+
+% x2p=Phi+eta(n_x1+1:end,:)*shocks;
+% n_u=length(u);
+% u=[u(:);sym(zeros(n_x2,1))];
+%
+% for i=1:n_x2
+% u(n_u+i)=sym([char(xp(n_x1+i)),'_aux']);
+% end
+%
+% f=subs(f,xp(n_x1+1:end),u(n_u+1:end));
+% warning('i am substituting x2p into auxiliary functions - need to check that it is correct')
+% pi_=subs(pi_,xp(n_x1+1:end),u(n_u+1:end));
+%
+%
+% pi_=[pi_(:);x2p(:)];
+
+% model.f=f;
+% model.auxvars=u;
+% model.auxfuns=pi_;
+
+new_eta=eta;
+new_eta(n_x1+1:end,:)=jacobian(subsPhi,shocks);
+
+%%%%%%%%%%%%%%
+symparams=[symparams(:);logicalparams(:)];
+model.n_params=numel(symparams);
+model.logical_params_loc=model.n_params+model.n_e-length(logicalparams)+(1:length(logicalparams));
+model.n_logicalparams=length(logicalparams);
+
+% add shocks to symparams
+symparams=[shocks(:);symparams(:)];
+
+n_u=length(u);
+model.n_u=n_u;
+tilf=f; % tilf(v,u) is a function of v and u
+% n=find_n(pi_,u); % number of substitutions needed to eliminate u
+[n,piu0]=find_n_new(pi_,u);
+model.piu0=piu0;
+
+% Identify variables that affect u
+% u_v=u; %u_v which is u as a function of v only u(v)
+uu=eye(n_u); % matrix to store which of u affect u
+uv=zeros(n_u,n_v);
+
+% piu0=double(logical(jacobian(pi_,u)~=0));
+piv0=double(logical(jacobian(pi_,v)~=0));
+piu=piu0;
+piv=piv0;
+
+
+for k=1:n
+ uu=uu+piu;
+ uv=uv+piv;
+ piv=piu*piv0;
+ piu=piu*piu0;
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+end
+model.uu=uu;
+
+pishocks0=double(sum(logical(jacobian(pi_,shocks)~=0),2));
+ushocks=uu*pishocks0;
+% for k=1:n
+% u_v=subs(u_v,u,pi_); % substitute pi_ into itself n times
+% uu=uu+logical(jacobian(u_v,u)~=0); % uu is a n_u-by-n_u matrix. the ij element is zero only if ui is independent of uj through all substitutions
+% uv=uv+logical(jacobian(u_v,v)~=0); % uv is a n_u-by-n_v matrix. the ij element is zero only if ui is independent of vj through all substitutions
+% end
+
+% Identify stochasic and predetermined functions and variables
+% warning('need to define all exog vars as stochastic')
+% if n_x2>0
+% stochexog=find(sum(1-logical(new_eta(n_x1+1:end,:)==0),2)); % stochastic exogenous variables
+% else
+% stochexog=[];
+% end
+% preexog=1:n_x2;
+% preexog(stochexog)=[]; % predetermined exogenous variables
+
+preexog=[];
+stochexog=reshape((1:n_x2),n_x2,1); % all exogenous vars are assumed stochastic.
+
+stochvars=[1:n_y,2*n_y+n_x1+stochexog']; % all stochastic variables
+
+tilfv=double(logical(jacobian(tilf,v)~=0));
+tilfu=double(logical(jacobian(tilf,u)~=0));
+tilfshocks=sum(double(logical(jacobian(tilf,shocks)~=0)),2);
+
+fv=double(logical(tilfv+tilfu*uv~=0)); % logical Jacobian of f w.r.t v
+fshocks=double(logical(tilfshocks+tilfu*ushocks~=0)); % logical Jacobian of f w.r.t shocks
+
+tilPhiv=double(logical(jacobian(Phi,v)~=0));
+tilPhiu=double(logical(jacobian(Phi,u)~=0));
+model.tilPhiu=tilPhiu;
+Phiv=double(logical(tilPhiv+tilPhiu*uv~=0)); % logical Jacobian of Phi w.r.t v
+
+if nnz(Phiv(:,1:n_y))>0
+ error('Function Phi cannot depend on future control variables')
+end
+
+if nnz(Phiv(:,2*n_y+n_x1+(1:n_x2)))>0
+ error('Function Phi cannot depend on future state variables')
+end
+
+
+tempind=sum( 1-logical(fv(:,stochvars)==0),2)+fshocks;
+
+
+stochfrows=find(tempind); % stochastic rows of f
+prefrows=1:n_f;
+
+
+prefrows(stochfrows)=[]; % predetermined rows of f
+
+% variables that affect the predetermined and stochastic rows of f
+
+prefvars=find(sum(1-logical(fv(prefrows,:)==0),1));
+stochfvars=find(sum(1-logical(fv(stochfrows,:)==0),1));
+
+Phivars=find(sum(1-logical(Phiv==0),1));
+
+currentFolder=pwd;
+if ~exist([pwd '\files'], 'dir')
+ mkdir('files');
+end
+
+cd 'files'
+
+% generate a function that computes eta
+gen_fun_vec(eta(:),[],symparams,['eta' uname],'row');
+
+
+% if order>=1
+% model.Phi_indc=getderivs_c(Phi,x,max(order,pert_order),symparams,'Phi');
+% end
+
+% Create an m file for u
+% newuv=jacobian(u_v,v); % calculate uv again
+newuv=uv;
+tempind=sum( 1-logical(newuv(:,stochvars)==0),2)+ushocks; % logical index of stochastic auxiliary variables
+% tempind(end-n_x2+1:end)=stochexog; % add the stochastic exogenous variables to the stochastic auxiliary variables
+stochurows=find(tempind); % stochastic rows of u
+model.stochurows=stochurows;
+preurows=1:n_u;
+preurows(stochurows)=[]; % predetermined rows of u
+model.preurows=preurows;
+preuvars=find(sum( logical(newuv(preurows,:)~=0),1)); % variables of predetermined rows of u
+stochuvars=find(sum( logical(newuv(stochurows,:)~=0),1)); % variables of stochastic rows of u
+
+% gen_fun_vec(u_v(preurows),symparams,v(preuvars),['preu' uname],'row');
+% gen_fun_vec(u_v(stochurows),symparams,v(stochuvars),['stochu' uname],'row');
+preurows_allsubs=logical(sum(uu(preurows,:),1));
+gen_fun_vec_subs(u(preurows),symparams,v(preuvars),pi_(preurows_allsubs),u(preurows_allsubs),['preu' uname],'row',piu0(preurows_allsubs,preurows_allsubs));
+
+stochurows_allsubs=logical(sum(uu(stochurows,:),1));
+gen_fun_vec_subs(u(stochurows),symparams,v(stochuvars),pi_(stochurows_allsubs),u(stochurows_allsubs),['stochu' uname],'row',piu0(stochurows_allsubs,stochurows_allsubs));
+
+model.preuvars=preuvars;
+model.stochuvars=stochuvars;
+
+
+% build z and find the Jacobian of z
+z=[v;u];
+
+% locate the logical variables in z
+
+logical_zvars=zeros(length(logicalvars),1);
+for i=1:length(logical_zvars)
+ logical_zvars(i)=find(logical(z==logicalvars(i)));
+end
+model.logical_zvars=logical_zvars;
+
+n_z=n_v+n_u;
+zz=[eye(n_v),zeros(n_v,n_u);uv,uu];
+for i=1:n_z
+ temp=zz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ zz(i,:)=temp;
+end
+zz=intarray(zz);
+model.maxzz=intarray(max(zz(:)));
+
+% build fv similar to zz
+fv=double(fv);
+for i=1:n_f
+ temp=fv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ fv(i,:)=temp;
+end
+model.fv=fv;
+
+% build Phiv similar to zz
+Phiv=double(Phiv);
+for i=1:n_x2
+ temp=Phiv(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ Phiv(i,:)=temp;
+end
+model.Phiv=Phiv;
+
+% tilfz=jacobian(tilf,z);
+tilfz=[tilfv,tilfu];
+
+% build tilfz
+% tilfz=double(logical(tilfz~=0)); % only direct effects
+for i=1:n_f
+ temp=tilfz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilfz(i,:)=temp;
+end
+model.tilfz=tilfz;
+model.maxtilfz=intarray(max(tilfz(:)));
+
+% build tilPhiz
+tilPhiz=[tilPhiv,tilPhiu];
+for i=1:n_x2
+ temp=tilPhiz(i,:);
+ temp(temp~=0)=1:nnz(temp);
+ tilPhiz(i,:)=temp;
+end
+% model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+
+% Create an m file for tilf
+pretilfzvars=find(sum(1-logical(tilfz(prefrows,:)==0),1));
+model.pretilfzvars=pretilfzvars; % variables in z that affect pretilf
+gen_fun_vec(tilf(prefrows),symparams,z(pretilfzvars),['pretilf' fname],'row');
+
+stochtilfzvars=find(sum(1-logical(tilfz(stochfrows,:)==0),1));
+model.stochtilfzvars=stochtilfzvars; % variables in z that affect stochtilf
+gen_fun_vec(tilf(stochfrows),symparams,z(stochtilfzvars),['stochtilf' fname],'row');
+
+% Differentiate PI and create m files
+
+PI=[v;pi_];
+prePI=PI;
+prePI(n_v+stochurows)=0; % stochastic rows of PI are set to zero. Note: the first n_v rows include stochastic variables but their derivatives w.r.t are ones or zeros.
+stochPI=PI;
+stochPI([1:n_v,n_v+preurows])=0; % nonstochastic rows are set to zero. See the note above.
+
+[model.prePI_ind_u]=getderivs_tensor(prePI,z,max(order+1,pert_order),symparams,['prePI' uname]);
+[model.stochPI_ind_u]=getderivs_tensor(stochPI,z,max(order+1,pert_order),symparams,['stochPI' uname]);
+
+prefuvars=find(sum(uu(logical(sum(logical(tilfu(prefrows,:)~=0),1)~=0),:),1));
+stochfuvars=find(sum(uu(logical(sum(logical(tilfu(stochfrows,:)~=0),1)~=0),:),1));
+
+Phiuvars=find(sum(uu(logical(sum(logical(tilPhiu~=0),1)~=0),:),1));
+
+model.prefuvars=prefuvars;
+model.stochfuvars=stochfuvars;
+model.Phiuvars=Phiuvars;
+
+prefzvars=[prefvars,n_v+prefuvars];
+stochfzvars=[stochfvars,n_v+stochfuvars];
+
+Phizvars=[Phivars,n_v+Phiuvars];
+
+model.n_prefzvars=length(prefzvars);
+model.n_stochfzvars=length(stochfzvars);
+model.n_Phizvars=length(Phizvars);
+
+[model.stochtilf_ind_u,model.stoch_n]=gen_chainderivs_tensor(tilf(stochfrows),v(stochfvars),u(stochfuvars),pi_(stochfuvars),max(order+1,pert_order),symparams,['stochtilf' fname]);
+[model.pretilf_ind_u,model.pre_n]=gen_chainderivs_tensor(tilf(prefrows),v(prefvars),u(prefuvars),pi_(prefuvars),max(order+1,pert_order),symparams,['pretilf' fname]);
+
+[model.Phi_ind_u,model.Phi_n]=gen_chainderivs_tensor(Phi,v(Phivars),u(Phiuvars),pi_(Phiuvars),max(order+1,pert_order),symparams,['Phi' fname]);
+
+% Create an m file for Phi and its derivatives w.r.t x
+gen_fun_vec(subsPhi,symparams,z(Phizvars),['Phi' uname],'row');
+
+gen_fun_vec(new_eta,symparams,z(Phizvars),['new_eta' uname],'row');
+
+
+% Store variables in struct model
+model.prefrows=prefrows;
+model.stochfrows=stochfrows;
+model.prefvars=prefvars;
+model.stochfvars=stochfvars;
+model.stochexog=stochexog;
+model.preexog=preexog;
+model.n_stochexog=length(stochexog);
+model.n_preexog=length(preexog);
+model.stochfzvars=stochfzvars;
+model.prefzvars=prefzvars;
+model.Phizvars=Phizvars;
+model.Phivars=Phivars;
+
+model.n_theta=n_theta;
+model.n_b=n_b;
+
+model.n_f=n_f;
+model.n_x=n_x;
+model.n_y=n_y;
+model.n_x1=n_x1;
+model.n_x2=n_x2;
+
+model.n_v=n_v;
+model.n_z=n_z;
+model.n_u=n_u;
+
+model.n_ind=1;
+
+model.U=cell(4,1);
+model.W=cell(4,1);
+maxorder=4;
+for i=2:maxorder+1
+ [model.U{i},model.W{i}]=create_UW(n_x,i);
+end
+
+model.stochzz=zz(model.stochfzvars,model.stochfzvars);
+model.prezz=zz(model.prefzvars,model.prefzvars);
+
+model.Phizz=zz(model.Phizvars,model.Phizvars);
+
+model.stochtilfz=tilfz(model.stochfrows,model.stochfzvars);
+model.pretilfz=tilfz(model.prefrows,model.prefzvars);
+
+model.tilPhiz=tilPhiz(:,Phizvars);
+model.maxtilPhiz=intarray(max(tilPhiz(:)));
+
+% calculate some big matrices now
+
+if order>=3
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+
+ save('tempfile')
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+
+ save('tempfile')
+ n_Phivars=length(Phivars);
+ clearvars -except n_Phivars
+
+ if n_Phivars>0
+ [ tempM ] = chainsM( n_Phivars,4 );
+ else
+ tempM=cell(4,1);
+ end
+ load('tempfile')
+ model.Phivars_chain4c_M2=tempM{2};
+ model.Phivars_chain4c_M3=tempM{3};
+ model.Phivars_chain4c_M4=tempM{4};
+ clear tempM
+
+
+ delete('tempfile.mat')
+end
+
+if order>=4
+ save('tempfile')
+ n_prefvars=length(prefvars);
+ clearvars -except n_prefvars
+
+ if n_prefvars>0
+ [ tempM ] = chainsM( n_prefvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.prefvars_chain5c_M1=tempM{1};
+ model.prefvars_chain5c_M2=tempM{2};
+ model.prefvars_chain5c_M3=tempM{3};
+ model.prefvars_chain5c_M4=tempM{4};
+ model.prefvars_chain5c_M5=tempM{5};
+ model.prefvars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+ save('tempfile')
+ n_stochfvars=length(stochfvars);
+ clearvars -except n_stochfvars
+
+ if n_stochfvars>0
+ [ tempM ] = chainsM( n_stochfvars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.stochfvars_chain5c_M1=tempM{1};
+ model.stochfvars_chain5c_M2=tempM{2};
+ model.stochfvars_chain5c_M3=tempM{3};
+ model.stochfvars_chain5c_M4=tempM{4};
+ model.stochfvars_chain5c_M5=tempM{5};
+ model.stochfvars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+ save('tempfile')
+ n_Phivars=length(Phivars);
+ clearvars -except n_Phivars
+
+ if n_Phivars>0
+ [ tempM ] = chainsM( n_Phivars,5 );
+ else
+ tempM=cell(6,1);
+ end
+ load('tempfile')
+ model.Phivars_chain5c_M1=tempM{1};
+ model.Phivars_chain5c_M2=tempM{2};
+ model.Phivars_chain5c_M3=tempM{3};
+ model.Phivars_chain5c_M4=tempM{4};
+ model.Phivars_chain5c_M5=tempM{5};
+ model.Phivars_chain5c_M6=tempM{6};
+
+ clear tempM
+
+
+ delete('tempfile.mat')
+end
+
+model.count_pre_n=model.pre_n-1;
+if model.count_pre_n<0
+ model.count_pre_n=0;
+end
+
+model.count_stoch_n=model.stoch_n-1;
+if model.count_stoch_n<0
+ model.count_stoch_n=0;
+end
+
+totindi=5+8;
+totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+totindi=totindi+3;
+totindi=totindi+4;
+totindi=totindi+2;
+totindi=totindi+2;
+totindi=totindi+1;
+totindi=totindi+9;
+totindi=totindi+8;
+totindi=totindi+8+model.count_stoch_n*(1+3+4+6)+1+4+6+9;
+totindi=totindi+2;
+totindi=totindi+9;
+totindi=totindi+7;
+
+model.totindi=totindi;
+
+rehash;
+
+model.symparams=symparams;
+
+cd(currentFolder)
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/shift_center.m b/105/replication_package/solution_methods/taylor_projection/shift_center.m
new file mode 100644
index 0000000000000000000000000000000000000000..91a027ef00bba2a737180f01dcaf0b5db90e226f
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/shift_center.m
@@ -0,0 +1,76 @@
+function [ coeffs ] = shift_center( coeffs,c0,newc0,order,model )
+%The function shifts the center of the approximating power series from c0
+%to newc0.
+% coeffs: vector of Polynomial coefficients
+% c0: old center of power series
+% newc0: new center of power series
+% n_f: number of power series
+% n_b: number of terms in power series (excluding symmetric monomials)
+% n_x: number of variables
+% order: Polynomial order of power series
+% U: cell variable with compression matrices
+% W: cell variable with uncompression matrices
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+
+n_b=model.n_b;
+n_x=model.n_x;
+U=model.U;
+W=model.W;
+
+coeffs=reshape(coeffs,[],n_b);
+GH0=coeffs(:,1);
+if order==1
+ GH1=coeffs(:,2:1+n_x);
+ [ GH0,GH1 ] = shiftpoly( newc0,c0,[],GH0,GH1 );
+ coeffs=[GH0,GH1];
+ coeffs=coeffs(:);
+elseif order==2
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ [ GH0,GH1,GH2 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2 );
+ coeffs=[GH0,GH1,GH2*U{2}];
+ coeffs=coeffs(:);
+elseif order==3
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ GH3=coeffs(:,2+n_x+model.unique2:1+n_x+model.unique2+model.unique3)*W{3};
+ [ GH0,GH1,GH2,GH3 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3 );
+ coeffs=[GH0,GH1,GH2*U{2},GH3*U{3}];
+ coeffs=coeffs(:);
+elseif order==4
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,2+n_x:1+n_x+model.unique2)*W{2};
+ GH3=coeffs(:,2+n_x+model.unique2:1+n_x+model.unique2+model.unique3)*W{3};
+ GH4=coeffs(:,2+n_x+model.unique2+model.unique3:1+n_x+model.unique2+model.unique3+model.unique4)*W{4};
+ [ GH0,GH1,GH2,GH3,GH4 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3,GH4 );
+ coeffs=[GH0,GH1,GH2*U{2},GH3*U{3},GH4*U{4}];
+ coeffs=coeffs(:);
+elseif order==5
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,nchoosek(n_x+1,1)+(1:nchoosek(n_x+1,2)))*W{2};
+ GH3=coeffs(:,nchoosek(n_x+2,2)+(1:nchoosek(n_x+2,3)))*W{3};
+ GH4=coeffs(:,nchoosek(n_x+3,3)+(1:nchoosek(n_x+3,4)))*W{4};
+ GH5=coeffs(:,nchoosek(n_x+4,4)+(1:nchoosek(n_x+4,5)))*W{5};
+ [ GH0,GH1,GH2,GH3,GH4,GH5 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3,GH4,GH5 );
+ coeffs=[GH0,GH1,GH2*U{2},GH3*U{3},GH4*U{4},GH5*U{5}];
+ coeffs=coeffs(:);
+elseif order==6
+ GH1=coeffs(:,2:1+n_x);
+ GH2=coeffs(:,nchoosek(n_x+1,1)+(1:nchoosek(n_x+1,2)))*W{2};
+ GH3=coeffs(:,nchoosek(n_x+2,2)+(1:nchoosek(n_x+2,3)))*W{3};
+ GH4=coeffs(:,nchoosek(n_x+3,3)+(1:nchoosek(n_x+3,4)))*W{4};
+ GH5=coeffs(:,nchoosek(n_x+4,4)+(1:nchoosek(n_x+4,5)))*W{5};
+ GH6=coeffs(:,nchoosek(n_x+5,5)+(1:nchoosek(n_x+5,6)))*W{6};
+ [ GH0,GH1,GH2,GH3,GH4,GH5,GH6 ] = shiftpoly( newc0,c0,[],GH0,GH1,GH2,GH3,GH4,GH5,GH6 );
+ coeffs=[GH0,GH1,GH2*U{2},GH3*U{3},GH4*U{4},GH5*U{5},GH6*U{6}];
+ coeffs=coeffs(:);
+elseif order>=7
+ error('order must not be larger than 6')
+end
+
+coeffs=full(coeffs);
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/shiftpoly.m b/105/replication_package/solution_methods/taylor_projection/shiftpoly.m
new file mode 100644
index 0000000000000000000000000000000000000000..0dbf216e2bd87408a20675871b26add3815ce5ea
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/shiftpoly.m
@@ -0,0 +1,71 @@
+function [ G0,varargout ] = shiftpoly( x,c,index,varargin )
+%[newG0,newG1,...]=shiftpoly(x,c,index,G0,G1,...) shifts the center of a given
+%polynomial from c to x. The coefficient matrices of the given Polynomial
+%are G0,G1,G2,..... Note that G2,G3,... must have symmetric columns.
+%Namely, these are the coefficients of the Taylor series about c.
+%The output is the coefficients of the new Polynomial.
+%If index is empty, the variables of the output Polynomial are the same as
+%the original Polynomial. To get a Polynomial in a subset of the original
+%variables (treating all other vars as constant), specify the index of the
+%new variables in index.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% changed on November 29, 2016 - x and c are vectorized.
+
+x=x(:);
+c=c(:);
+
+N=length(varargin)-1;
+n_x=length(x);
+if isempty(index)
+ index=1:n_x;
+end
+
+coeffs=cell2mat(varargin);
+
+% create cell
+cellX=cell(1,N+1);
+m=0;
+for i=1:N+1
+ newm=m+n_x^(i-1);
+ cellX{i}=sparse(size(coeffs,2),n_x^(i-1));
+ cellX{i}(m+1:newm,:)=factorial(i-1)*speye(n_x^(i-1));
+ m=newm;
+end
+
+x_c=x-c;
+lastkron=1;
+m=1;
+for i=1:N % i is the Kronecker power of x-c. All N powers need to be calculated
+ newm=m+n_x^i;
+ lastkron=kron(lastkron,x_c);
+ mj=m;
+ for j=1:N+1-i % j-1 is the derivative order. The i Kronecker power appears in derivatives up to order N+1-i
+
+ newmj=mj+n_x^(i+j-1);
+ if j==1
+ A=1;
+ else
+ A=prod(i+1:i+j-1);
+ end
+ cellX{j}(mj+1:newmj,:)=A*kron(lastkron,speye(n_x^(j-1)));
+ mj=newmj;
+ end
+ m=newm;
+end
+
+xtilx=speye(n_x);
+xtilx=xtilx(:,index);
+
+G0=coeffs*cellX{1};
+
+varargout=cell(1,N);
+lastkron=1;
+for i=1:N
+ lastkron=kron(lastkron,xtilx);
+ varargout{i}=coeffs*cellX{i+1}*lastkron/factorial(i);
+
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/subsf.m b/105/replication_package/solution_methods/taylor_projection/subsf.m
new file mode 100644
index 0000000000000000000000000000000000000000..801aa6d36a7f14a4ef328bd23150bf642cb85801
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/subsf.m
@@ -0,0 +1,13 @@
+function [ newf ] = subsf( f,auxvars,auxfuns )
+%Substitute out auxiliary variables.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+f_temp=[]; newf=f;
+while ~isequal(f_temp,newf)
+ f_temp=newf;
+ newf=subs(newf,auxvars,auxfuns);
+end
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tp.m b/105/replication_package/solution_methods/taylor_projection/tp.m
new file mode 100644
index 0000000000000000000000000000000000000000..538299eaa8e9f85bb7252e298a2029c0c722febb
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tp.m
@@ -0,0 +1,1139 @@
+function [T,J,model]=tp(coeffs,x0,model,params,eta,c0,nep,P,varargin)
+
+% This function computes the nonlinear system of Taylor projection and the
+% Jacobian.
+% Input args: coeffs=Polynomial coefficients (denoted Theta in the paper).
+% The coefficients should be provided as a vector of unique Taylor
+% coefficients.
+% x0=point at which the system is evaluated
+% model=variable generated by prepare_tp
+% params=parameters of the model
+% eta=the matrix eta
+% c0=center of the power series.
+% nep=a matrix of the realizations of the shocks. each row is a different shock.
+% P=a vector of probabilities (weights) of each realization.
+% varargin=option to add precomputed variables that are independent of coeffs.
+% Output args: T=a vector of the model conditions and the derivatives.
+% J=Jacobian of T.
+% model=the variable model updated.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=model.order(1);
+
+% make sure all inputs are full
+coeffs=full(coeffs);
+x0=full(x0);
+params=full(params);
+eta=full(eta);
+c0=full(c0);
+nep=full(nep);
+P=full(P);
+
+c0_old=c0;
+c0_new=x0;
+
+if c0~=x0 % shift the center of the power series to x0
+ warning('shifting center, Jacobian may be incorrect')
+ [ coeffs ] = shift_center( coeffs,c0_old,c0_new,order,model );
+ coeffs=full(coeffs);
+ c0=c0_new;
+end
+
+if isempty(varargin)
+ [ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta,model ] = precompute(x0,c0,model,order );
+else
+ g_theta=varargin{1};
+ h_theta=varargin{2};
+ gx_theta=varargin{3};
+ hx_theta=varargin{4};
+ gxxc_theta=varargin{5};
+ hxxc_theta=varargin{6};
+ gxxxc_theta=varargin{7};
+ hxxxc_theta=varargin{8};
+end
+
+indi=5; %count indi from 5, due to precompute.
+
+if ~isfield(model,'jacobian')
+ model.jacobian='exact';
+end
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+if ~isfield(model,'maxload')
+ maxload=intarray(length(P));
+else
+ maxload=intarray(model.maxload);
+end
+
+params=params(:);
+P=P(:);
+
+n_f=model.n_f; % no. of model conditions
+n_x=model.n_x; % no. of state variables
+n_y=model.n_y; % no. of control variables
+n_x2=model.n_x2; % no. of exogenous state variables
+n_x1=model.n_x1; % no. of endogenous state variabels
+n_v=model.n_v; % total no. of variables v=(yp,y,xp,x)
+n_theta=model.n_theta; % no. of Polynomial coefficients
+n_b=model.n_b; % no. of terms in the basis function
+n_nodes=size(nep,2); % no. nodes in the discrete shocks
+n_z=model.n_z; % no. of auxiliary variables
+
+coeffs=reshape(coeffs,n_f,n_b);
+g_coeffs=coeffs(1:n_y,:);
+
+%create stochy: index of future control variables that affect stochastic equations
+tempv=zeros(n_v,1);
+tempv(model.stochfvars)=model.stochfvars;
+tempv(n_y+1:end)=0;
+stochy=nonzeros(tempv);
+n_stochy=length(stochy);
+stochg_coeffs=coeffs(stochy,:);
+
+% U=model.U;
+
+unique2=[]; unique3=[];
+
+prefvars=model.prefvars; % index of variables that affect nonstochastic equations.
+stochfvars=model.stochfvars;% index of variables that affect stochastic equations.
+n_prefvars=length(prefvars);
+n_stochfvars=length(stochfvars);
+
+% lower block of v_theta, vx_theta and so on
+
+v_theta_lower_terms=vconcat(vconcat(g_theta,h_theta),sptensor(n_x,n_theta));
+
+if order>=1
+ vx_theta_lower_terms=vconcat(vconcat(gx_theta,hx_theta),sptensor(n_x,[n_x,n_theta]));
+end
+if order>=2
+ unique2=model.unique2;
+ vxxc_theta_lower_terms=vconcat(vconcat(gxxc_theta,hxxc_theta),sptensor(n_x,[unique2,n_theta]));
+end
+if order>=3
+ unique3=model.unique3;
+ vxxxc_theta_lower_terms=vconcat(vconcat(gxxxc_theta,hxxxc_theta),sptensor(n_x,[unique3,n_theta]));
+end
+
+% current state
+nx=x0;
+
+% evaluate policy functions
+g=coeffs(1:n_y,1);% only constant term is nonzero
+h1=coeffs(n_y+1:end,1);
+h=zeros(n_x,1);
+
+% derivatives of policy functions at x0 (assuming c0=x0)
+if order>=1
+ gx=coeffs(1:n_y,2:1+n_x);
+ h1x=coeffs(n_y+1:end,2:1+n_x);
+end
+
+if order>=2
+ gxxc=coeffs(1:n_y,2+n_x:1+n_x+unique2)*2;
+ h1xxc=coeffs(n_y+1:end,2+n_x:1+n_x+unique2)*2;
+end
+if order>=3
+ gxxxc=coeffs(1:n_y,2+n_x+unique2:1+n_x+unique2+unique3)*6;
+ h1xxxc=coeffs(n_y+1:end,2+n_x+unique2:1+n_x+unique2+unique3)*6;
+end
+
+% control vars
+ny=g;
+
+% STEP 1: COMPUTE NONSTOCHASTIC EQUATIONS AND DERIVATIVES, AND THEIR JACOBIAN
+
+% build h(x)
+h(1:n_x1,1)=h1; % predetermined endogenous state vars
+h(n_x1+1:end,1)=Phi_fun(nx,params); % expected value of exogenous state vars. shocks are added later
+
+% expected value of next period state variables.
+nxp=h;
+
+% derivatives of h at x0
+if order>=1
+ hx=vconcat(sptensor(h1x),Phi_d_c1(nx(:)',params,model.Phi_indc));
+end
+if order>=2
+ hxxc=vconcat(sptensor(h1xxc),Phi_d_c2(nx(:)',params,model.Phi_indc));
+end
+if order>=3
+ hxxxc=vconcat(sptensor(h1xxxc),Phi_d_c3(nx(:)',params,model.Phi_indc));
+end
+
+% evaluate residuals R0
+nv=[zeros(n_y,1);ny;nxp;nx]; % model variables, yp are zero for now, and nxp is an expected value. stochastic components will be added later.
+
+n_u=model.n_u;
+nu=zeros(n_u,1);
+npreu=preu_fun(nv(model.preuvars),params); % all predetermined u
+nu(model.preurows)=npreu;
+nz=[nv;nu]; % auxiliary variables
+pref=pretilf_fun(nz(model.pretilfzvars),params); % since i already have z, i use pretilf to evaluate f.
+
+
+% compute derivatives of prePI and pretilf w.r.t z (prePI=nonstochastic rows of PI, pretilf=nonstochastic rows of f)
+
+prePIz_full=prePI_d1(nz',params,model.prePI_ind_u);
+pretilfz=pretilf_tilf_d1([nv(prefvars);nu(model.prefuvars)]',params,model.pretilf_ind_u);
+if order>=1
+ prePIzz_full=prePI_d2(nz',params,model.prePI_ind_u);
+ pretilfzz=pretilf_tilf_d2([nv(prefvars);nu(model.prefuvars)]',params,model.pretilf_ind_u);
+end
+if order>=2
+ prePIzzz_full=prePI_d3(nz',params,model.prePI_ind_u);
+ pretilfzzz=pretilf_tilf_d3([nv(prefvars);nu(model.prefuvars)]',params,model.pretilf_ind_u);
+end
+if order>=3
+ prePIzzzz_full=prePI_d4(nz',params,model.prePI_ind_u);
+ pretilfzzzz=pretilf_tilf_d4([nv(prefvars);nu(model.prefuvars)]',params,model.pretilf_ind_u);
+end
+
+% extract derivatives of prePI w.r.t v from prePIz, prePIzz, ...
+if order>=0
+ [prePIz,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefvars,0,model.ind{indi});
+ indi=indi+1;
+end
+if order>=1
+ [prePIzz,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+end
+if order>=2
+ [prePIzzz,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain3c_M2')
+ [ tempM ] = chainsM( n_prefvars,3 );
+ model.prefvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if order>=3
+ [prePIzzzz,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain4c_M2')
+ [ tempM ] = chainsM( n_prefvars,4 );
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+
+
+% Use high order chain rules to compute derivatives of prePI w.r.t v
+totindi=5+8;
+if order==0
+ indi=totindi;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+elseif order==1
+ indi=totindi+(model.pre_n-1)*(1)+1;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+elseif order==2
+ indi=totindi+(model.pre_n-1)*(1+3)+1+4;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+elseif order==3
+ indi=totindi+(model.pre_n-1)*(1+3+4)+1+4+6;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=chain4c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvvc,model.ind{indi}]=chain4c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvv,model.ind{indi} ] = uncompressderivs( prefvvvvc,4,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+end
+totindi=totindi+(model.pre_n-1)*(1+3+4+6)+1+4+6+9;
+indi=totindi;
+
+
+preR0=pref;
+
+% compute R1 (first order derivatives of R w.r.t x)
+if order>=1
+ vx=vconcat(sptensor(n_y,n_x),sptensor(gx));
+ vx=vconcat(vx,hx);
+ vx=vconcat(vx,spteye(n_x));
+
+ prevx=takerows(vx,prefvars);
+ if isempty(pref)
+ preR1=zeros(0,n_x);
+ else
+ [preR1,model.ind{indi}]=chain1_tensor(prefv,prevx,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ preR1=sptensor2spmat(preR1);
+ end
+end
+
+% compute R2 (second order derivatives of R w.r.t x)
+if order>=2
+ vxxc=vconcat(sptensor(n_y,unique2),sptensor(gxxc));
+ vxxc=vconcat(vxxc,hxxc);
+ vxxc=vconcat(vxxc,sptensor(n_x,unique2));
+ prevxxc=takerows(vxxc,prefvars);
+ prevx=colsort(prevx);
+ if isempty(pref)
+ preR2=zeros(0,unique2);
+ else
+ [preR2,model.ind{indi}]=chain2c_tensor(prefv,prefvv,prevx,prevxxc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ preR2=sptensor2spmat(preR2);
+ end
+end
+
+% compute R3 (third order derivatives of R w.r.t x)
+if order>=3
+ vxxxc=vconcat(sptensor(n_y,unique3),sptensor(gxxxc));
+ vxxxc=vconcat(vxxxc,hxxxc);
+ vxxxc=vconcat(vxxxc,sptensor(n_x,unique3));
+ prevxxxc=takerows(vxxxc,prefvars);
+
+ if ~isfield(model,'x_chain3c_M2')
+ [~,W2x]=create_UW(n_x,2);
+ [U3x,~]=create_UW(n_x,3);
+ OMEGAx=create_OMEGA(n_x,3);
+ model.x_chain3c_M2=spmat2sptensor(kron(speye(n_x),W2x)*OMEGAx.OMEGA1*U3x);
+ clear W2x U3x
+ end
+
+ if isempty(pref)
+ preR3=zeros(0,unique3);
+ else
+ [preR3,model.ind{indi}]=chain3c_tensor(prefv,prefvv,prefvvv,prevx,prevxxc,prevxxxc,model.x_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ preR3=sptensor2spmat(preR3);
+ end
+
+end
+totindi=totindi+3;
+indi=totindi;
+% Jacobian of the nonstochastic equations and derivatives
+
+v_theta=vconcat(sptensor(n_y,n_theta),v_theta_lower_terms);
+prev_theta=takerows(v_theta,prefvars);
+
+[ preJ0,model.ind{indi} ] = chain0_theta_tensor( prefv,prev_theta,model.ind{indi},n_ind,maxload,'vec' );
+indi=indi+1;
+% preJ0=sptensor2spmat(preJ0);
+
+if order>=1
+ vx_theta=vconcat(sptensor(n_y,[n_x,n_theta]),vx_theta_lower_terms);
+ prevx_theta=takerows(vx_theta,prefvars);
+ prevx_theta=unfold(prevx_theta);
+ if isempty(pref)
+% preJ1=zeros(0,n_x*n_theta);
+ preJ1=sptensor(zeros(0,1),zeros(0,2),zeros(1,0),0,[n_x,n_theta]);
+ else
+ [ preJ1,model.ind{indi} ] = chain1_theta_tensor( prefv,prefvv,...
+ prevx,prev_theta,prevx_theta,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+% preJ1=sptensor2spmat(preJ1);
+ end
+end
+if order>=2
+ vxxc_theta=vconcat(sptensor(n_y,[unique2,n_theta]),vxxc_theta_lower_terms);
+ prevxxc_theta=takerows(vxxc_theta,prefvars);
+ prevxxc_theta=unfold(prevxxc_theta);
+
+ if ~isfield(model,'chain2c_theta_M2')
+ GAMMA=create_GAMMA(n_x,n_theta,2);
+ U2=create_UW(n_x,2);
+ model.chain2c_theta_M2=spmat2sptensor(GAMMA.GAMMA1*U2);
+ clear GAMMA U2
+ end
+
+ if isempty(pref)
+% preJ2=zeros(0,unique2*n_theta);
+ preJ2=sptensor(zeros(0,1),zeros(0,2),zeros(1,0),0,[unique2,n_theta]);
+ else
+ [ preJ2,model.ind{indi} ] = chain2c_theta_tensor( prefv,prefvv,prefvvv,...
+ prevx,prevxxc,...
+ prev_theta,prevx_theta,prevxxc_theta,...
+ model.chain2c_theta_M2,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+% preJ2=sptensor2spmat(preJ2);
+ end
+end
+if order>=3
+ vxxxc_theta=vconcat(sptensor(n_y,[unique3,n_theta]),vxxxc_theta_lower_terms);
+ prevxxxc_theta=takerows(vxxxc_theta,prefvars);
+ prevxxxc_theta=unfold(prevxxxc_theta);
+
+ if ~isfield(model,'chain3c_theta_M2')
+ GAMMA=create_GAMMA(n_x,n_theta,3);
+ [~,W2]=create_UW(n_x,2);
+ U3=create_UW(n_x,3);
+ model.chain3c_theta_M2=spmat2sptensor(kron(W2,speye(n_x))*GAMMA.GAMMA2*U3);
+ model.chain3c_theta_M3=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA3*U3);
+ model.chain3c_theta_M4=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA4*U3);
+ tempind=1:unique2*n_x;
+ tempmat=speye(unique2*n_x);
+ model.chain3c_theta_M5=spmat2sptensor(tempmat(:,permute(reshape(tempind,n_x,unique2),[2,1]))*kron(speye(n_x),W2)*GAMMA.GAMMA5*U3);
+ clear GAMMA W2 U3 GAMMA
+
+ end
+
+ if isempty(pref)
+% preJ3=zeros(0,unique3*n_theta);
+ preJ3=sptensor(zeros(0,1),zeros(0,2),zeros(1,0),0,[unique3,n_theta]);
+ else
+ [ preJ3,model.ind{indi} ] = chain3c_theta_tensor( prefv,prefvv,prefvvv,prefvvvv,...
+ prevx,prevxxc,prevxxxc,...
+ prev_theta,prevx_theta,prevxxc_theta,prevxxxc_theta,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+% preJ3=sptensor2spmat(preJ3);
+ end
+end
+totindi=totindi+4;
+indi=totindi;
+
+% STEP 2: COMPUTE STOCHASTIC EQUATIONS AND DERIVATIVES, AND THEIR JACOBIAN,
+% AND TAKE EXPECTED VALUE
+
+% prepare vectorized expressions for the stochastic part.
+
+nx_vec=repmat(nx,1,n_nodes); % n_nodes=the number of nodes of the discrete shocks.
+
+% next period state
+nxp_vec=repmat(h,1,n_nodes)+eta*nep;
+nxp_c0_vec=nxp_vec-repmat(c0,1,n_nodes);
+
+nxp_c0=sptensor(nxp_c0_vec(:,1)); % convert to 1D tensor
+nxp_c0.vals=nxp_c0_vec'; % assign the correct values in vals.
+
+if ~isfield(model,'M2')
+ model.M2=[];
+ model.M3=[];
+ model.M3x=[];
+ model.TW2=[];
+ model.TW3=[];
+ if order>=2
+ model.M2=fold(spmat2sptensor(model.W{2}*model.W{2}'*model.U{2}'),n_x,n_x);
+ model.TW2=fold(spmat2sptensor(model.W{2}),n_x,n_x);
+ model.TW2U2=spmat2sptensor(model.W{2}*model.U{2});
+ end
+ if order>=3
+ model.M3=fold(spmat2sptensor(model.W{3}*model.W{3}'*model.U{3}'),n_x,n_x,n_x);
+ model.M3x=fold(spmat2sptensor(3*model.W{3}*kron(model.W{2}'*model.U{2}',speye(n_x))),n_x,n_x,n_x);
+ model.TW3=fold(spmat2sptensor(model.W{3}),n_x,n_x,n_x);
+ model.TW3U3=spmat2sptensor(model.W{3}*model.U{3});
+ end
+end
+
+if ~isfield(model,'M3')
+ model.M3=[];
+ model.M3x=[];
+ model.TW3=[];
+end
+
+[Xp_vecT,Xpx_vecT,Xpxx_vecT,Xpxxx_vecT,Xpxxxx_vecT,model.ind{indi}]=create_X_tensor(order,nxp_c0,...
+ model.M2,model.M3,model.M3x,model.TW2,model.TW3,unique2,unique3,model.ind{indi},n_ind,maxload,'vec');
+indi=indi+1;
+
+if strcmp(model.jacobian,'approximate')
+ nx_c0=sptensor(n_x,1);
+ nx_c0.vals=repmat(nx_c0.vals,n_nodes,1);
+ [X_vecT,Xx_vecT,Xxx_vecT,Xxxx_vecT,Xxxxx_vecT,model.ind{indi}]=create_X_tensor(order,nx_c0,...
+ model.M2,model.M3,model.M3x,model.TW2,model.TW3,unique2,unique3,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+end
+totindi=totindi+2;
+indi=totindi;
+
+
+gp_vec=g_coeffs*Xp_vecT.vals';
+
+stochg_coeffsT=sptensor(stochg_coeffs);
+[stochgpx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpx_vecT,model.ind{indi},n_ind,maxload,'vec');
+indi=indi+1;
+
+% control vars in t+1
+nyp_vec=gp_vec;
+
+% evaluate residuals R0
+nv_vec=[nyp_vec;repmat(ny,1,n_nodes);nxp_vec;nx_vec];
+nstochv_vec=nv_vec(stochfvars,:); % stochastic vars.
+
+nstochu_vec=stochu_fun(nv_vec(model.stochuvars,:),params); % all stochastic u vars
+nu_vec=repmat(nu,1,n_nodes);
+nu_vec(model.stochurows,:)=nstochu_vec;
+nz_vec=[nv_vec;nu_vec];
+stochf_vec=stochtilf_fun(nz_vec(model.stochtilfzvars,:),params);
+
+% compute derivatives of stochPI and stochtilf w.r.t z
+
+stochPIz_vec=stochPI_d1(nz_vec',params,model.stochPI_ind_u);
+prePIz_full.vals=repmat(prePIz_full.vals,n_nodes,1);
+
+i1=tfind(prePIz_full);
+i2=tfind(stochPIz_vec);
+PIz_vec=sptensor([i1;i2],[prePIz_full.cols;stochPIz_vec.cols],[prePIz_full.vals,stochPIz_vec.vals],n_z,[n_z]);
+stochtilfz_vec=stochtilf_tilf_d1([nv_vec(stochfvars,:);nu_vec(model.stochfuvars,:)]',params,model.stochtilf_ind_u);
+
+
+if order>=1
+ stochPIzz_vec=stochPI_d2(nz_vec',params,model.stochPI_ind_u);
+ prePIzz_full.vals=repmat(prePIzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzz_full);
+ i2=tfind(stochPIzz_vec);
+ PIzz_vec=sptensor([i1;i2],[prePIzz_full.cols;stochPIzz_vec.cols],[prePIzz_full.vals,stochPIzz_vec.vals],n_z,[n_z,n_z]);
+ stochtilfzz_vec=stochtilf_tilf_d2([nv_vec(stochfvars,:);nu_vec(model.stochfuvars,:)]',params,model.stochtilf_ind_u);
+end
+if order>=2
+ stochPIzzz_vec=stochPI_d3(nz_vec',params,model.stochPI_ind_u);
+ prePIzzz_full.vals=repmat(prePIzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzz_full);
+ i2=tfind(stochPIzzz_vec);
+ PIzzz_vec=sptensor([i1;i2],[prePIzzz_full.cols;stochPIzzz_vec.cols],[prePIzzz_full.vals,stochPIzzz_vec.vals],n_z,[n_z,n_z,n_z]);
+ stochtilfzzz_vec=stochtilf_tilf_d3([nv_vec(stochfvars,:);nu_vec(model.stochfuvars,:)]',params,model.stochtilf_ind_u);
+end
+if order>=3
+ stochPIzzzz_vec=stochPI_d4(nz_vec',params,model.stochPI_ind_u);
+ prePIzzzz_full.vals=repmat(prePIzzzz_full.vals,n_nodes,1);
+
+ i1=tfind(prePIzzzz_full);
+ i2=tfind(stochPIzzzz_vec);
+ PIzzzz_vec=sptensor([i1;i2],[prePIzzzz_full.cols;stochPIzzzz_vec.cols],[prePIzzzz_full.vals,stochPIzzzz_vec.vals],n_z,[n_z,n_z,n_z,n_z]);
+ stochtilfzzzz_vec=stochtilf_tilf_d4([nv_vec(stochfvars,:);nu_vec(model.stochfuvars,:)]',params,model.stochtilf_ind_u);
+end
+
+totindi=totindi+1;
+indi=totindi;
+
+EstochR0=stochf_vec*P; %expected value of stochR0
+h_thetaT=h_theta;
+[chain0_theta_stochgpT,model.ind{indi}]=contraction1(stochgpx_vecT,h_thetaT,model.ind{indi},n_ind,maxload,'vec');
+indi=indi+1;
+
+totindi=totindi+1;
+indi=totindi;
+
+% compute derivatives of g w.r.t x at next period state (nxp)
+if order>=1
+ if order>1
+ [stochgpxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxx_vecT=sptensor(n_stochy,n_x^2,n_nodes);
+ end
+ hxT=hx;
+ [chain1_stochgpT,model.ind{indi}]=contraction1(stochgpx_vecT,hxT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hx_thetaT=unfold(hx_theta);
+
+ stochgpxx_vecT=fold(stochgpxx_vecT,n_x,n_x);
+ [chain1_theta_stochgpT,model.ind{indi}]=chain1_theta_tensor(stochgpx_vecT,stochgpxx_vecT,hxT,h_thetaT,hx_thetaT,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+end
+if order>=2
+ if order>2
+ [stochgpxxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxxx_vecT=sptensor(n_stochy,n_x^3,n_nodes);
+ end
+ hxxcT=hxxc;
+ hxT=colsort(hxT);
+ [chain2_stochgpT,model.ind{indi}]=chain2c_tensor(stochgpx_vecT,stochgpxx_vecT,hxT,hxxcT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hxxc_thetaT=unfold(hxxc_theta);
+ stochgpxxx_vecT=fold(stochgpxxx_vecT,n_x,n_x,n_x);
+
+ [chain2c_theta_stochgpT,model.ind{indi}]=chain2c_theta_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,hxT,hxxcT,h_thetaT,hx_thetaT,hxxc_thetaT,...
+ model.chain2c_theta_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+end
+if order>=3
+ if order>3
+ [stochgpxxxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxxxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxxxx_vecT=sptensor(n_stochy,n_x^4,n_nodes);
+ end
+ hxxxcT=hxxxc;
+
+ [chain3_stochgpT,model.ind{indi}]=chain3c_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,...
+ hxT,hxxcT,hxxxcT,...
+ model.x_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hxxxc_thetaT=unfold(hxxxc_theta);
+ stochgpxxxx_vecT=fold(stochgpxxxx_vecT,n_x,n_x,n_x,n_x);
+
+ [chain3c_theta_stochgpT,model.ind{indi}]=chain3c_theta_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,stochgpxxxx_vecT,...
+ hxT,hxxcT,hxxxcT,h_thetaT,hx_thetaT,hxxc_thetaT,hxxxc_thetaT,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+end
+totindi=totindi+9;
+indi=totindi;
+
+
+% extract PIv,Pivv,... from PIz,PIzz,...
+if order>=0
+ [stochPIz_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfvars,0,model.ind{indi});
+ indi=indi+1;
+end
+if order>=1
+ [stochPIzz_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+end
+if order>=2
+ [stochPIzzz_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain3c_M2')
+ [ tempM ] = chainsM( n_stochfvars,3 );
+ model.stochfvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+end
+if order>=3
+ [stochPIzzzz_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain4c_M2')
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+end
+totindi=totindi+8;
+indi=totindi;
+
+
+% compute derivatives of stochf w.r.t v by high order chain rules, and
+% multiply by the weights P (probabilities).
+
+if order==0
+ indi=totindi;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ stochfv_vec.vals=multcol(stochfv_vec.vals,P);
+elseif order==1
+ indi=totindi+(model.stoch_n-1)*(1)+1;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,P);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,P);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+elseif order==2
+ indi=totindi+(model.stoch_n-1)*(1+3)+1+4;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,P);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,P);
+ stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,P);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+elseif order==3
+ indi=totindi+(model.stoch_n-1)*(1+3+4)+1+4+6;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,P);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,P);
+ stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,P);
+ stochfvvvvc_vec.vals=multcol(stochfvvvvc_vec.vals,P);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ [ stochfvvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvvc_vec,4,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvvc_vec
+
+end
+totindi=totindi+8+(model.stoch_n-1)*(1+3+4+6)+1+4+6+9;
+indi=totindi;
+
+temp=reshape(1:n_theta,n_f,n_b);
+stochtheta=temp(stochy,:);
+stochtheta=stochtheta(:);
+n_stochtheta=length(stochtheta);
+
+% exact/approximate Jacobian of gp,gpx,...
+IstochyT=spteye(n_stochy);
+if strcmp(model.jacobian,'exact')
+ [stochgp_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xp_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+else
+ [stochgp_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(X_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+end
+
+nnzgp_theta_vecT=unfold(changecols(changerows(stochgp_stochtheta_vecT,stochy,n_y),stochy,n_f,1)); %n_y,n_theta with only nnz values
+nnzchain0_theta_gpT=changerows(chain0_theta_stochgpT,stochy,n_y);
+
+v_theta_lower_terms_vecT=v_theta_lower_terms;
+v_theta_lower_terms_vecT.vals=repmat(v_theta_lower_terms_vecT.vals,n_nodes,1);
+
+v_theta_vecT=vconcat(tplus(nnzchain0_theta_gpT,nnzgp_theta_vecT,maxload),v_theta_lower_terms_vecT);
+clear nnzchain0_theta_gpT nnzgp_theta_vecT
+stochv_theta_vecT=takerows(v_theta_vecT,stochfvars);
+
+clear v_theta_vecT
+
+totindi=totindi+2;
+indi=totindi;
+% derivatives of v w.r.t x
+if order>=1
+ vxT=vx;
+ stochvxT=takerows(vxT,stochfvars(n_stochy+1:end));
+ stochvxT.vals=repmat(stochvxT.vals,n_nodes,1);
+ stochvxT=vconcat(chain1_stochgpT,stochvxT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ stochgpx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpx_stochtheta_vecT),n_stochy,n_x),1),2));%n_stochy*n_stochtheta,n_x
+ %
+ [chain1_gp_theta_vecT,model.ind{indi}]=contraction1(stochgpx_stochtheta_vecT,hxT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain1_gp_theta_vecT=ptr2col(ptr2d(chain1_gp_theta_vecT,n_stochy,n_stochtheta),2);%n_stochy,n_x,n_stochtheta
+ nnzchain1_gp_theta_vecT=col2ptr(changecols(changerows(chain1_gp_theta_vecT,stochy,n_y),stochtheta,n_theta,2),1); %n_y*n_x,n_theta with only nnz values
+
+ nnzchain1_theta_gpT=col2ptr(changerows(chain1_theta_stochgpT,stochy,n_y),1);% n_y,n_x,n_theta
+
+ vx_theta_lower_terms_vecT=vx_theta_lower_terms;
+ vx_theta_lower_terms_vecT.vals=repmat(vx_theta_lower_terms_vecT.vals,n_nodes,1);
+
+ vx_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain1_theta_gpT,nnzchain1_gp_theta_vecT,maxload),1));
+ clear nnzchain1_theta_gpT nnzchain1_gp_theta_vecT
+ vx_theta_vecT=vconcat(vx_theta_upper_terms_vecT,unfold(vx_theta_lower_terms_vecT));
+
+ clear vx_theta_upper_terms_vecT vx_theta_lower_terms_vecT
+
+ stochvx_theta_vecT=takerows(vx_theta_vecT,stochfvars);
+
+ clear vx_theta_vecT
+end
+if order>=2
+ vxxcT=vxxc;
+ stochvxxcT=takerows(vxxcT,stochfvars(n_stochy+1:end));
+ stochvxxcT.vals=repmat(stochvxxcT.vals,n_nodes,1);
+ stochvxxcT=vconcat(chain2_stochgpT,stochvxxcT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ stochgpxx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpxx_stochtheta_vecT),n_stochy,n_x^2),1),2));%n_stochy*n_stochtheta,n_x^2
+ stochgpxx_stochtheta_vecT=fold(stochgpxx_stochtheta_vecT,n_x,n_x);
+
+ [chain2c_stochgp_stochtheta_vecT,model.ind{indi}]=chain2c_tensor(stochgpx_stochtheta_vecT,stochgpxx_stochtheta_vecT,...
+ hxT,hxxcT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain2c_stochgp_stochtheta_vecT=ptr2col(ptr2d(chain2c_stochgp_stochtheta_vecT,n_stochy,n_stochtheta),2);%n_stochy,unique2,n_stochtheta
+ nnzchain2c_gp_theta_vecT=col2ptr(changecols(changerows(chain2c_stochgp_stochtheta_vecT,stochy,n_y),stochtheta,n_theta,2),1); %n_y*unique2,n_theta with only nnz values
+ clear chain2c_stochgp_stochtheta_vecT
+
+ nnzchain2c_theta_gpT=col2ptr(changerows(chain2c_theta_stochgpT,stochy,n_y),1);% n_y,unique2,n_theta
+
+ vxxc_theta_lower_terms_vecT=unfold(vxxc_theta_lower_terms);
+ vxxc_theta_lower_terms_vecT.vals=repmat(vxxc_theta_lower_terms_vecT.vals,n_nodes,1);
+
+ vxxc_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain2c_theta_gpT,nnzchain2c_gp_theta_vecT,maxload),1));
+ clear nnzchain2c_theta_gpT nnzchain2c_gp_theta_vecT
+ vxxc_theta_vecT=vconcat(vxxc_theta_upper_terms_vecT,vxxc_theta_lower_terms_vecT);
+
+ clear vxxc_theta_upper_terms_vecT vxxc_theta_lower_terms_vecT
+
+ stochvxxc_theta_vecT=takerows(vxxc_theta_vecT,stochfvars);
+
+ clear vxxc_theta_vecT
+end
+if order>=3
+ vxxxcT=vxxxc;
+ stochvxxxcT=takerows(vxxxcT,stochfvars(n_stochy+1:end));
+ stochvxxxcT.vals=repmat(stochvxxxcT.vals,n_nodes,1);
+ stochvxxxcT=vconcat(chain3_stochgpT,stochvxxxcT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpxxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpxxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpxxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xxxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ stochgpxxx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpxxx_stochtheta_vecT),n_stochy,n_x^3),1),2));%n_stochy*n_stochtheta,n_x^2
+ stochgpxxx_stochtheta_vecT=fold(stochgpxxx_stochtheta_vecT,n_x,n_x,n_x);
+
+ [chain3c_stochgp_stochtheta_vecT,model.ind{indi}]=chain3c_tensor(stochgpx_stochtheta_vecT,stochgpxx_stochtheta_vecT,stochgpxxx_stochtheta_vecT,...
+ hxT,hxxcT,hxxxcT,...
+ model.x_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain3c_stochgp_stochtheta_vecT=ptr2col(ptr2d(chain3c_stochgp_stochtheta_vecT,n_stochy,n_stochtheta),2);%n_stochy,unique3,n_stochtheta
+ nnzchain3c_gp_theta_vecT=col2ptr(changecols(changerows(chain3c_stochgp_stochtheta_vecT,stochy,n_y),stochtheta,n_theta,2),1); %n_y*unique3,n_theta with only nnz values
+
+ clear chain3c_stochgp_stochtheta_vecT
+
+ nnzchain3c_theta_gpT=col2ptr(changerows(chain3c_theta_stochgpT,stochy,n_y),1);% n_y,unique3,n_theta
+
+ clear chain3c_theta_stochgpT
+
+ vxxxc_theta_lower_terms_vecT=unfold(vxxxc_theta_lower_terms);
+ vxxxc_theta_lower_terms_vecT.vals=repmat(vxxxc_theta_lower_terms_vecT.vals,n_nodes,1);
+
+ vxxxc_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain3c_theta_gpT,nnzchain3c_gp_theta_vecT,maxload),1));
+
+ clear nnzchain3c_theta_gpT nnzchain3c_gp_theta_vecT
+ vxxxc_theta_vecT=vconcat(vxxxc_theta_upper_terms_vecT,vxxxc_theta_lower_terms_vecT);
+
+ clear vxxxc_theta_upper_terms_vecT vxxxc_theta_lower_terms_vecT
+
+ stochvxxxc_theta_vecT=takerows(vxxxc_theta_vecT,stochfvars);
+
+ clear vxxxc_theta_vecT
+end
+totindi=totindi+9;
+indi=totindi;
+
+[ EstochJ0,model.ind{indi} ] = chain0_theta_tensor( stochfv_vec,stochv_theta_vecT,model.ind{indi},n_ind,maxload,'sum' );
+indi=indi+1;
+
+% EstochJ0=sptensor2spmat(EstochJ0);
+
+% EstochR1,EstochR2,EstochR3,EstochJ1,EstochJ2,EstochJ3
+if order>=1
+ [ EstochR1,model.ind{indi} ] = chain1_tensor( stochfv_vec,stochvxT,model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+ EstochR1=sptensor2spmat(EstochR1);
+
+ [ EstochJ1,model.ind{indi} ] = chain1_theta_tensor( stochfv_vec,stochfvv_vec,...
+ stochvxT,stochv_theta_vecT,stochvx_theta_vecT,...
+ model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+% EstochJ1=sptensor2spmat(EstochJ1);
+end
+if order>=2
+ stochvxT=colsort(stochvxT);
+ [ EstochR2,model.ind{indi} ] = chain2c_tensor( stochfv_vec,stochfvv_vec,...
+ stochvxT,stochvxxcT,model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+ EstochR2=sptensor2spmat(EstochR2);
+
+ [ EstochJ2,model.ind{indi} ] = chain2c_theta_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,...
+ stochvxT,stochvxxcT,...
+ stochv_theta_vecT,stochvx_theta_vecT,stochvxxc_theta_vecT,...
+ model.chain2c_theta_M2,...
+ model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+% EstochJ2=sptensor2spmat(EstochJ2);
+
+end
+if order>=3
+ [ EstochR3,model.ind{indi} ] = chain3c_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,...
+ model.x_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+ EstochR3=sptensor2spmat(EstochR3);
+
+ [ EstochJ3,model.ind{indi} ] = chain3c_theta_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,stochfvvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,...
+ stochv_theta_vecT,stochvx_theta_vecT,stochvxxc_theta_vecT,stochvxxxc_theta_vecT,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'sum' );
+ indi=indi+1;
+% EstochJ3=sptensor2spmat(EstochJ3);
+end
+totindi=totindi+7;
+
+% build the system and the Jacobian
+
+R0=spalloc(n_f,1,n_f);
+
+R0(model.prefrows)=preR0;
+R0(model.stochfrows)=EstochR0;
+
+J0=vconcat(preJ0,EstochJ0);
+oldrows=1:J0.tsize(1);
+newrows=zeros(1,J0.tsize(1));
+newrows([model.prefrows(:);model.stochfrows(:)])=oldrows;
+J0=permuterows(J0,newrows);
+
+T=R0;
+J=J0;
+
+if order>=1
+ R1=spalloc(n_f,n_x,nnz(preR1)+nnz(EstochR1));
+ R1(model.prefrows,:)=preR1;
+ R1(model.stochfrows,:)=EstochR1;
+
+ J1=vconcat(preJ1,EstochJ1);
+ J1=permuterows(J1,newrows);
+
+ J1=ptr2d(J1,1,n_f);
+ J1=ptr2col(J1,1);
+ J1=fold(unfold(J1),n_f*n_x,n_theta);
+ J1=ptr1d(col2ptr(J1,1));
+
+ J=vconcat(J,J1);
+
+ T=[T;R1(:)];
+end
+if order>=2
+ R2=spalloc(n_f,size(preR2,2),nnz(preR2)+nnz(EstochR2));
+ R2(model.prefrows,:)=preR2;
+ R2(model.stochfrows,:)=EstochR2;
+
+ J2=vconcat(preJ2,EstochJ2);
+ J2=permuterows(J2,newrows);
+
+ J2=ptr2d(J2,1,n_f);
+ J2=ptr2col(J2,1);
+ J2=fold(unfold(J2),n_f*unique2,n_theta);
+ J2=ptr1d(col2ptr(J2,1));
+
+ J=vconcat(J,J2);
+
+ T=[T;R2(:)];
+end
+if order>=3
+ R3=spalloc(n_f,size(preR3,2),nnz(preR3)+nnz(EstochR3));
+ J3=vconcat(preJ3,EstochJ3);
+ J3=permuterows(J3,newrows);
+
+ J3=ptr2d(J3,1,n_f);
+ J3=ptr2col(J3,1);
+ J3=fold(unfold(J3),n_f*unique3,n_theta);
+ J3=ptr1d(col2ptr(J3,1));
+
+ J=vconcat(J,J3);
+
+ R3(model.prefrows,:)=preR3;
+ R3(model.stochfrows,:)=EstochR3;
+
+ T=[T;R3(:)];
+end
+
+J=sptensor2spmat(J);
+
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/tpMS.m b/105/replication_package/solution_methods/taylor_projection/tpMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..23fe2c80ea85b4c2e9a0e9c9bfe3b63348538741
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpMS.m
@@ -0,0 +1,102 @@
+function [T,J,model]=tpMS(coeffs,x0,model,params,msparams,transition,c0,nep,P)
+
+if ~isequal(x0,c0)
+ error('x0 must be equal to c0')
+end
+
+% msparams should have n_regimes columns
+
+if size(msparams,2)~=model.n_regimes
+ error('msparams should have n_regimes columns')
+end
+
+msparams=msparams';
+
+paramsvec=repmat(params(:)',model.n_regimes^2,1); % n_regimes*n_regimes,[]
+
+[s,sp]=ndgrid([1:model.n_regimes],[1:model.n_regimes]);
+s=s(:);
+sp=sp(:);
+paramsvec=[paramsvec,msparams(s,:),msparams(sp,:)]; %n_s,n_sp,n_params
+
+paramsvec=[paramsvec,zeros(model.n_regimes^2,model.n_logicalparams)];
+
+coeffs=reshape(full(coeffs),model.n_theta,model.n_regimes);
+coeffsvec=coeffs(:,s)';
+coeffspvec=coeffs(:,sp)';
+
+
+
+x0vec=repmat(x0(:)',model.n_regimes^2,1);
+c0vec=repmat(c0(:)',model.n_regimes^2,1);
+
+nep=full(nep);
+P=full(P);
+
+% ms conditions
+if isfield(model,'jacobian')
+ model.jacobian=model.jacobian;
+end
+[T,J,model]=tpvec(coeffsvec,x0vec,model,paramsvec,c0vec,nep,P,coeffspvec);
+
+
+T.vals=reshape(T.vals,model.n_regimes,model.n_regimes,[]);
+T.vals=T.vals.*reshape(repmat(transition,1,size(T.vals,3)),model.n_regimes,model.n_regimes,size(T.vals,3)); % multiply by the transition matrix
+
+J.vals=reshape(J.vals,model.n_regimes,model.n_regimes,[]);
+J.vals=J.vals.*reshape(repmat(transition,1,size(J.vals,3)),model.n_regimes,model.n_regimes,size(J.vals,3)); % multiply by the transition matrix
+J.vals=reshape(J.vals,model.n_regimes^2,[]);
+
+% sum across sp
+T.vals=reshape(sum(T.vals,2),model.n_regimes,[]);
+
+[rows,cols,vals]=tfind(T);
+rows=double(rows);
+cols=double(cols);
+
+ncond=prod(T.tsize);
+addrows=repmat((0:model.n_regimes-1)*ncond,length(rows),1);
+newrows=repmat(rows,model.n_regimes,1)+addrows(:);
+vals=vals';
+vals=vals(:);
+
+Trows=newrows(:);
+Tcols=ones(length(Trows),1);
+Tvals=vals;
+Trowdim=model.n_regimes*ncond;
+
+[rows,cols,vals]=tfind(J);
+
+rows=double(rows);
+cols=double(cols);
+
+% Comment: I do not sum across sp. This will be done by the sparse
+% function.
+
+% find cols that belong to current period coeffs and future period coeffs
+current_cols=logical(cols<=model.n_theta);
+future_cols=logical(cols>model.n_theta);
+
+newcols=repmat(cols(:)',model.n_regimes^2,1);
+
+newcols(:,current_cols)=newcols(:,current_cols)+repmat((s(:)-1)*model.n_theta,1,nnz(current_cols));
+newcols(:,future_cols)=newcols(:,future_cols)-model.n_theta+repmat((sp(:)-1)*model.n_theta,1,nnz(future_cols));
+
+newrows=repmat(rows(:)',model.n_regimes^2,1);
+
+newrows=reshape(newrows,model.n_regimes,[]);
+newrows=newrows+repmat((0:model.n_regimes-1)'*ncond,1,size(newrows,2));
+
+vals=vals(:);
+
+Jrows=newrows(:);
+Jcols=newcols(:);
+Jvals=vals;
+
+Jrowdim=model.n_regimes*ncond;
+Jcoldim=model.n_regimes*model.n_theta;
+
+T=sparse(Trows,Tcols,Tvals,Trowdim,1);
+J=sparse(Jrows,Jcols,Jvals,Jrowdim,Jcoldim);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/tpMSvec.m b/105/replication_package/solution_methods/taylor_projection/tpMSvec.m
new file mode 100644
index 0000000000000000000000000000000000000000..ea0c3ed2af3c28872830751c235a7c8843e7768c
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpMSvec.m
@@ -0,0 +1,145 @@
+function [T,J,model]=tpMSvec(coeffs,x0,model,params,msparams,transition,c0,nep,P)
+
+% This function is a vectorized version of tpMS. The MS system is computed
+% for n_s different values of coeffs/x0/params, column-wise. The MS pattern
+% is preserved (i.e. future coeffs are separate from current coeffs)
+% INPUTS:
+% coeffs (n_s,n_theta,n_regimes)
+% x0 (n_s,n_x)
+% params (n_s,n_params)
+% c0 (n_s,n_x)
+% msparams (n_msparams,n_regimes)
+% OUTPUTS T and J are sparse tensors.
+% (c) Oren Levintal, September 29, 2017.
+
+if numel(x0)==model.n_x && numel(coeffs)==model.n_theta*model.n_regimes && numel(params)==model.n_params
+ n_s=1;
+else % x0,coeffs,params have a row dimension of 1 or n_s
+ temp=[size(x0,1),size(coeffs,1),size(params,1),size(c0,1)];
+ n_s=max(temp);
+ if min(temp)~=n_s
+ error('incompatible s dimension')
+ end
+end
+
+if ~isequal(x0,c0)
+ error('x0 must be equal to c0')
+end
+
+% msparams should have n_regimes columns
+
+if size(msparams,2)~=model.n_regimes
+ error('msparams should have n_regimes columns')
+end
+
+msparams=msparams'; %n_regimes,n_msparams
+
+paramsvec=reshape(repmat(params(:)',model.n_regimes^2,1),model.n_regimes^2*n_s,[]); % n_regimes*n_regimes,n_s*n_params
+
+[s,sp]=ndgrid([1:model.n_regimes],[1:model.n_regimes]);
+s=s(:);
+sp=sp(:);
+paramsvec=[paramsvec,repmat([msparams(s,:),msparams(sp,:)],n_s,1)];
+
+paramsvec=[paramsvec,zeros(model.n_regimes^2*n_s,model.n_logicalparams)];
+
+coeffs=reshape(full(coeffs),n_s*model.n_theta,model.n_regimes);
+coeffsvec=coeffs(:,s);
+coeffsvec=reshape(coeffsvec,n_s,model.n_theta,model.n_regimes^2);
+coeffsvec=permute(coeffsvec,[3,1,2]);
+coeffsvec=reshape(coeffsvec,model.n_regimes^2*n_s,[]);
+
+coeffspvec=coeffs(:,sp);
+coeffspvec=reshape(coeffspvec,n_s,model.n_theta,model.n_regimes^2);
+coeffspvec=permute(coeffspvec,[3,1,2]);
+coeffspvec=reshape(coeffspvec,model.n_regimes^2*n_s,[]);
+
+
+x0vec=repmat(x0(:)',model.n_regimes^2,1); %n_regimes^2,n_s*n_x
+x0vec=reshape(x0vec,model.n_regimes^2*n_s,[]); %n_regimes^2*n_s,n_x
+c0vec=repmat(c0(:)',model.n_regimes^2,1); %n_regimes^2,n_s*n_x
+c0vec=reshape(c0vec,model.n_regimes^2*n_s,[]); %n_regimes^2*n_s,n_x
+
+nep=full(nep);
+P=full(P);
+
+% ms conditions
+if isfield(model,'jacobian')
+ model.jacobian=model.jacobian;
+end
+
+% row dimensions should be n_regimes*n_regimes*n_s
+
+[T,J,model]=tpvec(coeffsvec,x0vec,model,paramsvec,c0vec,nep,P,coeffspvec);
+
+
+T.vals=reshape(T.vals,model.n_regimes,model.n_regimes,[]);
+T.vals=T.vals.*reshape(repmat(transition,1,size(T.vals,3)),model.n_regimes,model.n_regimes,size(T.vals,3)); % multiply by the transition matrix
+
+J.vals=reshape(J.vals,model.n_regimes,model.n_regimes,[]);
+J.vals=J.vals.*reshape(repmat(transition,1,size(J.vals,3)),model.n_regimes,model.n_regimes,size(J.vals,3)); % multiply by the transition matrix
+J.vals=reshape(J.vals,model.n_regimes^2*n_s,[]);
+
+% sum across sp and reshape
+T.vals=reshape(sum(T.vals,2),model.n_regimes*n_s,[]);
+
+[rows,cols,vals]=tfind(T);
+rows=double(rows);
+cols=double(cols);
+
+ncond=prod(T.tsize);
+addrows=repmat((0:model.n_regimes-1)*ncond,length(rows),1);
+newrows=repmat(rows,model.n_regimes,1)+addrows(:);
+vals=reshape(vals,model.n_regimes,n_s,[]);
+vals=permute(vals,[2,3,1]); %n_s,n_vals,n_regimes
+vals=reshape(vals,n_s,[]); %n_s,n_vals*n_regimes
+
+
+Trows=newrows(:);
+Tcols=ones(length(Trows),1);
+Tvals=vals;
+Trowdim=model.n_regimes*ncond;
+
+
+
+
+[rows,cols,vals]=tfind(J);
+
+rows=double(rows);
+cols=double(cols);
+
+% Comment: I do not sum across sp. This is done later by post-multiplying
+% the crs Jacobian matrix (with duplicate entries) by the identity matrix.
+
+% find cols that belong to current period coeffs and future period coeffs
+current_cols=logical(cols<=model.n_theta);
+future_cols=logical(cols>model.n_theta);
+
+newcols=repmat(cols(:)',model.n_regimes^2,1);
+
+newcols(:,current_cols)=newcols(:,current_cols)+repmat((s(:)-1)*model.n_theta,1,nnz(current_cols));
+newcols(:,future_cols)=newcols(:,future_cols)-model.n_theta+repmat((sp(:)-1)*model.n_theta,1,nnz(future_cols));
+
+newrows=repmat(rows(:)',model.n_regimes^2,1);
+
+newrows=reshape(newrows,model.n_regimes,[]);
+newrows=newrows+repmat((0:model.n_regimes-1)'*ncond,1,size(newrows,2));
+
+vals=reshape(vals,model.n_regimes^2,n_s,[]);
+vals=permute(vals,[2,1,3]);
+vals=reshape(vals,n_s,[]);
+
+Jrows=newrows(:);
+Jcols=newcols(:);
+Jvals=vals;
+
+Jrowdim=model.n_regimes*ncond;
+Jcoldim=model.n_regimes*model.n_theta;
+
+T=sptensor(Trows,Tcols,Tvals,Trowdim,1);
+J=sptensor(Jrows,Jcols,Jvals,Jrowdim,Jcoldim);
+J=contraction1(J,spteye(Jcoldim)); % this function sums across entries with same row and column (like the function sparse where there are duplicate entries)
+% T=sparse(Trows,Tcols,Tvals,Trowdim,1);
+% J=sparse(Jrows,Jcols,Jvals,Jrowdim,Jcoldim);
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/tpscale.m b/105/replication_package/solution_methods/taylor_projection/tpscale.m
new file mode 100644
index 0000000000000000000000000000000000000000..573ab5525c90918f60fc631af8c1bf79cc33f6fc
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpscale.m
@@ -0,0 +1,46 @@
+function [ scaledT,scaledJ,Wcols,Wrows,model ] = tpscale( weighted_coeffs,x0,model,params,eta,c0,nep,P,Wcols,Wrows,varargin )
+%This function computes the scaled system and its Jacobian. If weights are
+%empty, the function computes and returns the weights. Otherwise, the
+%supplied weights are used.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=model.order(1);
+
+if isempty(Wcols) && isempty(Wrows)
+ % if weights are not supplied assume no weights.
+ coeffs=weighted_coeffs;
+elseif ~isempty(Wcols) && ~isempty(Wrows)
+ % if all weights are supplied, unscale weighted_coeffs
+ coeffs=weighted_coeffs./Wcols;
+else
+ error('missing weights');
+end
+
+if isempty(varargin) % precomputed variables are not available
+ [T,J,model]=tp(coeffs,x0,model,params,eta,c0,nep,P);
+else
+ g_theta=varargin{1};
+ h_theta=varargin{2};
+ gx_theta=varargin{3};
+ hx_theta=varargin{4};
+ gxxc_theta=varargin{5};
+ hxxc_theta=varargin{6};
+ gxxxc_theta=varargin{7};
+ hxxxc_theta=varargin{8};
+ [T,J,model]=tp(coeffs,x0,model,params,eta,c0,nep,P,...
+ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta);
+end
+
+if isempty(Wcols)
+ Wcols=max(abs(J))';
+ Wrows=max(abs([J*spdiags(1./Wcols,0,model.n_theta,model.n_theta)]'))';
+end
+
+scaledT=T./Wrows;
+
+scaledJ=spdiags(1./Wrows,0,model.n_theta,model.n_theta)*J*spdiags(1./Wcols,0,model.n_theta,model.n_theta);
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tpscaleMS.m b/105/replication_package/solution_methods/taylor_projection/tpscaleMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..89c69dfb018688cec454e9f679bca83844fc2d40
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpscaleMS.m
@@ -0,0 +1,40 @@
+function [ scaledT,scaledJ,Wcols,Wrows,model ] = tpscaleMS( weighted_coeffs,x0,model,params,msparams,transition,c0,nep,P,Wcols,Wrows)
+%This function computes the scaled system and its Jacobian. If weights are
+%empty, the function computes and returns the weights. Otherwise, the
+%supplied weights are used.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=model.order(1);
+
+if isempty(Wcols) && isempty(Wrows)
+ % if weights are not supplied assume no weights.
+ coeffs=weighted_coeffs;
+elseif ~isempty(Wcols) && ~isempty(Wrows)
+ % if all weights are supplied, unscale weighted_coeffs
+ coeffs=weighted_coeffs./Wcols;
+else
+ error('missing weights');
+end
+
+[T,J,model]=tpMS(coeffs,x0,model,params,msparams,transition,c0,nep,P);
+
+if isempty(Wcols)
+ Wcols=max(abs(J))';
+ if min(Wcols)==0
+ Wcols=ones(size(Wcols));
+ end
+ Wrows=max(abs([J*spdiags(1./Wcols,0,model.n_theta*model.n_regimes,model.n_theta*model.n_regimes)]'))';
+ if min(Wrows)==0
+ Wrows=ones(size(Wrows));
+ end
+end
+
+scaledT=T./Wrows;
+[mJ,nJ]=size(J);
+% scaledJ=spdiags(1./Wrows,0,model.n_theta*model.n_regimes,model.n_theta*model.n_regimes)*J*spdiags(1./Wcols,0,model.n_theta*model.n_regimes,model.n_theta*model.n_regimes);
+scaledJ=spdiags(1./Wrows,0,mJ,mJ)*J*spdiags(1./Wcols,0,nJ,nJ);
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tpscaleMSi.m b/105/replication_package/solution_methods/taylor_projection/tpscaleMSi.m
new file mode 100644
index 0000000000000000000000000000000000000000..ce08d51f3288331bdaa404f621009d8ec6249c9b
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpscaleMSi.m
@@ -0,0 +1,105 @@
+function [ scaledT,scaledJ,Wcols,Wrows,model ] = tpscaleMSi( weighted_coeffs,x0,model,params,paramsi,msparams,transition,c0,nep,P,Wcols,Wrows)
+%This function computes the scaled system and its Jacobian. If weights are
+%empty, the function computes and returns the weights. Otherwise, the
+%supplied weights are used.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+
+order=model.order(1);
+
+if isempty(Wcols) && isempty(Wrows)
+ % if weights are not supplied assume no weights.
+ coeffs=weighted_coeffs;
+elseif ~isempty(Wcols) && ~isempty(Wrows)
+ % if all weights are supplied, unscale weighted_coeffs
+ coeffs=weighted_coeffs./Wcols;
+else
+ error('missing weights');
+end
+
+if ~isempty(paramsi)
+ n_s=size(paramsi,2);
+else
+ n_s=1;
+end
+
+if ~isfield(model,'active_vars')
+ coeffs=repmat(coeffs(:)',n_s,1);
+ coeffs=reshape(coeffs,n_s,model.n_theta,model.n_regimes);
+else
+ coeffs=reshape(coeffs,[],model.n_b);
+ coeffs=coeffs(model.active_vars(:),:);
+ coeffs=reshape(coeffs,n_s,[]);
+end
+x0=repmat(x0(:)',n_s,1);
+c0=repmat(c0(:)',n_s,1);
+
+params=[repmat(params(:)',n_s,1),paramsi'];
+
+[Ti,Ji,model]=tpMSvec(coeffs,x0,model,params,msparams,transition,c0,nep,P);
+
+if ~isfield(model,'active_vars')
+ T=Ti;
+ T.vals=Ti.vals(1,:);
+ J=Ji;
+ J.vals=Ji.vals(1,:);
+
+ for j=2:n_s
+ Tj=Ti;
+ Tj.vals=Ti.vals(j,:);
+ T=vconcat(T,Tj);
+ Jj=Ji;
+ Jj.vals=Ji.vals(j,:);
+ J=vconcat(J,Jj);
+ end
+else
+ %%%%%%%%%%%%%%%
+ %%% The coefficients must be of dimensions model.n_vars,n_b, where model.n_vars is
+ %%% the number of variables, and n_b size
+ %%% of basis function
+ %%%%%%%%%%%%%%%
+ T=Ti;
+ T.vals=Ti.vals(1,:);
+ J=Ji;
+ J.vals=Ji.vals(1,:);
+ countcoeffs=reshape(1:model.n_vars*model.n_b,[],model.n_b);
+ J=changecols(J,reshape(countcoeffs(model.active_vars(1,:),:),1,[]),model.n_vars*model.n_b,1);
+ for j=2:n_s
+ Tj=Ti;
+ Tj.vals=Ti.vals(j,:);
+ T=vconcat(T,Tj);
+ Jj=Ji;
+ Jj.vals=Ji.vals(j,:);
+ Jj=changecols(Jj,reshape(countcoeffs(model.active_vars(j,:),:),1,[]),model.n_vars*model.n_b,1);
+ J=vconcat(J,Jj);
+ end
+end
+T=sptensor2spmat(T);
+J=sptensor2spmat(J);
+
+if isfield(model,'special_code')
+ T=[T;model.moreT];
+ J=[J;model.moreJ];
+end
+
+
+[mJ,nJ]=size(J);
+
+if isempty(Wcols)
+ Wcols=max(abs(J))';
+ if min(Wcols)==0
+ Wcols=ones(size(Wcols));
+ end
+ Wrows=max(abs([J*spdiags(1./Wcols,0,nJ,nJ)]'))';
+ if min(Wrows)==0
+ Wrows=ones(size(Wrows));
+ end
+end
+
+scaledT=T./Wrows;
+scaledJ=spdiags(1./Wrows,0,mJ,mJ)*J*spdiags(1./Wcols,0,nJ,nJ);
+
+
+
+end
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tpsolve.m b/105/replication_package/solution_methods/taylor_projection/tpsolve.m
new file mode 100644
index 0000000000000000000000000000000000000000..1f8a51bd13dafa1b3068d46474fcdde2391d0a11
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpsolve.m
@@ -0,0 +1,160 @@
+function [ncoeffs,model,T,J,iter]=tpsolve(coeffs,x0,model,params,varargin)
+% function [ncoeffs,model,T,J,iter]=tpsolve(coeffs,x0,model,params,c0,nep,P,tolX,tolF,maxiter,varargin)
+if nargin==10
+ type='normal';
+ c0=varargin{1};
+ nep=varargin{2};
+ P=varargin{3};
+ tolX=varargin{4};
+ tolF=varargin{5};
+ maxiter=varargin{6};
+ OPTIONS=[];
+elseif nargin==11
+ type='normal';
+ c0=varargin{1};
+ nep=varargin{2};
+ P=varargin{3};
+ tolX=varargin{4};
+ tolF=varargin{5};
+ maxiter=varargin{6};
+ OPTIONS=varargin{7};
+elseif nargin==12
+ type='MS';
+ msparams=varargin{1};
+ transition=varargin{2};
+ c0=varargin{3};
+ nep=varargin{4};
+ P=varargin{5};
+ tolX=varargin{6};
+ tolF=varargin{7};
+ maxiter=varargin{8};
+ OPTIONS=[];
+elseif nargin==13
+ type='MS';
+ msparams=varargin{1};
+ transition=varargin{2};
+ c0=varargin{3};
+ nep=varargin{4};
+ P=varargin{5};
+ tolX=varargin{6};
+ tolF=varargin{7};
+ maxiter=varargin{8};
+ OPTIONS=varargin{9};
+else
+ error('wrong number of input arguments')
+end
+
+if isempty(nep) || isempty(P)
+ P=1;
+ nep=0;
+end
+
+if strcmp(type,'normal')
+ coeffs=coeffs(:);
+ if length(coeffs)~=model.n_theta
+ error(['The first argument is wrong. The initial guess should be a vector of ' num2str(model.n_theta) ' elements.'])
+ end
+ x0=x0(:);
+ if length(x0)~=model.n_x
+ error(['The second argument is wrong. The approximation point should be a vector of ' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if ~isstruct(model)
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ elseif ~isfield(model,'n_x')
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ end
+
+% params=[params(:);zeros(model.n_logicalparams,1)];
+
+ if length(params)~=model.n_params-model.n_logicalparams
+ error(['The fourth argument is wrong. The number of model parameters should be ' num2str(model.n_params) '.'])
+ end
+ c0=c0(:);
+ if length(c0)~=model.n_x
+ error(['The fifth argument is wrong. The center of the approximating polynomial should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if size(nep,1)~=model.n_e
+ error(['The sixth argument is wrong. It should be a matrix with ' num2str(model.n_e) ' rows (=the number of shocks).'])
+ end
+ P=P(:);
+ if size(nep,2)~=length(P)
+ error('The sixth or seventh arguments are wrong. The number of columns in the sixth argument should be equal to the number of elements in the seventh argument.')
+ end
+ if numel(tolX)~=1 || ~isnumeric(tolX)
+ error('The eighth argument should be a numeric scalar')
+ end
+ if numel(tolF)~=1 || ~isnumeric(tolF)
+ error('The ninth argument should be a numeric scalar')
+ end
+ if numel(maxiter)~=1 || ~isnumeric(maxiter)
+ error('The tenth argument should be a numeric scalar')
+ end
+
+
+ msparams=zeros(0,1);
+ transition=1;
+ if isempty(OPTIONS)
+ [ncoeffs,model,T,J,iter]=tpsolveMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter);
+ else
+ [ncoeffs,model,T,J,iter]=tpsolveMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter,OPTIONS);
+ end
+
+else
+
+ if size(coeffs,1)~=model.n_theta || size(coeffs,2)~=model.n_regimes
+ message=sprintf(['The first argument is wrong. The initial guess should be a ' num2str(model.n_theta) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of polynomial coefficients per regime is ' num2str(model.n_theta) ' and the number of regimes is ' num2str(model.n_regimes)'.']);
+ error(message);
+ end
+ x0=x0(:);
+ if length(x0)~=model.n_x
+ error(['The second argument is wrong. The approximation point should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if ~isstruct(model)
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ elseif ~isfield(model,'n_x')
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ end
+% params=[params(:);zeros(model.n_logicalparams,1)];
+
+ if length(params)~=model.n_params_no_ms-model.n_logicalparams
+ error(['The fourth argument is wrong. The number of model parameters should be ' num2str(model.n_params_no_ms) '.'])
+ end
+ if isempty(msparams)
+ msparams=zeros(0,model.n_regimes);
+ end
+ if size(msparams,1)~=model.n_msparams || size(msparams,2)~=model.n_regimes
+ error(sprintf(['The fifth argument is wrong. It should be a ' num2str(model.n_msparams) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of Markov switching parameters is ' num2str(model.n_msparams) ' and the number of regimes is ' num2str(model.n_regimes) '.']))
+ end
+ if size(transition,1)~=model.n_regimes || size(transition,2)~=model.n_regimes
+ error(['The sixth argument is wrong. The transition matrix should have ' num2str(model.n_regimes) ' rows and columns.'])
+ end
+ c0=c0(:);
+ if length(c0)~=model.n_x
+ error(['The seventh argument is wrong. The center of the approximating polynomial should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if size(nep,1)~=model.n_e
+ error(['The eighth argument is wrong. It should be a matrix with ' num2str(model.n_e) ' rows (=the number of shocks).'])
+ end
+ P=P(:);
+ if size(nep,2)~=length(P)
+ error('The eighth or ninth arguments are wrong. The number of columns in the eighth argument should be equal to the number of elements in the ninth argument.')
+ end
+ if numel(tolX)~=1 || ~isnumeric(tolX)
+ error('The tenth argument should be a numeric scalar')
+ end
+ if numel(tolF)~=1 || ~isnumeric(tolF)
+ error('The elevnth argument should be a numeric scalar')
+ end
+ if numel(maxiter)~=1 || ~isnumeric(maxiter)
+ error('The twelfth argument should be a numeric scalar')
+ end
+ if isempty(OPTIONS)
+ [ncoeffs,model,T,J,iter]=tpsolveMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter);
+ else
+ [ncoeffs,model,T,J,iter]=tpsolveMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter,OPTIONS);
+ end
+
+
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tpsolve2.m b/105/replication_package/solution_methods/taylor_projection/tpsolve2.m
new file mode 100644
index 0000000000000000000000000000000000000000..26a119ff32936d4aaa0c471a7f6f7d292ad29334
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpsolve2.m
@@ -0,0 +1,155 @@
+function [ncoeffs,model,T,J,iter]=tpsolve2(coeffs,x0,model,params,varargin)
+% function [ncoeffs,model,T,J,iter]=tpsolve(coeffs,x0,model,params,c0,nep,P,tolX,tolF,maxiter,varargin)
+if nargin==10
+ type='normal';
+ c0=varargin{1};
+ nep=varargin{2};
+ P=varargin{3};
+ tolX=varargin{4};
+ tolF=varargin{5};
+ maxiter=varargin{6};
+ OPTIONS=[];
+elseif nargin==11
+ type='normal';
+ c0=varargin{1};
+ nep=varargin{2};
+ P=varargin{3};
+ tolX=varargin{4};
+ tolF=varargin{5};
+ maxiter=varargin{6};
+ OPTIONS=varargin{7};
+elseif nargin==12
+ type='MS';
+ msparams=varargin{1};
+ transition=varargin{2};
+ c0=varargin{3};
+ nep=varargin{4};
+ P=varargin{5};
+ tolX=varargin{6};
+ tolF=varargin{7};
+ maxiter=varargin{8};
+ OPTIONS=[];
+elseif nargin==13
+ type='MS';
+ msparams=varargin{1};
+ transition=varargin{2};
+ c0=varargin{3};
+ nep=varargin{4};
+ P=varargin{5};
+ tolX=varargin{6};
+ tolF=varargin{7};
+ maxiter=varargin{8};
+ OPTIONS=varargin{9};
+else
+ error('wrong number of input arguments')
+end
+
+if strcmp(type,'normal')
+ coeffs=coeffs(:);
+ if length(coeffs)~=model.n_theta
+ error(['The first argument is wrong. The initial guess should be a vector of ' num2str(model.n_theta) ' elements.'])
+ end
+ x0=x0(:);
+ if length(x0)~=model.n_x
+ error(['The second argument is wrong. The approximation point should be a vector of ' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if ~isstruct(model)
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ elseif ~isfield(model,'n_x')
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ end
+
+% params=[params(:);zeros(model.n_logicalparams,1)];
+
+ if length(params)~=model.n_params-model.n_logicalparams
+ error(['The fourth argument is wrong. The number of model parameters should be ' num2str(model.n_params) '.'])
+ end
+ c0=c0(:);
+ if length(c0)~=model.n_x
+ error(['The fifth argument is wrong. The center of the approximating polynomial should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if size(nep,1)~=model.n_e
+ error(['The sixth argument is wrong. It should be a matrix with ' num2str(model.n_e) ' rows (=the number of shocks).'])
+ end
+ P=P(:);
+ if size(nep,2)~=length(P)
+ error('The sixth or seventh arguments are wrong. The number of columns in the sixth argument should be equal to the number of elements in the seventh argument.')
+ end
+ if numel(tolX)~=1 || ~isnumeric(tolX)
+ error('The eighth argument should be a numeric scalar')
+ end
+ if numel(tolF)~=1 || ~isnumeric(tolF)
+ error('The ninth argument should be a numeric scalar')
+ end
+ if numel(maxiter)~=1 || ~isnumeric(maxiter)
+ error('The tenth argument should be a numeric scalar')
+ end
+
+
+ msparams=zeros(0,1);
+ transition=1;
+ if isempty(OPTIONS)
+ [ncoeffs,model,T,J,iter]=tpsolveMS2(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter);
+ else
+ [ncoeffs,model,T,J,iter]=tpsolveMS2(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter,OPTIONS);
+ end
+
+else
+
+ if size(coeffs,1)~=model.n_theta || size(coeffs,2)~=model.n_regimes
+ message=sprintf(['The first argument is wrong. The initial guess should be a ' num2str(model.n_theta) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of polynomial coefficients per regime is ' num2str(model.n_theta) ' and the number of regimes is ' num2str(model.n_regimes)'.']);
+ error(message);
+ end
+ x0=x0(:);
+ if length(x0)~=model.n_x
+ error(['The second argument is wrong. The approximation point should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if ~isstruct(model)
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ elseif ~isfield(model,'n_x')
+ error('The third argument is wrong. It should be a structure generated by prepare_tp.')
+ end
+% params=[params(:);zeros(model.n_logicalparams,1)];
+
+ if length(params)~=model.n_params_no_ms-model.n_logicalparams
+ error(['The fourth argument is wrong. The number of model parameters should be ' num2str(model.n_params_no_ms) '.'])
+ end
+ if isempty(msparams)
+ msparams=zeros(0,model.n_regimes);
+ end
+ if size(msparams,1)~=model.n_msparams || size(msparams,2)~=model.n_regimes
+ error(sprintf(['The fifth argument is wrong. It should be a ' num2str(model.n_msparams) '-by-' num2str(model.n_regimes) ' matrix. \nThe number of Markov switching parameters is ' num2str(model.n_msparams) ' and the number of regimes is ' num2str(model.n_regimes) '.']))
+ end
+ if size(transition,1)~=model.n_regimes || size(transition,2)~=model.n_regimes
+ error(['The sixth argument is wrong. The transition matrix should have ' num2str(model.n_regimes) ' rows and columns.'])
+ end
+ c0=c0(:);
+ if length(c0)~=model.n_x
+ error(['The seventh argument is wrong. The center of the approximating polynomial should be a vector of' num2str(model.n_x) ' elements (=the number of state variables).'])
+ end
+ if size(nep,1)~=model.n_e
+ error(['The eighth argument is wrong. It should be a matrix with ' num2str(model.n_e) ' rows (=the number of shocks).'])
+ end
+ P=P(:);
+ if size(nep,2)~=length(P)
+ error('The eighth or ninth arguments are wrong. The number of columns in the eighth argument should be equal to the number of elements in the ninth argument.')
+ end
+ if numel(tolX)~=1 || ~isnumeric(tolX)
+ error('The tenth argument should be a numeric scalar')
+ end
+ if numel(tolF)~=1 || ~isnumeric(tolF)
+ error('The elevnth argument should be a numeric scalar')
+ end
+ if numel(maxiter)~=1 || ~isnumeric(maxiter)
+ error('The twelfth argument should be a numeric scalar')
+ end
+ if isempty(OPTIONS)
+ [ncoeffs,model,T,J,iter]=tpsolveMS2(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter);
+ else
+ [ncoeffs,model,T,J,iter]=tpsolveMS2(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter,OPTIONS);
+ end
+
+
+end
+
+
diff --git a/105/replication_package/solution_methods/taylor_projection/tpsolveMS.m b/105/replication_package/solution_methods/taylor_projection/tpsolveMS.m
new file mode 100644
index 0000000000000000000000000000000000000000..624c223559ca3bc9b9e59bfdb7b334dee3ee9950
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/tpsolveMS.m
@@ -0,0 +1,151 @@
+function [ncoeffs,model,T,J,iter]=tpsolveMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,tolX,tolF,maxiter,varargin)
+
+% The function computes the polynomial coefficients by the Newton method or
+% by fsolve/lsqnonlin.
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% Changed on March 19, 2017 - adjusted for Markov switching parameters
+
+
+x0=x0(:);
+
+params=params(:);
+
+c0=c0(:);
+
+P=P(:);
+
+display=1;
+if isfield(model,'display')
+ if strcmp(model.display,'off')
+ display=0;
+ end
+end
+
+
+order=model.order(1);
+
+% make sure all inputs are full
+coeffs=full(coeffs);
+x0=full(x0);
+params=full(params);
+msparams=full(msparams);
+c0=full(c0);
+P=full(P);
+
+n_x=model.n_x;
+
+% shift the center of the Polynomials to x0
+
+c0_old=c0;
+c0_new=x0;
+if ~isequal(c0_old,x0)
+ coeffs=reshape(coeffs,(model.n_y+model.n_x1)*model.n_b,model.n_regimes);
+ coeffs=reshape(coeffs',model.n_regimes*(model.n_y+model.n_x1),model.n_b);
+ [ coeffs ] = shift_center( coeffs,c0_old,c0_new,order,model );
+ coeffs=reshape(coeffs,model.n_regimes,(model.n_y+model.n_x1)*model.n_b);
+ coeffs=full(coeffs');
+ c0=c0_new;
+end
+coeffs=coeffs(:);
+
+% precompute expressions that are independent of coeffs
+% [ g_theta,h_theta,gx_theta,hx_theta,gxxc_theta,hxxc_theta,gxxxc_theta,hxxxc_theta,model ] = precompute(x0,c0,model,order );
+
+iter=1;
+
+% start without weights.
+
+Wcols=[]; Wrows=[]; coeffs=full(coeffs);
+
+[T,J,Wcols,Wrows,model]=tpscaleMS(coeffs,x0,model,params,msparams,transition,c0,nep,P,Wcols,Wrows);
+normT=norm(T);
+% rcond(full(J))
+bestT=normT;
+best_weighted_coeffs=Wcols.*coeffs;
+
+if maxiter>0
+ ncoeffs=coeffs-full(J\T)./Wcols;
+ d=ncoeffs-coeffs;
+ normd=norm(d);
+ optimality=norm(T'*J,inf);
+ if display==1
+ disp(['iter norm(system) norm(step) optimality measure'])
+
+ disp([' ' num2str(iter) ' ' num2str(normT,'%3.2e') ' ' num2str(normd,'%3.2e') ' ' num2str(optimality,'%3.2e')] )
+ end
+
+else
+ normd=inf;
+end
+
+% continue to convergence
+while normd > max(tolX,eps) && normT>max(tolF,eps) && iter max(tolX,eps) && normT>max(tolF,eps) && iter0
+% Rcond=rcond(full(J))
+% condtol=1e-16;
+% if Rcond>condtol
+ ncoeffs=coeffs-full(J\T)./Wcols;
+% else
+% warning('doing vpa')
+% digits=ceil(-log10(Rcond))+10;
+% ncoeffs=coeffs-double(vpa(full(J),digits)\vpa(full(T),digits))./Wcols;
+% end
+ d=ncoeffs-coeffs;
+ normd=norm(d);
+ optimality=norm(T'*J,inf);
+
+ if display==1
+ disp(['iter norm(system) norm(step) optimality measure'])
+
+ disp([' ' num2str(iter) ' ' num2str(normT,'%3.2e') ' ' num2str(normd,'%3.2e') ' ' num2str(optimality,'%3.2e')] )
+ end
+
+else
+ normd=inf;
+end
+% continue to convergence
+while normd > max(tolX,eps) && normT>max(tolF,eps) && itercondtol
+ ncoeffs=coeffs-full(J\T)./Wcols;
+% else
+% warning('doing vpa')
+% digits=ceil(-log10(Rcond))+10;
+% ncoeffs=coeffs-double(vpa(full(J),digits)\vpa(full(T),digits))./Wcols;
+% end
+
+ d=ncoeffs-coeffs;
+ optimality=norm(T'*J,inf);
+ normd=norm(d);
+ if display==1
+ disp([' ' num2str(iter) ' ' num2str(normT,'%3.2e') ' ' num2str(normd,'%3.2e') ' ' num2str(optimality,'%3.2e')] )
+ end
+end
+
+coeffs=best_weighted_coeffs./Wcols;
+
+% if Newton method did not converge with the maximum number of iterations,
+% switch to fsolve (default) or lsqnonlin.
+if logical(normd < max(tolX,eps) || normT=1
+ gx_theta.vals=repmat(gx_theta.vals,n_s,1);
+ hx_theta.vals=repmat(hx_theta.vals,n_s,1);
+end
+if order>=2
+ gxxc_theta.vals=repmat(gxxc_theta.vals,n_s,1);
+ hxxc_theta.vals=repmat(hxxc_theta.vals,n_s,1);
+end
+if order>=3
+ gxxxc_theta.vals=repmat(gxxxc_theta.vals,n_s,1);
+ hxxxc_theta.vals=repmat(hxxxc_theta.vals,n_s,1);
+end
+if order>=4
+ gxxxxc_theta.vals=repmat(gxxxxc_theta.vals,n_s,1);
+ hxxxxc_theta.vals=repmat(hxxxxc_theta.vals,n_s,1);
+end
+
+if ms==1
+ g_theta.tsize(end)=model.n_theta*2; % in ms models we duplicate the Jacobian. The first block corresponds to coefficients of current period, and the second block to next period.
+ h_theta.tsize(end)=model.n_theta*2;
+ if order>=1
+ gx_theta.tsize(end)=model.n_theta*2;
+ hx_theta.tsize(end)=model.n_theta*2;
+ end
+ if order>=2
+ gxxc_theta.tsize(end)=model.n_theta*2;
+ hxxc_theta.tsize(end)=model.n_theta*2;
+ end
+ if order>=3
+ gxxxc_theta.tsize(end)=model.n_theta*2;
+ hxxxc_theta.tsize(end)=model.n_theta*2;
+ end
+ if order>=4
+ gxxxxc_theta.tsize(end)=model.n_theta*2;
+ hxxxxc_theta.tsize(end)=model.n_theta*2;
+ end
+end
+
+
+indi=5; %count indi from 5, due to precompute.
+
+
+if ~isfield(model,'n_ind')
+ n_ind=1;
+else
+ n_ind=model.n_ind;
+end
+if ~isfield(model,'maxload')
+ maxload=intarray(length(P)*n_s);
+else
+ maxload=intarray(model.maxload);
+end
+model.maxload=maxload;
+
+params=paramsvec;
+P=P(:);
+
+n_f=model.n_f; % no. of model conditions
+n_x=model.n_x; % no. of state variables
+n_y=model.n_y; % no. of control variables
+n_x2=model.n_x2; % no. of exogenous state variables
+n_x1=model.n_x1; % no. of endogenous state variabels
+n_v=model.n_v; % total no. of variables v=(yp,y,xp,x)
+n_theta=model.n_theta; % no. of Polynomial coefficients
+n_b=model.n_b; % no. of terms in the basis function
+n_nodes=size(nep,2); % no. nodes in the discrete shocks
+n_z=model.n_z; % no. of auxiliary variables
+n_e=model.n_e;
+
+n_prefrows=length(model.prefrows);
+n_stochfrows=length(model.stochfrows);
+
+n_params=model.n_params;
+
+if model.hybrid==1 || model.hybrid==3
+ n_params=n_params+n_e; % shocks are treated as parameters
+end
+
+coeffs=reshape(coeffsvec,n_s,[],n_b);
+% g_coeffs=coeffs(:,1:n_y,:);
+
+%create stochy: index of future control variables that affect stochastic equations
+tempv=zeros(n_v,1);
+tempv(model.stochfvars)=model.stochfvars;
+tempv(n_y+1:end)=0;
+stochy=nonzeros(tempv); % this is the stochastic y variables that affect f, but it does not include stochastic y variables that affect logical expressions only
+n_stochy=length(stochy);
+if ms==0
+ stochg_coeffs=coeffs(:,stochy,:);
+else
+ coeffspvec=full(reshape(coeffsp,n_s,[],n_b));
+ stochg_coeffs=coeffspvec(:,stochy,:);
+end
+
+if ~isfield(model,'ind4')
+ model.ind4=cell(100+model.count_pre_n+model.count_stoch_n,1); % indices for 4th order computations
+end
+indi4=1;
+
+unique2=[]; unique3=[]; unique4=[];
+
+prefvars=model.prefvars; % index of variables that affect nonstochastic equations.
+stochfvars=model.stochfvars;% index of variables that affect stochastic equations.
+n_prefvars=length(prefvars);
+n_stochfvars=length(stochfvars);
+
+if model.pde==3 % compute derivatives of derivs w.r.t x and theta
+ factor=ms+1;
+ if order==0
+ gx__theta=sptensor(model.n_tildy1st,n_theta*factor,n_s);
+ else
+ rows=1:model.n_tildy1st;
+ rows=rows(:);
+ cols=n_y+(model.tildy1st_ind);
+ cols=cols(:);
+ vals=ones(n_s,length(rows));
+ gx__theta=sptensor(rows,cols,vals,model.n_tildy1st,n_theta*factor);
+ end
+ if order<=1
+ gxx__theta=sptensor(model.n_tildy2nd,n_theta*factor,n_s);
+ else
+ rows=1:model.n_tildy2nd;
+ rows=rows(:);
+ cols=n_y+n_y*n_x+(1:n_y*model.unique2);
+ cols=full(reshape(cols,n_y,model.unique2)*model.W{2});
+ cols=cols(model.tildy2nd_ind);
+ cols=cols(:);
+ vals=2*ones(n_s,length(rows));
+ gxx__theta=sptensor(rows,cols,vals,model.n_tildy2nd,n_theta*factor);
+ end
+ gx__theta=vconcat(gxx__theta,gx__theta);
+ g_theta=vconcat(gx__theta,g_theta); % derivatives and levels
+ if order>=1
+ if order==1
+ gx_x_theta=sptensor(model.n_tildy1st,[n_x,n_theta*factor],n_s);
+ else
+ rows=1:model.n_tildy1st*n_x;
+ cols=n_y+n_y*n_x+(1:n_y*model.unique2);
+ cols=full(reshape(cols,n_y,model.unique2)*model.W{2});
+ cols=reshape(cols,n_y*n_x,n_x);
+ cols=cols(model.tildy1st_ind,:);
+ [rows1,rows2]=ind2sub([model.n_tildy1st,n_x],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=2*ones(n_s,length(rows));
+ gx_x_theta=sptensor(rows,cols,vals,model.n_tildy1st,[n_x,n_theta*factor]);
+ end
+ if order<=2
+ gxx_x_theta=sptensor(model.n_tildy2nd,[n_x,n_theta*factor],n_s);
+ else
+ rows=1:model.n_tildy2nd*n_x;
+ rows=rows(:);
+ cols=n_y+n_y*n_x+n_y*model.unique2+(1:n_y*model.unique3);
+ cols=full(reshape(cols,n_y,model.unique3)*model.W{3});
+ cols=reshape(cols,n_y*n_x^2,n_x);
+ cols=cols(model.tildy2nd_ind,:);
+ cols=cols(:);
+ [rows1,rows2]=ind2sub([model.n_tildy2nd,n_x],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=6*ones(n_s,length(rows));
+ gxx_x_theta=sptensor(rows,cols,vals,model.n_tildy2nd,[n_x,n_theta*factor]);
+ end
+ gx_x_theta=vconcat(gxx_x_theta,gx_x_theta);
+ gx_theta=vconcat(gx_x_theta,gx_theta);
+ end
+ if order>=2
+ if order==2
+ gx_xxc_theta=sptensor(model.n_tildy1st,[model.unique2,n_theta*factor],n_s);
+ else
+ rows=1:model.n_tildy1st*model.unique2;
+ cols=n_y+n_y*n_x+n_y*model.unique2+(1:n_y*model.unique3);
+ cols=full(reshape(cols,n_y,model.unique3)*model.W{3});
+ cols=reshape(cols,n_y*n_x,n_x^2);
+ cols=cols(model.tildy1st_ind,:);
+ cols=full(cols*model.U{2});
+
+ [rows1,rows2]=ind2sub([model.n_tildy1st,model.unique2],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=6*ones(n_s,length(rows));
+ gx_xxc_theta=sptensor(rows,cols,vals,model.n_tildy1st,[model.unique2,n_theta*factor]);
+ end
+ if order<=3
+ gxx_xxc_theta=sptensor(model.n_tildy2nd,[model.unique2,n_theta*factor],n_s);
+ else
+ rows=1:model.n_tildy2nd*model.unique2;
+ rows=rows(:);
+ cols=n_y+n_y*n_x+n_y*model.unique2+n_y*model.unique3+(1:n_y*model.unique4);
+ cols=full(reshape(cols,n_y,model.unique4)*model.W{4});
+ cols=full(reshape(cols,n_y*n_x^2,n_x^2)*model.U{2});
+ cols=cols(model.tildy2nd_ind,:);
+ cols=cols(:);
+ [rows1,rows2]=ind2sub([model.n_tildy2nd,model.unique2],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=24*ones(n_s,length(rows));
+ gxx_xxc_theta=sptensor(rows,cols,vals,model.n_tildy2nd,[model.unique2,n_theta*factor]);
+ end
+ gx_xxc_theta=vconcat(gxx_xxc_theta,gx_xxc_theta);
+ gxxc_theta=vconcat(gx_xxc_theta,gxxc_theta);
+ end
+ if order>=3
+ if order==3
+ gx_xxxc_theta=sptensor(model.n_tildy1st,[model.unique3,n_theta*factor],n_s);
+ else
+ rows=1:model.n_tildy1st*model.unique3;
+ cols=n_y+n_y*(n_x+model.unique2+model.unique3)+(1:n_y*model.unique4);
+ cols=full(reshape(cols,n_y,model.unique4)*model.W{4});
+ cols=reshape(cols,n_y*n_x,n_x^3);
+ cols=cols(model.tildy1st_ind,:);
+ cols=full(cols*model.U{3});
+
+ [rows1,rows2]=ind2sub([model.n_tildy1st,model.unique3],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=24*ones(n_s,length(rows));
+ gx_xxxc_theta=sptensor(rows,cols,vals,model.n_tildy1st,[model.unique3,n_theta*factor]);
+ end
+ if order<=4
+ gxx_xxxc_theta=sptensor(model.n_tildy2nd,[model.unique3,n_theta*factor],n_s);
+ else
+ error('order cannot exceed 4')
+ end
+ gx_xxxc_theta=vconcat(gxx_xxxc_theta,gx_xxxc_theta);
+ gxxxc_theta=vconcat(gx_xxxc_theta,gxxxc_theta);
+ end
+ if order>=4
+ if order==4
+ gx_xxxxc_theta=sptensor(model.n_tildy1st,[model.unique4,n_theta*factor],n_s);
+ gxx_xxxxc_theta=sptensor(model.n_tildy2nd,[model.unique4,n_theta*factor],n_s);
+ else
+ error('order cannot exceed 4')
+ end
+ gx_xxxxc_theta=vconcat(gxx_xxxxc_theta,gx_xxxxc_theta);
+ gxxxxc_theta=vconcat(gx_xxxxc_theta,gxxxxc_theta);
+ end
+ if model.pde>=2
+ if model.pde==2
+ AmatT=feval('AmatT_d1',zeros(n_s,n_y*(1+n_x)),params,model.Amat_ind);
+ elseif model.pde==3
+ AmatT=feval('AmatT_d1',zeros(n_s,n_y+model.n_tildy1st+model.n_tildy2nd),params,model.Amat_ind);
+ end
+ g_theta=contraction1(AmatT,g_theta);
+ if order>=1
+ gx_theta=contraction1(AmatT,unfold(gx_theta));
+ gx_theta=fold(gx_theta,n_x,n_theta*factor);
+ end
+ if order>=2
+ gxxc_theta=contraction1(AmatT,unfold(gxxc_theta));
+ gxxc_theta=fold(gxxc_theta,model.unique2,n_theta*factor);
+ end
+ if order>=3
+ gxxxc_theta=contraction1(AmatT,unfold(gxxxc_theta));
+ gxxxc_theta=fold(gxxxc_theta,model.unique3,n_theta*factor);
+ end
+ if order>=4
+ gxxxxc_theta=contraction1(AmatT,unfold(gxxxxc_theta));
+ gxxxxc_theta=fold(gxxxxc_theta,model.unique4,n_theta*factor);
+ end
+ end
+elseif model.pde>=1 % compute derivatives of dy w.r.t x and theta
+ factor=ms+1;
+ if order==0
+ gx__theta=sptensor(n_y*n_x,n_theta*factor,n_s);
+ else
+ rows=1:n_y*n_x;
+ rows=rows(:);
+ cols=n_y+(1:n_y*n_x);
+ cols=cols(:);
+ vals=ones(n_s,length(rows));
+ gx__theta=sptensor(rows,cols,vals,n_y*n_x,n_theta*factor);
+ end
+ g_theta=vconcat(gx__theta,g_theta); % derivatives and levels
+ if order>=1
+ if order==1
+ gx_x_theta=sptensor(n_y*n_x,[n_x,n_theta*factor],n_s);
+ else
+ rows=1:n_y*n_x^2;
+ cols=n_y+n_y*n_x+(1:n_y*model.unique2);
+ cols=full(reshape(cols,n_y,model.unique2)*model.W{2});
+ [rows1,rows2]=ind2sub([n_y*n_x,n_x],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=2*ones(n_s,length(rows));
+ gx_x_theta=sptensor(rows,cols,vals,n_y*n_x,[n_x,n_theta*factor]);
+ end
+ gx_theta=vconcat(gx_x_theta,gx_theta);
+ end
+ if order>=2
+ if order==2
+ gx_xxc_theta=sptensor(n_y*n_x,[model.unique2,n_theta*factor],n_s);
+ else
+ rows=1:n_y*n_x*model.unique2;
+ cols=n_y+n_y*n_x+n_y*model.unique2+(1:n_y*model.unique3);
+ cols=full(reshape(cols,n_y,model.unique3)*model.W{3});
+ cols=reshape(cols,n_y*n_x,n_x^2);
+ cols=full(cols*model.U{2});
+
+ [rows1,rows2]=ind2sub([n_y*n_x,model.unique2],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=6*ones(n_s,length(rows));
+ gx_xxc_theta=sptensor(rows,cols,vals,n_y*n_x,[model.unique2,n_theta*factor]);
+ end
+ gxxc_theta=vconcat(gx_xxc_theta,gxxc_theta);
+ end
+ if order>=3
+ if order==3
+ gx_xxxc_theta=sptensor(n_y*n_x,[model.unique3,n_theta*factor],n_s);
+ else
+ rows=1:n_y*n_x*model.unique3;
+ cols=n_y+n_y*(n_x+model.unique2+model.unique3)+(1:n_y*model.unique4);
+ cols=full(reshape(cols,n_y,model.unique4)*model.W{4});
+ cols=reshape(cols,n_y*n_x,n_x^3);
+ cols=full(cols*model.U{3});
+
+ [rows1,rows2]=ind2sub([n_y*n_x,model.unique3],rows(:));
+ rows=rows1(:);
+ cols=[rows2(:),cols(:)];
+ vals=24*ones(n_s,length(rows));
+ gx_xxxc_theta=sptensor(rows,cols,vals,n_y*n_x,[model.unique3,n_theta*factor]);
+ end
+ gxxxc_theta=vconcat(gx_xxxc_theta,gxxxc_theta);
+ end
+ if order>=4
+ if order==4
+ gx_xxxxc_theta=sptensor(n_y*n_x,[model.unique4,n_theta*factor],n_s);
+ else
+ error('order cannot exceed 4')
+ end
+ gxxxxc_theta=vconcat(gx_xxxxc_theta,gxxxxc_theta);
+ end
+ if model.pde==2
+ AmatT=feval('AmatT_d1',zeros(n_s,n_y*(1+n_x)),params,model.Amat_ind);
+
+ g_theta=contraction1(AmatT,g_theta);
+ if order>=1
+ gx_theta=contraction1(AmatT,unfold(gx_theta));
+ gx_theta=fold(gx_theta,n_x,n_theta*factor);
+ end
+ if order>=2
+ gxxc_theta=contraction1(AmatT,unfold(gxxc_theta));
+ gxxc_theta=fold(gxxc_theta,model.unique2,n_theta*factor);
+ end
+ if order>=3
+ gxxxc_theta=contraction1(AmatT,unfold(gxxxc_theta));
+ gxxxc_theta=fold(gxxxc_theta,model.unique3,n_theta*factor);
+ end
+ if order>=4
+ gxxxxc_theta=contraction1(AmatT,unfold(gxxxxc_theta));
+ gxxxxc_theta=fold(gxxxxc_theta,model.unique4,n_theta*factor);
+ end
+ end
+end
+% lower block of v_theta, vx_theta and so on
+v_theta_lower_terms=vconcat(vconcat(g_theta,h_theta),sptensor(n_x,(ms+1)*n_theta,n_s));
+if order>=1
+ vx_theta_lower_terms=vconcat(vconcat(gx_theta,hx_theta),sptensor(n_x,[n_x,(ms+1)*n_theta],n_s));
+end
+if order>=2
+ unique2=model.unique2;
+ vxxc_theta_lower_terms=vconcat(vconcat(gxxc_theta,hxxc_theta),sptensor(n_x,[unique2,(ms+1)*n_theta],n_s));
+end
+if order>=3
+ unique3=model.unique3;
+ vxxxc_theta_lower_terms=vconcat(vconcat(gxxxc_theta,hxxxc_theta),sptensor(n_x,[unique3,(ms+1)*n_theta],n_s));
+end
+if order>=4
+ unique4=model.unique4;
+ vxxxxc_theta_lower_terms=vconcat(vconcat(gxxxxc_theta,hxxxxc_theta),sptensor(n_x,[unique4,(ms+1)*n_theta],n_s));
+end
+
+
+
+% current state
+nx=x0vec;
+
+% evaluate policy functions
+% if model.pde==2
+% n_y=model.n_tily;
+% end
+
+g=coeffs(:,1:n_y,1);% only constant term is nonzero
+h1=coeffs(:,n_y+1:end,1);
+h=zeros(n_s,n_x);
+
+% derivatives of policy functions at x0 (assuming c0=x0)
+if order>=1
+ gx=coeffs(:,1:n_y,2:1+n_x);
+ if model.pde==3
+ if order==1
+ gx_x=sptensor(model.n_tildy1st,n_x,n_s);
+ gxx_x=sptensor(model.n_tildy2nd,n_x,n_s);
+ gx_x=vconcat(gxx_x,gx_x);
+ end
+ elseif model.pde>=1
+ if order==1
+ gx_x=sptensor(n_y*n_x,n_x,n_s);
+ end
+ end
+ tempT=sptensor(reshape(gx(1,:,:),n_y,n_x));
+ tempT.vals=reshape(permute(gx,[1,3,2]),n_s,n_x*n_y); % permute is needed because tensors are in row format
+ gx=tempT;
+
+
+ h1x=coeffs(:,n_y+1:end,2:1+n_x);
+ tempT=sptensor(reshape(h1x(1,:,:),n_x1,n_x));
+ tempT.vals=reshape(permute(h1x,[1,3,2]),n_s,n_x*n_x1); % permute is needed because tensors are in row format
+ h1x=tempT;
+end
+
+if order>=2
+ gxxc=coeffs(:,1:n_y,2+n_x:1+n_x+unique2)*2;
+ if model.pde==3
+ gx_x=full(reshape(gxxc,n_s*n_y,unique2)*model.W{2});
+ gx_x=reshape(gx_x,n_s,n_y*n_x,n_x);
+ gx_x=gx_x(:,model.tildy1st_ind,:);
+ tempT=sptensor(reshape(gx_x(1,:,:),model.n_tildy1st,n_x));
+ tempT.vals=reshape(permute(gx_x,[1,3,2]),n_s,n_x*model.n_tildy1st); % permute is needed because tensors are in row format
+ gx_x=tempT;
+ if order==2
+ gx_xxc=sptensor(model.n_tildy1st,unique2,n_s);
+ gxx_x=sptensor(model.n_tildy2nd,n_x,n_s);
+ gxx_xxc=sptensor(model.n_tildy2nd,unique2,n_s);
+ gx_x=vconcat(gxx_x,gx_x);
+ gx_xxc=vconcat(gxx_xxc,gx_xxc);
+
+ end
+ elseif model.pde>=1
+ gx_x=full(reshape(gxxc,n_s*n_y,unique2)*model.W{2});
+ gx_x=reshape(gx_x,n_s,n_y*n_x,n_x);
+ tempT=sptensor(reshape(gx_x(1,:,:),n_y*n_x,n_x));
+ tempT.vals=reshape(permute(gx_x,[1,3,2]),n_s,n_x*n_y*n_x); % permute is needed because tensors are in row format
+ gx_x=tempT;
+ if order==2
+ gx_xxc=sptensor(n_y*n_x,unique2,n_s);
+ end
+ end
+ tempT=sptensor(reshape(gxxc(1,:,:),n_y,unique2));
+ tempT.vals=reshape(permute(gxxc,[1,3,2]),n_s,unique2*n_y); % permute is needed because tensors are in row format
+ gxxc=tempT;
+
+ h1xxc=coeffs(:,n_y+1:end,2+n_x:1+n_x+unique2)*2;
+ tempT=sptensor(reshape(h1xxc(1,:,:),n_x1,unique2));
+ tempT.vals=reshape(permute(h1xxc,[1,3,2]),n_s,unique2*n_x1); % permute is needed because tensors are in row format
+ h1xxc=tempT;
+end
+if order>=3
+ gxxxc=coeffs(:,1:n_y,2+n_x+unique2:1+n_x+unique2+unique3)*6;
+ if model.pde==3
+ gx_xx=full(reshape(gxxxc,n_s*n_y,unique3)*model.W{3});
+ gx_xx=reshape(gx_xx,n_s*n_y*n_x,n_x^2);
+ gx_xxc=full(gx_xx*model.U{2});
+ gx_xxc=reshape(gx_xxc,n_s,n_y*n_x,unique2);
+ gx_xxc=gx_xxc(:,model.tildy1st_ind,:);
+ tempT=sptensor(reshape(gx_xxc(1,:,:),model.n_tildy1st,unique2));
+ tempT.vals=reshape(permute(gx_xxc,[1,3,2]),n_s,unique2*model.n_tildy1st); % permute is needed because tensors are in row format
+ gx_xxc=tempT;
+
+ gxx_x=full(reshape(gxxxc,n_s*n_y,unique3)*model.W{3});
+ gxx_x=reshape(gxx_x,n_s,n_y*n_x^2,n_x);
+ gxx_x=gxx_x(:,model.tildy2nd_ind,:);
+ tempT=sptensor(reshape(gxx_x(1,:,:),model.n_tildy2nd,n_x));
+ tempT.vals=reshape(permute(gxx_x,[1,3,2]),n_s,n_x*model.n_tildy2nd); % permute is needed because tensors are in row format
+ gxx_x=tempT;
+
+ if order==3
+ gx_xxxc=sptensor(model.n_tildy1st,unique3,n_s);
+ gxx_xxc=sptensor(model.n_tildy2nd,unique2,n_s);
+ gxx_xxxc=sptensor(model.n_tildy2nd,unique3,n_s);
+ gx_x=vconcat(gxx_x,gx_x);
+ gx_xxc=vconcat(gxx_xxc,gx_xxc);
+ gx_xxxc=vconcat(gxx_xxxc,gx_xxxc);
+ end
+ elseif model.pde>=1
+ gx_xx=full(reshape(gxxxc,n_s*n_y,unique3)*model.W{3});
+ gx_xxc=full(reshape(gx_xx,n_s*n_y*n_x,n_x^2)*model.U{2});
+ gx_xxc=reshape(gx_xxc,n_s,n_y*n_x,unique2);
+ tempT=sptensor(reshape(gx_xxc(1,:,:),n_y*n_x,unique2));
+ tempT.vals=reshape(permute(gx_xxc,[1,3,2]),n_s,unique2*n_y*n_x); % permute is needed because tensors are in row format
+ gx_xxc=tempT;
+ if order==3
+ gx_xxxc=sptensor(n_y*n_x,unique3,n_s);
+ end
+ end
+ tempT=sptensor(reshape(gxxxc(1,:,:),n_y,unique3));
+ tempT.vals=reshape(permute(gxxxc,[1,3,2]),n_s,unique3*n_y); % permute is needed because tensors are in row format
+ gxxxc=tempT;
+
+ h1xxxc=coeffs(:,n_y+1:end,2+n_x+unique2:1+n_x+unique2+unique3)*6;
+ tempT=sptensor(reshape(h1xxxc(1,:,:),n_x1,unique3));
+ tempT.vals=reshape(permute(h1xxxc,[1,3,2]),n_s,unique3*n_x1); % permute is needed because tensors are in row format
+ h1xxxc=tempT;
+end
+if order>=4
+ gxxxxc=coeffs(:,1:n_y,2+n_x+unique2+unique3:1+n_x+unique2+unique3+unique4)*24;
+ if model.pde==3
+ gx_xxx=full(reshape(gxxxxc,n_s*n_y,unique4)*model.W{4});
+ gx_xxx=reshape(gx_xxx,n_s*n_y*n_x,n_x^3);
+ gx_xxxc=full(gx_xxx*model.U{3});
+ gx_xxxc=reshape(gx_xxxc,n_s,n_y*n_x,unique3);
+ gx_xxxc=gx_xxxc(:,model.tildy1st_ind,:);
+ tempT=sptensor(reshape(gx_xxxc(1,:,:),model.n_tildy1st,unique3));
+ tempT.vals=reshape(permute(gx_xxxc,[1,3,2]),n_s,unique3*model.n_tildy1st); % permute is needed because tensors are in row format
+ gx_xxxc=tempT;
+
+ gxx_xx=full(reshape(gxxxxc,n_s*n_y,unique4)*model.W{4});
+ gxx_xx=reshape(gxx_xx,n_s*n_y*n_x^2,n_x^2);
+ gxx_xxc=full(gxx_xx*model.U{2});
+ gxx_xxc=reshape(gxx_xxc,n_s,n_y*n_x^2,unique2);
+ gxx_xxc=gxx_xxc(:,model.tildy2nd_ind,:);
+ tempT=sptensor(reshape(gxx_xxc(1,:,:),model.n_tildy2nd,unique2));
+ tempT.vals=reshape(permute(gxx_xxc,[1,3,2]),n_s,unique2*model.n_tildy2nd); % permute is needed because tensors are in row format
+ gxx_xxc=tempT;
+
+ if order==4
+ gx_xxxxc=sptensor(model.n_tildy1st,unique4,n_s);
+ gxx_xxxc=sptensor(model.n_tildy2nd,unique3,n_s);
+ gxx_xxxxc=sptensor(model.n_tildy2nd,unique4,n_s);
+ gx_x=vconcat(gxx_x,gx_x);
+ gx_xxc=vconcat(gxx_xxc,gx_xxc);
+ gx_xxxc=vconcat(gxx_xxxc,gx_xxxc);
+ gx_xxxxc=vconcat(gxx_xxxxc,gx_xxxxc);
+ end
+ elseif model.pde>=1
+ gx_xxx=full(reshape(gxxxxc,n_s*n_y,unique4)*model.W{4});
+ gx_xxxc=full(reshape(gx_xxx,n_s*n_y*n_x,n_x^3)*model.U{3});
+ gx_xxxc=reshape(gx_xxxc,n_s,n_y*n_x,unique3);
+ tempT=sptensor(reshape(gx_xxxc(1,:,:),n_y*n_x,unique3));
+ tempT.vals=reshape(permute(gx_xxxc,[1,3,2]),n_s,unique3*n_y*n_x); % permute is needed because tensors are in row format
+ gx_xxxc=tempT;
+ if order==4
+ gx_xxxxc=sptensor(n_y*n_x,unique4,n_s);
+ end
+ end
+ tempT=sptensor(reshape(gxxxxc(1,:,:),n_y,unique4));
+ tempT.vals=reshape(permute(gxxxxc,[1,3,2]),n_s,unique4*n_y); % permute is needed because tensors are in row format
+ gxxxxc=tempT;
+
+ h1xxxxc=coeffs(:,n_y+1:end,2+n_x+unique2+unique3:1+n_x+unique2+unique3+unique4)*24;
+ tempT=sptensor(reshape(h1xxxxc(1,:,:),n_x1,unique4));
+ tempT.vals=reshape(permute(h1xxxxc,[1,3,2]),n_s,unique4*n_x1); % permute is needed because tensors are in row format
+ h1xxxxc=tempT;
+end
+% control vars
+if model.pde==0
+ ny=g;
+elseif model.pde==3
+ if order==0
+ ny=full([zeros(1,model.n_tildy2nd+model.n_tildy1st),g]);
+ elseif order==1
+ temp=reshape(permute(reshape(gx.vals,n_s,n_x,n_y),[1,3,2]),n_s,n_y*n_x);
+ temp=temp(:,model.tildy1st_ind);
+ ny=full([zeros(n_s,model.n_tildy2nd),temp,g]);
+ elseif order>=2
+ temp1=reshape(permute(reshape(gx.vals,n_s,n_x,n_y),[1,3,2]),n_s,n_y*n_x);
+ temp1=temp1(:,model.tildy1st_ind);
+ temp2=reshape(permute(reshape(gxxc.vals,n_s,unique2,n_y),[1,3,2]),n_s*n_y,unique2);
+ temp2=full(temp2*model.W{2});
+ temp2=reshape(temp2,n_s,n_y*n_x^2);
+ temp2=temp2(:,model.tildy2nd_ind);
+ ny=full([temp2,temp1,g]);
+ end
+else
+ if order==0
+ ny=full([zeros(1,n_y*n_x),g]);
+ else
+ ny=full([reshape(permute(reshape(gx.vals,n_s,n_x,n_y),[1,3,2]),n_s,n_y*n_x),g]);
+ end
+end
+
+if model.pde>=2
+% n_y=old_n_y;
+ tildy_tily=ny;
+ if model.pde==2
+ tildy_tilyT=sptensor(zeros(n_y*(1+n_x),1));
+ else
+ tildy_tilyT=sptensor(zeros(n_y+model.n_tildy1st+model.n_tildy2nd,1));
+ end
+ tildy_tilyT.vals=tildy_tily;
+ nyT=contraction1(AmatT,tildy_tilyT); % this is the vector of the original [dy;y]
+ ny=nyT.vals;
+end
+% STEP 1: COMPUTE NONSTOCHASTIC EQUATIONS AND DERIVATIVES, AND THEIR JACOBIAN
+
+% build h(x)
+h(:,1:n_x1,1)=h1; % predetermined endogenous state vars
+
+if model.hybrid==0
+ uname=['Phi' model.uname '_fun'];
+ h(:,n_x1+1:end,1)=feval(uname,nx,params); % expected value of exogenous state vars. shocks are added later
+
+ % derivatives of h at x0
+ if order>=1
+ hx=vconcat(h1x,Phi_d_c1(nx,params,model.Phi_indc));
+ end
+ if order>=2
+ hxxc=vconcat(h1xxc,Phi_d_c2(nx,params,model.Phi_indc));
+ end
+ if order>=3
+ hxxxc=vconcat(h1xxxc,Phi_d_c3(nx,params,model.Phi_indc));
+ end
+ if order>=4
+ hxxxxc=vconcat(h1xxxxc,Phi_d_c4(nx,params,model.Phi_indc));
+ end
+else
+ % derivatives of h at x0
+ if order>=1
+ hx=vconcat(h1x,sptensor(n_x2,n_x,n_s));
+ end
+ if order>=2
+ hxxc=vconcat(h1xxc,sptensor(n_x2,model.unique2,n_s));
+ end
+ if order>=3
+ hxxxc=vconcat(h1xxxc,sptensor(n_x2,model.unique3,n_s));
+ end
+ if order>=4
+ hxxxxc=vconcat(h1xxxxc,sptensor(n_x2,model.unique4,n_s));
+ end
+end
+
+% expected value of next period state variables.
+nxp=h;
+
+% evaluate residuals R0
+if model.pde==0
+ nv=[zeros(n_s,n_y),ny,nxp,nx]; % model variables, yp are zero for now, and nxp is an expected value. stochastic components will be added later.
+elseif model.pde==1
+ nv=[zeros(n_s,n_y*(n_x+1)),ny,nxp,nx];
+elseif model.pde>=2
+ nv=[zeros(n_s,model.n_y_extended),ny,nxp,nx];
+end
+
+n_u=model.n_u;
+nu=zeros(n_s,n_u);
+uname=['preu' model.uname '_fun'];
+npreu=feval(uname,nv(:,model.preuvars),params); % all predetermined u
+nu(:,model.preurows)=npreu;
+
+% This block is not necessary, because f is independent of x2p (they are treated
+% as auxiliary variables and substituted out)
+% if model.hybrid==1
+% nxp(:,n_x1+1:end)=nu(:,end-n_x2+1:end); % last block of auxiliary variables are the hybrid state variables
+% nv=[zeros(n_s,n_y),ny,nxp,nx];
+% end
+
+nz=[nv,nu]; % auxiliary variables
+params(:,model.logical_params_loc)=double(logical(nz(:,model.logical_zvars)>0));
+
+if isempty(model.prefrows)
+ preR0=sptensor(0,1,n_s);
+ preR1=sptensor(0,n_x,n_s);
+ preR2=sptensor(0,unique2,n_s);
+ preR3=sptensor(0,unique3,n_s);
+ preR4=sptensor(0,unique4,n_s);
+ preJ0=sptensor(0,(ms+1)*n_theta,n_s);
+ preJ1=sptensor(0,[n_x,(ms+1)*n_theta],n_s);
+ preJ2=sptensor(0,[unique2,(ms+1)*n_theta],n_s);
+ preJ3=sptensor(0,[unique3,(ms+1)*n_theta],n_s);
+ preJ4=sptensor(0,[unique4,(ms+1)*n_theta],n_s);
+
+ % compute variables that will be necessary later
+ uname=['prePI' model.uname '_d1'];
+
+ prePIz_full=feval(uname,nz,params,model.prePI_ind_u);
+ if order>=1
+ uname=['prePI' model.uname '_d2'];
+ prePIzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ vx=vconcat(sptensor(n_y,n_x,n_s),gx);
+ vx=vconcat(vx,hx);
+ vx=vconcat(vx,spteye(n_x,n_s));
+
+ end
+ if order>=2
+ uname=['prePI' model.uname '_d3'];
+ prePIzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ if ~isfield(model,'chain2c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,2);
+ U2=create_UW(n_x,2);
+ model.chain2c_theta_M2=spmat2sptensor(GAMMA.GAMMA1*U2);
+ clear GAMMA U2
+ end
+ vxxc=vconcat(sptensor(n_y,unique2,n_s),gxxc);
+ vxxc=vconcat(vxxc,hxxc);
+ vxxc=vconcat(vxxc,sptensor(n_x,unique2,n_s));
+ end
+ if order>=3
+ uname=['prePI' model.uname '_d4'];
+ prePIzzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ if ~isfield(model,'x_chain3c_M2')
+ [~,W2x]=create_UW(n_x,2);
+ [U3x,~]=create_UW(n_x,3);
+ OMEGAx=create_OMEGA(n_x,3);
+ model.x_chain3c_M2=spmat2sptensor(kron(speye(n_x),W2x)*OMEGAx.OMEGA1*U3x);
+ clear W2x U3x
+ end
+ if ~isfield(model,'chain3c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,3);
+ [~,W2]=create_UW(n_x,2);
+ U3=create_UW(n_x,3);
+ model.chain3c_theta_M2=spmat2sptensor(kron(W2,speye(n_x))*GAMMA.GAMMA2*U3);
+ model.chain3c_theta_M3=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA3*U3);
+ model.chain3c_theta_M4=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA4*U3);
+ tempind=1:unique2*n_x;
+ tempmat=speye(unique2*n_x);
+ model.chain3c_theta_M5=spmat2sptensor(tempmat(:,permute(reshape(tempind,n_x,unique2),[2,1]))*kron(speye(n_x),W2)*GAMMA.GAMMA5*U3);
+ clear GAMMA W2 U3 GAMMA
+
+ end
+ vxxxc=vconcat(sptensor(n_y,unique3,n_s),gxxxc);
+ vxxxc=vconcat(vxxxc,hxxxc);
+ vxxxc=vconcat(vxxxc,sptensor(n_x,unique3,n_s));
+
+ end
+ if order>=4
+ uname=['prePI' model.uname '_d5'];
+ prePIzzzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ if ~isfield(model,'x_chain3c_M2')
+ [~,W2x]=create_UW(n_x,2);
+ [U3x,~]=create_UW(n_x,3);
+ OMEGAx=create_OMEGA(n_x,3);
+ model.x_chain3c_M2=spmat2sptensor(kron(speye(n_x),W2x)*OMEGAx.OMEGA1*U3x);
+ clear W2x U3x
+ end
+ if ~isfield(model,'chain3c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,3);
+ [~,W2]=create_UW(n_x,2);
+ U3=create_UW(n_x,3);
+ model.chain3c_theta_M2=spmat2sptensor(kron(W2,speye(n_x))*GAMMA.GAMMA2*U3);
+ model.chain3c_theta_M3=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA3*U3);
+ model.chain3c_theta_M4=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA4*U3);
+ tempind=1:unique2*n_x;
+ tempmat=speye(unique2*n_x);
+ model.chain3c_theta_M5=spmat2sptensor(tempmat(:,permute(reshape(tempind,n_x,unique2),[2,1]))*kron(speye(n_x),W2)*GAMMA.GAMMA5*U3);
+ clear GAMMA W2 U3 GAMMA
+
+ end
+ vxxxxc=vconcat(sptensor(n_y,unique4,n_s),gxxxxc);
+ vxxxxc=vconcat(vxxxxc,hxxxxc);
+ vxxxxc=vconcat(vxxxxc,sptensor(n_x,unique4,n_s));
+
+ end
+% v_theta=[];
+ v_theta=sptensor(0,(ms+1)*n_theta,n_s);
+ if model.hybrid==3
+ v_theta=vconcat(sptensor(n_y,(ms+1)*n_theta,n_s),v_theta_lower_terms);
+ if order>=1
+ vx_theta=vconcat(sptensor(n_y,[n_x,(ms+1)*n_theta],n_s),vx_theta_lower_terms);
+ end
+ if order>=2
+ vxxc_theta=vconcat(sptensor(n_y,[unique2,(ms+1)*n_theta],n_s),vxxc_theta_lower_terms);
+ end
+ if order>=3
+ vxxxc_theta=vconcat(sptensor(n_y,[unique3,(ms+1)*n_theta],n_s),vxxxc_theta_lower_terms);
+ end
+ if order>=4
+ vxxxxc_theta=vconcat(sptensor(n_y,[unique4,(ms+1)*n_theta],n_s),vxxxxc_theta_lower_terms);
+ if ~isfield(model,'x_chain4c_M2')
+ [~,W2new]=create_UW(unique2,2);
+ [~,W2x]=create_UW(n_x,2);
+ [~,W3x]=create_UW(n_x,3);
+ [U4x,~]=create_UW(n_x,4);
+ OMEGAx=create_OMEGA(n_x,4);
+ model.x_chain4c_M2=spmat2sptensor(kron(W2x,W2x)*OMEGAx.OMEGA2*U4x);
+ model.x_chain4c_M3=spmat2sptensor(kron(speye(n_x),W3x)*OMEGAx.OMEGA3*U4x);
+ model.x_chain4c_M4=spmat2sptensor(W2new*kron(W2x,W2x)*OMEGAx.OMEGA4*U4x);
+ clear W2new W2x W3x U4x OMEGAx
+ end
+ if ~isfield(model,'chain4c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,4);
+ [~,W2]=create_UW(n_x,2);
+ [~,W3]=create_UW(n_x,3);
+ U4=create_UW(n_x,4);
+ [~,W2new]=create_UW(unique2,2);
+ model.chain4c_theta_M2=spmat2sptensor(kron(W3,speye(n_x))*GAMMA.GAMMA16*U4);
+ model.chain4c_theta_M3=spmat2sptensor(kron(W2,W2)*GAMMA.GAMMA2*U4);
+ model.chain4c_theta_M5=spmat2sptensor(kron(speye(n_x^2),W2)*GAMMA.GAMMA17*GAMMA.GAMMA2*U4);
+ model.chain4c_theta_M6=spmat2sptensor(kron(speye(n_x),W3)*GAMMA.GAMMA3*U4);
+ model.chain4c_theta_M9=spmat2sptensor(W2new*kron(W2,W2)*GAMMA.GAMMA4*U4);
+ model.chain4c_theta_M10=spmat2sptensor(kron(W2,W2)*GAMMA.GAMMA18*GAMMA.GAMMA4*U4);
+
+ clear GAMMA W2 W3 U4 W2new
+
+ end
+ end
+ end
+
+ totindi=5+8;
+ totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+ totindi=totindi+3;
+ totindi=totindi+4;
+
+ indi=totindi;
+else
+
+ fname=['pretilf' model.fname '_fun'];
+ pref=feval(fname,nz(:,model.pretilfzvars),params); % since i already have z, i use pretilf to evaluate f.
+
+
+ % compute derivatives of prePI and pretilf w.r.t z (prePI=nonstochastic rows of PI, pretilf=nonstochastic rows of f)
+ uname=['prePI' model.uname '_d1'];
+ prePIz_full=feval(uname,nz,params,model.prePI_ind_u);
+
+ fname=['pretilf' model.fname '_tilf_d1'];
+ pretilfz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ if order>=1
+ uname=['prePI' model.uname '_d2'];
+ prePIzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d2'];
+ pretilfzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+ if order>=2
+ uname=['prePI' model.uname '_d3'];
+ prePIzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d3'];
+ pretilfzzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+ if order>=3
+ uname=['prePI' model.uname '_d4'];
+ prePIzzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d4'];
+ pretilfzzzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+ if order>=4
+ uname=['prePI' model.uname '_d5'];
+ prePIzzzzz_full=feval(uname,nz,params,model.prePI_ind_u);
+ fname=['pretilf' model.fname '_tilf_d5'];
+ pretilfzzzzz=feval(fname,[nv(:,prefvars),nu(:,model.prefuvars)],params,model.pretilf_ind_u);
+ end
+
+ % extract derivatives of prePI w.r.t v from prePIz, prePIzz, ...
+ if order>=0
+ [prePIz,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=extract(prePIz_full,model.prefzvars,model.prefvars,0,model.ind{indi});
+ indi=indi+1;
+ end
+ if order>=1
+ [prePIzz,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=extract(prePIzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ end
+ if order>=2
+ [prePIzzz,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=extract(prePIzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain3c_M2')
+ [ tempM ] = chainsM( n_prefvars,3 );
+ model.prefvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+ end
+ if order>=3
+ [prePIzzzz,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefzvars,0,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=extract(prePIzzzz_full,model.prefzvars,model.prefvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'prefvars_chain4c_M2')
+ [ tempM ] = chainsM( n_prefvars,4 );
+ model.prefvars_chain4c_M2=tempM{2};
+ model.prefvars_chain4c_M3=tempM{3};
+ model.prefvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+ end
+ if order>=4
+ [prePIzzzzz,model.ind4{indi4}]=extract(prePIzzzzz_full,model.prefzvars,model.prefzvars,0,model.ind4{indi4});
+ indi4=indi4+1;
+ [prePIvvvvvc,model.ind4{indi4}]=extract(prePIzzzzz_full,model.prefzvars,model.prefvars,1,model.ind4{indi4});
+ indi4=indi4+1;
+ end
+
+ % Use high order chain rules to compute derivatives of prePI w.r.t v
+ totindi=5+8;
+ if order==0
+ indi=totindi;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ model.prefv=prefv;
+ elseif order==1
+ indi=totindi+model.count_pre_n*(1)+1;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ model.prefv=prefv;
+ model.prefvv=prefvv;
+
+ elseif order==2
+ indi=totindi+model.count_pre_n*(1+3)+1+4;
+ for i=2:model.pre_n
+% tic
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+% toc
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ model.prefv=prefv;
+ model.prefvv=prefvv;
+ model.prefvvv=prefvvv;
+
+ elseif order==3
+ indi=totindi+model.count_pre_n*(1+3+4)+1+4+6;
+% tic
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvc,model.ind{indi}]=chain4c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+% toc
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvvc,model.ind{indi}]=chain4c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvv,model.ind{indi} ] = uncompressderivs( prefvvvvc,4,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ model.prefv=prefv;
+ model.prefvv=prefvv;
+ model.prefvvv=prefvvv;
+ model.prefvvvv=prefvvvv;
+
+
+ elseif order==4
+ indi=totindi+model.count_pre_n*(1+3+4)+1+4+6;
+ for i=2:model.pre_n
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+ [prePIvvvvvc,model.ind4{indi4}]=chain5c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,prePIzzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,prePIvvvvvc,...
+ model.prefvars_chain5c_M1,model.prefvars_chain5c_M2,model.prefvars_chain5c_M3,model.prefvars_chain5c_M4,model.prefvars_chain5c_M5,model.prefvars_chain5c_M6,...
+ model.ind4{indi4},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi4=indi4+1;
+ [prePIvvvvc,model.ind{indi}]=chain4c_tensor(prePIz,prePIzz,prePIzzz,prePIzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.prezz,model.maxzz);
+ indi=indi+1;
+ [prePIvvvc,model.ind{indi}]=chain3c_tensor(prePIz,prePIzz,prePIzzz,...
+ prePIv,prePIvvc,prePIvvvc,model.prefvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=chain2c_tensor(prePIz,prePIzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prePIv,model.ind{indi}]=chain1_tensor(prePIz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [prePIv,model.ind{indi}]=colsort(prePIv,model.ind{indi});
+ indi=indi+1;
+ [prePIvvc,model.ind{indi}]=colsort(prePIvvc,model.ind{indi});
+ indi=indi+1;
+
+ [prefv,model.ind{indi}]=chain1_tensor(pretilfz,prePIv,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [prefvvc,model.ind{indi}]=chain2c_tensor(pretilfz,pretilfzz,prePIv,prePIvvc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvc,model.ind{indi}]=chain3c_tensor(pretilfz,pretilfzz,pretilfzzz,...
+ prePIv,prePIvvc,prePIvvvc,...
+ model.prefvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [prefvvvvc,model.ind{indi}]=chain4c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,...
+ model.prefvars_chain4c_M2,model.prefvars_chain4c_M3,model.prefvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi=indi+1;
+
+ [prefvvvvvc,model.ind4{indi4}]=chain5c_tensor(pretilfz,pretilfzz,pretilfzzz,pretilfzzzz,pretilfzzzzz,...
+ prePIv,prePIvvc,prePIvvvc,prePIvvvvc,prePIvvvvvc,...
+ model.prefvars_chain5c_M1,model.prefvars_chain5c_M2,model.prefvars_chain5c_M3,model.prefvars_chain5c_M4,model.prefvars_chain5c_M5,model.prefvars_chain5c_M6,...
+ model.ind4{indi4},n_ind,maxload,'vec',model.pretilfz,model.maxtilfz);
+ indi4=indi4+1;
+
+ [ prefvv,model.ind{indi} ] = uncompressderivs( prefvvc,2,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvv,model.ind{indi} ] = uncompressderivs( prefvvvc,3,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvv,model.ind{indi} ] = uncompressderivs( prefvvvvc,4,n_prefvars,model.fv(model.prefrows,prefvars),model.ind{indi} );
+ indi=indi+1;
+
+ [ prefvvvvv,model.ind4{indi4} ] = uncompressderivs( prefvvvvvc,5,n_prefvars,model.fv(model.prefrows,prefvars),model.ind4{indi4} );
+ indi4=indi4+1;
+
+ model.prefv=prefv;
+ model.prefvv=prefvv;
+ model.prefvvv=prefvvv;
+ model.prefvvvv=prefvvvv;
+
+ end
+ totindi=totindi+model.count_pre_n*(1+3+4+6)+1+4+6+9;
+ indi=totindi;
+
+ if model.steady_state==1
+ if size(prefv.vals,1)~=1
+ error('cannot compute steady state on vectorized tensors')
+ end
+ nzprefv=prefv;
+ nzprefv.vals(:)=1;
+ nzprefv=sptensor2spmat(nzprefv);
+ nzprefv_full=zeros(n_prefrows,model.n_v);
+ nzprefv_full(:,model.prefvars)=full(nzprefv);
+ nzprefv_full(:,2*model.n_y+(1:model.n_x1))=nzprefv_full(:,2*model.n_y+(1:model.n_x1))+nzprefv_full(:,2*model.n_y+model.n_x+(1:model.n_x1));
+ nzprefv=nzprefv_full(:,model.prefvars);
+ [i,j]=find(nzprefv);
+
+ prefv=sptensor2spmat(prefv);
+ prefv_full=zeros(n_prefrows,model.n_v);
+ prefv_full(:,model.prefvars)=full(prefv);
+ prefv_full(:,2*model.n_y+(1:model.n_x1))=prefv_full(:,2*model.n_y+(1:model.n_x1))+prefv_full(:,2*model.n_y+model.n_x+(1:model.n_x1));
+ prefv=prefv_full(:,model.prefvars);
+
+ vals=prefv(logical(nzprefv(:)));
+
+ prefv=sptensor(i(:),j(:),vals(:)',size(prefv,1),size(prefv,2));
+ end
+
+ tempT=sptensor(zeros(n_prefrows,1));
+ tempT.vals=full(pref); % n_s,n_prefrows
+ preR0=tempT;
+
+ % compute R1 (first order derivatives of R w.r.t x)
+ if order>=1
+ if model.pde==0
+ vx=vconcat(sptensor(n_y,n_x,n_s),gx);
+ elseif model.pde==1
+ vx=vconcat(sptensor(n_y*(n_x+1),n_x,n_s),gx_x);
+ vx=vconcat(vx,gx);
+ elseif model.pde>=2
+ gx_x_gx=contraction1(AmatT,vconcat(gx_x,gx));
+ vx=vconcat(sptensor(model.n_y_extended,n_x,n_s),gx_x_gx);
+ end
+ vx=vconcat(vx,hx);
+ vx=vconcat(vx,spteye(n_x,n_s));
+ model.vx=vx;
+
+ prevx=takerows(vx,prefvars);
+ if isempty(pref)
+ preR1=sptensor(0,n_x,n_s);
+ else
+ [preR1,model.ind{indi}]=chain1_tensor(prefv,prevx,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ end
+
+ % compute R2 (second order derivatives of R w.r.t x)
+ if order>=2
+ if model.pde==0
+ vxxc=vconcat(sptensor(n_y,unique2,n_s),gxxc);
+ elseif model.pde==1
+ vxxc=vconcat(sptensor(n_y*(n_x+1),unique2,n_s),gx_xxc);
+ vxxc=vconcat(vxxc,gxxc);
+ elseif model.pde>=2
+ gx_xxc_gxxc=contraction1(AmatT,vconcat(gx_xxc,gxxc));
+ vxxc=vconcat(sptensor(model.n_y_extended,unique2,n_s),gx_xxc_gxxc);
+ end
+ vxxc=vconcat(vxxc,hxxc);
+ vxxc=vconcat(vxxc,sptensor(n_x,unique2,n_s));
+ model.vxxc=vxxc;
+ prevxxc=takerows(vxxc,prefvars);
+ [prevx,model.ind4{indi4}]=colsort(prevx,model.ind4{indi4}); % i use model.ind4 because i forgot to put it in model.ind
+ indi4=indi4+1;
+ if isempty(pref)
+ preR2=sptensor(0,unique2,n_s);
+ else
+ [preR2,model.ind{indi}]=chain2c_tensor(prefv,prefvv,prevx,prevxxc,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ end
+
+ % compute R3 (third order derivatives of R w.r.t x)
+ if order>=3
+ if model.pde==0
+ vxxxc=vconcat(sptensor(n_y,unique3,n_s),gxxxc);
+ elseif model.pde==1
+ vxxxc=vconcat(sptensor(n_y*(n_x+1),unique3,n_s),gx_xxxc);
+ vxxxc=vconcat(vxxxc,gxxxc);
+ elseif model.pde>=2
+ gx_xxxc_gxxxc=contraction1(AmatT,vconcat(gx_xxxc,gxxxc));
+ vxxxc=vconcat(sptensor(model.n_y_extended,unique3,n_s),gx_xxxc_gxxxc);
+ end
+ vxxxc=vconcat(vxxxc,hxxxc);
+ vxxxc=vconcat(vxxxc,sptensor(n_x,unique3,n_s));
+ model.vxxxc=vxxxc;
+ prevxxxc=takerows(vxxxc,prefvars);
+
+ if ~isfield(model,'x_chain3c_M2')
+ [~,W2x]=create_UW(n_x,2);
+ [U3x,~]=create_UW(n_x,3);
+ OMEGAx=create_OMEGA(n_x,3);
+ model.x_chain3c_M2=spmat2sptensor(kron(speye(n_x),W2x)*OMEGAx.OMEGA1*U3x);
+ clear W2x U3x OMEGAx
+ end
+
+ if isempty(pref)
+ preR3=sptensor(0,unique3,n_s);
+ else
+ [preR3,model.ind{indi}]=chain3c_tensor(prefv,prefvv,prefvvv,prevx,prevxxc,prevxxxc,model.x_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ end
+
+ % compute R4 (fourth order derivatives of R w.r.t x)
+ if order>=4
+ if model.pde==0
+ vxxxxc=vconcat(sptensor(n_y,unique4,n_s),gxxxxc);
+ elseif model.pde==1
+ vxxxxc=vconcat(sptensor(n_y*(n_x+1),unique4,n_s),gx_xxxxc);
+ vxxxxc=vconcat(vxxxxc,gxxxxc);
+ elseif model.pde>=2
+ gx_xxxxc_gxxxxc=contraction1(AmatT,vconcat(gx_xxxxc,gxxxxc));
+ vxxxxc=vconcat(sptensor(model.n_y_extended,unique4,n_s),gx_xxxxc_gxxxxc);
+ end
+ vxxxxc=vconcat(vxxxxc,hxxxxc);
+ vxxxxc=vconcat(vxxxxc,sptensor(n_x,unique4,n_s));
+ model.vxxxxc=vxxxxc;
+ prevxxxxc=takerows(vxxxxc,prefvars);
+
+ if ~isfield(model,'x_chain4c_M2')
+ [~,W2new]=create_UW(unique2,2);
+ [~,W2x]=create_UW(n_x,2);
+ [~,W3x]=create_UW(n_x,3);
+ [U4x,~]=create_UW(n_x,4);
+ OMEGAx=create_OMEGA(n_x,4);
+ model.x_chain4c_M2=spmat2sptensor(kron(W2x,W2x)*OMEGAx.OMEGA2*U4x);
+ model.x_chain4c_M3=spmat2sptensor(kron(speye(n_x),W3x)*OMEGAx.OMEGA3*U4x);
+ model.x_chain4c_M4=spmat2sptensor(W2new*kron(W2x,W2x)*OMEGAx.OMEGA4*U4x);
+ clear W2new W2x W3x U4x OMEGAx
+ end
+
+ if isempty(pref)
+ preR4=sptensor(0,unique4,n_s);
+ else
+ [prevxxc,model.ind4{indi4}]=colsort(prevxxc,model.ind4{indi4});
+ indi4=indi4+1;
+
+ [preR4,model.ind4{indi4}]=chain4c_tensor(prefv,prefvv,prefvvv,prefvvvv,prevx,prevxxc,prevxxxc,prevxxxxc,...
+ model.x_chain4c_M2,model.x_chain4c_M3,model.x_chain4c_M4,model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+ end
+
+ end
+ totindi=totindi+3;
+ indi=totindi;
+ % Jacobian of the nonstochastic equations and derivatives
+
+ if model.pde==0
+ v_theta=vconcat(sptensor(n_y,(ms+1)*n_theta,n_s),v_theta_lower_terms);
+ elseif model.pde==1
+ v_theta=vconcat(sptensor(n_y*(n_x+1),(ms+1)*n_theta,n_s),v_theta_lower_terms);
+ elseif model.pde>=2
+ v_theta=vconcat(sptensor(model.n_y_extended,(ms+1)*n_theta,n_s),v_theta_lower_terms);
+ end
+
+ prev_theta=takerows(v_theta,prefvars);
+
+ [ preJ0,model.ind{indi} ] = chain0_theta_tensor( prefv,prev_theta,model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+
+ if order>=1
+ if model.pde==0
+ vx_theta=vconcat(sptensor(n_y,[n_x,(ms+1)*n_theta],n_s),vx_theta_lower_terms);
+ elseif model.pde==1
+ vx_theta=vconcat(sptensor(n_y*(n_x+1),[n_x,(ms+1)*n_theta],n_s),vx_theta_lower_terms);
+ elseif model.pde>=2
+ vx_theta=vconcat(sptensor(model.n_y_extended,[n_x,(ms+1)*n_theta],n_s),vx_theta_lower_terms);
+ end
+ model.vx_theta=vx_theta;
+ prevx_theta=takerows(vx_theta,prefvars);
+ prevx_theta=unfold(prevx_theta);
+ if isempty(pref)
+ preJ1=sptensor(zeros(0,1),zeros(0,2),zeros(n_s,0),0,[n_x,(ms+1)*n_theta]);
+ else
+ [ preJ1,model.ind{indi} ] = chain1_theta_tensor( prefv,prefvv,...
+ prevx,prev_theta,prevx_theta,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ end
+ end
+ if order>=2
+ if model.pde==0
+ vxxc_theta=vconcat(sptensor(n_y,[unique2,(ms+1)*n_theta],n_s),vxxc_theta_lower_terms);
+ elseif model.pde==1
+ vxxc_theta=vconcat(sptensor(n_y*(n_x+1),[unique2,(ms+1)*n_theta],n_s),vxxc_theta_lower_terms);
+ elseif model.pde>=2
+ vxxc_theta=vconcat(sptensor(model.n_y_extended,[unique2,(ms+1)*n_theta],n_s),vxxc_theta_lower_terms);
+ end
+ model.vxxc_theta=vxxc_theta;
+ prevxxc_theta=takerows(vxxc_theta,prefvars);
+ prevxxc_theta=unfold(prevxxc_theta);
+
+ if ~isfield(model,'chain2c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,2);
+ U2=create_UW(n_x,2);
+ model.chain2c_theta_M2=spmat2sptensor(GAMMA.GAMMA1*U2);
+ clear GAMMA U2
+ end
+
+ if isempty(pref)
+ preJ2=sptensor(zeros(0,1),zeros(0,2),zeros(n_s,0),0,[unique2,(ms+1)*n_theta]);
+ else
+ [ preJ2,model.ind{indi} ] = chain2c_theta_tensor( prefv,prefvv,prefvvv,...
+ prevx,prevxxc,...
+ prev_theta,prevx_theta,prevxxc_theta,...
+ model.chain2c_theta_M2,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ end
+ end
+ if order>=3
+ if model.pde==0
+ vxxxc_theta=vconcat(sptensor(n_y,[unique3,(ms+1)*n_theta],n_s),vxxxc_theta_lower_terms);
+ elseif model.pde==1
+ vxxxc_theta=vconcat(sptensor(n_y*(n_x+1),[unique3,(ms+1)*n_theta],n_s),vxxxc_theta_lower_terms);
+ elseif model.pde>=2
+ vxxxc_theta=vconcat(sptensor(model.n_y_extended,[unique3,(ms+1)*n_theta],n_s),vxxxc_theta_lower_terms);
+ end
+ model.vxxxc_theta=vxxxc_theta;
+ prevxxxc_theta=takerows(vxxxc_theta,prefvars);
+ prevxxxc_theta=unfold(prevxxxc_theta);
+
+ if ~isfield(model,'chain3c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,3);
+ [~,W2]=create_UW(n_x,2);
+ U3=create_UW(n_x,3);
+ model.chain3c_theta_M2=spmat2sptensor(kron(W2,speye(n_x))*GAMMA.GAMMA2*U3);
+ model.chain3c_theta_M3=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA3*U3);
+ model.chain3c_theta_M4=spmat2sptensor(kron(speye(n_x),W2)*GAMMA.GAMMA4*U3);
+ tempind=1:unique2*n_x;
+ tempmat=speye(unique2*n_x);
+ model.chain3c_theta_M5=spmat2sptensor(tempmat(:,permute(reshape(tempind,n_x,unique2),[2,1]))*kron(speye(n_x),W2)*GAMMA.GAMMA5*U3);
+ clear GAMMA W2 U3
+
+ end
+
+ if isempty(pref)
+ preJ3=sptensor(zeros(0,1),zeros(0,2),zeros(n_s,0),0,[unique3,(ms+1)*n_theta]);
+ else
+ [ preJ3,model.ind{indi} ] = chain3c_theta_tensor( prefv,prefvv,prefvvv,prefvvvv,...
+ prevx,prevxxc,prevxxxc,...
+ prev_theta,prevx_theta,prevxxc_theta,prevxxxc_theta,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ end
+ end
+ if order>=4
+ if model.pde==0
+ vxxxxc_theta=vconcat(sptensor(n_y,[unique4,(ms+1)*n_theta],n_s),vxxxxc_theta_lower_terms);
+ elseif model.pde==1
+ vxxxxc_theta=vconcat(sptensor(n_y*(n_x+1),[unique4,(ms+1)*n_theta],n_s),vxxxxc_theta_lower_terms);
+ elseif model.pde>=2
+ vxxxxc_theta=vconcat(sptensor(model.n_y_extended,[unique4,(ms+1)*n_theta],n_s),vxxxxc_theta_lower_terms);
+ end
+ model.vxxxxc_theta=vxxxxc_theta;
+ prevxxxxc_theta=takerows(vxxxxc_theta,prefvars);
+ prevxxxxc_theta=unfold(prevxxxxc_theta);
+
+ if ~isfield(model,'chain4c_theta_M2')
+ GAMMA=create_GAMMA(n_x,(ms+1)*n_theta,4);
+ [~,W2]=create_UW(n_x,2);
+ [~,W3]=create_UW(n_x,3);
+ U4=create_UW(n_x,4);
+ [~,W2new]=create_UW(unique2,2);
+ model.chain4c_theta_M2=spmat2sptensor(kron(W3,speye(n_x))*GAMMA.GAMMA16*U4);
+ model.chain4c_theta_M3=spmat2sptensor(kron(W2,W2)*GAMMA.GAMMA2*U4);
+ model.chain4c_theta_M5=spmat2sptensor(kron(speye(n_x^2),W2)*GAMMA.GAMMA17*GAMMA.GAMMA2*U4);
+ model.chain4c_theta_M6=spmat2sptensor(kron(speye(n_x),W3)*GAMMA.GAMMA3*U4);
+ model.chain4c_theta_M9=spmat2sptensor(W2new*kron(W2,W2)*GAMMA.GAMMA4*U4);
+ model.chain4c_theta_M10=spmat2sptensor(kron(W2,W2)*GAMMA.GAMMA18*GAMMA.GAMMA4*U4);
+
+ clear GAMMA W2 W3 U4 W2new
+
+ end
+
+ if isempty(pref)
+ preJ4=sptensor(zeros(0,1),zeros(0,2),zeros(n_s,0),0,[unique4,(ms+1)*n_theta]);
+ else
+ [ preJ4,model.ind4{indi4} ] = chain4c_theta_tensor( prefv,prefvv,prefvvv,prefvvvv,prefvvvvv,...
+ prevx,prevxxc,prevxxxc,prevxxxxc,...
+ prev_theta,prevx_theta,prevxxc_theta,prevxxxc_theta,prevxxxxc_theta,...
+ model.chain4c_theta_M2,model.chain4c_theta_M3,model.chain4c_theta_M5,model.chain4c_theta_M6,model.chain4c_theta_M9,model.chain4c_theta_M10,...
+ model.ind4{indi4},n_ind,maxload,'vec' );
+ indi4=indi4+1;
+ end
+ end
+ totindi=totindi+4;
+ indi=totindi;
+end
+
+% STEP 2: COMPUTE STOCHASTIC EQUATIONS AND DERIVATIVES, AND THEIR JACOBIAN,
+% AND TAKE EXPECTED VALUE
+
+% prepare vectorized expressions for the stochastic part.
+if isempty(model.stochfrows)
+ EstochR0=sptensor(0,1,n_s);
+ EstochR1=sptensor(0,n_x,n_s);
+ EstochR2=sptensor(0,unique2,n_s);
+ EstochR3=sptensor(0,unique3,n_s);
+ EstochR4=sptensor(0,unique4,n_s);
+ EstochJ0=sptensor(0,(ms+1)*n_theta,n_s);
+ EstochJ1=sptensor(0,[n_x,(ms+1)*n_theta],n_s);
+ EstochJ2=sptensor(0,[unique2,(ms+1)*n_theta],n_s);
+ EstochJ3=sptensor(0,[unique3,(ms+1)*n_theta],n_s);
+ EstochJ4=sptensor(0,[unique4,(ms+1)*n_theta],n_s);
+else
+ nx_vec=repmat(nx(:)',n_nodes,1); % n_nodes=the number of nodes of the discrete shocks.
+ nx_vec=reshape(nx_vec,n_nodes*n_s,[]);
+
+ % next period state
+ if model.hybrid==0
+ nxp_vec=repmat(h(:),1,n_nodes)+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ elseif model.hybrid==1
+ h_vec=repmat(h(:),1,n_nodes); %n_s*n_x,n_nodes
+
+ params_vec=[repmat(nep',n_s,1),reshape(repmat(reshape(params(:,n_e+1:end),1,[]),n_nodes,1),n_nodes*n_s,[])]; %n_nodes*n_s,n_params
+ uname=['Phi' model.uname '_fun'];
+ tempvars=[nx,ny,nu(:,model.preurows)]; %n_s,n_x+n_y
+ tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_s*n_nodes,n_x+n_y+n_preurows
+ Phi_vec=feval(uname,tempvars,params_vec); %n_s*n_nodes,n_x2
+ Phi_vec=permute(reshape(Phi_vec,n_s,n_nodes,n_x2),[1,3,2]); %n_s,n_x2,n_nodes
+ h_vec=reshape(h_vec,n_s,n_x,n_nodes);
+ h_vec(:,n_x1+1:end,:)=Phi_vec;
+ h_vec=reshape(h_vec,n_s*n_x,n_nodes);
+ nxp_vec=h_vec+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ elseif model.hybrid==3
+ h_vec=repmat(h(:),1,n_nodes); %n_s*n_x,n_nodes
+
+ params_vec=[repmat(nep',n_s,1),reshape(repmat(reshape(params(:,n_e+1:end),1,[]),n_nodes,1),n_nodes*n_s,[])]; %n_nodes*n_s,n_params
+ uname=['Phi' model.uname '_fun'];
+ tempvars=nz(:,model.Phizvars); %n_s,n_x+n_y
+ tempvars=reshape(repmat(tempvars(:)',n_nodes,1),n_nodes*n_s,[]); %n_nodes*n_s,n_x+n_y+n_preurows
+ Phi_vec=feval(uname,tempvars,params_vec); %n_nodes*n_s,n_x2
+ Phi_vec=permute(reshape(Phi_vec,n_nodes,n_s,n_x2),[2,3,1]); %n_s,n_x2,n_nodes
+ h_vec=reshape(h_vec,n_s,n_x,n_nodes);
+ h_vec(:,n_x1+1:end,:)=Phi_vec;
+ h_vec=reshape(h_vec,n_s*n_x,n_nodes);
+ nxp_vec=h_vec+reshape(etavec,[],n_e)*nep; %n_s*n_x,n_nodes
+ end
+
+ nxp_c0_vec=nxp_vec-reshape(repmat(c0vec,1,n_nodes),n_s*n_x,n_nodes);
+
+ nxp_vec_permuted=reshape(permute(reshape(nxp_vec,n_s,n_x,n_nodes),[3,1,2]),n_nodes*n_s,n_x);
+
+ tempxp=1:n_x;
+ tempxp=tempxp(:);
+ nxp_c0=sptensor(tempxp); % convert to 1D tensor
+ tempvals=reshape(nxp_c0_vec,n_s,n_x,n_nodes);
+ tempvals=permute(tempvals,[3,1,2]);
+ tempvals=reshape(tempvals,n_nodes*n_s,n_x);
+ nxp_c0.vals=tempvals; % assign the correct values in vals.
+
+ if ~isfield(model,'M2')
+ model.M2=[];
+ model.M3=[];
+ model.M3x=[];
+ model.TW2=[];
+ model.TW3=[];
+ model.M4=[];
+ model.M4x=[];
+ model.M4xx=[];
+ model.M4xxx=[];
+ if order>=2
+ model.M2=fold(spmat2sptensor(model.W{2}*model.W{2}'*model.U{2}'),n_x,n_x);
+ model.TW2=fold(spmat2sptensor(model.W{2}),n_x,n_x);
+ model.TW2U2=spmat2sptensor(model.W{2}*model.U{2});
+ end
+ if order>=3
+ model.M3=fold(spmat2sptensor(model.W{3}*model.W{3}'*model.U{3}'),n_x,n_x,n_x);
+ model.M3x=fold(spmat2sptensor(3*model.W{3}*kron(model.W{2}'*model.U{2}',speye(n_x))),n_x,n_x,n_x);
+ model.TW3=fold(spmat2sptensor(model.W{3}),n_x,n_x,n_x);
+ model.TW3U3=spmat2sptensor(model.W{3}*model.U{3});
+ end
+ if order>=4
+ model.M4=fold(spmat2sptensor(model.W{4}*model.W{4}'*model.U{4}'),n_x,n_x,n_x,n_x);
+ model.M4x=fold(spmat2sptensor(4*model.W{4}*kron(model.W{3}'*model.U{3}',speye(n_x))),n_x,n_x,n_x,n_x);
+ model.M4xx=fold(spmat2sptensor(12*model.W{4}*kron(model.W{2}'*model.U{2}',speye(n_x^2))),n_x,n_x,n_x,n_x);
+ model.M4xxx=fold(spmat2sptensor(24*model.W{4}),n_x,n_x,n_x,n_x);
+ end
+ end
+
+ [Xp_vecT,Xpx_vecT,Xpxx_vecT,Xpxxx_vecT,Xpxxxx_vecT,Xpxxxxx_vecT,model.ind{indi}]=create_X_tensor(order,nxp_c0,...
+ model.M2,model.M3,model.M3x,model.TW2,model.TW3,model.M4,model.M4x,model.M4xx,model.M4xxx,unique2,unique3,unique4,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ if strcmp(model.jacobian,'approximate')
+ nx_c0=sptensor(n_x,1);
+ nx_c0.vals=repmat(nx_c0.vals,n_nodes*n_s,1);
+ [X_vecT,Xx_vecT,Xxx_vecT,Xxxx_vecT,Xxxxx_vecT,Xxxxxx_vecT,model.ind{indi}]=create_X_tensor(order,nx_c0,...
+ model.M2,model.M3,model.M3x,model.TW2,model.TW3,model.M4,model.M4x,model.M4xx,model.M4xxx,unique2,unique3,unique4,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ totindi=totindi+2;
+ indi=totindi;
+
+
+ stochg_coeffsT=sptensor(ones(n_stochy,n_b));
+ tempvals=stochg_coeffs; %n_s,n_stochy,n_b
+ tempvals=permute(tempvals,[1,3,2]); % n_s,n_b,n_stochy
+ tempvals=repmat(tempvals(:)',n_nodes,1); % n_nodes,n_s*n_b*n_stochy
+ tempvals=reshape(tempvals,n_nodes*n_s,n_b*n_stochy);
+ stochg_coeffsT.vals=tempvals;
+
+ if model.n_logicalparams==0
+ [stochgp_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xp_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ gp_vec=changerows(stochgp_vecT,stochy,n_y);
+ temp=zeros(n_nodes*n_s,n_y);
+ temp(:,stochy)=gp_vec.vals;
+ else
+ g_coeffsT=sptensor(ones(n_y,n_b));
+ g_coeffs=coeffspvec(:,1:n_y,:);
+
+ tempvals=g_coeffs; %n_s,n_y,n_b
+ tempvals=permute(tempvals,[1,3,2]); % n_s,n_b,n_y
+ tempvals=repmat(tempvals(:)',n_nodes,1); % n_nodes,n_s*n_b*n_y
+ tempvals=reshape(tempvals,n_nodes*n_s,n_b*n_y);
+ g_coeffsT.vals=tempvals;
+
+ [gp_vecT,model.ind{indi}]=contraction1(g_coeffsT,Xp_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ gp_vec=changerows(gp_vecT,1:n_y,n_y);
+ temp=zeros(n_nodes*n_s,n_y);
+ temp(:,1:n_y)=gp_vec.vals;
+
+ end
+ gp_vec=temp; % n_nodes*n_s,n_y
+
+ [stochgpx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ % control vars in t+1
+ nyp_vec=gp_vec;
+
+ % evaluate residuals R0
+ nv_vec=[nyp_vec,reshape(repmat(ny(:)',n_nodes,1),n_nodes*n_s,[]),nxp_vec_permuted,nx_vec];
+ % nstochv_vec=nv_vec(:,stochfvars); % stochastic vars.
+
+ if model.hybrid==0
+ params_vec=reshape(repmat(params(:)',n_nodes,1),n_nodes*n_s,n_params);
+ end
+
+ uname=['stochu' model.uname '_fun'];
+ nstochu_vec=feval(uname,nv_vec(:,model.stochuvars),params_vec); % all stochastic u vars
+ nu_vec=reshape(repmat(nu(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ nu_vec(:,model.stochurows)=nstochu_vec;
+ nz_vec=[nv_vec,nu_vec];
+ params_vec(:,model.logical_params_loc)=double(logical(nz_vec(:,model.logical_zvars)>0));
+
+ fname=['stochtilf' model.fname '_fun'];
+ stochf_vec=feval(fname,nz_vec(:,model.stochtilfzvars),params_vec);
+
+ % compute derivatives of stochPI and stochtilf w.r.t z
+ uname=['stochPI' model.uname '_d1'];
+ stochPIz_vec=feval(uname,nz_vec,params_vec,model.stochPI_ind_u);
+ prePIz_full.vals=reshape(repmat(prePIz_full.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ i1=tfind(prePIz_full);
+ i2=tfind(stochPIz_vec);
+ PIz_vec=sptensor([i1;i2],[prePIz_full.cols;stochPIz_vec.cols],[prePIz_full.vals,stochPIz_vec.vals],n_z,[n_z]);
+
+ fname=['stochtilf' model.fname '_tilf_d1'];
+ stochtilfz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params_vec,model.stochtilf_ind_u);
+
+
+ if order>=1
+ uname=['stochPI' model.uname '_d2'];
+ stochPIzz_vec=feval(uname,nz_vec,params_vec,model.stochPI_ind_u);
+ prePIzz_full.vals=reshape(repmat(prePIzz_full.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ i1=tfind(prePIzz_full);
+ i2=tfind(stochPIzz_vec);
+ PIzz_vec=sptensor([i1;i2],[prePIzz_full.cols;stochPIzz_vec.cols],[prePIzz_full.vals,stochPIzz_vec.vals],n_z,[n_z,n_z]);
+
+ fname=['stochtilf' model.fname '_tilf_d2'];
+ stochtilfzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params_vec,model.stochtilf_ind_u);
+ end
+ if order>=2
+ uname=['stochPI' model.uname '_d3'];
+ stochPIzzz_vec=feval(uname,nz_vec,params_vec,model.stochPI_ind_u);
+ prePIzzz_full.vals=reshape(repmat(prePIzzz_full.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ i1=tfind(prePIzzz_full);
+ i2=tfind(stochPIzzz_vec);
+ PIzzz_vec=sptensor([i1;i2],[prePIzzz_full.cols;stochPIzzz_vec.cols],[prePIzzz_full.vals,stochPIzzz_vec.vals],n_z,[n_z,n_z,n_z]);
+ fname=['stochtilf' model.fname '_tilf_d3'];
+ stochtilfzzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params_vec,model.stochtilf_ind_u);
+ end
+ if order>=3
+ uname=['stochPI' model.uname '_d4'];
+ stochPIzzzz_vec=feval(uname,nz_vec,params_vec,model.stochPI_ind_u);
+ prePIzzzz_full.vals=reshape(repmat(prePIzzzz_full.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ i1=tfind(prePIzzzz_full);
+ i2=tfind(stochPIzzzz_vec);
+ PIzzzz_vec=sptensor([i1;i2],[prePIzzzz_full.cols;stochPIzzzz_vec.cols],[prePIzzzz_full.vals,stochPIzzzz_vec.vals],n_z,[n_z,n_z,n_z,n_z]);
+ fname=['stochtilf' model.fname '_tilf_d4'];
+ stochtilfzzzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params_vec,model.stochtilf_ind_u);
+ end
+ if order>=4
+ uname=['stochPI' model.uname '_d5'];
+ stochPIzzzzz_vec=feval(uname,nz_vec,params_vec,model.stochPI_ind_u);
+ prePIzzzzz_full.vals=reshape(repmat(prePIzzzzz_full.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ i1=tfind(prePIzzzzz_full);
+ i2=tfind(stochPIzzzzz_vec);
+ PIzzzzz_vec=sptensor([i1;i2],[prePIzzzzz_full.cols;stochPIzzzzz_vec.cols],[prePIzzzzz_full.vals,stochPIzzzzz_vec.vals],n_z,[n_z,n_z,n_z,n_z,n_z]);
+ fname=['stochtilf' model.fname '_tilf_d5'];
+ stochtilfzzzzz_vec=feval(fname,[nv_vec(:,stochfvars),nu_vec(:,model.stochfuvars)],params_vec,model.stochtilf_ind_u);
+ end
+
+ totindi=totindi+2;
+ indi=totindi;
+
+ % stochf_vec is n_nodes*n_s,n_stochf
+ EstochR0=P'*reshape(stochf_vec,n_nodes,[]); %expected value of stochR0
+ EstochR0=reshape(EstochR0,n_s,[]);
+
+ tempT=sptensor(zeros(n_stochfrows,1));
+ tempT.vals=full(EstochR0);
+ EstochR0=tempT;
+
+ % compute derivatives of Phi w.r.t x and theta for a model with hybrid
+ % state variables
+ if model.hybrid==1 || model.hybrid==3
+ get_hybridPhi_derivs_v;
+ get_hybridPhi_derivs_x_theta;
+
+ end
+
+
+ h_thetaT=h_theta;
+ h_thetaT.vals=reshape(repmat(h_thetaT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phitheta
+ h_thetaT=vconcat(takerows(h_thetaT,1:n_x1),Phitheta);
+ end
+
+ [chain0_theta_stochgpT,model.ind{indi}]=contraction1(stochgpx_vecT,h_thetaT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ totindi=totindi+1;
+ indi=totindi;
+
+ % compute derivatives of g w.r.t x at next period state (nxp)
+ if order>=1
+ if order>1
+ [stochgpxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxx_vecT=sptensor(n_stochy,n_x^2,n_nodes);
+ end
+ hxT=hx;
+ hxT.vals=reshape(repmat(hxT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phix
+ hxT=vconcat(takerows(hxT,1:n_x1),Phix);
+ end
+
+ [chain1_stochgpT,model.ind{indi}]=contraction1(stochgpx_vecT,hxT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hx_thetaT=unfold(hx_theta);
+ hx_thetaT.vals=reshape(repmat(hx_thetaT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixtheta
+ hx_thetaT=vconcat(takerows(hx_thetaT,1:n_x1),unfold(Phixtheta));
+ end
+
+
+ stochgpxx_vecT=fold(stochgpxx_vecT,n_x,n_x);
+ [chain1_theta_stochgpT,model.ind{indi}]=chain1_theta_tensor(stochgpx_vecT,stochgpxx_vecT,hxT,h_thetaT,hx_thetaT,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ if order>=2
+ if order>2
+ [stochgpxxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxxx_vecT=sptensor(n_stochy,n_x^3,n_nodes);
+ end
+ hxxcT=hxxc;
+ hxxcT.vals=reshape(repmat(hxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxc
+ hxxcT=vconcat(takerows(hxxcT,1:n_x1),Phixxc);
+ end
+
+ [hxT,model.ind4{indi4}]=colsort(hxT,model.ind4{indi4});
+ indi4=indi4+1;
+ [chain2_stochgpT,model.ind{indi}]=chain2c_tensor(stochgpx_vecT,stochgpxx_vecT,hxT,hxxcT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hxxc_thetaT=unfold(hxxc_theta);
+ hxxc_thetaT.vals=reshape(repmat(hxxc_thetaT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxctheta
+ hxxc_thetaT=vconcat(takerows(hxxc_thetaT,1:n_x1),unfold(Phixxctheta));
+ end
+
+ stochgpxxx_vecT=fold(stochgpxxx_vecT,n_x,n_x,n_x);
+
+ [chain2c_theta_stochgpT,model.ind{indi}]=chain2c_theta_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,hxT,hxxcT,h_thetaT,hx_thetaT,hxxc_thetaT,...
+ model.chain2c_theta_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ if order>=3
+ if order>3
+ [stochgpxxxx_vecT,model.ind{indi}]=contraction1(stochg_coeffsT,Xpxxxx_vecT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ stochgpxxxx_vecT=sptensor(n_stochy,n_x^4,n_nodes);
+ end
+ hxxxcT=hxxxc;
+ hxxxcT.vals=reshape(repmat(hxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxxc
+ hxxxcT=vconcat(takerows(hxxxcT,1:n_x1),Phixxxc);
+ end
+
+ [chain3_stochgpT,model.ind{indi}]=chain3c_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,...
+ hxT,hxxcT,hxxxcT,...
+ model.x_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ hxxxc_thetaT=unfold(hxxxc_theta);
+ hxxxc_thetaT.vals=reshape(repmat(hxxxc_thetaT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxxctheta
+ hxxxc_thetaT=vconcat(takerows(hxxxc_thetaT,1:n_x1),unfold(Phixxxctheta));
+ end
+
+ stochgpxxxx_vecT=fold(stochgpxxxx_vecT,n_x,n_x,n_x,n_x);
+
+ [chain3c_theta_stochgpT,model.ind{indi}]=chain3c_theta_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,stochgpxxxx_vecT,...
+ hxT,hxxcT,hxxxcT,h_thetaT,hx_thetaT,hxxc_thetaT,hxxxc_thetaT,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ if order>=4
+ if order>4
+ [stochgpxxxxx_vecT,model.ind4{indi4}]=contraction1(stochg_coeffsT,Xpxxxxx_vecT,model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+ else
+ stochgpxxxxx_vecT=sptensor(n_stochy,n_x^5,n_nodes);
+ end
+ hxxxxcT=hxxxxc;
+ hxxxxcT.vals=reshape(repmat(hxxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxxxc
+ hxxxxcT=vconcat(takerows(hxxxxcT,1:n_x1),Phixxxxc);
+ end
+
+ [hxxcT,model.ind4{indi4}]=colsort(hxxcT,model.ind4{indi4});
+ indi4=indi4+1;
+
+ [chain4_stochgpT,model.ind4{indi4}]=chain4c_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,stochgpxxxx_vecT,...
+ hxT,hxxcT,hxxxcT,hxxxxcT,...
+ model.x_chain4c_M2,model.x_chain4c_M3,model.x_chain4c_M4,model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+
+ hxxxxc_thetaT=unfold(hxxxxc_theta);
+ hxxxxc_thetaT.vals=reshape(repmat(hxxxxc_thetaT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==1 || model.hybrid==3 % add Phixxxxctheta
+ hxxxxc_thetaT=vconcat(takerows(hxxxxc_thetaT,1:n_x1),unfold(Phixxxxctheta));
+ end
+
+ stochgpxxxxx_vecT=fold(stochgpxxxxx_vecT,n_x,n_x,n_x,n_x,n_x);
+
+ [chain4c_theta_stochgpT,model.ind4{indi4}]=chain4c_theta_tensor(stochgpx_vecT,stochgpxx_vecT,stochgpxxx_vecT,stochgpxxxx_vecT,stochgpxxxxx_vecT,...
+ hxT,hxxcT,hxxxcT,hxxxxcT,h_thetaT,hx_thetaT,hxxc_thetaT,hxxxc_thetaT,hxxxxc_thetaT,...
+ model.chain4c_theta_M2,model.chain4c_theta_M3,model.chain4c_theta_M5,model.chain4c_theta_M6,model.chain4c_theta_M9,model.chain4c_theta_M10,...
+ model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+ end
+ totindi=totindi+9;
+ indi=totindi;
+
+ % extract PIv,Pivv,... from PIz,PIzz,...
+ if order>=0
+ [stochPIz_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=extract(PIz_vec,model.stochfzvars,model.stochfvars,0,model.ind{indi});
+ indi=indi+1;
+ end
+ if order>=1
+ [stochPIzz_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=extract(PIzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ end
+ if order>=2
+ [stochPIzzz_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=extract(PIzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain3c_M2')
+ [ tempM ] = chainsM( n_stochfvars,3 );
+ model.stochfvars_chain3c_M2=tempM{2};
+ clear tempM
+ end
+ end
+ if order>=3
+ [stochPIzzzz_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=extract(PIzzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind{indi});
+ indi=indi+1;
+ if ~isfield(model,'stochfvars_chain4c_M2')
+ [ tempM ] = chainsM( n_stochfvars,4 );
+ model.stochfvars_chain4c_M2=tempM{2};
+ model.stochfvars_chain4c_M3=tempM{3};
+ model.stochfvars_chain4c_M4=tempM{4};
+ clear tempM
+ end
+ end
+ if order>=4
+ [stochPIzzzzz_vec,model.ind4{indi4}]=extract(PIzzzzz_vec,model.stochfzvars,model.stochfzvars,0,model.ind4{indi4});
+ indi4=indi4+1;
+ [stochPIvvvvvc_vec,model.ind4{indi4}]=extract(PIzzzzz_vec,model.stochfzvars,model.stochfvars,1,model.ind4{indi4});
+ indi4=indi4+1;
+ end
+ totindi=totindi+8;
+ indi=totindi;
+
+
+ % compute derivatives of stochf w.r.t v by high order chain rules, and
+ % multiply by the weights P (probabilities).
+ Pvec=repmat(P(:),n_s,1);
+ if order==0
+ indi=totindi;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+
+ model.stochfv_vec=stochfv_vec;
+
+ elseif order==1
+ indi=totindi+model.count_stoch_n*(1)+1;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ elseif order==2
+ indi=totindi+model.count_stoch_n*(1+3)+1+4;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+ stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ elseif order==3
+ indi=totindi+model.count_stoch_n*(1+3+4)+1+4+6;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi=indi+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+ stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+ stochfvvvvc_vec.vals=multcol(stochfvvvvc_vec.vals,Pvec);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ [ stochfvvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvvc_vec,4,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvvc_vec
+ elseif order==4
+ indi=totindi+model.count_stoch_n*(1+3+4)+1+4+6;
+ for i=2:model.stoch_n
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvvvvc_vec,model.ind4{indi4}]=chain5c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,stochPIzzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,stochPIvvvvvc_vec,...
+ model.stochfvars_chain5c_M1,model.stochfvars_chain5c_M2,model.stochfvars_chain5c_M3,model.stochfvars_chain5c_M4,model.stochfvars_chain5c_M5,model.stochfvars_chain5c_M6,...
+ model.ind4{indi4},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi4=indi4+1;
+ [stochPIvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,stochPIzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochzz,model.maxzz);
+ indi=indi+1;
+ [stochPIvvvc_vec,model.ind{indi}]=chain3c_tensor(stochPIz_vec,stochPIzz_vec,stochPIzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,model.stochfvars_chain3c_M2,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=chain2c_tensor(stochPIz_vec,stochPIzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochPIv_vec,model.ind{indi}]=chain1_tensor(stochPIz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+ [stochPIv_vec,model.ind{indi}]=colsort(stochPIv_vec,model.ind{indi});
+ indi=indi+1;
+ [stochPIvvc_vec,model.ind{indi}]=colsort(stochPIvvc_vec,model.ind{indi});
+ indi=indi+1;
+
+ [stochfv_vec,model.ind{indi}]=chain1_tensor(stochtilfz_vec,stochPIv_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ [stochfvvc_vec,model.ind{indi}]=chain2c_tensor(stochtilfz_vec,stochtilfzz_vec,stochPIv_vec,stochPIvvc_vec,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvc_vec,model.ind{indi}]=chain3c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,...
+ model.stochfvars_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ [stochfvvvvc_vec,model.ind{indi}]=chain4c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,...
+ model.stochfvars_chain4c_M2,model.stochfvars_chain4c_M3,model.stochfvars_chain4c_M4,...
+ model.ind{indi},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi=indi+1;
+ [stochfvvvvvc_vec,model.ind4{indi4}]=chain5c_tensor(stochtilfz_vec,stochtilfzz_vec,stochtilfzzz_vec,stochtilfzzzz_vec,stochtilfzzzzz_vec,...
+ stochPIv_vec,stochPIvvc_vec,stochPIvvvc_vec,stochPIvvvvc_vec,stochPIvvvvvc_vec,...
+ model.stochfvars_chain5c_M1,model.stochfvars_chain5c_M2,model.stochfvars_chain5c_M3,model.stochfvars_chain5c_M4,model.stochfvars_chain5c_M5,model.stochfvars_chain5c_M6,...
+ model.ind4{indi4},n_ind,maxload,'vec',model.stochtilfz,model.maxtilfz);
+ indi4=indi4+1;
+
+ stochfv_vec.vals=multcol(stochfv_vec.vals,Pvec);
+ stochfvvc_vec.vals=multcol(stochfvvc_vec.vals,Pvec);
+ stochfvvvc_vec.vals=multcol(stochfvvvc_vec.vals,Pvec);
+ stochfvvvvc_vec.vals=multcol(stochfvvvvc_vec.vals,Pvec);
+ stochfvvvvvc_vec.vals=multcol(stochfvvvvvc_vec.vals,Pvec);
+
+ [ stochfvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvc_vec,2,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvc_vec
+
+ [ stochfvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvc_vec,3,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvc_vec
+
+ [ stochfvvvv_vec,model.ind{indi} ] = uncompressderivs( stochfvvvvc_vec,4,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind{indi} );
+ indi=indi+1;
+ clear stochfvvvvc_vec
+
+ [ stochfvvvvv_vec,model.ind4{indi4} ] = uncompressderivs( stochfvvvvvc_vec,5,n_stochfvars,model.fv(model.stochfrows,stochfvars),model.ind4{indi4} );
+ indi4=indi4+1;
+ clear stochfvvvvvc_vec
+
+ end
+ totindi=totindi+8+model.count_stoch_n*(1+3+4+6)+1+4+6+9;
+ indi=totindi;
+
+
+ if model.steady_state==1
+ if size(stochfv_vec.vals,1)~=1
+ error('cannot compute steady state on vectorized tensors')
+ end
+ nzstochfv=stochfv_vec;
+ nzstochfv.vals(:)=1;
+ nzstochfv=sptensor2spmat(nzstochfv);
+ nzstochfv_full=zeros(n_stochfrows,model.n_v);
+ nzstochfv_full(:,model.stochfvars)=full(nzstochfv);
+ nzstochfv_full(:,2*model.n_y+(1:model.n_x1))=nzstochfv_full(:,2*model.n_y+(1:model.n_x1))+nzstochfv_full(:,2*model.n_y+model.n_x+(1:model.n_x1));
+ nzstochfv=nzstochfv_full(:,model.stochfvars);
+ [i,j]=find(nzstochfv);
+
+ stochfv=sptensor2spmat(stochfv_vec);
+ stochfv_full=zeros(n_stochfrows,model.n_v);
+ stochfv_full(:,model.stochfvars)=full(stochfv);
+ stochfv_full(:,2*model.n_y+(1:model.n_x1))=stochfv_full(:,2*model.n_y+(1:model.n_x1))+stochfv_full(:,2*model.n_y+model.n_x+(1:model.n_x1));
+ stochfv=stochfv_full(:,model.stochfvars);
+
+ vals=stochfv(logical(nzstochfv(:)));
+
+ stochfv_vec=sptensor(i(:),j(:),vals(:)',size(stochfv,1),size(stochfv,2));
+ end
+
+
+ temp=reshape((1:n_theta)+ms*n_theta,[],n_b);
+ stochtheta=temp(stochy,:);
+ stochtheta=stochtheta(:);
+ n_stochtheta=length(stochtheta);
+
+ % exact/approximate Jacobian of gp,gpx,...
+ IstochyT=spteye(n_stochy);
+ if strcmp(model.jacobian,'exact')
+ [stochgp_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xp_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgp_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(X_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ if ms==0
+ nnzgp_theta_vecT=unfold(changecols(changerows(stochgp_stochtheta_vecT,stochy,n_y),stochy,n_y+n_x1,1)); %n_y,n_theta with only nnz values
+ else
+
+ nnzgp_theta_vecT=unfold(changecols(changerows(unfold(stochgp_stochtheta_vecT),stochy,n_y),stochtheta,(ms+1)*n_theta,1)); %n_y,n_theta with only nnz values
+ end
+ nnzchain0_theta_gpT=changerows(chain0_theta_stochgpT,stochy,n_y);
+
+ v_theta_lower_terms_vecT=v_theta_lower_terms;
+ v_theta_lower_terms_vecT.vals=reshape(repmat(v_theta_lower_terms_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==3 % not necessary for model.hybrid==1 because x2p does not appear in any of the equations
+ temp=vconcat(takerows(v_theta_lower_terms_vecT,1:n_y+n_x1),Phitheta);
+ temp=vconcat(temp,takerows(v_theta_lower_terms_vecT,n_y+n_x+(1:n_x)));
+ v_theta_lower_terms_vecT=temp;
+ end
+
+ v_theta_vecT=vconcat(tplus(nnzchain0_theta_gpT,nnzgp_theta_vecT,maxload),v_theta_lower_terms_vecT);
+ clear nnzchain0_theta_gpT nnzgp_theta_vecT
+ stochv_theta_vecT=takerows(v_theta_vecT,stochfvars);
+
+ clear v_theta_vecT
+
+ totindi=totindi+2;
+ indi=totindi;
+ % derivatives of v w.r.t x
+ if order>=1
+ vxT=vx;
+ if model.hybrid==0 || model.hybrid==1
+ stochvxT=takerows(vxT,stochfvars(n_stochy+1:end));
+ stochvxT.vals=reshape(repmat(stochvxT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ elseif model.hybrid==3
+ vxT.vals=reshape(repmat(vxT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ temp=vconcat(takerows(vxT,1:2*n_y+n_x1),Phix);
+ temp=vconcat(temp,takerows(vxT,2*n_y+n_x+(1:n_x)));
+ vxT=temp;
+ stochvxT=takerows(vxT,stochfvars(n_stochy+1:end));
+ end
+ stochvxT=vconcat(chain1_stochgpT,stochvxT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ stochgpx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpx_stochtheta_vecT),n_stochy,n_x),1),2));%n_stochy*n_stochtheta,n_x
+ %
+ [chain1_gp_theta_vecT,model.ind{indi}]=contraction1(stochgpx_stochtheta_vecT,hxT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain1_gp_theta_vecT=ptr2col(ptr2d(chain1_gp_theta_vecT,n_stochy,n_stochtheta),2);%n_stochy,n_x,n_stochtheta
+ nnzchain1_gp_theta_vecT=col2ptr(changecols(changerows(chain1_gp_theta_vecT,stochy,n_y),stochtheta,(ms+1)*n_theta,2),1); %n_y*n_x,n_theta with only nnz values
+
+ nnzchain1_theta_gpT=col2ptr(changerows(chain1_theta_stochgpT,stochy,n_y),1);% n_y,n_x,n_theta
+
+ vx_theta_lower_terms_vecT=vx_theta_lower_terms;
+ vx_theta_lower_terms_vecT.vals=reshape(repmat(vx_theta_lower_terms_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==3
+ temp=vconcat(takerows(vx_theta_lower_terms_vecT,1:n_y+n_x1),Phixtheta);
+ temp=vconcat(temp,takerows(vx_theta_lower_terms_vecT,n_y+n_x+(1:n_x)));
+ vx_theta_lower_terms_vecT=temp;
+ end
+
+ vx_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain1_theta_gpT,nnzchain1_gp_theta_vecT,maxload),1));
+ clear nnzchain1_theta_gpT nnzchain1_gp_theta_vecT
+ vx_theta_vecT=vconcat(vx_theta_upper_terms_vecT,unfold(vx_theta_lower_terms_vecT));
+
+ clear vx_theta_upper_terms_vecT vx_theta_lower_terms_vecT
+
+ stochvx_theta_vecT=takerows(vx_theta_vecT,stochfvars);
+
+ clear vx_theta_vecT
+ end
+ if order>=2
+ vxxcT=vxxc;
+ if model.hybrid==0 || model.hybrid==1
+ stochvxxcT=takerows(vxxcT,stochfvars(n_stochy+1:end));
+ stochvxxcT.vals=reshape(repmat(stochvxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ elseif model.hybrid==3
+ vxxcT.vals=reshape(repmat(vxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ temp=vconcat(takerows(vxxcT,1:2*n_y+n_x1),Phixxc);
+ temp=vconcat(temp,takerows(vxxcT,2*n_y+n_x+(1:n_x)));
+ vxxcT=temp;
+ stochvxxcT=takerows(vxxcT,stochfvars(n_stochy+1:end));
+ end
+
+ stochvxxcT=vconcat(chain2_stochgpT,stochvxxcT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+ stochgpxx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpxx_stochtheta_vecT),n_stochy,n_x^2),1),2));%n_stochy*n_stochtheta,n_x^2
+ stochgpxx_stochtheta_vecT=fold(stochgpxx_stochtheta_vecT,n_x,n_x);
+
+ [chain2c_stochgp_stochtheta_vecT,model.ind{indi}]=chain2c_tensor(stochgpx_stochtheta_vecT,stochgpxx_stochtheta_vecT,...
+ hxT,hxxcT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain2c_stochgp_stochtheta_vecT=ptr2col(ptr2d(chain2c_stochgp_stochtheta_vecT,n_stochy,n_stochtheta),2);%n_stochy,unique2,n_stochtheta
+ nnzchain2c_gp_theta_vecT=col2ptr(changecols(changerows(chain2c_stochgp_stochtheta_vecT,stochy,n_y),stochtheta,(ms+1)*n_theta,2),1); %n_y*unique2,n_theta with only nnz values
+ clear chain2c_stochgp_stochtheta_vecT
+
+ nnzchain2c_theta_gpT=col2ptr(changerows(chain2c_theta_stochgpT,stochy,n_y),1);% n_y,unique2,n_theta
+
+ vxxc_theta_lower_terms_vecT=unfold(vxxc_theta_lower_terms);
+ vxxc_theta_lower_terms_vecT.vals=reshape(repmat(vxxc_theta_lower_terms_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==3
+ temp=vconcat(takerows(vxxc_theta_lower_terms_vecT,1:n_y+n_x1),unfold(Phixxctheta));
+ temp=vconcat(temp,takerows(vxxc_theta_lower_terms_vecT,n_y+n_x+(1:n_x)));
+ vxxc_theta_lower_terms_vecT=temp;
+ end
+
+ vxxc_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain2c_theta_gpT,nnzchain2c_gp_theta_vecT,maxload),1));
+ clear nnzchain2c_theta_gpT nnzchain2c_gp_theta_vecT
+ vxxc_theta_vecT=vconcat(vxxc_theta_upper_terms_vecT,vxxc_theta_lower_terms_vecT);
+
+ clear vxxc_theta_upper_terms_vecT vxxc_theta_lower_terms_vecT
+
+ stochvxxc_theta_vecT=takerows(vxxc_theta_vecT,stochfvars);
+
+ clear vxxc_theta_vecT
+ end
+ if order>=3
+ vxxxcT=vxxxc;
+ if model.hybrid==0 || model.hybrid==1
+ stochvxxxcT=takerows(vxxxcT,stochfvars(n_stochy+1:end));
+ stochvxxxcT.vals=reshape(repmat(stochvxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ elseif model.hybrid==3
+ vxxxcT.vals=reshape(repmat(vxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ temp=vconcat(takerows(vxxxcT,1:2*n_y+n_x1),Phixxxc);
+ temp=vconcat(temp,takerows(vxxxcT,2*n_y+n_x+(1:n_x)));
+ vxxxcT=temp;
+ stochvxxxcT=takerows(vxxxcT,stochfvars(n_stochy+1:end));
+ end
+
+
+ stochvxxxcT=vconcat(chain3_stochgpT,stochvxxxcT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpxxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xpxxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ else
+ [stochgpxxx_stochtheta_vecT,model.ind{indi}]=tkron(ttranspose(Xxxx_vecT),IstochyT,model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+ end
+
+
+ stochgpxxx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpxxx_stochtheta_vecT),n_stochy,n_x^3),1),2));%n_stochy*n_stochtheta,n_x^2
+ stochgpxxx_stochtheta_vecT=fold(stochgpxxx_stochtheta_vecT,n_x,n_x,n_x);
+
+ [chain3c_stochgp_stochtheta_vecT,model.ind{indi}]=chain3c_tensor(stochgpx_stochtheta_vecT,stochgpxx_stochtheta_vecT,stochgpxxx_stochtheta_vecT,...
+ hxT,hxxcT,hxxxcT,...
+ model.x_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec');
+ indi=indi+1;
+
+ chain3c_stochgp_stochtheta_vecT=ptr2col(ptr2d(chain3c_stochgp_stochtheta_vecT,n_stochy,n_stochtheta),2);%n_stochy,unique3,n_stochtheta
+ nnzchain3c_gp_theta_vecT=col2ptr(changecols(changerows(chain3c_stochgp_stochtheta_vecT,stochy,n_y),stochtheta,(ms+1)*n_theta,2),1); %n_y*unique3,n_theta with only nnz values
+
+ clear chain3c_stochgp_stochtheta_vecT
+
+ nnzchain3c_theta_gpT=col2ptr(changerows(chain3c_theta_stochgpT,stochy,n_y),1);% n_y,unique3,n_theta
+
+ clear chain3c_theta_stochgpT
+
+ vxxxc_theta_lower_terms_vecT=unfold(vxxxc_theta_lower_terms);
+ vxxxc_theta_lower_terms_vecT.vals=reshape(repmat(vxxxc_theta_lower_terms_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==3
+ temp=vconcat(takerows(vxxxc_theta_lower_terms_vecT,1:n_y+n_x1),unfold(Phixxxctheta));
+ temp=vconcat(temp,takerows(vxxxc_theta_lower_terms_vecT,n_y+n_x+(1:n_x)));
+ vxxxc_theta_lower_terms_vecT=temp;
+ end
+
+ vxxxc_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain3c_theta_gpT,nnzchain3c_gp_theta_vecT,maxload),1));
+
+ clear nnzchain3c_theta_gpT nnzchain3c_gp_theta_vecT
+ vxxxc_theta_vecT=vconcat(vxxxc_theta_upper_terms_vecT,vxxxc_theta_lower_terms_vecT);
+
+ clear vxxxc_theta_upper_terms_vecT vxxxc_theta_lower_terms_vecT
+
+ stochvxxxc_theta_vecT=takerows(vxxxc_theta_vecT,stochfvars);
+
+ clear vxxxc_theta_vecT
+ end
+ if order>=4
+ vxxxxcT=vxxxxc;
+ if model.hybrid==0 || model.hybrid==1
+ stochvxxxxcT=takerows(vxxxxcT,stochfvars(n_stochy+1:end));
+ stochvxxxxcT.vals=reshape(repmat(stochvxxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ elseif model.hybrid==3
+ vxxxxcT.vals=reshape(repmat(vxxxxcT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+ temp=vconcat(takerows(vxxxxcT,1:2*n_y+n_x1),Phixxxxc);
+ temp=vconcat(temp,takerows(vxxxxcT,2*n_y+n_x+(1:n_x)));
+ vxxxxcT=temp;
+ stochvxxxxcT=takerows(vxxxxcT,stochfvars(n_stochy+1:end));
+ end
+
+ stochvxxxxcT=vconcat(chain4_stochgpT,stochvxxxxcT);
+
+ if strcmp(model.jacobian,'exact')
+ [stochgpxxxx_stochtheta_vecT,model.ind4{indi4}]=tkron(ttranspose(Xpxxxx_vecT),IstochyT,model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+ else
+ [stochgpxxxx_stochtheta_vecT,model.ind4{indi4}]=tkron(ttranspose(Xxxxx_vecT),IstochyT,model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+ end
+
+
+ stochgpxxxx_stochtheta_vecT=ptr1d(col2ptr(ptr2col(ptr2d(unfold(stochgpxxxx_stochtheta_vecT),n_stochy,n_x^4),1),2));%n_stochy*n_stochtheta,n_x^4
+ stochgpxxxx_stochtheta_vecT=fold(stochgpxxxx_stochtheta_vecT,n_x,n_x,n_x,n_x);
+
+ [chain4c_stochgp_stochtheta_vecT,model.ind4{indi4}]=chain4c_tensor(stochgpx_stochtheta_vecT,stochgpxx_stochtheta_vecT,stochgpxxx_stochtheta_vecT,stochgpxxxx_stochtheta_vecT,...
+ hxT,hxxcT,hxxxcT,hxxxxcT,...
+ model.x_chain4c_M2,model.x_chain4c_M3,model.x_chain4c_M4,...
+ model.ind4{indi4},n_ind,maxload,'vec');
+ indi4=indi4+1;
+
+ chain4c_stochgp_stochtheta_vecT=ptr2col(ptr2d(chain4c_stochgp_stochtheta_vecT,n_stochy,n_stochtheta),2);%n_stochy,unique4,n_stochtheta
+ nnzchain4c_gp_theta_vecT=col2ptr(changecols(changerows(chain4c_stochgp_stochtheta_vecT,stochy,n_y),stochtheta,(ms+1)*n_theta,2),1); %n_y*unique4,n_theta with only nnz values
+
+ clear chain4c_stochgp_stochtheta_vecT
+
+ nnzchain4c_theta_gpT=col2ptr(changerows(chain4c_theta_stochgpT,stochy,n_y),1);% n_y,unique4,n_theta
+
+ clear chain4c_theta_stochgpT
+
+ vxxxxc_theta_lower_terms_vecT=unfold(vxxxxc_theta_lower_terms);
+ vxxxxc_theta_lower_terms_vecT.vals=reshape(repmat(vxxxxc_theta_lower_terms_vecT.vals(:)',n_nodes,1),n_nodes*n_s,[]);
+
+ if model.hybrid==3
+ temp=vconcat(takerows(vxxxxc_theta_lower_terms_vecT,1:n_y+n_x1),unfold(Phixxxxctheta));
+ temp=vconcat(temp,takerows(vxxxxc_theta_lower_terms_vecT,n_y+n_x+(1:n_x)));
+ vxxxxc_theta_lower_terms_vecT=temp;
+ end
+
+ vxxxxc_theta_upper_terms_vecT=unfold(ptr2col(tplus(nnzchain4c_theta_gpT,nnzchain4c_gp_theta_vecT,maxload),1));
+
+ clear nnzchain4c_theta_gpT nnzchain4c_gp_theta_vecT
+ vxxxxc_theta_vecT=vconcat(vxxxxc_theta_upper_terms_vecT,vxxxxc_theta_lower_terms_vecT);
+
+ clear vxxxxc_theta_upper_terms_vecT vxxxxc_theta_lower_terms_vecT
+
+ stochvxxxxc_theta_vecT=takerows(vxxxxc_theta_vecT,stochfvars);
+
+ clear vxxxxc_theta_vecT
+ end
+ totindi=totindi+9;
+ indi=totindi;
+
+ [ EstochJ0,model.ind{indi} ] = chain0_theta_tensor( stochfv_vec,stochv_theta_vecT,model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+
+ EstochJ0.vals=reshape(sum(reshape(EstochJ0.vals,n_nodes,[]),1),n_s,[]);
+
+ if order>=1
+ [ EstochR1,model.ind{indi} ] = chain1_tensor( stochfv_vec,stochvxT,model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochR1.vals=reshape(sum(reshape(EstochR1.vals,n_nodes,[]),1),n_s,[]);
+
+
+
+ [ EstochJ1,model.ind{indi} ] = chain1_theta_tensor( stochfv_vec,stochfvv_vec,...
+ stochvxT,stochv_theta_vecT,stochvx_theta_vecT,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochJ1.vals=reshape(sum(reshape(EstochJ1.vals,n_nodes,[]),1),n_s,[]);
+ end
+ if order>=2
+ [stochvxT,model.ind4{indi4}]=colsort(stochvxT,model.ind4{indi4});
+ indi4=indi4+1;
+ [ EstochR2,model.ind{indi} ] = chain2c_tensor( stochfv_vec,stochfvv_vec,...
+ stochvxT,stochvxxcT,model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochR2.vals=reshape(sum(reshape(EstochR2.vals,n_nodes,[]),1),n_s,[]);
+
+ [ EstochJ2,model.ind{indi} ] = chain2c_theta_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,...
+ stochvxT,stochvxxcT,...
+ stochv_theta_vecT,stochvx_theta_vecT,stochvxxc_theta_vecT,...
+ model.chain2c_theta_M2,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochJ2.vals=reshape(sum(reshape(EstochJ2.vals,n_nodes,[]),1),n_s,[]);
+ end
+ if order>=3
+ [ EstochR3,model.ind{indi} ] = chain3c_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,...
+ model.x_chain3c_M2,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochR3.vals=reshape(sum(reshape(EstochR3.vals,n_nodes,[]),1),n_s,[]);
+
+ [ EstochJ3,model.ind{indi} ] = chain3c_theta_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,stochfvvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,...
+ stochv_theta_vecT,stochvx_theta_vecT,stochvxxc_theta_vecT,stochvxxxc_theta_vecT,...
+ model.chain3c_theta_M2,model.chain3c_theta_M3,model.chain3c_theta_M4,model.chain3c_theta_M5,...
+ model.ind{indi},n_ind,maxload,'vec' );
+ indi=indi+1;
+ EstochJ3.vals=reshape(sum(reshape(EstochJ3.vals,n_nodes,[]),1),n_s,[]);
+ end
+ if order>=4
+ [stochvxxcT,model.ind4{indi4}]=colsort(stochvxxcT,model.ind4{indi4});
+ indi4=indi4+1;
+ [ EstochR4,model.ind4{indi4} ] = chain4c_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,stochfvvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,stochvxxxxcT,...
+ model.x_chain4c_M2,model.x_chain4c_M3,model.x_chain4c_M4,...
+ model.ind4{indi4},n_ind,maxload,'vec' );
+ indi4=indi4+1;
+ EstochR4.vals=reshape(sum(reshape(EstochR4.vals,n_nodes,[]),1),n_s,[]);
+
+ [ EstochJ4,model.ind4{indi4} ] = chain4c_theta_tensor( stochfv_vec,stochfvv_vec,stochfvvv_vec,stochfvvvv_vec,stochfvvvvv_vec,...
+ stochvxT,stochvxxcT,stochvxxxcT,stochvxxxxcT,...
+ stochv_theta_vecT,stochvx_theta_vecT,stochvxxc_theta_vecT,stochvxxxc_theta_vecT,stochvxxxxc_theta_vecT,...
+ model.chain4c_theta_M2,model.chain4c_theta_M3,model.chain4c_theta_M5,model.chain4c_theta_M6,model.chain4c_theta_M9,model.chain4c_theta_M10,...
+ model.ind4{indi4},n_ind,maxload,'vec' );
+ indi4=indi4+1;
+ EstochJ4.vals=reshape(sum(reshape(EstochJ4.vals,n_nodes,[]),1),n_s,[]);
+ end
+ totindi=totindi+7;
+end
+
+% build the system and the Jacobian
+
+R0=vconcat(preR0,EstochR0);
+oldrows=1:R0.tsize(1);
+newrows=zeros(1,R0.tsize(1));
+newrows([model.prefrows(:);model.stochfrows(:)])=oldrows;
+R0=permuterows(R0,newrows);
+
+J0=vconcat(preJ0,EstochJ0);
+J0=permuterows(J0,newrows);
+
+
+
+T=R0;
+J=J0;
+
+if order>=1
+ R1=vconcat(preR1,EstochR1);
+ R1=permuterows(R1,newrows);
+
+ R1=ptr2d(R1,1,n_f);
+ R1=ptr2col(R1,1);
+ R1=fold(unfold(R1),n_f*n_x,1);
+ R1=ptr1d(col2ptr(R1,1));
+
+ T=vconcat(T,R1);
+
+ J1=vconcat(preJ1,EstochJ1);
+ J1=permuterows(J1,newrows);
+
+ J1=ptr2d(J1,1,n_f);
+ J1=ptr2col(J1,1);
+ J1=fold(unfold(J1),n_f*n_x,(ms+1)*n_theta);
+ J1=ptr1d(col2ptr(J1,1));
+
+ J=vconcat(J,J1);
+end
+if order>=2
+ R2=vconcat(preR2,EstochR2);
+ R2=permuterows(R2,newrows);
+
+ R2=ptr2d(R2,1,n_f);
+ R2=ptr2col(R2,1);
+ R2=fold(unfold(R2),n_f*unique2,1);
+ R2=ptr1d(col2ptr(R2,1));
+
+ T=vconcat(T,R2);
+
+ J2=vconcat(preJ2,EstochJ2);
+ J2=permuterows(J2,newrows);
+
+ J2=ptr2d(J2,1,n_f);
+ J2=ptr2col(J2,1);
+ J2=fold(unfold(J2),n_f*unique2,(ms+1)*n_theta);
+ J2=ptr1d(col2ptr(J2,1));
+
+ J=vconcat(J,J2);
+end
+if order>=3
+ R3=vconcat(preR3,EstochR3);
+ R3=permuterows(R3,newrows);
+
+ R3=ptr2d(R3,1,n_f);
+ R3=ptr2col(R3,1);
+ R3=fold(unfold(R3),n_f*unique3,1);
+ R3=ptr1d(col2ptr(R3,1));
+
+ T=vconcat(T,R3);
+
+ J3=vconcat(preJ3,EstochJ3);
+ J3=permuterows(J3,newrows);
+
+ J3=ptr2d(J3,1,n_f);
+ J3=ptr2col(J3,1);
+ J3=fold(unfold(J3),n_f*unique3,(ms+1)*n_theta);
+ J3=ptr1d(col2ptr(J3,1));
+
+ J=vconcat(J,J3);
+
+end
+if order>=4
+ R4=vconcat(preR4,EstochR4);
+ R4=permuterows(R4,newrows);
+
+ R4=ptr2d(R4,1,n_f);
+ R4=ptr2col(R4,1);
+ R4=fold(unfold(R4),n_f*unique4,1);
+ R4=ptr1d(col2ptr(R4,1));
+
+ T=vconcat(T,R4);
+
+ J4=vconcat(preJ4,EstochJ4);
+ J4=permuterows(J4,newrows);
+
+ J4=ptr2d(J4,1,n_f);
+ J4=ptr2col(J4,1);
+ J4=fold(unfold(J4),n_f*unique4,(ms+1)*n_theta);
+ J4=ptr1d(col2ptr(J4,1));
+
+ J=vconcat(J,J4);
+
+end
+model.coeffs=coeffs;
+model.nv=nv;
+model.v_theta=v_theta;
+
+if isfield(model,'special_code')
+ eval(model.special_code);
+end
+
+end
\ No newline at end of file
diff --git a/105/replication_package/solution_methods/taylor_projection/uncompressderivs.m b/105/replication_package/solution_methods/taylor_projection/uncompressderivs.m
new file mode 100644
index 0000000000000000000000000000000000000000..4e65aa707b1f4821f7c7cd82450ea0bf5591860e
--- /dev/null
+++ b/105/replication_package/solution_methods/taylor_projection/uncompressderivs.m
@@ -0,0 +1,92 @@
+function [ derivs_uncompressed,ind ] = uncompressderivs( derivs,order,n_v,nnzmat,ind )
+%derivs is a sparse tensor that stores unique derivatives of function f w.r.t v.
+%order=derivative order
+%n_v=length(v);
+%nnzmat= a matrix that stores variables that affect f.
+%ind=auxiliary index
+%
+% � Copyright, Oren Levintal, June 13, 2016.
+% on January 20, 2017 - extended to fifth order
+% on September 12, 2017 - bug corrected for the case of empty tensors.
+l=derivs.tsize(1);
+if isempty(ind)
+ original_derivs=derivs;
+ if size(derivs.ptr,2)>1
+ error('2D ptr not supported')
+ end
+
+ n_vals=size(derivs.vals,2);
+ derivs.vals=1:n_vals;
+ sortind=zeros(1,n_vals*factorial(order));
+ newcols=zeros(n_vals*factorial(order),order);
+ nz=1;
+ newptr=zeros(l+1,1);
+ newptr(1)=nz;
+ subinds='i1';
+ subindsvec='i1(:)';
+ for j=2:order
+ subinds=[subinds ',i' num2str(j)];
+ subindsvec=[subindsvec ',i' num2str(j) '(:)'];
+ end
+ for i=1:l
+ deriv_i=takerows(derivs,i); % take row i
+ nnzmati=nnzmat(i,:);
+ ni=nnz(nnzmati);
+ % convert from compress form to unique form without using c2u
+ % function because it takes n_v^order memory, and i want only
+ % ni^order.
+ eval(['[' subinds ']=ndgrid(find(nnzmati));'])
+ eval(['nnzind=sub2ind(repmat(n_v,1,order),' subindsvec ');'])
+ nnzind=sparse(nnzind,ones(length(nnzind),1),ones(length(nnzind),1),n_v^order,1);
+ [loc,nnzind]=nnz_UW(n_v,order,nnzind,'ind');
+ smat=sparse(loc,ones(length(loc),1),nnzind,nchoosek(n_v+order-1,order),1);
+ eval(['[' subinds ']=ind2sub(repmat(n_v,1,order),full(smat(deriv_i.cols)));'])
+ eval(['allind=[' subindsvec '];'])
+ deriv_i.cols=intarray(allind); % this is the unique form
+ %%%%
+ % change column indices
+ deriv_i.cols=intarray(nnzmati(deriv_i.cols));
+ deriv_i.tsize=intarray([1,repmat(ni,1,order)]);
+ if ni>0 % if column dimension is nonzero (which is the normal case)
+ % u2c
+ deriv_i=u2c(deriv_i);
+ [~,W]=create_UW(ni,order);
+ deriv_i=contraction1(unfold(deriv_i),spmat2sptensor(W));
+ end
+ %change column indices back to original
+ if order==2
+ deriv_i=fold(deriv_i,ni,ni);
+ elseif order==3
+ deriv_i=fold(deriv_i,ni,ni,ni);
+ elseif order==4
+ deriv_i=fold(deriv_i,ni,ni,ni,ni);
+ elseif order==5
+ deriv_i=fold(deriv_i,ni,ni,ni,ni,ni);
+ else
+ error('order should be between 2 and 5')
+ end
+ temp=find(nnzmati);
+ deriv_i.cols=temp(deriv_i.cols);
+
+ n_valsi=size(deriv_i.vals,2);
+ sortind(nz:nz+n_valsi-1)=deriv_i.vals;
+ newcols(nz:nz+n_valsi-1,:)=deriv_i.cols;
+ nz=nz+n_valsi;
+ newptr(i+1)=nz;
+ end
+
+ ind.sortind=sortind(1:nz-1);
+ ind.newcols=intarray(newcols(1:nz-1,:));
+ ind.ptr=intarray(newptr);
+ derivs=original_derivs;
+end
+
+derivs_uncompressed=sptensor;
+derivs_uncompressed.vals=derivs.vals(:,ind.sortind);
+derivs_uncompressed.cols=ind.newcols;
+derivs_uncompressed.ptr=ind.ptr;
+derivs_uncompressed.tsize=intarray([l,repmat(n_v,1,order)]);
+
+
+end
+
diff --git a/105/should_reproduce.txt b/105/should_reproduce.txt
new file mode 100644
index 0000000000000000000000000000000000000000..49384932f5fa6a36368d9c797e8088319871df4e
--- /dev/null
+++ b/105/should_reproduce.txt
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ffcf205a879662dcb27e51b78cc5b41710889af588695d45808c69245dbb184
+size 74