538 lines
17 KiB
Matlab
538 lines
17 KiB
Matlab
function [H, dA, dOm, Hss, gp, d2A, d2Om, H2ss] = getH(A, B, M_,oo_,kronflag,indx,indexo)
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% computes derivative of reduced form linear model w.r.t. deep params
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%
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% Copyright (C) 2010-2011 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if nargin<3 || isempty(kronflag), kronflag = 0; end
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if nargin<4 || isempty(indx), indx = [1:M_.param_nbr];, end,
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if nargin<5 || isempty(indexo), indexo = [];, end,
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[I,J]=find(M_.lead_lag_incidence');
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yy0=oo_.dr.ys(I);
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% yy0=[];
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% for j=1:size(M_.lead_lag_incidence,1);
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% yy0 = [ yy0; oo_.dr.ys(find(M_.lead_lag_incidence(j,:)))];
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% end
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dyssdtheta=zeros(length(oo_.dr.ys),M_.param_nbr);
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if nargout>5,
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[residual, gg1, gg2] = feval([M_.fname,'_static'],oo_.dr.ys, oo_.exo_steady_state', M_.params);
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[df, gp, d2f] = feval([M_.fname,'_params_derivs'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1, dyssdtheta);
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d2f = get_all_resid_2nd_derivs(d2f,length(oo_.dr.ys),M_.param_nbr);
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d2f = d2f(:,indx,indx);
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if isempty(find(gg2)),
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for j=1:length(indx),
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d2yssdtheta(:,:,j) = -gg1\d2f(:,:,j);
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end
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else
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gam = d2f*0;
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for j=1:length(indx),
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d2yssdtheta(:,:,j) = -gg1\(d2f(:,:,j)+gam(:,:,j));
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end
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end
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else
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[residual, gg1] = feval([M_.fname,'_static'],oo_.dr.ys, oo_.exo_steady_state', M_.params);
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df = feval([M_.fname,'_params_derivs'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1, dyssdtheta);
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end
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dyssdtheta = -gg1\df;
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if any(any(isnan(dyssdtheta))),
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[U,T] = schur(gg1);
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global options_
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qz_criterium=options_.qz_criterium;
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e1 = abs(ordeig(T)) < qz_criterium-1;
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k = sum(e1); % Number non stationary variables.
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n = length(e1)-k; % Number of stationary variables.
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[U,T] = ordschur(U,T,e1);
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T = T(k+1:end,k+1:end);
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dyssdtheta = -U(:,k+1:end)*(T\U(:,k+1:end)')*df;
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if nargout>5,
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for j=1:length(indx),
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d2yssdtheta(:,:,j) = -U(:,k+1:end)*(T\U(:,k+1:end)')*d2f(:,:,j);
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end
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end
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end
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if nargout>5,
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[df, gp, d2f, gpp] = feval([M_.fname,'_params_derivs'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1, dyssdtheta);
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H2ss = d2yssdtheta(oo_.dr.order_var,:,:);
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[residual, g1, g2, g3] = feval([M_.fname,'_dynamic'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1);
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else
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[df, gp] = feval([M_.fname,'_params_derivs'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1, dyssdtheta);
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[residual, g1, g2 ] = feval([M_.fname,'_dynamic'],yy0, oo_.exo_steady_state', ...
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M_.params, oo_.dr.ys, 1);
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end
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Hss = dyssdtheta(oo_.dr.order_var,indx);
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dyssdtheta = dyssdtheta(I,:);
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[nr, nc]=size(g2);
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[m, nelem]=size(g1);
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nc = sqrt(nc);
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ns = max(max(M_.lead_lag_incidence));
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gp2 = gp*0;
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for j=1:nr,
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[I J]=ind2sub([nc nc],find(g2(j,:)));
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for i=1:nc,
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is = find(I==i);
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is = is(find(J(is)<=ns));
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if ~isempty(is),
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g20=full(g2(j,find(g2(j,:))));
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gp2(j,i,:)=g20(is)*dyssdtheta(J(is),:);
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end
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end
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end
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gp = gp+gp2;
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gp = gp(:,:,indx);
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param_nbr = length(indx);
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if nargout>5,
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param_nbr_2 = param_nbr*(param_nbr+1)/2;
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end
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m = size(A,1);
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n = size(B,2);
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klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
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k11 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);
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a = g1(:,nonzeros(k11'));
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da = gp(:,nonzeros(k11'),:);
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if nargout > 5,
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nelem = size(g1,2);
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g22 = get_all_2nd_derivs(gpp,m,nelem,M_.param_nbr);
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g22 = g22(:,:,indx,indx);
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d2a = g22(:,nonzeros(k11'),:,:);
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end
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kstate = oo_.dr.kstate;
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GAM1 = zeros(M_.endo_nbr,M_.endo_nbr);
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Dg1 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr);
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% nf = find(M_.lead_lag_incidence(M_.maximum_endo_lag+2,:));
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% GAM1(:, nf) = -g1(:,M_.lead_lag_incidence(M_.maximum_endo_lag+2,nf));
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k1 = find(kstate(:,2) == M_.maximum_endo_lag+2 & kstate(:,3));
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GAM1(:, kstate(k1,1)) = -a(:,kstate(k1,3));
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Dg1(:, kstate(k1,1), :) = -da(:,kstate(k1,3),:);
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if nargout > 5,
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D2g1 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr,param_nbr);
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D2g1(:, kstate(k1,1), :, :) = -d2a(:,kstate(k1,3),:,:);
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end
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% k = find(kstate(:,2) > M_.maximum_endo_lag+2 & kstate(:,3));
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% kk = find(kstate(:,2) > M_.maximum_endo_lag+2 & ~kstate(:,3));
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% nauxe = 0;
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% if ~isempty(k),
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% ax(:,k)= -a(:,kstate(k,3));
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% ax(:,kk)= 0;
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% dax(:,k,:)= -da(:,kstate(k,3),:);
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% dax(:,kk,:)= 0;
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% nauxe=size(ax,2);
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% GAM1 = [ax GAM1];
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% Dg1 = cat(2,dax,Dg1);
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% clear ax
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% end
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[junk,cols_b,cols_j] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+1, ...
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oo_.dr.order_var));
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GAM0 = zeros(M_.endo_nbr,M_.endo_nbr);
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Dg0 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr);
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GAM0(:,cols_b) = g1(:,cols_j);
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Dg0(:,cols_b,:) = gp(:,cols_j,:);
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if nargout > 5,
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D2g0 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr,param_nbr);
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D2g0(:, cols_b, :, :) = g22(:,cols_j,:,:);
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end
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% GAM0 = g1(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,:));
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k2 = find(kstate(:,2) == M_.maximum_endo_lag+1 & kstate(:,4));
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GAM2 = zeros(M_.endo_nbr,M_.endo_nbr);
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Dg2 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr);
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% nb = find(M_.lead_lag_incidence(1,:));
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% GAM2(:, nb) = -g1(:,M_.lead_lag_incidence(1,nb));
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GAM2(:, kstate(k2,1)) = -a(:,kstate(k2,4));
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Dg2(:, kstate(k2,1), :) = -da(:,kstate(k2,4),:);
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if nargout > 5,
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D2g2 = zeros(M_.endo_nbr,M_.endo_nbr,param_nbr,param_nbr);
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D2g2(:, kstate(k2,1), :, :) = -d2a(:,kstate(k2,4),:,:);
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end% naux = 0;
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% k = find(kstate(:,2) < M_.maximum_endo_lag+1 & kstate(:,4));
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% kk = find(kstate(:,2) < M_.maximum_endo_lag+1 );
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% if ~isempty(k),
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% ax(:,k)= -a(:,kstate(k,4));
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% ax = ax(:,kk);
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% dax(:,k,:)= -da(:,kstate(k,4),:);
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% dax = dax(:,kk,:);
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% naux = size(ax,2);
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% GAM2 = [GAM2 ax];
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% Dg2 = cat(2,Dg2,dax);
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% end
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%
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% GAM0 = blkdiag(GAM0,eye(naux));
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% Dg0 = cat(1,Dg0,zeros(naux+nauxe,M_.endo_nbr,param_nbr));
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% Dg0 = cat(2,Dg0,zeros(m+nauxe,naux,param_nbr));
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% Dg0 = cat(2,zeros(m+nauxe,nauxe,param_nbr),Dg0);
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%
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% GAM2 = [GAM2 ; A(M_.endo_nbr+1:end,:)];
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% Dg2 = cat(1,Dg2,zeros(naux+nauxe,m,param_nbr));
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% Dg2 = cat(2,zeros(m+nauxe,nauxe,param_nbr),Dg2);
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% GAM2 = [zeros(m+nauxe,nauxe) [GAM2; zeros(nauxe,m)]];
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% GAM0 = [[zeros(m,nauxe);(eye(nauxe))] [GAM0; zeros(nauxe,m)]];
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GAM3 = -g1(:,length(yy0)+1:end);
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% GAM3 = -g1(oo_.dr.order_var,length(yy0)+1:end);
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% GAM3 = [GAM3; zeros(naux+nauxe,size(GAM3,2))];
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% Dg3 = -gp(oo_.dr.order_var,length(yy0)+1:end,:);
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Dg3 = -gp(:,length(yy0)+1:end,:);
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if nargout>5,
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D2g3 = -g22(:,length(yy0)+1:end,:,:);
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clear g22 d2a
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end
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% Dg3 = cat(1,Dg3,zeros(naux+nauxe,size(GAM3,2),param_nbr));
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% auxe = zeros(0,1);
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% k0 = kstate(find(kstate(:,2) >= M_.maximum_endo_lag+2),:);;
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% i0 = find(k0(:,2) == M_.maximum_endo_lag+2);
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% for i=M_.maximum_endo_lag+3:M_.maximum_endo_lag+2+M_.maximum_endo_lead,
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% i1 = find(k0(:,2) == i);
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% n1 = size(i1,1);
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% j = zeros(n1,1);
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% for j1 = 1:n1
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% j(j1) = find(k0(i0,1)==k0(i1(j1),1));
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% end
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% auxe = [auxe; i0(j)];
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% i0 = i1;
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% end
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% auxe = [(1:size(auxe,1))' auxe(end:-1:1)];
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% n_ir1 = size(auxe,1);
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% nr = m + n_ir1;
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% GAM1 = [[GAM1 zeros(size(GAM1,1),naux)]; zeros(naux+nauxe,m+nauxe)];
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% GAM1(m+1:end,:) = sparse(auxe(:,1),auxe(:,2),ones(n_ir1,1),n_ir1,nr);
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% Dg1 = cat(2,Dg1,zeros(M_.endo_nbr,naux,param_nbr));
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% Dg1 = cat(1,Dg1,zeros(naux+nauxe,m+nauxe,param_nbr));
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% Ax = A;
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% A1 = A;
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% Bx = B;
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% B1 = B;
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% for j=1:M_.maximum_endo_lead-1,
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% A1 = A1*A;
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% B1 = A*B1;
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% k = find(kstate(:,2) == M_.maximum_endo_lag+2+j );
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% Ax = [A1(kstate(k,1),:); Ax];
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% Bx = [B1(kstate(k,1),:); Bx];
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% end
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% Ax = [zeros(m+nauxe,nauxe) Ax];
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% A0 = A;
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% A=Ax; clear Ax A1;
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% B0=B;
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% B = Bx; clear Bx B1;
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m = size(A,1);
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n = size(B,2);
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% Dg1 = zeros(m,m,param_nbr);
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% Dg1(:, nf, :) = -gp(:,M_.lead_lag_incidence(3,nf),:);
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% Dg0 = gp(:,M_.lead_lag_incidence(2,:),:);
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% Dg2 = zeros(m,m,param_nbr);
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% Dg2(:, nb, :) = -gp(:,M_.lead_lag_incidence(1,nb),:);
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% Dg3 = -gp(:,length(yy0)+1:end,:);
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if kronflag==1, % kronecker products
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Dg0=reshape(Dg0,m^2,param_nbr);
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Dg1=reshape(Dg1,m^2,param_nbr);
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Dg2=reshape(Dg2,m^2,param_nbr);
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for j=1:param_nbr,
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Dg3(:,:,j)=Dg3(:,:,j)*M_.Sigma_e;
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end
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Dg3=reshape(Dg3,m*n,param_nbr);
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Om = B*M_.Sigma_e*B';
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Im = eye(m);
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Dm = duplication(m);
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DmPl = inv(Dm'*Dm)*Dm';
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Kmm = commutation(m,m);
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Kmn = commutation(m,n);
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Da = [eye(m^2),zeros(m^2,m*(m+1)/2)];
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Dom = [zeros(m*(m+1)/2,m^2),eye(m*(m+1)/2)];
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Df1Dtau = ( kron(Im,GAM0) - kron(A',GAM1) - kron(Im,GAM1*A) )*Da;
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Df1Dthet = kron(A',Im)*Dg0 - kron( (A')^2,Im)*Dg1 - Dg2;
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Df2Dtau = DmPl*( kron(GAM0,GAM0) - kron(GAM0,GAM1*A) - kron(GAM1*A,GAM0) + kron(GAM1*A,GAM1*A) )*Dm*Dom - ...
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DmPl*( kron(GAM0*Om,GAM1) + kron(GAM1,GAM0*Om)*Kmm - kron(GAM1*A*Om,GAM1) - kron(GAM1,GAM1*A*Om)*Kmm )*Da;
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Df2Dthet = DmPl*( kron(GAM0*Om,Im) + kron(Im,GAM0*Om)*Kmm - kron(Im,GAM1*A*Om)*Kmm - kron(GAM1*A*Om,Im) )*Dg0 - ...
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DmPl*( kron(GAM0*Om*A',Im) + kron(Im,GAM0*Om*A')*Kmm - kron(Im,GAM1*A*Om*A')*Kmm - kron(GAM1*A*Om*A',Im) )*Dg1 -...
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DmPl*( kron(GAM3,Im) + kron(Im,GAM3)*Kmn )*Dg3;
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DfDtau = [Df1Dtau;Df2Dtau];
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DfDthet = [Df1Dthet;Df2Dthet];
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H = -DfDtau\DfDthet;
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x = reshape(H(1:m*m,:),m,m,param_nbr);
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y = reshape(Dm*H(m*m+1:end,:),m,m,param_nbr);
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if nauxe,
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x = x(nauxe+1:end,nauxe+1:end,:);
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y = y(nauxe+1:end,nauxe+1:end,:);
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dA = x;
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dOm = y;
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m = size(y,1);
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x = reshape(x,m*m,param_nbr);
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Dm = duplication(m);
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DmPl = inv(Dm'*Dm)*Dm';
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y = DmPl*reshape(y,m*m,param_nbr);
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H = [x;y];
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else
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dA = x;
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dOm = y;
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end
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Hx = [];
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if ~isempty(indexo),
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dSig = zeros(M_.exo_nbr,M_.exo_nbr);
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dOm = cat(3,zeros(size(dOm,1),size(dOm,1),length(indexo)),dOm);
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for j=1:length(indexo)
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dSig(indexo(j),indexo(j)) = 2*sqrt(M_.Sigma_e(indexo(j),indexo(j)));
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y = B*dSig*B';
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y = y(nauxe+1:end,nauxe+1:end);
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Hx(:,j) = [zeros((m-nauxe)^2,1); dyn_vech(y)];
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if nargout>1,
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dOm(:,:,j) = y;
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end
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dSig(indexo(j),indexo(j)) = 0;
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end
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end
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H = [ [zeros(M_.endo_nbr,length(indexo)) Hss]; [Hx H]];
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elseif kronflag==-1, % perturbation
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fun = 'thet2tau';
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params0 = M_.params;
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H = fjaco(fun,[sqrt(diag(M_.Sigma_e(indexo,indexo))); M_.params(indx)],indx,indexo);
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assignin('base','M_', M_);
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assignin('base','oo_', oo_);
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else % generalized sylvester equation
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% solves a*x+b*x*c=d
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a = (GAM0-GAM1*A);
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inva = inv(a);
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b = -GAM1;
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c = A;
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elem = zeros(m,m,param_nbr);
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d = elem;
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for j=1:param_nbr,
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elem(:,:,j) = (Dg0(:,:,j)-Dg1(:,:,j)*A);
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d(:,:,j) = Dg2(:,:,j)-elem(:,:,j)*A;
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end
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xx=sylvester3(a,b,c,d);
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flag=1;
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icount=0;
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while flag && icount<4,
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[xx, flag]=sylvester3a(xx,a,b,c,d);
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icount=icount+1;
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end
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H=zeros(m*m+m*(m+1)/2,param_nbr+length(indexo));
|
|
if nargout>1,
|
|
dOm = zeros(m,m,param_nbr+length(indexo));
|
|
dA=zeros(m,m,param_nbr+length(indexo));
|
|
dB=zeros(m,n,param_nbr);
|
|
end
|
|
if ~isempty(indexo),
|
|
dSig = zeros(M_.exo_nbr,M_.exo_nbr,length(indexo));
|
|
for j=1:length(indexo)
|
|
dSig(indexo(j),indexo(j),j) = 2*sqrt(M_.Sigma_e(indexo(j),indexo(j)));
|
|
y = B*dSig(:,:,j)*B';
|
|
% y = y(nauxe+1:end,nauxe+1:end);
|
|
% H(:,j) = [zeros((m-nauxe)^2,1); dyn_vech(y)];
|
|
H(:,j) = [zeros(m^2,1); dyn_vech(y)];
|
|
if nargout>1,
|
|
dOm(:,:,j) = y;
|
|
end
|
|
% dSig(indexo(j),indexo(j)) = 0;
|
|
end
|
|
end
|
|
for j=1:param_nbr,
|
|
x = xx(:,:,j);
|
|
y = inva * (Dg3(:,:,j)-(elem(:,:,j)-GAM1*x)*B);
|
|
if nargout>1,
|
|
dB(:,:,j) = y;
|
|
end
|
|
y = y*M_.Sigma_e*B'+B*M_.Sigma_e*y';
|
|
% x = x(nauxe+1:end,nauxe+1:end);
|
|
% y = y(nauxe+1:end,nauxe+1:end);
|
|
if nargout>1,
|
|
dA(:,:,j+length(indexo)) = x;
|
|
dOm(:,:,j+length(indexo)) = y;
|
|
end
|
|
H(:,j+length(indexo)) = [x(:); dyn_vech(y)];
|
|
end
|
|
% for j=1:param_nbr,
|
|
% disp(['Derivatives w.r.t. ',M_.param_names(indx(j),:),', ',int2str(j),'/',int2str(param_nbr)])
|
|
% elem = (Dg0(:,:,j)-Dg1(:,:,j)*A);
|
|
% d = Dg2(:,:,j)-elem*A;
|
|
% x=sylvester3(a,b,c,d);
|
|
% % x=sylvester3a(x,a,b,c,d);
|
|
% y = inva * (Dg3(:,:,j)-(elem-GAM1*x)*B);
|
|
% y = y*B'+B*y';
|
|
% x = x(nauxe+1:end,nauxe+1:end);
|
|
% y = y(nauxe+1:end,nauxe+1:end);
|
|
% H(:,j) = [x(:); dyn_vech(y)];
|
|
% end
|
|
H = [[zeros(M_.endo_nbr,length(indexo)) Hss]; H];
|
|
|
|
end
|
|
|
|
if nargout > 5,
|
|
tot_param_nbr = param_nbr + length(indexo);
|
|
tot_param_nbr_2 = tot_param_nbr*(tot_param_nbr+1)/2;
|
|
d = zeros(m,m,param_nbr_2);
|
|
d2A = zeros(m,m,tot_param_nbr,tot_param_nbr);
|
|
d2Om = zeros(m,m,tot_param_nbr,tot_param_nbr);
|
|
d2B = zeros(m,n,tot_param_nbr,tot_param_nbr);
|
|
cc=triu(ones(param_nbr,param_nbr));
|
|
[i2,j2]=find(cc);
|
|
cc = blkdiag( zeros(length(indexo),length(indexo)), cc);
|
|
[ipar2]=find(cc);
|
|
ctot=triu(ones(tot_param_nbr,tot_param_nbr));
|
|
ctot(1:length(indexo),1:length(indexo))=eye(length(indexo));
|
|
[itot2, jtot2]=find(ctot);
|
|
jcount=0;
|
|
for j=1:param_nbr,
|
|
for i=j:param_nbr,
|
|
elem1 = (D2g0(:,:,j,i)-D2g1(:,:,j,i)*A);
|
|
elem1 = D2g2(:,:,j,i)-elem1*A;
|
|
elemj0 = Dg0(:,:,j)-Dg1(:,:,j)*A;
|
|
elemi0 = Dg0(:,:,i)-Dg1(:,:,i)*A;
|
|
elem2 = -elemj0*xx(:,:,i)-elemi0*xx(:,:,j);
|
|
elem2 = elem2 + ( Dg1(:,:,j)*xx(:,:,i) + Dg1(:,:,i)*xx(:,:,j) )*A;
|
|
elem2 = elem2 + GAM1*( xx(:,:,i)*xx(:,:,j) + xx(:,:,j)*xx(:,:,i));
|
|
jcount=jcount+1;
|
|
d(:,:,jcount) = elem1+elem2;
|
|
end
|
|
end
|
|
xx2=sylvester3(a,b,c,d);
|
|
flag=1;
|
|
icount=0;
|
|
while flag && icount<4,
|
|
[xx2, flag]=sylvester3a(xx2,a,b,c,d);
|
|
icount = icount + 1;
|
|
end
|
|
jcount = 0;
|
|
for j=1:param_nbr,
|
|
for i=j:param_nbr,
|
|
jcount=jcount+1;
|
|
x = xx2(:,:,jcount);
|
|
elem1 = (D2g0(:,:,j,i)-D2g1(:,:,j,i)*A);
|
|
elem1 = elem1 -( Dg1(:,:,j)*xx(:,:,i) + Dg1(:,:,i)*xx(:,:,j) );
|
|
elemj0 = Dg0(:,:,j)-Dg1(:,:,j)*A-GAM1*xx(:,:,j);
|
|
elemi0 = Dg0(:,:,i)-Dg1(:,:,i)*A-GAM1*xx(:,:,i);
|
|
elem0 = elemj0*dB(:,:,i)+elemi0*dB(:,:,j);
|
|
y = inva * (D2g3(:,:,j,i)-elem0-(elem1-GAM1*x)*B);
|
|
d2B(:,:,j+length(indexo),i+length(indexo)) = y;
|
|
d2B(:,:,i+length(indexo),j+length(indexo)) = y;
|
|
y = y*M_.Sigma_e*B'+B*M_.Sigma_e*y'+ ...
|
|
dB(:,:,j)*M_.Sigma_e*dB(:,:,i)'+dB(:,:,i)*M_.Sigma_e*dB(:,:,j)';
|
|
% x = x(nauxe+1:end,nauxe+1:end);
|
|
% y = y(nauxe+1:end,nauxe+1:end);
|
|
d2A(:,:,j+length(indexo),i+length(indexo)) = x;
|
|
d2A(:,:,i+length(indexo),j+length(indexo)) = x;
|
|
d2Om(:,:,j+length(indexo),i+length(indexo)) = y;
|
|
d2Om(:,:,i+length(indexo),j+length(indexo)) = y;
|
|
end
|
|
end
|
|
if ~isempty(indexo),
|
|
d2Sig = zeros(M_.exo_nbr,M_.exo_nbr,length(indexo));
|
|
for j=1:length(indexo)
|
|
d2Sig(indexo(j),indexo(j),j) = 2;
|
|
y = B*d2Sig(:,:,j)*B';
|
|
d2Om(:,:,j,j) = y;
|
|
% y = y(nauxe+1:end,nauxe+1:end);
|
|
% H(:,j) = [zeros((m-nauxe)^2,1); dyn_vech(y)];
|
|
% H(:,j) = [zeros(m^2,1); dyn_vech(y)];
|
|
% dOm(:,:,j) = y;
|
|
for i=1:param_nbr,
|
|
y = dB(:,:,i)*dSig(:,:,j)*B'+B*dSig(:,:,j)*dB(:,:,i)';
|
|
d2Om(:,:,j,i+length(indexo)) = y;
|
|
d2Om(:,:,i+length(indexo),j) = y;
|
|
end
|
|
end
|
|
end
|
|
end
|
|
|
|
return
|
|
|
|
function g22 = get_2nd_deriv(gpp,m,n,i,j),
|
|
|
|
g22=zeros(m,n);
|
|
is=find(gpp(:,3)==i);
|
|
is=is(find(gpp(is,4)==j));
|
|
|
|
if ~isempty(is),
|
|
g22(gpp(is,1),gpp(is,2))=gpp(is,5);
|
|
end
|
|
return
|
|
|
|
function g22 = get_all_2nd_derivs(gpp,m,n,npar),
|
|
|
|
g22=zeros(m,n,npar,npar);
|
|
% c=ones(npar,npar);
|
|
% c=triu(c);
|
|
% ic=find(c);
|
|
|
|
for is=1:length(gpp),
|
|
% d=zeros(npar,npar);
|
|
% d(gpp(is,3),gpp(is,4))=1;
|
|
% indx = find(ic==find(d));
|
|
g22(gpp(is,1),gpp(is,2),gpp(is,3),gpp(is,4))=gpp(is,5);
|
|
g22(gpp(is,1),gpp(is,2),gpp(is,4),gpp(is,3))=gpp(is,5);
|
|
end
|
|
|
|
return
|
|
|
|
function r22 = get_all_resid_2nd_derivs(rpp,m,npar),
|
|
|
|
r22=zeros(m,npar,npar);
|
|
% c=ones(npar,npar);
|
|
% c=triu(c);
|
|
% ic=find(c);
|
|
|
|
for is=1:length(rpp),
|
|
% d=zeros(npar,npar);
|
|
% d(rpp(is,2),rpp(is,3))=1;
|
|
% indx = find(ic==find(d));
|
|
r22(rpp(is,1),rpp(is,2),rpp(is,3))=rpp(is,4);
|
|
r22(rpp(is,1),rpp(is,3),rpp(is,2))=rpp(is,4);
|
|
end
|
|
|
|
return |