make extended path algorithm 1 as a self contained problem usable by dynare_solve

time-shift
Michel Juillard 2014-05-12 10:18:43 +02:00
parent c3efb214ef
commit 26f2b301b0
3 changed files with 329 additions and 272 deletions

194
matlab/ep/ep_problem_2.m Normal file
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@ -0,0 +1,194 @@
function [res,A,info] = ep_problem_2(y,x,pm)
info = 0;
res = [];
A = [];
dynamic_model = pm.dynamic_model;
ny = pm.ny;
params = pm.params;
steady_state = pm.steady_state;
order = pm.order;
nodes = pm.nodes;
nnodes = pm.nnodes;
weights = pm.weights;
h_correction = pm.h_correction;
dimension = pm.dimension;
world_nbr = pm.world_nbr;
nnzA = pm.nnzA;
periods = pm.periods;
i_rows = pm.i_rows';
i_cols = pm.i_cols;
nyp = pm.nyp;
nyf = pm.nyf;
hybrid_order = pm.hybrid_order;
i_cols_1 = pm.i_cols_1;
i_cols_j = pm.i_cols_j;
icA = pm.icA;
i_cols_T = pm.i_cols_T;
i_cols_p = i_cols(1:nyp);
i_cols_s = i_cols(nyp+(1:ny));
i_cols_f = i_cols(nyp+ny+(1:nyf));
i_cols_A = i_cols;
i_cols_Ap0 = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af0 = i_cols_f - ny;
i_hc = i_cols_f - 2*ny;
nzA = cell(periods,world_nbr);
res = zeros(ny,periods,world_nbr);
Y = zeros(ny*(periods+2),world_nbr);
Y(1:ny,1) = pm.y0;
Y(end-ny+1:end,:) = repmat(steady_state,1,world_nbr);
Y(pm.i_upd_y) = y;
offset_r0 = 0;
for i = 1:order+1
i_w_p = 1;
for j = 1:(1+(nnodes-1)*(i-1))
innovation = x;
if i <= order && j == 1
% first world, integrating future shocks
if nargin > 1
A1 = sparse([],[],[],i*ny,dimension,nnzA*world_nbr);
end
for k=1:nnodes
if nargin > 1
if i == 2
i_cols_Ap = i_cols_Ap0;
elseif i > 2
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes- ...
1)*(i-2)*(i-3)/2);
end
if k == 1
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2);
else
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2+(i-1)*(nnodes-1) ...
+ k - 1);
end
end
if i > 1
innovation(i+1,:) = nodes(k,:);
end
if k == 1
k1 = 1;
else
k1 = (nnodes-1)*(i-1)+k;
end
if hybrid_order == 2 && (k > 1 || i == order)
z = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)+h_correction(i_hc)];
else
z = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)];
end
if nargin > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
end
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,1) = res(:,i,1)+weights(k)*d1;
end
if nargin > 1
[ir,ic,v] = find(A1);
nzA{i,j} = [ir,ic,v]';
end
elseif j > 1 + (nnodes-1)*(i-2)
% new world, using previous state of world 1 and hit
% by shocks from nodes
if nargin > 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
end
k = j - (nnodes-1)*(i-2);
innovation(i+1,:) = nodes(k,:);
z = [Y(i_cols_p,1);
Y(i_cols_s,j);
Y(i_cols_f,j)];
if nargin > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
[ir,ic,v] = find(jacobian(:,i_cols_j));
nzA{i,j} = [i_rows(ir),i_cols_A(ic), v]';
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,j) = d1;
if nargin > 1
i_cols_Af = i_cols_Af + ny;
end
else
% existing worlds other than 1
if nargin > 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2+j-1);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
end
z = [Y(i_cols_p,j);
Y(i_cols_s,j);
Y(i_cols_f,j)];
if nargin > 1
[d1,jacobian] = dynamic_model(z,innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
[ir,ic,v] = find(jacobian(:,i_cols_j));
nzA{i,j} = [i_rows(ir),i_cols_A(ic),v]';
else
d1 = dynamic_model(z,innovation,params,steady_state,i+1);
end
res(:,i,j) = d1;
i_cols_Af = i_cols_Af + ny;
end
i_rows = i_rows + ny;
if mod(j,nnodes) == 0
i_w_p = i_w_p + 1;
end
if nargin > 1 && i > 1
i_cols_As = i_cols_As + ny;
end
offset_r0 = offset_r0 + ny;
end
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
end
for j=1:world_nbr
i_rows_y = i_cols+(order+1)*ny;
offset_c = ny*(order+(nnodes-1)*(order-1)*order/2+j-1);
offset_r = offset_r0+(j-1)*ny;
for i=order+2:periods
if nargin > 1
[d1,jacobian] = dynamic_model(Y(i_rows_y,j),x,params, ...
steady_state,i+1);
if i < periods
[ir,ic,v] = find(jacobian(:,i_cols_j));
else
[ir,ic,v] = find(jacobian(:,i_cols_T));
end
nzA{i,j} = [offset_r+ir,offset_c+icA(ic), v]';
else
d1 = dynamic_model(Y(i_rows_y,j),x,params, ...
steady_state,i+1);
end
res(:,i,j) = d1;
i_rows_y = i_rows_y + ny;
offset_c = offset_c + world_nbr*ny;
offset_r = offset_r + world_nbr*ny;
end
end
if nargin > 1
iA = [nzA{:}]';
A = sparse(iA(:,1),iA(:,2),iA(:,3),dimension,dimension);
end
res = res(pm.i_upd_r);

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@ -1,4 +1,4 @@
function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model_1(endo_simul,exo_simul,EpOptions,pfm,order,varargin)
function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model_1(endo_simul,exo_simul,Options,pfm,order,varargin)
% Copyright (C) 2012-2013 Dynare Team
%
@ -17,281 +17,135 @@ function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model_1(endo
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
if nargin < 6
homotopy_parameter = 1;
else
homotopy_parameter = varargin{1};
global options_
if nargin < 6
homotopy_parameter = 1;
else
homotopy_parameter = varargin{1};
end
flag = 0;
err = 0;
stop = 0;
EpOptions = Options.ep;
params = pfm.params;
steady_state = pfm.steady_state;
ny = pfm.ny;
periods = pfm.periods;
dynamic_model = pfm.dynamic_model;
lead_lag_incidence = pfm.lead_lag_incidence;
nyp = pfm.nyp;
nyf = pfm.nyf;
i_cols_1 = pfm.i_cols_1;
i_cols_A1 = pfm.i_cols_A1;
i_cols_j = pfm.i_cols_j;
i_cols_T = nonzeros(lead_lag_incidence(1:2,:)');
hybrid_order = pfm.hybrid_order;
dr = pfm.dr;
nodes = pfm.nodes;
weights = pfm.weights;
nnodes = pfm.nnodes;
maxit = pfm.maxit_;
tolerance = pfm.tolerance;
verbose = pfm.verbose;
number_of_shocks = size(exo_simul,2);
% make sure that there is a node equal to zero
% and permute nodes and weights to have zero first
k = find(sum(abs(nodes),2) < 1e-12);
if ~isempty(k)
nodes = [nodes(k,:); nodes(1:k-1,:); nodes(k+1:end,:)];
weights = [weights(k); weights(1:k-1); weights(k+1:end)];
else
error('there is no nodes equal to zero')
end
if hybrid_order > 0
if hybrid_order == 2
h_correction = 0.5*dr.ghs2(dr.inv_order_var);
end
flag = 0;
err = 0;
stop = 0;
else
h_correction = 0;
end
params = pfm.params;
steady_state = pfm.steady_state;
ny = pfm.ny;
periods = pfm.periods;
dynamic_model = pfm.dynamic_model;
lead_lag_incidence = pfm.lead_lag_incidence;
nyp = pfm.nyp;
nyf = pfm.nyf;
i_cols_1 = pfm.i_cols_1;
i_cols_A1 = pfm.i_cols_A1;
i_cols_j = pfm.i_cols_j;
i_cols_T = nonzeros(lead_lag_incidence(1:2,:)');
hybrid_order = pfm.hybrid_order;
dr = pfm.dr;
[nodes,weights,nnodes] = setup_integration_nodes(EpOptions,pfm);
maxit = pfm.maxit_;
tolerance = pfm.tolerance;
verbose = pfm.verbose;
if verbose
disp ([' -----------------------------------------------------']);
disp (['MODEL SIMULATION :']);
fprintf('\n');
end
number_of_shocks = size(exo_simul,2);
% Each column of Y represents a different world
% The upper right cells are unused
% The first row block is ny x 1
% The second row block is ny x nnodes
% The third row block is ny x nnodes^2
% and so on until size ny x nnodes^order
world_nbr = 1+(nnodes-1)*order;
Y = endo_simul(:,2:end-1);
Y = repmat(Y,1,world_nbr);
pfm.y0 = endo_simul(:,1);
% make sure that there is a node equal to zero
% and permute nodes and weights to have zero first
k = find(sum(abs(nodes),2) < 1e-12);
if ~isempty(k)
nodes = [nodes(k,:); nodes(1:k-1,:); nodes(k+1:end,:)];
weights = [weights(k); weights(1:k-1); weights(k+1:end)];
else
error('there is no nodes equal to zero')
end
if hybrid_order > 0
if hybrid_order == 2
h_correction = 0.5*dr.ghs2(dr.inv_order_var);
end
% The columns of A map the elements of Y such that
% each block of Y with ny rows are unfolded column wise
% number of blocks
block_nbr = (order+(nnodes-1)*(order-1)*order/2+(periods-order)*world_nbr);
% dimension of the problem
dimension = ny*block_nbr;
pfm.block_nbr = block_nbr;
pfm.dimension = dimension;
if order == 0
i_upd_r = (1:ny*periods);
i_upd_y = i_upd_r + ny;
else
i_upd_r = zeros(dimension,1);
i_upd_y = i_upd_r;
i_upd_r(1:ny) = (1:ny);
i_upd_y(1:ny) = ny+(1:ny);
i1 = ny+1;
i2 = 2*ny;
n1 = ny+1;
n2 = 2*ny;
for i=2:periods
k = n1:n2;
for j=1:(1+(nnodes-1)*min(i-1,order))
i_upd_r(i1:i2) = k+(j-1)*ny*periods;
i_upd_y(i1:i2) = k+ny+(j-1)*ny*(periods+2);
i1 = i2+1;
i2 = i2+ny;
end
n1 = n2+1;
n2 = n2+ny;
end
end
icA = [find(lead_lag_incidence(1,:)) find(lead_lag_incidence(2,:))+world_nbr*ny ...
find(lead_lag_incidence(3,:))+2*world_nbr*ny]';
h1 = clock;
pfm.order = order;
pfm.world_nbr = world_nbr;
pfm.nodes = nodes;
pfm.nnodes = nnodes;
pfm.weights = weights;
pfm.h_correction = h_correction;
pfm.i_rows = 1:ny;
i_cols = find(lead_lag_incidence');
pfm.i_cols = i_cols;
pfm.nyp = nyp;
pfm.nyf = nyf;
pfm.hybrid_order = hybrid_order;
pfm.i_cols_1 = i_cols_1;
pfm.i_cols_h = i_cols_j;
pfm.icA = icA;
pfm.i_cols_T = i_cols_T;
pfm.i_upd_r = i_upd_r;
pfm.i_upd_y = i_upd_y;
if verbose
disp ([' -----------------------------------------------------']);
disp (['MODEL SIMULATION :']);
fprintf('\n');
end
z = endo_simul(find(lead_lag_incidence'));
[d1,jacobian] = dynamic_model(z,exo_simul,params,steady_state,2);
% Each column of Y represents a different world
% The upper right cells are unused
% The first row block is ny x 1
% The second row block is ny x nnodes
% The third row block is ny x nnodes^2
% and so on until size ny x nnodes^order
world_nbr = 1+(nnodes-1)*order;
Y = repmat(endo_simul(:),1,world_nbr);
% The columns of A map the elements of Y such that
% each block of Y with ny rows are unfolded column wise
dimension = ny*(order+(nnodes-1)*(order-1)*order/2+(periods-order)*world_nbr);
if order == 0
i_upd_r = (1:ny*periods);
i_upd_y = i_upd_r + ny;
else
i_upd_r = zeros(dimension,1);
i_upd_y = i_upd_r;
i_upd_r(1:ny) = (1:ny);
i_upd_y(1:ny) = ny+(1:ny);
i1 = ny+1;
i2 = 2*ny;
n1 = ny+1;
n2 = 2*ny;
for i=2:periods
k = n1:n2;
for j=1:(1+(nnodes-1)*min(i-1,order))
i_upd_r(i1:i2) = k+(j-1)*ny*periods;
i_upd_y(i1:i2) = k+ny+(j-1)*ny*(periods+2);
i1 = i2+1;
i2 = i2+ny;
end
n1 = n2+1;
n2 = n2+ny;
end
end
icA = [find(lead_lag_incidence(1,:)) find(lead_lag_incidence(2,:))+world_nbr*ny ...
find(lead_lag_incidence(3,:))+2*world_nbr*ny]';
h1 = clock;
for iter = 1:maxit
h2 = clock;
A1 = sparse([],[],[],ny*(order+(nnodes-1)*(order-1)*order/2),dimension,(order+1)*world_nbr*nnz(jacobian));
res = zeros(ny,periods,world_nbr);
i_rows = 1:ny;
i_cols = find(lead_lag_incidence');
i_cols_p = i_cols(1:nyp);
i_cols_s = i_cols(nyp+(1:ny));
i_cols_f = i_cols(nyp+ny+(1:nyf));
i_cols_A = i_cols;
i_cols_Ap0 = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af0 = i_cols_f - ny;
i_hc = i_cols_f - 2*ny;
for i = 1:order+1
i_w_p = 1;
for j = 1:(1+(nnodes-1)*(i-1))
innovation = exo_simul;
if i <= order && j == 1
% first world, integrating future shocks
for k=1:nnodes
if i == 2
i_cols_Ap = i_cols_Ap0;
elseif i > 2
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes- ...
1)*(i-2)*(i-3)/2);
end
if k == 1
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2);
else
i_cols_Af = i_cols_Af0 + ny*(i-1+(nnodes-1)*i*(i-1)/ ...
2+(i-1)*(nnodes-1) ...
+ k - 1);
end
if i > 1
innovation(i+1,:) = nodes(k,:);
end
if k == 1
k1 = 1;
else
k1 = (nnodes-1)*(i-1)+k;
end
if hybrid_order == 2 && (k > 1 || i == order)
y = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)+h_correction(i_hc)];
else
y = [Y(i_cols_p,1);
Y(i_cols_s,1);
Y(i_cols_f,k1)];
end
[d1,jacobian] = dynamic_model(y,homotopy_parameter*innovation, ...
params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = A1(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
end
res(:,i,1) = res(:,i,1)+weights(k)*d1;
end
elseif j > 1 + (nnodes-1)*(i-2)
% new world, using previous state of world 1 and hit
% by shocks from nodes
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
k = j - (nnodes-1)*(i-2);
innovation(i+1,:) = nodes(k,:);
y = [Y(i_cols_p,1);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,homotopy_parameter*innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(:,i,j) = d1;
i_cols_Af = i_cols_Af + ny;
else
% existing worlds other than 1
i_cols_Ap = i_cols_Ap0 + ny*(i-2+(nnodes-1)*(i-2)*(i-3)/2+j-1);
i_cols_Af = i_cols_Af0 + ny*(i+(nnodes-1)*i*(i-1)/2+j-2);
y = [Y(i_cols_p,j);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,homotopy_parameter*innovation,params,steady_state,i+1);
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A1(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(:,i,j) = d1;
i_cols_Af = i_cols_Af + ny;
end
i_rows = i_rows + ny;
if mod(j,nnodes) == 0
i_w_p = i_w_p + 1;
end
if i > 1
i_cols_As = i_cols_As + ny;
end
end
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
end
nzA = cell(periods,world_nbr);
parfor j=1:world_nbr
i_rows_y = find(lead_lag_incidence')+(order+1)*ny;
offset_c = ny*(order+(nnodes-1)*(order-1)*order/2+j-1);
offset_r = (j-1)*ny;
for i=order+2:periods
[d1,jacobian] = dynamic_model(Y(i_rows_y,j), ...
exo_simul,params, ...
steady_state,i+1);
if i == periods
[ir,ic,v] = find(jacobian(:,i_cols_T));
else
[ir,ic,v] = find(jacobian(:,i_cols_j));
end
nzA{i,j} = [offset_r+ir,offset_c+icA(ic), v]';
res(:,i,j) = d1;
i_rows_y = i_rows_y + ny;
offset_c = offset_c + world_nbr*ny;
offset_r = offset_r + world_nbr*ny;
end
end
err = max(abs(res(i_upd_r)));
if verbose
[err1, k1] = max(abs(res));
[err2, k2] = max(abs(err1));
[err3, k3] = max(abs(err2));
disp([iter err k1(:,k2(:,:,k3),k3) k2(:,:,k3) k3])
end
if err < tolerance
stop = 1;
flag = 0;% Convergency obtained.
endo_simul = reshape(Y(:,1),ny,periods+2);%Y(ny+(1:ny),1);
if verbose
save ep_test_s1 exo_simul endo_simul Y
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp([' Convergency obtained.']) ;
fprintf('\n') ;
end
break
end
A2 = [nzA{:}]';
if any(isnan(A2(:,3))) || any(any(any(isnan(res))))
if verbose
disp(['solve_stochastic_foresight_model_1 encountered ' ...
'NaN'])
save ep_test_s2 exo_simul endo_simul
pause
end
flag = 1;
return
end
A = [A1; sparse(A2(:,1),A2(:,2),A2(:,3),ny*(periods-order-1)*world_nbr,dimension)];
if verbose
disp(sprintf('condest %g',condest(A)))
end
dy = -A\res(i_upd_r);
Y(i_upd_y) = Y(i_upd_y) + dy;
end
if ~stop
if verbose
fprintf('\n') ;
disp([' Total time of simulation :' num2str(etime(clock,h1))]) ;
fprintf('\n') ;
disp(['WARNING : maximum number of iterations is reached (modify options_.simul.maxit).']) ;
fprintf('\n') ;
disp(sprintf('err: %f',err));
save ep_test_s2 exo_simul endo_simul
pause
end
flag = 1;% more iterations are needed.
endo_simul = 1;
end
if verbose
disp (['-----------------------------------------------------']) ;
end
options_.solve_algo = 9;
options_.steady.maxit = 100;
y = repmat(steady_state,block_nbr,1);
y = dynare_solve(@ep_problem_2,y,1,exo_simul,pfm);
endo_simul(:,2) = y(1:ny);

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@ -0,0 +1,9 @@
function [X,w]=stroud_judd_7.5.8(d)
E = eye(d);
X = cell(2*d,1);
m = 1;
for i=1:d
X{m} = E(:,i);
m = m+1;
X{m} = -E(:,i);