From a17c3f10575f0ab8904ab3a53bb6c13d0052cfd9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=A9bastien=20Villemot?= <sebastien@dynare.org>
Date: Thu, 26 Sep 2024 17:20:13 +0200
Subject: [PATCH] MCP solver: use sparse representation for the model
Ref. #1859
---
.../perfect_foresight_mcp_problem.m | 151 +++++++-----------
.../solve_stacked_problem.m | 29 ++--
2 files changed, 81 insertions(+), 99 deletions(-)
diff --git a/matlab/perfect-foresight-models/perfect_foresight_mcp_problem.m b/matlab/perfect-foresight-models/perfect_foresight_mcp_problem.m
index 13bb412050..d6bbda7c7e 100644
--- a/matlab/perfect-foresight-models/perfect_foresight_mcp_problem.m
+++ b/matlab/perfect-foresight-models/perfect_foresight_mcp_problem.m
@@ -1,50 +1,43 @@
-function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_function, Y0, YT, ...
- exo_simul, params, steady_state, ...
- maximum_lag, T, ny, i_cols, ...
- i_cols_J1, i_cols_1, i_cols_T, ...
- i_cols_j, i_cols_0,i_cols_J0, eq_index)
-% function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_function, Y0, YT, ...
-% exo_simul, params, steady_state, ...
-% maximum_lag, T, ny, i_cols, ...
-% i_cols_J1, i_cols_1, i_cols_T, ...
-% i_cols_j,eq_index)
+function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_resid_function, ...
+ dynamic_g1_function, Y0, YT, ...
+ exo_simul, params, steady_state, ...
+ dynamic_g1_sparse_rowval, ...
+ dynamic_g1_sparse_colval, ...
+ dynamic_g1_sparse_colptr, ...
+ maximum_lag, T, ny, eq_index)
+% function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_resid_function, ...
+% dynamic_g1_function, Y0, YT, ...
+% exo_simul, params, steady_state, ...
+% dynamic_g1_sparse_rowval, ...
+% dynamic_g1_sparse_colval, ...
+% dynamic_g1_sparse_colptr, ...
+% maximum_lag, T, ny, eq_index)
% Computes the residuals and the Jacobian matrix for a perfect foresight problem over T periods
% in a mixed complementarity problem context
%
% INPUTS
-% y [double] N*1 array, terminal conditions for the endogenous variables
-% dynamic_function [handle] function handle to _dynamic-file
-% Y0 [double] N*1 array, initial conditions for the endogenous variables
-% YT [double] N*1 array, terminal conditions for the endogenous variables
-% exo_simul [double] nperiods*M_.exo_nbr matrix of exogenous variables (in declaration order)
-% for all simulation periods
-% params [double] nparams*1 array, parameter values
-% steady_state [double] endo_nbr*1 vector of steady state values
-% maximum_lag [scalar] maximum lag present in the model
-% T [scalar] number of simulation periods
-% ny [scalar] number of endogenous variables
-% i_cols [double] indices of variables appearing in M_.lead_lag_incidence
-% and that need to be passed to _dynamic-file
-% i_cols_J1 [double] indices of contemporaneous and forward looking variables
-% appearing in M_.lead_lag_incidence
-% i_cols_1 [double] indices of contemporaneous and forward looking variables in
-% M_.lead_lag_incidence in dynamic Jacobian (relevant in first period)
-% i_cols_T [double] columns of dynamic Jacobian related to contemporaneous and backward-looking
-% variables (relevant in last period)
-% i_cols_j [double] indices of variables in M_.lead_lag_incidence
-% in dynamic Jacobian (relevant in intermediate periods)
-% eq_index [double] N*1 array, index vector describing residual mapping resulting
-% from complementarity setup
+% y [double] (ny*T)*1 array, path for the endogenous variables
+% dynamic_resid_function [handle] function handle to dynamic residuals
+% dynamic_g1_function [handle] function handle to dynamic Jacobian
+% Y0 [double] ny*1 array, initial conditions for the endogenous variables
+% YT [double] ny*1 array, terminal conditions for the endogenous variables
+% exo_simul [double] (max_lag+nperiods+max_lead)*M_.exo_nbr matrix of exogenous
+% variables (in declaration order) for all simulation periods
+% params [double] nparams*1 array, parameter values
+% steady_state [double] ny*1 vector of steady state values
+% dynamic_g1_sparse_rowval [integer vector] eponymous field in M_
+% dynamic_g1_sparse_colval [integer vector] eponymous field in M_
+% dynamic_g1_sparse_colptr [integer vector] eponymous field in M_
+% maximum_lag [scalar] maximum lag present in the model
+% T [scalar] number of simulation periods
+% ny [scalar] number of endogenous variables
+% eq_index [double] ny*1 array, index vector describing residual mapping resulting
+% from complementarity setup
% OUTPUTS
-% residuals [double] (N*T)*1 array, residuals of the stacked problem
-% JJacobian [double] (N*T)*(N*T) array, Jacobian of the stacked problem
-% ALGORITHM
-% None
-%
-% SPECIAL REQUIREMENTS
-% None.
+% residuals [double] (ny*T)*1 array, residuals of the stacked problem
+% JJacobian [double] (ny*T)*(ny*T) array, Jacobian of the stacked problem
-% Copyright © 1996-2020 Dynare Team
+% Copyright © 1996-2024 Dynare Team
%
% This file is part of Dynare.
%
@@ -61,65 +54,43 @@ function [residuals,JJacobian] = perfect_foresight_mcp_problem(y, dynamic_functi
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
+YY = reshape([Y0; y; YT], ny, T+2);
-YY = [Y0; y; YT];
-
-residuals = zeros(T*ny,1);
+residuals = NaN(T*ny,1);
if nargout == 2
iJacobian = cell(T,1);
end
-i_rows = 1:ny;
offset = 0;
-i_cols_J = i_cols;
-for it = maximum_lag+(1:T)
- if nargout == 1
- res = dynamic_function(YY(i_cols),exo_simul, params, ...
- steady_state,it);
- residuals(i_rows) = res(eq_index);
- elseif nargout == 2
- [res,jacobian] = dynamic_function(YY(i_cols),exo_simul, params, steady_state,it);
- residuals(i_rows) = res(eq_index);
- if T==1 && it==maximum_lag+1
- [rows, cols, vals] = find(jacobian(eq_index,i_cols_0));
- if size(jacobian, 1) == 1 % find() will return row vectors in this case
- rows = rows';
- cols = cols';
- vals = vals';
- end
- iJacobian{1} = [rows, i_cols_J0(cols), vals];
- elseif it == maximum_lag+1
- [rows,cols,vals] = find(jacobian(eq_index,i_cols_1));
- if numel(eq_index) == 1 % find() will return row vectors in this case
- rows = rows';
- cols = cols';
- vals = vals';
- end
- iJacobian{1} = [offset+rows, i_cols_J1(cols), vals];
- elseif it == maximum_lag+T
- [rows,cols,vals] = find(jacobian(eq_index,i_cols_T));
- if numel(eq_index) == 1 % find() will return row vectors in this case
- rows = rows';
- cols = cols';
- vals = vals';
- end
- iJacobian{T} = [offset+rows, i_cols_J(i_cols_T(cols)), vals];
+for t = 1:T
+ y3n = YY(:, t+(0:2));
+ x = exo_simul(t+maximum_lag, :);
+
+ [res, TT_order, TT] = dynamic_resid_function(y3n, x, params, steady_state);
+ residuals(offset + (1:ny)) = res(eq_index);
+
+ if nargout == 2
+ jacobian = dynamic_g1_function(y3n, x, params, steady_state, dynamic_g1_sparse_rowval, dynamic_g1_sparse_colval, dynamic_g1_sparse_colptr, TT_order, TT);
+ if T == 1 % static model
+ [rows, cols, vals] = find(jacobian(eq_index, ny+(1:ny)));
+ elseif t == 1
+ [rows, cols, vals] = find(jacobian(eq_index, ny+(1:2*ny)));
+ elseif t == T
+ [rows, cols, vals] = find(jacobian(eq_index, 1:2*ny));
+ cols = cols - ny;
else
- [rows,cols,vals] = find(jacobian(eq_index,i_cols_j));
- if numel(eq_index) == 1 % find() will return row vectors in this case
- rows = rows';
- cols = cols';
- vals = vals';
- end
- iJacobian{it-maximum_lag} = [offset+rows, i_cols_J(cols), vals];
- i_cols_J = i_cols_J + ny;
+ [rows, cols, vals] = find(jacobian(eq_index, 1:3*ny));
+ cols = cols - ny;
+ end
+ if numel(eq_index) == 1 % find() will return row vectors in this case
+ rows = rows';
+ cols = cols';
+ vals = vals';
end
- offset = offset + ny;
+ iJacobian{t} = [offset+rows, offset+cols, vals];
end
-
- i_rows = i_rows + ny;
- i_cols = i_cols + ny;
+ offset = offset + ny;
end
if nargout == 2
diff --git a/matlab/perfect-foresight-models/solve_stacked_problem.m b/matlab/perfect-foresight-models/solve_stacked_problem.m
index cd5996343e..4ec67beacf 100644
--- a/matlab/perfect-foresight-models/solve_stacked_problem.m
+++ b/matlab/perfect-foresight-models/solve_stacked_problem.m
@@ -31,8 +31,17 @@ function [endogenousvariables, success, maxerror] = solve_stacked_problem(endoge
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
-[options_, y0, yT, z, i_cols, i_cols_J1, i_cols_T, i_cols_j, i_cols_1, i_cols_0, i_cols_J0, dynamicmodel] = ...
- initialize_stacked_problem(endogenousvariables, options_, M_, steadystate);
+if M_.maximum_lag > 0
+ y0 = endogenousvariables(:, M_.maximum_lag);
+else
+ y0 = NaN(M_.endo_nbr, 1);
+end
+if M_.maximum_lead > 0
+ yT = endogenousvariables(:, M_.maximum_lag+options_.periods+1);
+else
+ yT = NaN(M_.endo_nbr, 1);
+end
+z = endogenousvariables(:,M_.maximum_lag+(1:options_.periods));
if (options_.solve_algo == 10 || options_.solve_algo == 11)% mixed complementarity problem
[lb, ub] = feval(sprintf('%s.dynamic_complementarity_conditions', M_.fname), M_.params);
@@ -47,14 +56,16 @@ if (options_.solve_algo == 10 || options_.solve_algo == 11)% mixed complementari
options_.mcppath.lb = repmat(lb,options_.periods,1);
options_.mcppath.ub = repmat(ub,options_.periods,1);
end
+ dynamic_resid_function = str2func([M_.fname,'.sparse.dynamic_resid']);
+ dynamic_g1_function = str2func([M_.fname,'.sparse.dynamic_g1']);
[y, check, res, ~, errorcode] = dynare_solve(@perfect_foresight_mcp_problem, z(:), ...
- options_.simul.maxit, options_.dynatol.f, options_.dynatol.x, ...
- options_, ...
- dynamicmodel, y0, yT, ...
- exogenousvariables, M_.params, steadystate, ...
- M_.maximum_lag, options_.periods, M_.endo_nbr, i_cols, ...
- i_cols_J1, i_cols_1, i_cols_T, i_cols_j, i_cols_0, i_cols_J0, ...
- M_.dynamic_mcp_equations_reordering);
+ options_.simul.maxit, options_.dynatol.f, options_.dynatol.x, ...
+ options_, ...
+ dynamic_resid_function, dynamic_g1_function, y0, yT, ...
+ exogenousvariables, M_.params, steadystate, ...
+ M_.dynamic_g1_sparse_rowval, M_.dynamic_g1_sparse_colval, M_.dynamic_g1_sparse_colptr, ...
+ M_.maximum_lag, options_.periods, M_.endo_nbr, ...
+ M_.dynamic_mcp_equations_reordering);
eq_to_ignore=find(isfinite(lb) | isfinite(ub));
else
--
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