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Add tests for matrix notation 

Closes: Enterprise/dynare#1
time-shift
Sébastien Villemot 2020-06-30 11:36:57 +02:00
parent 2acacf61f1
commit 8d4a80956c
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GPG Key ID: 2CECE9350ECEBE4A
17 changed files with 767 additions and 3 deletions
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2
preprocessor

@ -1 +1 @@
Subproject commit 78881c9244a087e23937acbfe0139014595d18aa
Subproject commit 8bfcc59af7331621e534c8ff58eb5afeadb070fe

3
tests/.gitignore vendored
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@ -94,6 +94,9 @@ wsOct
!/kronecker/test_kron.m
!/load_octave_packages.m
!/ls2003/data_ca1.m
!/matrix_notation/extFunNoDerivsMatrix.m
!/matrix_notation/extFunFirstDerivMatrix.m
!/matrix_notation/extFunWithFirstAndSecondDerivsMatrix.m
!/measurement_errors/data_ca1.m
!/measurement_errors/fs2000_corr_me_ml_mcmc/fsdat_simul.m
!/missing/simulate_data_with_missing_observations.m

39
tests/Makefile.am
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@ -396,7 +396,18 @@ MODFILES = \
bgp/nk-1/nk.mod \
bgp/ramsey-1/ramsey.mod \
dynare-command-options/ramst.mod \
particle/local_state_space_iteration_k_test.mod
particle/local_state_space_iteration_k_test.mod \
matrix_notation/deterministic_matrix.mod \
matrix_notation/deterministic_scalar.mod \
matrix_notation/stochastic_matrix.mod \
matrix_notation/stochastic_scalar.mod \
matrix_notation/benchmark.mod \
matrix_notation/no_deriv_given_matrix_dll.mod \
matrix_notation/no_deriv_given_matrix.mod \
matrix_notation/first_deriv_given_matrix_dll.mod \
matrix_notation/first_deriv_given_matrix.mod \
matrix_notation/first_and_2nd_deriv_given_matrix_dll.mod \
matrix_notation/first_and_2nd_deriv_given_matrix.mod
ECB_MODFILES = \
var-expectations/1/example.mod \
@ -777,6 +788,23 @@ trend-component-and-var-models/tcm8.o.trs: trend-component-and-var-models/tcm6.o
discretionary_policy/dennis_1_estim.m.trs: discretionary_policy/dennis_1.m.trs
discretionary_policy/dennis_1_estim.o.trs: discretionary_policy/dennis_1.o.trs
matrix_notation/deterministic_scalar.m.trs: matrix_notation/deterministic_matrix.m.trs
matrix_notation/deterministic_scalar.o.trs: matrix_notation/deterministic_matrix.o.trs
matrix_notation/stochastic_scalar.m.trs: matrix_notation/stochastic_matrix.m.trs
matrix_notation/stochastic_scalar.o.trs: matrix_notation/stochastic_matrix.o.trs
matrix_notation/first_deriv_given_matrix.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/first_deriv_given_matrix.o.trs: matrix_notation/benchmark.o.trs
matrix_notation/first_deriv_given_matrix_dll.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/first_deriv_given_matrix_dll.o.trs: matrix_notation/benchmark.o.trs
matrix_notation/first_and_2nd_deriv_given_matrix.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/first_and_2nd_deriv_given_matrix.o.trs: matrix_notation/benchmark.o.trs
matrix_notation/first_and_2nd_deriv_given_matrix_dll.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/first_and_2nd_deriv_given_matrix_dll.o.trs: matrix_notation/benchmark.o.trs
matrix_notation/no_deriv_given_matrix.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/no_deriv_given_matrix.o.trs: matrix_notation/benchmark.o.trs
matrix_notation/no_deriv_given_matrix_dll.m.trs: matrix_notation/benchmark.m.trs
matrix_notation/no_deriv_given_matrix_dll.o.trs: matrix_notation/benchmark.o.trs
observation_trends_and_prefiltering/MCMC: m/observation_trends_and_prefiltering/MCMC o/observation_trends_and_prefiltering/MCMC
m/observation_trends_and_prefiltering/MCMC: $(patsubst %.mod, %.m.trs, $(filter observation_trends_and_prefiltering/MCMC/%.mod, $(MODFILES)))
o/observation_trends_and_prefiltering/MCMC: $(patsubst %.mod, %.o.trs, $(filter observation_trends_and_prefiltering/MCMC/%.mod, $(MODFILES)))
@ -985,6 +1013,10 @@ estimation/univariate: m/estimation/univariate o/estimation/univariate
m/estimation/univariate: $(patsubst %.mod, %.m.trs, $(filter estimation/univariate/%.mod, $(MODFILES)))
o/estimation/univariate: $(patsubst %.mod, %.o.trs, $(filter estimation/univariate/%.mod, $(MODFILES)))
matrix_notation: m/matrix_notation o/matrix_notation
m/matrix_notation: $(patsubst %.mod, %.m.trs, $(filter matrix_notation/%.mod, $(MODFILES)))
o/matrix_notation: $(patsubst %.mod, %.o.trs, $(filter matrix_notation/%.mod, $(MODFILES)))
# ECB files
M_ECB_TRS_FILES = $(patsubst %.mod, %.m.trs, $(ECB_MODFILES))
@ -1168,7 +1200,10 @@ EXTRA_DIST = \
histval_initval_file/my_assert.m \
histval_initval_file/ramst_data.xls \
histval_initval_file/ramst_data.xlsx \
histval_initval_file/ramst_initval_file_data.m
histval_initval_file/ramst_initval_file_data.m \
matrix_notation/extFunFirstDerivMatrix.m \
matrix_notation/extFunNoDerivsMatrix.m \
matrix_notation/extFunWithFirstAndSecondDerivsMatrix.m
if ENABLE_MATLAB
check-local: check-matlab

44
tests/matrix_notation/benchmark.mod Normal file
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@ -0,0 +1,44 @@
/* This file is used as a benchmark against with the other tests with external
functions are compared.
It is almost the same as example1.mod, except that the shocks process is
nonlinear (in order to have a non-zero Hessian of the
external function) */
var y, c, k, h, a, b;
varexo e, u;
parameters beta, alpha, delta, theta, psi, rho, tau;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
k = exp(b)*(y-c)+(1-delta)*k(-1) ;
a = rho*a(-1)^2+5*tau*b(-1)^2 + e;
b = 3*tau/2*a(-1)^2+7*rho/3*b(-1)^2 + u;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
end;
shocks;
var e; stderr 0.009;
var u; stderr 0.009;
var e, u = phi*0.009*0.009;
end;
stoch_simul;

38
tests/matrix_notation/deterministic_matrix.mod Normal file
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@ -0,0 +1,38 @@
// Do not forget to update deterministic_scalar.mod when this file is modified
var(rows=3) X, Y, Z;
var t;
varexo(rows=3) E, U, V;
parameters(rows=3, cols=3) P;
P = [.1, .2, -.3; -.1, .5, .1; .2, -.3, .9];
model;
X = P*X(-1)+E;
transpose(Y) = transpose(Y(-1))*transpose(P)+transpose(U);
Z = V;
t = Y[1](-1) + Y[2](+1);
end;
shocks;
var E;
periods 1 2;
values [0.5; 0.6; 0.7] [0.2; 0.3; 0.4];
var U[1];
periods 3;
values 0.8;
var U[2];
periods 3;
values 0.7;
var V[:];
periods 1;
values 0.1;
end;
perfect_foresight_setup(periods=50);
perfect_foresight_solver;
write_latex_dynamic_model;

70
tests/matrix_notation/deterministic_scalar.mod Normal file
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@ -0,0 +1,70 @@
// Scalar translation of deterministic_matrix.mod
// The declaration orders are the same as those of the expanded matrix version
var t X_1 X_2 X_3 Y_1 Y_2 Y_3 Z_1 Z_2 Z_3;
varexo E_1 E_2 E_3 U_1 U_2 U_3 V_1 V_2 V_3;
parameters P_1_1 P_1_2 P_1_3 P_2_1 P_2_2 P_2_3 P_3_1 P_3_2 P_3_3;
P_1_1 = .1;
P_1_2 = .2;
P_1_3 = -.3;
P_2_1 = -.1;
P_2_2 = .5;
P_2_3 = .1;
P_3_1 = .2;
P_3_2 = -.3;
P_3_3 = .9;
model;
X_1 = P_1_1*X_1(-1) + P_1_2*X_2(-1) + P_1_3*X_3(-1) + E_1;
X_2 = P_2_1*X_1(-1) + P_2_2*X_2(-1) + P_2_3*X_3(-1) + E_2;
X_3 = P_3_1*X_1(-1) + P_3_2*X_2(-1) + P_3_3*X_3(-1) + E_3;
Y_1 = P_1_1*Y_1(-1) + P_1_2*Y_2(-1) + P_1_3*Y_3(-1) + U_1;
Y_2 = P_2_1*Y_1(-1) + P_2_2*Y_2(-1) + P_2_3*Y_3(-1) + U_2;
Y_3 = P_3_1*Y_1(-1) + P_3_2*Y_2(-1) + P_3_3*Y_3(-1) + U_3;
Z_1 = V_1;
Z_2 = V_2;
Z_3 = V_3;
t = Y_1(-1) + Y_2(+1);
end;
shocks;
var E_1;
periods 1 2;
values 0.5 0.2;
var E_2;
periods 1 2;
values 0.6 0.3;
var E_3;
periods 1 2;
values 0.7 0.4;
var U_1;
periods 3;
values 0.8;
var U_2;
periods 3;
values 0.7;
var V_1;
periods 1;
values 0.1;
var V_2;
periods 1;
values 0.1;
var V_3;
periods 1;
values 0.1;
end;
perfect_foresight_setup(periods=50);
perfect_foresight_solver;
L = load('deterministic_matrix_results.mat');
if max(max(abs(L.oo_.endo_simul - oo_.endo_simul))) > 1e-12
error('Failure in matrix expansion')
end

4
tests/matrix_notation/extFunFirstDerivMatrix.m Normal file
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@ -0,0 +1,4 @@
function dy=extFunFirstDerivMatrix(a,b,c)
dy = [ c(1)^2 0 5*c(2)^2 0 2*a(1)*c(1) 10*b(1)*c(2);
0 3*c(1)^2 0 7*c(2)^2 6*a(2)*c(1) 14*b(2)*c(2) ];
end

3
tests/matrix_notation/extFunNoDerivsMatrix.m Normal file
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@ -0,0 +1,3 @@
function y=extFunNoDerivsMatrix(a,b,c)
y=[a(1), 5*b(1); 3*a(2) 7*b(2)]*c.^2;
end

20
tests/matrix_notation/extFunWithFirstAndSecondDerivsMatrix.m Normal file
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@ -0,0 +1,20 @@
function [y dy d2y]=extFunWithFirstAndSecondDerivsMatrix(a,b,c)
y=[a(1), 5*b(1); 3*a(2), 7*b(2)]*c.^2;
dy = [ c(1)^2 0 5*c(2)^2 0 2*a(1)*c(1) 10*b(1)*c(2);
0 3*c(1)^2 0 7*c(2)^2 6*a(2)*c(1) 14*b(2)*c(2) ];
d2y=zeros(2,6,6);
d2y(1,1,5) = 2*c(1);
d2y(1,3,6) = 10*c(2);
d2y(1,5,1) = 2*c(1);
d2y(1,5,5) = 2*a(1);
d2y(1,6,3) = 10*c(2);
d2y(1,6,6) = 10*b(1);
d2y(2,2,5) = 6*c(1);
d2y(2,4,6) = 14*c(2);
d2y(2,5,2) = 6*c(1);
d2y(2,5,5) = 6*a(2);
d2y(2,6,4) = 14*c(2);
d2y(2,6,6) = 14*b(2);
end

71
tests/matrix_notation/first_and_2nd_deriv_given_matrix.mod Normal file
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@ -0,0 +1,71 @@
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunWithFirstAndSecondDerivsMatrix, in_arg_dim=[2,2,2],
out_arg_dim=2, first_deriv_provided, second_deriv_provided);
model;
[endogenous='c',name='law of motion of capital']
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunWithFirstAndSecondDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

71
tests/matrix_notation/first_and_2nd_deriv_given_matrix_dll.mod Normal file
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@ -0,0 +1,71 @@
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunWithFirstAndSecondDerivsMatrix, in_arg_dim=[2,2,2],
out_arg_dim=2, first_deriv_provided, second_deriv_provided);
model(use_dll);
[endogenous='c',name='law of motion of capital']
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunWithFirstAndSecondDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

72
tests/matrix_notation/first_deriv_given_matrix.mod Normal file
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@ -0,0 +1,72 @@
// --+ options: json=compute +--
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunNoDerivsMatrix, in_arg_dim=[2,2,2],
out_arg_dim=2, first_deriv_provided=extFunFirstDerivMatrix);
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunNoDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

73
tests/matrix_notation/first_deriv_given_matrix_dll.mod Normal file
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@ -0,0 +1,73 @@
// --+ options: json=compute +--
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunNoDerivsMatrix, in_arg_dim=[2,2,2],
out_arg_dim=2, first_deriv_provided=extFunFirstDerivMatrix);
model(use_dll);
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunNoDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

71
tests/matrix_notation/no_deriv_given_matrix.mod Normal file
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@ -0,0 +1,71 @@
// --+ options: json=compute +--
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunNoDerivsMatrix, in_arg_dim=[2,2,2], out_arg_dim=2);
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunNoDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

71
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// --+ options: json=compute +--
var y, c, k, h;
var(rows = 2) A; // A == [a; b]
varexo(rows = 2) E; // E == [e; u]
parameters beta, alpha, delta, theta, psi;
parameters(rows=2,cols=2) P;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
P = [rho, tau; tau/2, rho/3];
external_function(nargs=3, name=extFunNoDerivsMatrix, in_arg_dim=[2,2,2], out_arg_dim=2);
model(use_dll);
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(A[2])*c)/(exp(A[2](+1))*c(+1)))
*(exp(A[2](+1))*alpha*y(+1)+(1-delta)*k));
y = exp(A[1])*(k(-1)^alpha)*(h^(1-alpha));
k = exp(A[2])*(y-c)+(1-delta)*k(-1) ;
A = extFunNoDerivsMatrix(P[:,1], transpose(P[:,2]), A(-1)) + E;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
A[1] = 0;
A[2] = 0;
E[:] = 0;
end;
shocks;
var E[:]; stderr 0.009;
var E[1], E[2] = phi*0.009*0.009;
end;
stoch_simul;
L = load('benchmark_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxu - oo_.dr.ghxu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghxx - oo_.dr.ghxx))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghuu - oo_.dr.ghuu))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.dr.ghs2 - oo_.dr.ghs2))) > 1e-12
error('Failure in matrix notation with external function')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix notation with external function')
end

46
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// Do not forget to update stochastic_scalar.mod when this file is modified
var(rows=3) X, Y, Z, T;
var r;
varexo(rows=3) E, U, V, W;
varexo f;
parameters(rows=3, cols=3) P;
varexo_det(rows=3) D;
P = [.1, .2, -.3; -.1, .5, .1; .2, -.3, .9];
model;
X = P*X(-1)+E;
transpose(Y) = transpose(Y(-1))*transpose(P)+transpose(U);
Z[1] = V[1];
Z[2] = V[2];
Z[3] = V[3];
T = D + W;
r = 0.9*r(+1)+f;
end;
shocks;
var E = [ 0.1, 0.2, 0.3 ];
var E[1], E[2] = 0.08;
var U[1] = 0.4;
var U[2]; stderr 0.5;
var U[3]; stderr 0.6;
corr U[1], U[2] = 0.09;
var V; stderr [ 1.1, 1.2, 1.3 ];
vcov W = [
1, 0.2, 0.3;
0.2, 5, 0.6;
0.3, 0.6, 9
];
var f = 3;
var f, E[2] = 0.5;
corr U[1], f = 0.7;
end;
stoch_simul(order=1, nodecomposition, irf=0);
write_latex_dynamic_model;

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// Scalar translation of stochastic_matrix.mod
// The declaration orders are the same as those of the expanded matrix version
var r X_1 X_2 X_3 Y_1 Y_2 Y_3 Z_1 Z_2 Z_3 T_1 T_2 T_3;
varexo f E_1 E_2 E_3 U_1 U_2 U_3 V_1 V_2 V_3 W_1 W_2 W_3;
parameters P_1_1 P_1_2 P_1_3 P_2_1 P_2_2 P_2_3 P_3_1 P_3_2 P_3_3;
varexo_det D_1 D_2 D_3;
P_1_1 = .1;
P_1_2 = .2;
P_1_3 = -.3;
P_2_1 = -.1;
P_2_2 = .5;
P_2_3 = .1;
P_3_1 = .2;
P_3_2 = -.3;
P_3_3 = .9;
model;
X_1 = P_1_1*X_1(-1) + P_1_2*X_2(-1) + P_1_3*X_3(-1) + E_1;
X_2 = P_2_1*X_1(-1) + P_2_2*X_2(-1) + P_2_3*X_3(-1) + E_2;
X_3 = P_3_1*X_1(-1) + P_3_2*X_2(-1) + P_3_3*X_3(-1) + E_3;
Y_1 = P_1_1*Y_1(-1) + P_1_2*Y_2(-1) + P_1_3*Y_3(-1) + U_1;
Y_2 = P_2_1*Y_1(-1) + P_2_2*Y_2(-1) + P_2_3*Y_3(-1) + U_2;
Y_3 = P_3_1*Y_1(-1) + P_3_2*Y_2(-1) + P_3_3*Y_3(-1) + U_3;
Z_1 = V_1;
Z_2 = V_2;
Z_3 = V_3;
T_1 = D_1 + W_1;
T_2 = D_2 + W_2;
T_3 = D_3 + W_3;
r = 0.9*r(+1)+f;
end;
shocks;
var E_1 = 0.1;
var E_2 = 0.2;
var E_3 = 0.3;
var E_1, E_2 = 0.08;
var U_1 = 0.4;
var U_2; stderr 0.5;
var U_3; stderr 0.6;
corr U_1, U_2 = 0.09;
var V_1; stderr 1.1;
var V_2; stderr 1.2;
var V_3; stderr 1.3;
var W_1 = 1;
var W_2 = 5;
var W_3 = 9;
var W_1, W_2 = 0.2;
var W_1, W_3 = 0.3;
var W_2, W_3 = 0.6;
var f = 3;
var f, E_2 = 0.5;
corr U_1, f = 0.7;
end;
stoch_simul(order=1, nodecomposition, irf=0);
L = load('stochastic_matrix_results.mat');
if max(max(abs(L.oo_.dr.ghu - oo_.dr.ghu))) > 1e-12
error('Failure in matrix expansion')
end
if max(max(abs(L.oo_.dr.ghx - oo_.dr.ghx))) > 1e-12
error('Failure in matrix expansion')
end
if max(max(abs(L.oo_.var - oo_.var))) > 1e-12
error('Failure in matrix expansion')
end