93 lines
2.8 KiB
Matlab
93 lines
2.8 KiB
Matlab
function chol_sigma=get_lower_cholesky_covariance(Sigma_e,add_tiny_number_to_cholesky)
|
|
% function chol_sigma=get_lower_cholesky_covariance(Sigma_e)
|
|
% Computes the lower triangular Cholesky decomposition of a covariance matrix,
|
|
% working around zero entries on the diagonal and perfect correlation
|
|
%
|
|
% INPUTS
|
|
% Sigma_e [double] covariance matrix
|
|
%
|
|
% OUTPUTS
|
|
% chol_sigma [cell] Cholesky factor
|
|
%
|
|
% ALGORITHM
|
|
% Add small value to diagonal to break perfect correlation
|
|
%
|
|
% SPECIAL REQUIREMENTS.
|
|
% None.
|
|
%
|
|
% Copyright © 2023 Dynare Team
|
|
%
|
|
% This file is part of Dynare.
|
|
%
|
|
% Dynare is free software: you can redistribute it and/or modify
|
|
% it under the terms of the GNU General Public License as published by
|
|
% the Free Software Foundation, either version 3 of the License, or
|
|
% (at your option) any later version.
|
|
%
|
|
% Dynare is distributed in the hope that it will be useful,
|
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
% GNU General Public License for more details.
|
|
%
|
|
% You should have received a copy of the GNU General Public License
|
|
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
|
|
|
|
if nargin<2
|
|
add_tiny_number_to_cholesky=1e-14;
|
|
end
|
|
std_deviation=sqrt(diag(Sigma_e));
|
|
non_zero_indices=find(std_deviation~=0); %find non-zero shocks;
|
|
try
|
|
chol_sigma=zeros(size(Sigma_e));
|
|
chol_sigma(non_zero_indices,non_zero_indices)=chol(Sigma_e(non_zero_indices,non_zero_indices),'lower');
|
|
catch
|
|
% cases with perfect correlation
|
|
fprintf('Non-positive definite covariance matrix encountered. Using add_tiny_number_to_cholesky one the diagonal.\n')
|
|
chol_sigma=zeros(size(Sigma_e));
|
|
chol_sigma(non_zero_indices,non_zero_indices)=chol(Sigma_e(non_zero_indices,non_zero_indices)+add_tiny_number_to_cholesky*eye(length(non_zero_indices)),'lower');
|
|
% correlation=diag(std_deviation(non_zero_indices))\Sigma_e(non_zero_indices,non_zero_indices)/diag(std_deviation(non_zero_indices));
|
|
end
|
|
|
|
return % --*-- Unit tests --*--
|
|
|
|
%@test:1
|
|
|
|
Sigma_e=diag(4*ones(3,1));
|
|
Sigma_e(2,2)=0;
|
|
chol_1=get_lower_cholesky_covariance(Sigma_e);
|
|
if max(max(abs(chol_1-diag([2,0,2]))))>eps
|
|
t(1)=false;
|
|
else
|
|
t(1)=true;
|
|
end
|
|
|
|
Sigma_e=ones(3,3);
|
|
chol_2=get_lower_cholesky_covariance(Sigma_e,1e-14);
|
|
chol_3=get_lower_cholesky_covariance(Sigma_e+1e-14*eye(3),1e-14);
|
|
if max(max(abs(chol_2-chol_3)))>eps || any(any(triu(chol_3,1)))
|
|
t(2)=false;
|
|
else
|
|
t(2)=true;
|
|
end
|
|
|
|
Sigma_e=ones(3,3);
|
|
Sigma_e(2,:)=0;
|
|
Sigma_e(:,2)=0;
|
|
chol_4=get_lower_cholesky_covariance(Sigma_e,1e-14);
|
|
if chol_4(2,2)~=0 || any(any(triu(chol_4,1)))
|
|
t(3)=false;
|
|
else
|
|
t(3)=true;
|
|
end
|
|
|
|
Sigma_e=[4 0.5 0; 0.5 9 0; 0 0 16];
|
|
chol_5=get_lower_cholesky_covariance(Sigma_e,1e-14);
|
|
if any(any(triu(chol_5,1))) %should be lower triangular
|
|
t(4)=false;
|
|
else
|
|
t(4)=true;
|
|
end
|
|
|
|
T = all(t);
|
|
%@eof:1
|