53 lines
2.0 KiB
Matlab
53 lines
2.0 KiB
Matlab
function G = rand_inverse_wishart(m, v, H_inv_upper_chol)
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% function G = rand_inverse_wishart(m, v, H_inv_upper_chol)
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% rand_inverse_wishart Pseudo random matrices drawn from an
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% inverse Wishart distribution
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% G = rand_inverse_wishart(m, v, H_inv_upper_chol)
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% Returns an m-by-m matrix drawn from an inverse-Wishart distribution.
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%
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% INPUTS:
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% m: dimension of G and H_inv_upper_chol.
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% v: degrees of freedom, greater or equal than m.
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% H_inv_chol: upper cholesky decomposition of the inverse of the
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% matrix parameter.
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% The upper cholesky of the inverse is requested here
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% in order to avoid to recompute it at every random draw.
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% H_inv_upper_chol = chol(inv(H))
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% OUTPUTS:
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% G: G ~ IW(m, v, H) where H = inv(H_inv_upper_chol'*H_inv_upper_chol)
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% or, equivalently, using the correspondence between Wishart and
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% inverse-Wishart: inv(G) ~ W(m, v, S) where
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% S = H_inv_upper_chol'*H_inv_upper_chol = inv(H)
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%
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% SPECIAL REQUIREMENT
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% none
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%
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% Copyright © 2003-2017 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 <https://www.gnu.org/licenses/>.
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X = randn(v, m) * H_inv_upper_chol;
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% At this point, X'*X is Wishart distributed
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% G = inv(X'*X);
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% Rather compute inv(X'*X) using the SVD
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[~,S,V] = svd(X, 0);
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SSi = 1 ./ (diag(S) .^ 2);
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G = (V .* repmat(SSi', m, 1)) * V'; |