function G = rand_inverse_wishart(m, v, H_inv_upper_chol)
% rand_inverse_wishart  Pseudo random matrices drawn from an
%                       inverse Wishart distribution
%
% G = rand_inverse_wishart(m, v, H_inv_upper_chol)
%
% Returns an m-by-m matrix drawn from an inverse-Wishart distribution.
%
% m:          dimension of G and H_inv_upper_chol.
% v:          degrees of freedom, greater or equal than m.
% H_inv_chol: upper cholesky decomposition of the inverse of the
%             matrix parameter.
%             The upper cholesky of the inverse is requested here
%             in order to avoid to recompute it at every random draw.
%             H_inv_upper_chol = chol(inv(H))
%
% In other words:
%  G ~ IW(m, v, H) where H = inv(H_inv_upper_chol'*H_inv_upper_chol)
% or, equivalently, using the correspondence between Wishart and
% inverse-Wishart:
%  inv(G) ~ W(m, v, S) where S = H_inv_upper_chol'*H_inv_upper_chol = inv(H)

    X = randn(v, m) * H_inv_upper_chol; 
    
    
    % At this point, X'*X is Wishart distributed
    % G = inv(X'*X);

    % Rather compute inv(X'*X) using the SVD
    [U,S,V] = svd(X, 0);
    SSi = 1 ./ (diag(S) .^ 2);
    G = (V .* repmat(SSi', m, 1)) * V';