%PINVF: Pseudoinverse based on r singular values of A.
% X = PINVF(A,r,tol) produces a matrix X of the same dimensions
% as A' so that A*X*A = A, X*A*X = X and AX and XA
% are Hermitian. The computation is based on SVD(A) and r
% singular values.
%
% X = pinvf(A,r,tol)
%
% See also RANK.
%
% L.G. Van Willigenburg, W.L. De Koning, 28-11-95.
%
function X = pinvf(A,r,tol)
[U,S,V] = svd(A,0);
if min(size(S)) == 1
S = S(1);
else
S = diag(S);
end
if nargin~=3
tol = max(size(A)) * S(1) * eps;
end
rt = sum(S > tol);
if nargin>1
rt=min(rt,r);
end
if (rt == 0)
X = zeros(size(A'));
else
S = diag(ones(rt,1)./S(1:rt));
X = V(:,1:rt)*S*U(:,1:rt)';
end
