svdtrunc(A, tol)

function [U sv tol] = svdtrunc(A, tol)
%SVDTRUNC Truncated SVD decomposition.
%	[U sv tol] = SVDTRUNC(A)
%	[U sv tol] = SVDTRUNC(A, tol)
%
%	A    - matrix
%	tol  - tolerance, only singular values > tol are kept (default: eps)
%
%	U    - truncated (left) singular vectors
%	sv   - list of truncated singular values
%	tol  - next singular value after truncation
%
%	eg. [U sv tol] = svdtrunc(rand(6,7), 0.5)
%
%	See also HOSVD, SVD.

if nargin == 1
	tol = eps;
end

% lanczos iterative algorithm for large sparse matrices:
%[U, S, V] = lansvd(A, n, 'L');
[U S] = svd(A, 'econ');
sv = diag(S);
ns = sum(sv > tol);

% tolerance == next singular value
if ns < length(sv)
	tol = sv(ns+1);
	sv = sv(1:ns);
	U = U(:,1:ns);
else
	tol = 0;
end

%Urest = U(:, ns+1:end);
%V = V(:, 1:ns);
%Vrest = V(:, ns+1:end);