rank2(A,tol)

function n = rank2(A,tol)
%  PURPOSE: estimates matrix rank of an triangular matrix
%
% ---------------------------------------------------
%  USAGE: n = rank2(A,tol)
%  where: 
%         A                         a matrix
%         tol                       uses the tolerance tol in estimating
%                                   matrix rank
%
%         n                         an estimate of matrix A rank
%
%   COMMENTS:
%       This routine gives fast estimation of matrix rank but less accurate
%       than Mathlab's rank. This routine is unable to distinguish very small
%       singular values from zero.
%
% Copyright  (c) Pawel Kowal (2006)
% All rights reserved
% LREM_SOLVE toolbox is available free for noncommercial academic use only.
% [e-mail]


[n,m]           = size(A);
if n==0 ||m==0
    n           = 0;
    return;
end    
if n==1 || m==1
    s           = abs(A(1,1));
else
s               = abs(diag(A));
end

n               = sum(s>tol);