// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) ????-2008 - INRIA
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution.  The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt

function [Q,M,rk]=fullrf(A,tol)
    //[Q,M,rk]=fullrf(A)
    //Full rank factorization : A=Q.M
    //with range(Q)=range(A) and ker(M)=ker(A),
    //Q full column rank , M full row rank
    // rk = rank(A) = #columns(Q) = #rows(M)
    //F.D.
    //!
    [lhs,rhs]=argn(0)
    na1=norm(A,1);
    if rhs==1 then tol=sqrt(%eps);end
    if na1 < 1.d-10 then Q=[];M=[];rk=0;return;end
    tol1=tol*na1;
    [U,s,V,rk]=svd(A,tol1);
    sq=sqrt(s);
    Q=U*sq;M=sq*V';
    Q=Q(:,1:rk);M=M(1:rk,:);
endfunction