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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 1987-2008 - INRIA - François DELEBECQUE
//
// 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-en.txt
function [w,rk]=rowcomp(A,flag,tol)
//Row compression of A <--> computation of im(A)
//flag and tol are optional parameters
//flag='qr' or 'svd' (default 'svd')
//tol tolerance parameter (sqrt(%eps)*norm(A,1) as default value)
//the rk first (top) rows of w span the row range of a
//the rk first columns of w' span the image of a
if A==[] then w=[];rk=0;return;end
[ma,na]=size(A)
rhs=argn(2)
if norm(A,1) < sqrt(%eps)/10 then rk=0,w=eye(ma,ma),return;end
select rhs
case 1 then// default values for flag and tol
flag='svd',tol=sqrt(%eps)*norm(A,1);
case 2 then //default value for tol
tol=sqrt(%eps)*norm(A,1)
else
if size(tol,'*')>1|~isreal(tol)|tol<0 then
error(msprintf(gettext("%s: Wrong values for input argument #%d: Non-negative scalar expected.\n"),'rowcomp',3));
end
end
select flag
case 'qr' then
[q,r,rk,e]=qr(A,tol);w=q';
case 'svd' then
[u,s,v,rk]=svd(A,tol);w=u' ;
else
error(msprintf(gettext("%s: Wrong value for input argument #%d: Must be in the set {%s}.\n"),'rowcomp',2,'''qr'',''svd'''));
end
endfunction
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