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// 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-en.txt
function kerA=kernel(A,tol,flag)
//Syntax : [x]=kernel(A [,tol [,flag]])
// flag = 'svd' or 'sqr' no flag if A sparse
if type(A)==1 then
[lhs,rhs]=argn(0);
[n,m]=size(A);
select rhs
case 1 then
[kerA,rk]=colcomp(A);
case 2 then
[kerA,rk]=colcomp(A,'svd',tol)
case 3 then
[kerA,rk]=colcomp(A,flag,tol)
end
kerA=kerA(:,1:m-rk);return;
end
if type(A)==5 then
[lhs,rhs]=argn(0);
[ma,na]=size(A);
if rhs==3 then
error(msprintf(gettext("%s: SVD and QR not implemented in sparse.\n"),'kernel'));
end
if rhs==2 then tol=1.d-10;else tol=%eps;end
%tol=tol*maxi(abs(A))*max(ma,na);
if ma<na then
A=[A;sparse([],[],[na-ma,na])];
end
if ma>na then
A=A'*A;ma=na;
end
[ptr,rkA]=lufact(A,[%tol,0.001]);
[P,L,U,Q]=luget(ptr);
ludel(ptr);
U=clean(U);
[ptrU,rk]=lufact(U,[%tol,.001]);
nma=max(na,ma);
Y=[sparse([],[],[rkA,nma-rkA]);speye(nma-rkA,nma-rkA)];
kerA=[];
for k=1:na-rkA
bb=full(Y(:,k));
ww=sparse(lusolve(ptrU,bb));
kerA=[kerA,ww];
end
ludel(ptrU);
if na<>rkA then
kerA=clean(Q'*kerA);
end
if ma>na then kerA=kerA(1:na,:);
end
else
error(msprintf(gettext("%s: This feature has not been implemented.\n"),'kernel'));
end
endfunction
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