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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_V2.1-en.txt
function spcho=chfact(A)
//cholesky factors, returned in a tlist
//spcho = {xlnz, nnzl, xsuper, xlindx, lindx, snode,
// split, tmpsiz, perm, invp, lnz}.
//
// invp=spcho('invp');xlnz=spcho('xlnz');
// xlindx=spcho('xlindx');lindx=spcho('lindx');lnz=spcho('lnz');
// P=sparse([(1:m)',invp],ones(invp),[m,m]);
// adjncy = spcompack(xlnz,xlindx,lindx);
// R=adj2sp(xlnz,adjncy,lnz);
// =>P*R*R'*P'=A
m = size(A,1);
if size(A,2) ~= m | type(A)~=5 | A == [] then,
error("Matrix must be square, sparse and nonempty.");
end;
neqns=m;
[xadj,adjncy,v]=sp2adj(A-diag(diag(A)));
[perm,invp,nofsub]=ordmmd(xadj,adjncy,neqns);
cachsz = 16;
spcho=symfct(xadj,adjncy,perm,invp,cachsz,neqns);
[xadjf,adjncyf,v]=sp2adj(A);
spcho=inpnv(xadjf,adjncyf,v,spcho);
level=8;
spcho=blkfc1(spcho,level);
endfunction
function [spcho]= blkfc1(spcho,level)
//retrieves Fortran variables (see sfinit.f,bfinit.f,symfct.f )
//[xlnz,nnzl,xsuper,xlindx,lindx,snode,split,tmpsiz,perm,invp,lnz]=spcho(2:12);
xsuper=spcho("xsuper");
nsuper=size(xsuper,1)-1;
snode=spcho("snode");
neqns=size(snode,1);
lnz=spcho("lnz");
nnzl=size(lnz,1);
iwsiz = 2*neqns+2*nsuper;
iwork = zeros(iwsiz,1);
tmpsiz = spcho("tmpsiz");
tmpvec= zeros(tmpsiz,1);
iflag=0;
// calling blkfc1i primitive
[lnz,iflag]=blkfc1i(neqns,nsuper,xsuper,snode,spcho("split"),spcho("xlindx"),spcho("lindx"),spcho("xlnz"),lnz,iwsiz,iwork,tmpsiz,tmpvec,iflag,level);
//
if max(abs(lnz)) > 5d63 then
warning(gettext(" Possible matrix is not positive definite."));
end;
select iflag
case -1 then,
error(gettext("Non-positive diagonal encountered, matrix is not positive definite.")),
case -2 then,
error(gettext("Insufficient working storage in blkfct, temp(*).")),
case -3 then,
error(gettext("Insufficient working storage in blkfct, iwork(*).")),
end;
//
spcho("lnz")=lnz;
endfunction
function rhs=blkslv(spcho,rhs)
//
//[xlnz,nnzl,xsuper,xlindx,lindx,snode,split,tmpsiz,perm,invp,lnz]=spcho(2:12);
xsuper=spcho("xsuper");
nsuper=size(xsuper,1)-1;
neqns =size(rhs,1);
rhs=blkslvi(nsuper,xsuper,spcho("xlindx"),spcho("lindx"),spcho("xlnz"),...
spcho("lnz"),rhs);
endfunction
function [spcho]=inpnv(xadjf,adjf,anzf,spcho)
//
//[xlnz,nnzl,xsuper,xlindx,lindx,snode,split,tmpsiz,perm,invp,lnz]=spcho(2:12);
//
xsuper=spcho("xsuper");
neqns=size(xadjf,1)-1,
nsuper=size(xsuper,1)-1,
//
offset=zeros(neqns,1);
lnz=zeros(spcho("nnzl"),1);
//
lnz = inpnvi(neqns,xadjf,adjf,anzf,spcho("perm"),spcho("invp"),nsuper,...
xsuper,spcho("xlindx"),spcho("lindx"),spcho("xlnz"),lnz,offset);
//
spcho("lnz")=lnz;
endfunction
function [spcho] = symfct(xadj,adjncy,perm,invp,cachsz,neqns)
//
// sfinit - input
//
nnza=size(adjncy,1);
iwsiz = 7*neqns+4;
iwork=zeros(iwsiz,1);
///
if size(perm)~= [neqns,1] then, error(gettext(" SYMFCT requires PERM to be neqns x 1")),
end;
if size(invp)~= [neqns,1] then, error(gettext(" SYMFCT requires INVN to be neqns x 1")),
end;
if size(cachsz)~= [1,1] then, error(gettext(" SYMFCT requires CACHSZ to be 1 x 1")),
end;
//
[perm,invp,colcnt,nnzl,nsub,nsuper,snode,xsuper,iflag]=...
sfinit(neqns,nnza,xadj,adjncy,perm,invp,iwsiz,iwork);
//
if iflag == -1 then error(gettext(" Insufficient working storage in sfinit")),end;
//
bb=xsuper(1:nsuper+1,1);
xsuper=bb
iwsiz = 2*nsuper+2*neqns+1;
iwork=zeros(iwsiz,1);
//
//
[xlindx,lindx,xlnz,iflag]=symfcti(neqns,nnza,xadj,adjncy,perm,...
invp,colcnt,nsuper,xsuper,snode,nsub,iwsiz,iwork)
if iflag == -1 then error(" Insufficient working storage in symfct"),end;
if iflag == -2 then error(" Inconsistancy in the input in symfct"),end;
//
[tmpsiz,split]=bfinit(neqns,nsuper,xsuper,snode,xlindx,lindx,cachsz)
spcho = tlist(["chol","xlnz","nnzl","xsuper","xlindx","lindx","snode","split",...
"tmpsiz","perm","invp","lnz"],...
xlnz,nnzl,xsuper,xlindx,lindx,snode,split,tmpsiz,perm,invp,[])
endfunction
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