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//------------------------------------------------------------------------------
// CHOLMOD/MATLAB/nesdis: MATLAB interface for CHOLMOD+METIS+CAMD+CCOLAMD
//------------------------------------------------------------------------------
// CHOLMOD/MATLAB Module. Copyright (C) 2005-2023, Timothy A. Davis.
// All Rights Reserved.
// SPDX-License-Identifier: GPL-2.0+
//------------------------------------------------------------------------------
// MATLAB(tm) is a Trademark of The MathWorks, Inc.
// METIS is Copyrighted by G. Karypis
// CHOLMOD's nested dissection, based on METIS_ComputeVertexSeparator, CAMD, and
// CCOLAMD.
//
// Usage:
//
// [p, cp, cmember] = nesdis (A) orders A, using tril(A)
// [p, cp, cmember] = nesdis (A,'sym') orders A, using tril(A)
// [p, cp, cmember] = nesdis (A,'row') orders A*A'
// [p, cp, cmember] = nesdis (A,'col') orders A'*A
//
// Nested dissection ordering. Returns a permutation p such that the Cholesky
// factorization of A(p,p), A(p,:)*A(p,:)', or A(:,p)'*A(:,p) is sparser than
// the unpermuted system. 'mode' defaults to 'sym'.
//
// An optional 3rd input argument:
//
// nesdis (A,mode,opts)
//
// specifies control parameters. opts(1) is the smallest subgraph that should
// not be partitioned (default is 200), opts(2) is 1 if connected components are
// to be split independently (default is 0). opts(3) controls when a separator
// is kept; it is kept if nsep < opts(3)*n, where nsep is the number of nodes in
// the separator and n is the number of nodes in the graph being cut (default is
// 1).
//
// opts(4) is 0 if the smallest subgraphs are not to be ordered. For the 'sym'
// case, or if mode is not present: 1 if to be ordered by CAMD, or 2 if to be
// ordered with CSYMAMD (default is 1). For the other cases: 0 for natural
// ordering, 1 if to be ordered by CCOLAMD.
//
// cp and cmember are optional. cmember(i)=c means that node i is in component
// c, where c is in the range of 1 to the number of components. length(cp) is
// the number of components found. cp is the separator tree; cp(c) is the
// parent of component c, or 0 if c is a root. There can be anywhere from
// 1 to n components, where n is the number of rows of A, A*A', or A'*A.
//
// Requires METIS and the CHOLMOD Partition Module.
#include "sputil2.h"
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
#ifndef NPARTITION
double dummy = 0 ;
int64_t *Perm, *Cmember, *CParent ;
cholmod_sparse *A, Amatrix ;
cholmod_common Common, *cm ;
int64_t n, transpose, c, ncomp ;
char buf [LEN] ;
//--------------------------------------------------------------------------
// start CHOLMOD and set defaults
//--------------------------------------------------------------------------
cm = &Common ;
cholmod_l_start (cm) ;
sputil2_config (SPUMONI, cm) ;
//--------------------------------------------------------------------------
// get inputs
//--------------------------------------------------------------------------
if (nargout > 3 || nargin < 1 || nargin > 3)
{
mexErrMsgTxt ("Usage: [p cp cmember] = nesdis (A, mode, opts)") ;
}
if (nargin > 2)
{
double *x = (double *) mxGetData (pargin [2]) ;
n = mxGetNumberOfElements (pargin [2]) ;
if (n > 0) cm->method [0].nd_small = x [0] ;
if (n > 1) cm->method [0].nd_components = x [1] ;
if (n > 2) cm->method [0].nd_oksep = x [2] ;
if (n > 3) cm->method [0].nd_camd = x [3] ;
}
//--------------------------------------------------------------------------
// get input matrix A
//--------------------------------------------------------------------------
A = sputil2_get_sparse_pattern (pargin [0], CHOLMOD_DOUBLE, &Amatrix, cm) ;
//--------------------------------------------------------------------------
// get A->stype, default is to use tril(A)
//--------------------------------------------------------------------------
A->stype = -1 ;
transpose = FALSE ;
if (nargin > 1)
{
buf [0] = '\0' ;
if (mxIsChar (pargin [1]))
{
mxGetString (pargin [1], buf, LEN) ;
}
c = buf [0] ;
if (tolower (c) == 'r')
{
// unsymmetric case (A*A') if string starts with 'r'
transpose = FALSE ;
A->stype = 0 ;
}
else if (tolower (c) == 'c')
{
// unsymmetric case (A'*A) if string starts with 'c'
transpose = TRUE ;
A->stype = 0 ;
}
else if (tolower (c) == 's')
{
// symmetric case (A) if string starts with 's'
transpose = FALSE ;
A->stype = -1 ;
}
else
{
mexErrMsgTxt ("nesdis: unrecognized mode") ;
}
}
if (A->stype && A->nrow != A->ncol)
{
mexErrMsgTxt ("nesdis: A must be square") ;
}
//--------------------------------------------------------------------------
// order the matrix with CHOLMOD's nested dissection
//--------------------------------------------------------------------------
if (transpose)
{
// C = A', and then order C*C' with cholmod_l_nested_dissection
cholmod_sparse *C = cholmod_l_transpose (A, 0, cm) ;
n = C->nrow ;
CParent = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
Cmember = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
Perm = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
ncomp = cholmod_l_nested_dissection (C, NULL, 0, Perm, CParent,
Cmember, cm) ;
cholmod_l_free_sparse (&C, cm) ;
}
else
{
// order A or A*A' with cholmod_l_nested_dissection
n = A->nrow ;
CParent = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
Cmember = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
Perm = cholmod_l_malloc (n, sizeof (int64_t), cm) ;
ncomp = cholmod_l_nested_dissection (A, NULL, 0, Perm, CParent,
Cmember, cm) ;
}
//--------------------------------------------------------------------------
// free workspace and return results
//--------------------------------------------------------------------------
sputil2_free_sparse (&A, &Amatrix, 0, cm) ;
if (ncomp < 0) mexErrMsgTxt ("nesdis failed") ;
pargout [0] = sputil2_put_int (Perm, n, 1) ;
if (nargout > 1)
{
pargout [1] = sputil2_put_int (CParent, ncomp, 1) ;
}
if (nargout > 2)
{
pargout [2] = sputil2_put_int (Cmember, n, 1) ;
}
cholmod_l_free (n, sizeof (int64_t), Perm, cm) ;
cholmod_l_free (n, sizeof (int64_t), CParent, cm) ;
cholmod_l_free (n, sizeof (int64_t), Cmember, cm) ;
cholmod_l_finish (cm) ;
if (SPUMONI > 0) cholmod_l_print_common (" ", cm) ;
#else
mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ;
#endif
}
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