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/* ========================================================================== */
/* === ldlsymbolmex.c: LDLSYMBOL mexFunction =============================== */
/* ========================================================================== */
/* MATLAB interface for symbolic LDL' factorization using the LDL sparse matrix
* package. This mexFunction is not required by the LDL mexFunction.
*
* MATLAB calling syntax is:
*
* [Lnz, Parent, flopcount] = ldlsymbol (A)
* [Lnz, Parent, flopcount] = ldlsymbol (A, P)
*
* P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example.
* Only the diagonal and upper triangular part of A or A(P,P) is accessed; the
* lower triangular part is ignored.
*
* The elimination tree is returned in the Parent array. The number of nonzeros
* in each column of L is returned in Lnz. This mexFunction replicates the
* following MATLAB computations, using ldl_symbolic:
*
* Lnz = symbfact (A) - 1 ;
* Parent = etree (A) ;
* flopcount = sum (Lnz .* (Lnz + 2)) ;
*
* or, if P is provided,
*
* B = A (P,P) ;
* Lnz = symbfact (B) - 1 ;
* Parent = etree (B) ;
* flopcount = sum (Lnz .* (Lnz + 2)) ;
*
* This code is faster than the above MATLAB statements, typically by a factor
* of 4 to 40 (median speedup of 9) in MATLAB 6.5 on a Pentium 4 Linux laptop
* (excluding the B=A(P,P) time), on a wide range of symmetric sparse matrices.
*
* LDL Version 1.2, Copyright (c) 2005 by Timothy A Davis,
* University of Florida. All Rights Reserved. See README for the License.
*/
#include "ldl.h"
#include "mex.h"
#include "matrix.h"
/* ========================================================================== */
/* === LDLSYMBOL mexFunction ================================================ */
/* ========================================================================== */
void mexFunction
(
int nargout,
mxArray *pargout[ ],
int nargin,
const mxArray *pargin[ ]
)
{
int i, n, *Pattern, *Flag, *Lp, *Ap, *Ai, *Lnz, *Parent,
*P, *Pinv, nn, k, j, permute ;
double flops, *p ;
/* ---------------------------------------------------------------------- */
/* get inputs and allocate workspace */
/* ---------------------------------------------------------------------- */
if (nargin == 0 || nargin > 2)
{
mexErrMsgTxt ("Usage:\n"
" [Lnz, Parent, flopcount] = ldl (A) ;\n"
" [Lnz, Parent, flopcount] = ldl (A, P) ;\n") ;
}
n = mxGetM (pargin [0]) ;
if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0])
|| !mxIsDouble (pargin [0]) || mxIsComplex (pargin [0]))
{
mexErrMsgTxt ("ldlsymbol: A must be sparse, square, and real") ;
}
nn = (n == 0) ? 1 : n ;
/* get sparse matrix A */
Ap = mxGetJc (pargin [0]) ;
Ai = mxGetIr (pargin [0]) ;
/* get fill-reducing ordering, if present */
permute = ((nargin > 1) && !mxIsEmpty (pargin [1])) ;
if (permute)
{
if (mxGetM (pargin [1]) * mxGetN (pargin [1]) != n ||
mxIsSparse (pargin [1]))
{
mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ;
}
P = (int *) mxMalloc (nn * sizeof (int)) ;
Pinv = (int *) mxMalloc (nn * sizeof (int)) ;
p = mxGetPr (pargin [1]) ;
for (k = 0 ; k < n ; k++)
{
P [k] = p [k] - 1 ; /* convert to 0-based */
}
}
else
{
P = (int *) NULL ;
Pinv = (int *) NULL ;
}
/* allocate first part of L */
Lp = (int *) mxMalloc ((n+1) * sizeof (int)) ;
Parent = (int *) mxMalloc (nn * sizeof (int)) ;
/* get workspace */
Flag = (int *) mxMalloc (nn * sizeof (int)) ;
Pattern = (int *) mxMalloc (nn * sizeof (int)) ;
Lnz = (int *) mxMalloc (nn * sizeof (int)) ;
/* make sure the input P is valid */
if (permute && !ldl_valid_perm (n, P, Flag))
{
mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ;
}
/* note that we assume that the input matrix is valid */
/* ---------------------------------------------------------------------- */
/* symbolic factorization to get Lp, Parent, Lnz, and optionally Pinv */
/* ---------------------------------------------------------------------- */
ldl_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv) ;
/* ---------------------------------------------------------------------- */
/* create outputs */
/* ---------------------------------------------------------------------- */
/* create the output Lnz vector */
pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
p = mxGetPr (pargout [0]) ;
for (j = 0 ; j < n ; j++)
{
p [j] = Lnz [j] ;
}
/* return elimination tree (add 1 to change from 0-based to 1-based) */
if (nargout > 1)
{
pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ;
p = mxGetPr (pargout [1]) ;
for (i = 0 ; i < n ; i++)
{
p [i] = Parent [i] + 1 ;
}
}
if (nargout > 2)
{
/* find flop count for ldl_numeric */
flops = 0 ;
for (k = 0 ; k < n ; k++)
{
flops += ((double) Lnz [k]) * (Lnz [k] + 2) ;
}
pargout [2] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
p = mxGetPr (pargout [2]) ;
p [0] = flops ;
}
if (permute)
{
mxFree (P) ;
mxFree (Pinv) ;
}
mxFree (Lp) ;
mxFree (Parent) ;
mxFree (Flag) ;
mxFree (Pattern) ;
mxFree (Lnz) ;
}
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