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// CXSparse/MATLAB/Test/cs_maxtransr_mex: maximum transversal
// CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs_mex.h"
/* find an augmenting path starting at column j and extend the match if found */
static
int64_t augment (int64_t k, cs_dl *A, int64_t *jmatch, int64_t *cheap, int64_t *w,
int64_t j)
{
int64_t found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ;
/* --- Start depth-first-search at node j ------------------------------- */
w [j] = k ; /* mark j as visited for kth path */
for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
{
i = Ai [p] ; /* try a cheap assignment (i,j) */
found = (jmatch [i] == -1) ;
}
cheap [j] = p ; /* start here next time for j */
/* --- Depth-first-search of neighbors of j ----------------------------- */
for (p = Ap [j] ; p < Ap [j+1] && !found ; p++)
{
i = Ai [p] ; /* consider row i */
if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */
found = augment (k, A, jmatch, cheap, w, jmatch [i]) ;
}
if (found) jmatch [i] = j ; /* augment jmatch if path found */
return (found) ;
}
/* find a maximum transveral */
static
int64_t *maxtrans (cs_dl *A) /* returns jmatch [0..m-1] */
{
int64_t i, j, k, n, m, *Ap, *jmatch, *w, *cheap ;
if (!A) return (NULL) ; /* check inputs */
n = A->n ; m = A->m ; Ap = A->p ;
jmatch = cs_dl_malloc (m, sizeof (int64_t)) ; /* allocate result */
w = cs_dl_malloc (2*n, sizeof (int64_t)) ; /* allocate workspace */
if (!w || !jmatch) return (cs_dl_idone (jmatch, NULL, w, 0)) ;
cheap = w + n ;
for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */
for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */
for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ;
return (cs_dl_idone (jmatch, NULL, w, 1)) ;
}
/* invert a maximum matching */
static int64_t *invmatch (int64_t *jmatch, int64_t m, int64_t n)
{
int64_t i, j, *imatch ;
if (!jmatch) return (NULL) ;
imatch = cs_dl_malloc (n, sizeof (int64_t)) ;
if (!imatch) return (NULL) ;
for (j = 0 ; j < n ; j++) imatch [j] = -1 ;
for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
return (imatch) ;
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs_dl *A, Amatrix ;
double *x ;
int64_t i, m, n, *imatch, *jmatch ;
if (nargout > 1 || nargin != 1)
{
mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ;
}
/* get inputs */
A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ;
m = A->m ;
n = A->n ;
jmatch = maxtrans (A) ;
imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */
pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
x = mxGetPr (pargout [0]) ;
for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ;
cs_dl_free (jmatch) ;
cs_dl_free (imatch) ;
}
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