/* glpspm.c (general sparse matrices) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
* Copyright (C) 2004-2018 Free Software Foundation, Inc.
* Written by Andrew Makhorin <mao@gnu.org>.
*
* GLPK is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* GLPK is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#include "env.h"
#include "hbm.h"
#include "rgr.h"
#include "spm.h"
/***********************************************************************
* NAME
*
* spm_create_mat - create general sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_create_mat(int m, int n);
*
* DESCRIPTION
*
* The routine spm_create_mat creates a general sparse matrix having
* m rows and n columns. Being created the matrix is zero (empty), i.e.
* has no elements.
*
* RETURNS
*
* The routine returns a pointer to the matrix created. */
SPM *spm_create_mat(int m, int n)
{ SPM *A;
xassert(0 <= m && m < INT_MAX);
xassert(0 <= n && n < INT_MAX);
A = xmalloc(sizeof(SPM));
A->m = m;
A->n = n;
if (m == 0 || n == 0)
{ A->pool = NULL;
A->row = NULL;
A->col = NULL;
}
else
{ int i, j;
A->pool = dmp_create_pool();
A->row = xcalloc(1+m, sizeof(SPME *));
for (i = 1; i <= m; i++) A->row[i] = NULL;
A->col = xcalloc(1+n, sizeof(SPME *));
for (j = 1; j <= n; j++) A->col[j] = NULL;
}
return A;
}
/***********************************************************************
* NAME
*
* spm_new_elem - add new element to sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPME *spm_new_elem(SPM *A, int i, int j, double val);
*
* DESCRIPTION
*
* The routine spm_new_elem adds a new element to the specified sparse
* matrix. Parameters i, j, and val specify the row number, the column
* number, and a numerical value of the element, respectively.
*
* RETURNS
*
* The routine returns a pointer to the new element added. */
SPME *spm_new_elem(SPM *A, int i, int j, double val)
{ SPME *e;
xassert(1 <= i && i <= A->m);
xassert(1 <= j && j <= A->n);
e = dmp_get_atom(A->pool, sizeof(SPME));
e->i = i;
e->j = j;
e->val = val;
e->r_prev = NULL;
e->r_next = A->row[i];
if (e->r_next != NULL) e->r_next->r_prev = e;
e->c_prev = NULL;
e->c_next = A->col[j];
if (e->c_next != NULL) e->c_next->c_prev = e;
A->row[i] = A->col[j] = e;
return e;
}
/***********************************************************************
* NAME
*
* spm_delete_mat - delete general sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* void spm_delete_mat(SPM *A);
*
* DESCRIPTION
*
* The routine deletes the specified general sparse matrix freeing all
* the memory allocated to this object. */
void spm_delete_mat(SPM *A)
{ /* delete sparse matrix */
if (A->pool != NULL) dmp_delete_pool(A->pool);
if (A->row != NULL) xfree(A->row);
if (A->col != NULL) xfree(A->col);
xfree(A);
return;
}
/***********************************************************************
* NAME
*
* spm_test_mat_e - create test sparse matrix of E(n,c) class
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_test_mat_e(int n, int c);
*
* DESCRIPTION
*
* The routine spm_test_mat_e creates a test sparse matrix of E(n,c)
* class as described in the book: Ole 0sterby, Zahari Zlatev. Direct
* Methods for Sparse Matrices. Springer-Verlag, 1983.
*
* Matrix of E(n,c) class is a symmetric positive definite matrix of
* the order n. It has the number 4 on its main diagonal and the number
* -1 on its four co-diagonals, two of which are neighbour to the main
* diagonal and two others are shifted from the main diagonal on the
* distance c.
*
* It is necessary that n >= 3 and 2 <= c <= n-1.
*
* RETURNS
*
* The routine returns a pointer to the matrix created. */
SPM *spm_test_mat_e(int n, int c)
{ SPM *A;
int i;
xassert(n >= 3 && 2 <= c && c <= n-1);
A = spm_create_mat(n, n);
for (i = 1; i <= n; i++)
spm_new_elem(A, i, i, 4.0);
for (i = 1; i <= n-1; i++)
{ spm_new_elem(A, i, i+1, -1.0);
spm_new_elem(A, i+1, i, -1.0);
}
for (i = 1; i <= n-c; i++)
{ spm_new_elem(A, i, i+c, -1.0);
spm_new_elem(A, i+c, i, -1.0);
}
return A;
}
/***********************************************************************
* NAME
*
* spm_test_mat_d - create test sparse matrix of D(n,c) class
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_test_mat_d(int n, int c);
*
* DESCRIPTION
*
* The routine spm_test_mat_d creates a test sparse matrix of D(n,c)
* class as described in the book: Ole 0sterby, Zahari Zlatev. Direct
* Methods for Sparse Matrices. Springer-Verlag, 1983.
*
* Matrix of D(n,c) class is a non-singular matrix of the order n. It
* has unity main diagonal, three co-diagonals above the main diagonal
* on the distance c, which are cyclically continued below the main
* diagonal, and a triangle block of the size 10x10 in the upper right
* corner.
*
* It is necessary that n >= 14 and 1 <= c <= n-13.
*
* RETURNS
*
* The routine returns a pointer to the matrix created. */
SPM *spm_test_mat_d(int n, int c)
{ SPM *A;
int i, j;
xassert(n >= 14 && 1 <= c && c <= n-13);
A = spm_create_mat(n, n);
for (i = 1; i <= n; i++)
spm_new_elem(A, i, i, 1.0);
for (i = 1; i <= n-c; i++)
spm_new_elem(A, i, i+c, (double)(i+1));
for (i = n-c+1; i <= n; i++)
spm_new_elem(A, i, i-n+c, (double)(i+1));
for (i = 1; i <= n-c-1; i++)
spm_new_elem(A, i, i+c+1, (double)(-i));
for (i = n-c; i <= n; i++)
spm_new_elem(A, i, i-n+c+1, (double)(-i));
for (i = 1; i <= n-c-2; i++)
spm_new_elem(A, i, i+c+2, 16.0);
for (i = n-c-1; i <= n; i++)
spm_new_elem(A, i, i-n+c+2, 16.0);
for (j = 1; j <= 10; j++)
for (i = 1; i <= 11-j; i++)
spm_new_elem(A, i, n-11+i+j, 100.0 * (double)j);
return A;
}
/***********************************************************************
* NAME
*
* spm_show_mat - write sparse matrix pattern in BMP file format
*
* SYNOPSIS
*
* #include "glpspm.h"
* int spm_show_mat(const SPM *A, const char *fname);
*
* DESCRIPTION
*
* The routine spm_show_mat writes pattern of the specified sparse
* matrix in uncompressed BMP file format (Windows bitmap) to a binary
* file whose name is specified by the character string fname.
*
* Each pixel corresponds to one matrix element. The pixel colors have
* the following meaning:
*
* Black structurally zero element
* White positive element
* Cyan negative element
* Green zero element
* Red duplicate element
*
* RETURNS
*
* If no error occured, the routine returns zero. Otherwise, it prints
* an appropriate error message and returns non-zero. */
int spm_show_mat(const SPM *A, const char *fname)
{ int m = A->m;
int n = A->n;
int i, j, k, ret;
char *map;
xprintf("spm_show_mat: writing matrix pattern to '%s'...\n",
fname);
xassert(1 <= m && m <= 32767);
xassert(1 <= n && n <= 32767);
map = xmalloc(m * n);
memset(map, 0x08, m * n);
for (i = 1; i <= m; i++)
{ SPME *e;
for (e = A->row[i]; e != NULL; e = e->r_next)
{ j = e->j;
xassert(1 <= j && j <= n);
k = n * (i - 1) + (j - 1);
if (map[k] != 0x08)
map[k] = 0x0C;
else if (e->val > 0.0)
map[k] = 0x0F;
else if (e->val < 0.0)
map[k] = 0x0B;
else
map[k] = 0x0A;
}
}
ret = rgr_write_bmp16(fname, m, n, map);
xfree(map);
return ret;
}
/***********************************************************************
* NAME
*
* spm_read_hbm - read sparse matrix in Harwell-Boeing format
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_read_hbm(const char *fname);
*
* DESCRIPTION
*
* The routine spm_read_hbm reads a sparse matrix in the Harwell-Boeing
* format from a text file whose name is the character string fname.
*
* Detailed description of the Harwell-Boeing format recognised by this
* routine can be found in the following report:
*
* I.S.Duff, R.G.Grimes, J.G.Lewis. User's Guide for the Harwell-Boeing
* Sparse Matrix Collection (Release I), TR/PA/92/86, October 1992.
*
* NOTE
*
* The routine spm_read_hbm reads the matrix "as is", due to which zero
* and/or duplicate elements can appear in the matrix.
*
* RETURNS
*
* If no error occured, the routine returns a pointer to the matrix
* created. Otherwise, the routine prints an appropriate error message
* and returns NULL. */
SPM *spm_read_hbm(const char *fname)
{ SPM *A = NULL;
HBM *hbm;
int nrow, ncol, nnzero, i, j, beg, end, ptr, *colptr, *rowind;
double val, *values;
char *mxtype;
hbm = hbm_read_mat(fname);
if (hbm == NULL)
{ xprintf("spm_read_hbm: unable to read matrix\n");
goto fini;
}
mxtype = hbm->mxtype;
nrow = hbm->nrow;
ncol = hbm->ncol;
nnzero = hbm->nnzero;
colptr = hbm->colptr;
rowind = hbm->rowind;
values = hbm->values;
if (!(strcmp(mxtype, "RSA") == 0 || strcmp(mxtype, "PSA") == 0 ||
strcmp(mxtype, "RUA") == 0 || strcmp(mxtype, "PUA") == 0 ||
strcmp(mxtype, "RRA") == 0 || strcmp(mxtype, "PRA") == 0))
{ xprintf("spm_read_hbm: matrix type '%s' not supported\n",
mxtype);
goto fini;
}
A = spm_create_mat(nrow, ncol);
if (mxtype[1] == 'S' || mxtype[1] == 'U')
xassert(nrow == ncol);
for (j = 1; j <= ncol; j++)
{ beg = colptr[j];
end = colptr[j+1];
xassert(1 <= beg && beg <= end && end <= nnzero + 1);
for (ptr = beg; ptr < end; ptr++)
{ i = rowind[ptr];
xassert(1 <= i && i <= nrow);
if (mxtype[0] == 'R')
val = values[ptr];
else
val = 1.0;
spm_new_elem(A, i, j, val);
if (mxtype[1] == 'S' && i != j)
spm_new_elem(A, j, i, val);
}
}
fini: if (hbm != NULL) hbm_free_mat(hbm);
return A;
}
/***********************************************************************
* NAME
*
* spm_count_nnz - determine number of non-zeros in sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* int spm_count_nnz(const SPM *A);
*
* RETURNS
*
* The routine spm_count_nnz returns the number of structural non-zero
* elements in the specified sparse matrix. */
int spm_count_nnz(const SPM *A)
{ SPME *e;
int i, nnz = 0;
for (i = 1; i <= A->m; i++)
for (e = A->row[i]; e != NULL; e = e->r_next) nnz++;
return nnz;
}
/***********************************************************************
* NAME
*
* spm_drop_zeros - remove zero elements from sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* int spm_drop_zeros(SPM *A, double eps);
*
* DESCRIPTION
*
* The routine spm_drop_zeros removes all elements from the specified
* sparse matrix, whose absolute value is less than eps.
*
* If the parameter eps is 0, only zero elements are removed from the
* matrix.
*
* RETURNS
*
* The routine returns the number of elements removed. */
int spm_drop_zeros(SPM *A, double eps)
{ SPME *e, *next;
int i, count = 0;
for (i = 1; i <= A->m; i++)
{ for (e = A->row[i]; e != NULL; e = next)
{ next = e->r_next;
if (e->val == 0.0 || fabs(e->val) < eps)
{ /* remove element from the row list */
if (e->r_prev == NULL)
A->row[e->i] = e->r_next;
else
e->r_prev->r_next = e->r_next;
if (e->r_next == NULL)
;
else
e->r_next->r_prev = e->r_prev;
/* remove element from the column list */
if (e->c_prev == NULL)
A->col[e->j] = e->c_next;
else
e->c_prev->c_next = e->c_next;
if (e->c_next == NULL)
;
else
e->c_next->c_prev = e->c_prev;
/* return element to the memory pool */
dmp_free_atom(A->pool, e, sizeof(SPME));
count++;
}
}
}
return count;
}
/***********************************************************************
* NAME
*
* spm_read_mat - read sparse matrix from text file
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_read_mat(const char *fname);
*
* DESCRIPTION
*
* The routine reads a sparse matrix from a text file whose name is
* specified by the parameter fname.
*
* For the file format see description of the routine spm_write_mat.
*
* RETURNS
*
* On success the routine returns a pointer to the matrix created,
* otherwise NULL. */
#if 1
SPM *spm_read_mat(const char *fname)
{ xassert(fname != fname);
return NULL;
}
#else
SPM *spm_read_mat(const char *fname)
{ SPM *A = NULL;
PDS *pds;
jmp_buf jump;
int i, j, k, m, n, nnz, fail = 0;
double val;
xprintf("spm_read_mat: reading matrix from '%s'...\n", fname);
pds = pds_open_file(fname);
if (pds == NULL)
{ xprintf("spm_read_mat: unable to open '%s' - %s\n", fname,
strerror(errno));
fail = 1;
goto done;
}
if (setjmp(jump))
{ fail = 1;
goto done;
}
pds_set_jump(pds, jump);
/* number of rows, number of columns, number of non-zeros */
m = pds_scan_int(pds);
if (m < 0)
pds_error(pds, "invalid number of rows\n");
n = pds_scan_int(pds);
if (n < 0)
pds_error(pds, "invalid number of columns\n");
nnz = pds_scan_int(pds);
if (nnz < 0)
pds_error(pds, "invalid number of non-zeros\n");
/* create matrix */
xprintf("spm_read_mat: %d rows, %d columns, %d non-zeros\n",
m, n, nnz);
A = spm_create_mat(m, n);
/* read matrix elements */
for (k = 1; k <= nnz; k++)
{ /* row index, column index, element value */
i = pds_scan_int(pds);
if (!(1 <= i && i <= m))
pds_error(pds, "row index out of range\n");
j = pds_scan_int(pds);
if (!(1 <= j && j <= n))
pds_error(pds, "column index out of range\n");
val = pds_scan_num(pds);
/* add new element to the matrix */
spm_new_elem(A, i, j, val);
}
xprintf("spm_read_mat: %d lines were read\n", pds->count);
done: if (pds != NULL) pds_close_file(pds);
if (fail && A != NULL) spm_delete_mat(A), A = NULL;
return A;
}
#endif
/***********************************************************************
* NAME
*
* spm_write_mat - write sparse matrix to text file
*
* SYNOPSIS
*
* #include "glpspm.h"
* int spm_write_mat(const SPM *A, const char *fname);
*
* DESCRIPTION
*
* The routine spm_write_mat writes the specified sparse matrix to a
* text file whose name is specified by the parameter fname. This file
* can be read back with the routine spm_read_mat.
*
* RETURNS
*
* On success the routine returns zero, otherwise non-zero.
*
* FILE FORMAT
*
* The file created by the routine spm_write_mat is a plain text file,
* which contains the following information:
*
* m n nnz
* row[1] col[1] val[1]
* row[2] col[2] val[2]
* . . .
* row[nnz] col[nnz] val[nnz]
*
* where:
* m is the number of rows;
* n is the number of columns;
* nnz is the number of non-zeros;
* row[k], k = 1,...,nnz, are row indices;
* col[k], k = 1,...,nnz, are column indices;
* val[k], k = 1,...,nnz, are element values. */
#if 1
int spm_write_mat(const SPM *A, const char *fname)
{ xassert(A != A);
xassert(fname != fname);
return 0;
}
#else
int spm_write_mat(const SPM *A, const char *fname)
{ FILE *fp;
int i, nnz, ret = 0;
xprintf("spm_write_mat: writing matrix to '%s'...\n", fname);
fp = fopen(fname, "w");
if (fp == NULL)
{ xprintf("spm_write_mat: unable to create '%s' - %s\n", fname,
strerror(errno));
ret = 1;
goto done;
}
/* number of rows, number of columns, number of non-zeros */
nnz = spm_count_nnz(A);
fprintf(fp, "%d %d %d\n", A->m, A->n, nnz);
/* walk through rows of the matrix */
for (i = 1; i <= A->m; i++)
{ SPME *e;
/* walk through elements of i-th row */
for (e = A->row[i]; e != NULL; e = e->r_next)
{ /* row index, column index, element value */
fprintf(fp, "%d %d %.*g\n", e->i, e->j, DBL_DIG, e->val);
}
}
fflush(fp);
if (ferror(fp))
{ xprintf("spm_write_mat: writing error on '%s' - %s\n", fname,
strerror(errno));
ret = 1;
goto done;
}
xprintf("spm_write_mat: %d lines were written\n", 1 + nnz);
done: if (fp != NULL) fclose(fp);
return ret;
}
#endif
/***********************************************************************
* NAME
*
* spm_transpose - transpose sparse matrix
*
* SYNOPSIS
*
* #include "glpspm.h"
* SPM *spm_transpose(const SPM *A);
*
* RETURNS
*
* The routine computes and returns sparse matrix B, which is a matrix
* transposed to sparse matrix A. */
SPM *spm_transpose(const SPM *A)
{ SPM *B;
int i;
B = spm_create_mat(A->n, A->m);
for (i = 1; i <= A->m; i++)
{ SPME *e;
for (e = A->row[i]; e != NULL; e = e->r_next)
spm_new_elem(B, e->j, i, e->val);
}
return B;
}
SPM *spm_add_sym(const SPM *A, const SPM *B)
{ /* add two sparse matrices (symbolic phase) */
SPM *C;
int i, j, *flag;
xassert(A->m == B->m);
xassert(A->n == B->n);
/* create resultant matrix */
C = spm_create_mat(A->m, A->n);
/* allocate and clear the flag array */
flag = xcalloc(1+C->n, sizeof(int));
for (j = 1; j <= C->n; j++)
flag[j] = 0;
/* compute pattern of C = A + B */
for (i = 1; i <= C->m; i++)
{ SPME *e;
/* at the beginning i-th row of C is empty */
/* (i-th row of C) := (i-th row of C) union (i-th row of A) */
for (e = A->row[i]; e != NULL; e = e->r_next)
{ /* (note that i-th row of A may have duplicate elements) */
j = e->j;
if (!flag[j])
{ spm_new_elem(C, i, j, 0.0);
flag[j] = 1;
}
}
/* (i-th row of C) := (i-th row of C) union (i-th row of B) */
for (e = B->row[i]; e != NULL; e = e->r_next)
{ /* (note that i-th row of B may have duplicate elements) */
j = e->j;
if (!flag[j])
{ spm_new_elem(C, i, j, 0.0);
flag[j] = 1;
}
}
/* reset the flag array */
for (e = C->row[i]; e != NULL; e = e->r_next)
flag[e->j] = 0;
}
/* check and deallocate the flag array */
for (j = 1; j <= C->n; j++)
xassert(!flag[j]);
xfree(flag);
return C;
}
void spm_add_num(SPM *C, double alfa, const SPM *A, double beta,
const SPM *B)
{ /* add two sparse matrices (numeric phase) */
int i, j;
double *work;
/* allocate and clear the working array */
work = xcalloc(1+C->n, sizeof(double));
for (j = 1; j <= C->n; j++)
work[j] = 0.0;
/* compute matrix C = alfa * A + beta * B */
for (i = 1; i <= C->n; i++)
{ SPME *e;
/* work := alfa * (i-th row of A) + beta * (i-th row of B) */
/* (note that A and/or B may have duplicate elements) */
for (e = A->row[i]; e != NULL; e = e->r_next)
work[e->j] += alfa * e->val;
for (e = B->row[i]; e != NULL; e = e->r_next)
work[e->j] += beta * e->val;
/* (i-th row of C) := work, work := 0 */
for (e = C->row[i]; e != NULL; e = e->r_next)
{ j = e->j;
e->val = work[j];
work[j] = 0.0;
}
}
/* check and deallocate the working array */
for (j = 1; j <= C->n; j++)
xassert(work[j] == 0.0);
xfree(work);
return;
}
SPM *spm_add_mat(double alfa, const SPM *A, double beta, const SPM *B)
{ /* add two sparse matrices (driver routine) */
SPM *C;
C = spm_add_sym(A, B);
spm_add_num(C, alfa, A, beta, B);
return C;
}
SPM *spm_mul_sym(const SPM *A, const SPM *B)
{ /* multiply two sparse matrices (symbolic phase) */
int i, j, k, *flag;
SPM *C;
xassert(A->n == B->m);
/* create resultant matrix */
C = spm_create_mat(A->m, B->n);
/* allocate and clear the flag array */
flag = xcalloc(1+C->n, sizeof(int));
for (j = 1; j <= C->n; j++)
flag[j] = 0;
/* compute pattern of C = A * B */
for (i = 1; i <= C->m; i++)
{ SPME *e, *ee;
/* compute pattern of i-th row of C */
for (e = A->row[i]; e != NULL; e = e->r_next)
{ k = e->j;
for (ee = B->row[k]; ee != NULL; ee = ee->r_next)
{ j = ee->j;
/* if a[i,k] != 0 and b[k,j] != 0 then c[i,j] != 0 */
if (!flag[j])
{ /* c[i,j] does not exist, so create it */
spm_new_elem(C, i, j, 0.0);
flag[j] = 1;
}
}
}
/* reset the flag array */
for (e = C->row[i]; e != NULL; e = e->r_next)
flag[e->j] = 0;
}
/* check and deallocate the flag array */
for (j = 1; j <= C->n; j++)
xassert(!flag[j]);
xfree(flag);
return C;
}
void spm_mul_num(SPM *C, const SPM *A, const SPM *B)
{ /* multiply two sparse matrices (numeric phase) */
int i, j;
double *work;
/* allocate and clear the working array */
work = xcalloc(1+A->n, sizeof(double));
for (j = 1; j <= A->n; j++)
work[j] = 0.0;
/* compute matrix C = A * B */
for (i = 1; i <= C->m; i++)
{ SPME *e, *ee;
double temp;
/* work := (i-th row of A) */
/* (note that A may have duplicate elements) */
for (e = A->row[i]; e != NULL; e = e->r_next)
work[e->j] += e->val;
/* compute i-th row of C */
for (e = C->row[i]; e != NULL; e = e->r_next)
{ j = e->j;
/* c[i,j] := work * (j-th column of B) */
temp = 0.0;
for (ee = B->col[j]; ee != NULL; ee = ee->c_next)
temp += work[ee->i] * ee->val;
e->val = temp;
}
/* reset the working array */
for (e = A->row[i]; e != NULL; e = e->r_next)
work[e->j] = 0.0;
}
/* check and deallocate the working array */
for (j = 1; j <= A->n; j++)
xassert(work[j] == 0.0);
xfree(work);
return;
}
SPM *spm_mul_mat(const SPM *A, const SPM *B)
{ /* multiply two sparse matrices (driver routine) */
SPM *C;
C = spm_mul_sym(A, B);
spm_mul_num(C, A, B);
return C;
}
PER *spm_create_per(int n)
{ /* create permutation matrix */
PER *P;
int k;
xassert(n >= 0);
P = xmalloc(sizeof(PER));
P->n = n;
P->row = xcalloc(1+n, sizeof(int));
P->col = xcalloc(1+n, sizeof(int));
/* initially it is identity matrix */
for (k = 1; k <= n; k++)
P->row[k] = P->col[k] = k;
return P;
}
void spm_check_per(PER *P)
{ /* check permutation matrix for correctness */
int i, j;
xassert(P->n >= 0);
for (i = 1; i <= P->n; i++)
{ j = P->row[i];
xassert(1 <= j && j <= P->n);
xassert(P->col[j] == i);
}
return;
}
void spm_delete_per(PER *P)
{ /* delete permutation matrix */
xfree(P->row);
xfree(P->col);
xfree(P);
return;
}
/* eof */