/* glpspm.c */

/***********************************************************************

*  This code is part of GLPK (GNU Linear Programming Kit).

*

*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

*  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

*  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

*  E-mail: <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 "glphbm.h"

#include "glprgr.h"

#include "glpspm.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 */