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/* advbas.c (construct advanced initial LP basis) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2008-2016 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 "env.h"
#include "prob.h"
#include "triang.h"
/***********************************************************************
* NAME
*
* glp_adv_basis - construct advanced initial LP basis
*
* SYNOPSIS
*
* void glp_adv_basis(glp_prob *P, int flags);
*
* DESCRIPTION
*
* The routine glp_adv_basis constructs an advanced initial LP basis
* for the specified problem object.
*
* The parameter flag is reserved for use in the future and should be
* specified as zero.
*
* NOTE
*
* The routine glp_adv_basis should be called after the constraint
* matrix has been scaled (if scaling is used). */
static int mat(void *info, int k, int ind[], double val[])
{ glp_prob *P = info;
int m = P->m;
int n = P->n;
GLPROW **row = P->row;
GLPCOL **col = P->col;
GLPAIJ *aij;
int i, j, len;
if (k > 0)
{ /* retrieve scaled row of constraint matrix */
i = +k;
xassert(1 <= i && i <= m);
len = 0;
if (row[i]->type == GLP_FX)
{ for (aij = row[i]->ptr; aij != NULL; aij = aij->r_next)
{ j = aij->col->j;
if (col[j]->type != GLP_FX)
{ len++;
ind[len] = j;
val[len] = aij->row->rii * aij->val * aij->col->sjj;
}
}
}
}
else
{ /* retrieve scaled column of constraint matrix */
j = -k;
xassert(1 <= j && j <= n);
len = 0;
if (col[j]->type != GLP_FX)
{ for (aij = col[j]->ptr; aij != NULL; aij = aij->c_next)
{ i = aij->row->i;
if (row[i]->type == GLP_FX)
{ len++;
ind[len] = i;
val[len] = aij->row->rii * aij->val * aij->col->sjj;
}
}
}
}
return len;
}
void glp_adv_basis(glp_prob *P, int flags)
{ int i, j, k, m, n, min_mn, size, *rn, *cn;
char *flag;
if (flags != 0)
xerror("glp_adv_basis: flags = %d; invalid flags\n", flags);
m = P->m; /* number of rows */
n = P->n; /* number of columns */
if (m == 0 || n == 0)
{ /* trivial case */
glp_std_basis(P);
goto done;
}
xprintf("Constructing initial basis...\n");
/* allocate working arrays */
min_mn = (m < n ? m : n);
rn = talloc(1+min_mn, int);
cn = talloc(1+min_mn, int);
flag = talloc(1+m, char);
/* make the basis empty */
for (i = 1; i <= m; i++)
{ flag[i] = 0;
glp_set_row_stat(P, i, GLP_NS);
}
for (j = 1; j <= n; j++)
glp_set_col_stat(P, j, GLP_NS);
/* find maximal triangular part of the constraint matrix;
to prevent including non-fixed rows and fixed columns in the
triangular part, such rows and columns are temporarily made
empty by the routine mat */
#if 1 /* FIXME: tolerance */
size = triang(m, n, mat, P, 0.001, rn, cn);
#endif
xassert(0 <= size && size <= min_mn);
/* include in the basis non-fixed structural variables, whose
columns constitute the triangular part */
for (k = 1; k <= size; k++)
{ i = rn[k];
xassert(1 <= i && i <= m);
flag[i] = 1;
j = cn[k];
xassert(1 <= j && j <= n);
glp_set_col_stat(P, j, GLP_BS);
}
/* include in the basis appropriate auxiliary variables, whose
unity columns preserve triangular form of the basis matrix */
for (i = 1; i <= m; i++)
{ if (flag[i] == 0)
{ glp_set_row_stat(P, i, GLP_BS);
if (P->row[i]->type != GLP_FX)
size++;
}
}
/* size of triangular part = (number of rows) - (number of basic
fixed auxiliary variables) */
xprintf("Size of triangular part is %d\n", size);
/* deallocate working arrays */
tfree(rn);
tfree(cn);
tfree(flag);
done: return;
}
/* eof */
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