alpar@1: /* glpini02.c */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #include "glpapi.h"
alpar@1: 
alpar@1: struct var
alpar@1: {     /* structural variable */
alpar@1:       int j;
alpar@1:       /* ordinal number */
alpar@1:       double q;
alpar@1:       /* penalty value */
alpar@1: };
alpar@1: 
alpar@1: static int fcmp(const void *ptr1, const void *ptr2)
alpar@1: {     /* this routine is passed to the qsort() function */
alpar@1:       struct var *col1 = (void *)ptr1, *col2 = (void *)ptr2;
alpar@1:       if (col1->q < col2->q) return -1;
alpar@1:       if (col1->q > col2->q) return +1;
alpar@1:       return 0;
alpar@1: }
alpar@1: 
alpar@1: static int get_column(glp_prob *lp, int j, int ind[], double val[])
alpar@1: {     /* Bixby's algorithm assumes that the constraint matrix is scaled
alpar@1:          such that the maximum absolute value in every non-zero row and
alpar@1:          column is 1 */
alpar@1:       int k, len;
alpar@1:       double big;
alpar@1:       len = glp_get_mat_col(lp, j, ind, val);
alpar@1:       big = 0.0;
alpar@1:       for (k = 1; k <= len; k++)
alpar@1:          if (big < fabs(val[k])) big = fabs(val[k]);
alpar@1:       if (big == 0.0) big = 1.0;
alpar@1:       for (k = 1; k <= len; k++) val[k] /= big;
alpar@1:       return len;
alpar@1: }
alpar@1: 
alpar@1: static void cpx_basis(glp_prob *lp)
alpar@1: {     /* main routine */
alpar@1:       struct var *C, *C2, *C3, *C4;
alpar@1:       int m, n, i, j, jk, k, l, ll, t, n2, n3, n4, type, len, *I, *r,
alpar@1:          *ind;
alpar@1:       double alpha, gamma, cmax, temp, *v, *val;
alpar@1:       xprintf("Constructing initial basis...\n");
alpar@1:       /* determine the number of rows and columns */
alpar@1:       m = glp_get_num_rows(lp);
alpar@1:       n = glp_get_num_cols(lp);
alpar@1:       /* allocate working arrays */
alpar@1:       C = xcalloc(1+n, sizeof(struct var));
alpar@1:       I = xcalloc(1+m, sizeof(int));
alpar@1:       r = xcalloc(1+m, sizeof(int));
alpar@1:       v = xcalloc(1+m, sizeof(double));
alpar@1:       ind = xcalloc(1+m, sizeof(int));
alpar@1:       val = xcalloc(1+m, sizeof(double));
alpar@1:       /* make all auxiliary variables non-basic */
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:       {  if (glp_get_row_type(lp, i) != GLP_DB)
alpar@1:             glp_set_row_stat(lp, i, GLP_NS);
alpar@1:          else if (fabs(glp_get_row_lb(lp, i)) <=
alpar@1:                   fabs(glp_get_row_ub(lp, i)))
alpar@1:             glp_set_row_stat(lp, i, GLP_NL);
alpar@1:          else
alpar@1:             glp_set_row_stat(lp, i, GLP_NU);
alpar@1:       }
alpar@1:       /* make all structural variables non-basic */
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  if (glp_get_col_type(lp, j) != GLP_DB)
alpar@1:             glp_set_col_stat(lp, j, GLP_NS);
alpar@1:          else if (fabs(glp_get_col_lb(lp, j)) <=
alpar@1:                   fabs(glp_get_col_ub(lp, j)))
alpar@1:             glp_set_col_stat(lp, j, GLP_NL);
alpar@1:          else
alpar@1:             glp_set_col_stat(lp, j, GLP_NU);
alpar@1:       }
alpar@1:       /* C2 is a set of free structural variables */
alpar@1:       n2 = 0, C2 = C + 0;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  type = glp_get_col_type(lp, j);
alpar@1:          if (type == GLP_FR)
alpar@1:          {  n2++;
alpar@1:             C2[n2].j = j;
alpar@1:             C2[n2].q = 0.0;
alpar@1:          }
alpar@1:       }
alpar@1:       /* C3 is a set of structural variables having excatly one (lower
alpar@1:          or upper) bound */
alpar@1:       n3 = 0, C3 = C2 + n2;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  type = glp_get_col_type(lp, j);
alpar@1:          if (type == GLP_LO)
alpar@1:          {  n3++;
alpar@1:             C3[n3].j = j;
alpar@1:             C3[n3].q = + glp_get_col_lb(lp, j);
alpar@1:          }
alpar@1:          else if (type == GLP_UP)
alpar@1:          {  n3++;
alpar@1:             C3[n3].j = j;
alpar@1:             C3[n3].q = - glp_get_col_ub(lp, j);
alpar@1:          }
alpar@1:       }
alpar@1:       /* C4 is a set of structural variables having both (lower and
alpar@1:          upper) bounds */
alpar@1:       n4 = 0, C4 = C3 + n3;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  type = glp_get_col_type(lp, j);
alpar@1:          if (type == GLP_DB)
alpar@1:          {  n4++;
alpar@1:             C4[n4].j = j;
alpar@1:             C4[n4].q = glp_get_col_lb(lp, j) - glp_get_col_ub(lp, j);
alpar@1:          }
alpar@1:       }
alpar@1:       /* compute gamma = max{|c[j]|: 1 <= j <= n} */
alpar@1:       gamma = 0.0;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  temp = fabs(glp_get_obj_coef(lp, j));
alpar@1:          if (gamma < temp) gamma = temp;
alpar@1:       }
alpar@1:       /* compute cmax */
alpar@1:       cmax = (gamma == 0.0 ? 1.0 : 1000.0 * gamma);
alpar@1:       /* compute final penalty for all structural variables within sets
alpar@1:          C2, C3, and C4 */
alpar@1:       switch (glp_get_obj_dir(lp))
alpar@1:       {  case GLP_MIN: temp = +1.0; break;
alpar@1:          case GLP_MAX: temp = -1.0; break;
alpar@1:          default: xassert(lp != lp);
alpar@1:       }
alpar@1:       for (k = 1; k <= n2+n3+n4; k++)
alpar@1:       {  j = C[k].j;
alpar@1:          C[k].q += (temp * glp_get_obj_coef(lp, j)) / cmax;
alpar@1:       }
alpar@1:       /* sort structural variables within C2, C3, and C4 in ascending
alpar@1:          order of penalty value */
alpar@1:       qsort(C2+1, n2, sizeof(struct var), fcmp);
alpar@1:       for (k = 1; k < n2; k++) xassert(C2[k].q <= C2[k+1].q);
alpar@1:       qsort(C3+1, n3, sizeof(struct var), fcmp);
alpar@1:       for (k = 1; k < n3; k++) xassert(C3[k].q <= C3[k+1].q);
alpar@1:       qsort(C4+1, n4, sizeof(struct var), fcmp);
alpar@1:       for (k = 1; k < n4; k++) xassert(C4[k].q <= C4[k+1].q);
alpar@1:       /*** STEP 1 ***/
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:       {  type = glp_get_row_type(lp, i);
alpar@1:          if (type != GLP_FX)
alpar@1:          {  /* row i is either free or inequality constraint */
alpar@1:             glp_set_row_stat(lp, i, GLP_BS);
alpar@1:             I[i] = 1;
alpar@1:             r[i] = 1;
alpar@1:          }
alpar@1:          else
alpar@1:          {  /* row i is equality constraint */
alpar@1:             I[i] = 0;
alpar@1:             r[i] = 0;
alpar@1:          }
alpar@1:          v[i] = +DBL_MAX;
alpar@1:       }
alpar@1:       /*** STEP 2 ***/
alpar@1:       for (k = 1; k <= n2+n3+n4; k++)
alpar@1:       {  jk = C[k].j;
alpar@1:          len = get_column(lp, jk, ind, val);
alpar@1:          /* let alpha = max{|A[l,jk]|: r[l] = 0} and let l' be such
alpar@1:             that alpha = |A[l',jk]| */
alpar@1:          alpha = 0.0, ll = 0;
alpar@1:          for (t = 1; t <= len; t++)
alpar@1:          {  l = ind[t];
alpar@1:             if (r[l] == 0 && alpha < fabs(val[t]))
alpar@1:                alpha = fabs(val[t]), ll = l;
alpar@1:          }
alpar@1:          if (alpha >= 0.99)
alpar@1:          {  /* B := B union {jk} */
alpar@1:             glp_set_col_stat(lp, jk, GLP_BS);
alpar@1:             I[ll] = 1;
alpar@1:             v[ll] = alpha;
alpar@1:             /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
alpar@1:             for (t = 1; t <= len; t++)
alpar@1:             {  l = ind[t];
alpar@1:                if (val[t] != 0.0) r[l]++;
alpar@1:             }
alpar@1:             /* continue to the next k */
alpar@1:             continue;
alpar@1:          }
alpar@1:          /* if |A[l,jk]| > 0.01 * v[l] for some l, continue to the
alpar@1:             next k */
alpar@1:          for (t = 1; t <= len; t++)
alpar@1:          {  l = ind[t];
alpar@1:             if (fabs(val[t]) > 0.01 * v[l]) break;
alpar@1:          }
alpar@1:          if (t <= len) continue;
alpar@1:          /* otherwise, let alpha = max{|A[l,jk]|: I[l] = 0} and let l'
alpar@1:             be such that alpha = |A[l',jk]| */
alpar@1:          alpha = 0.0, ll = 0;
alpar@1:          for (t = 1; t <= len; t++)
alpar@1:          {  l = ind[t];
alpar@1:             if (I[l] == 0 && alpha < fabs(val[t]))
alpar@1:                alpha = fabs(val[t]), ll = l;
alpar@1:          }
alpar@1:          /* if alpha = 0, continue to the next k */
alpar@1:          if (alpha == 0.0) continue;
alpar@1:          /* B := B union {jk} */
alpar@1:          glp_set_col_stat(lp, jk, GLP_BS);
alpar@1:          I[ll] = 1;
alpar@1:          v[ll] = alpha;
alpar@1:          /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
alpar@1:          for (t = 1; t <= len; t++)
alpar@1:          {  l = ind[t];
alpar@1:             if (val[t] != 0.0) r[l]++;
alpar@1:          }
alpar@1:       }
alpar@1:       /*** STEP 3 ***/
alpar@1:       /* add an artificial variable (auxiliary variable for equality
alpar@1:          constraint) to cover each remaining uncovered row */
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:          if (I[i] == 0) glp_set_row_stat(lp, i, GLP_BS);
alpar@1:       /* free working arrays */
alpar@1:       xfree(C);
alpar@1:       xfree(I);
alpar@1:       xfree(r);
alpar@1:       xfree(v);
alpar@1:       xfree(ind);
alpar@1:       xfree(val);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_cpx_basis - construct Bixby's initial LP basis
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  void glp_cpx_basis(glp_prob *lp);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine glp_cpx_basis constructs an advanced initial basis for
alpar@1: *  the specified problem object.
alpar@1: *
alpar@1: *  The routine is based on Bixby's algorithm described in the paper:
alpar@1: *
alpar@1: *  Robert E. Bixby. Implementing the Simplex Method: The Initial Basis.
alpar@1: *  ORSA Journal on Computing, Vol. 4, No. 3, 1992, pp. 267-84. */
alpar@1: 
alpar@1: void glp_cpx_basis(glp_prob *lp)
alpar@1: {     if (lp->m == 0 || lp->n == 0)
alpar@1:          glp_std_basis(lp);
alpar@1:       else
alpar@1:          cpx_basis(lp);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /* eof */