lemon-project-template-glpk

comparison deps/glpk/src/glpini02.c @ 11:4fc6ad2fb8a6

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Test GLPK in src/main.cc
author Alpar Juttner <alpar@cs.elte.hu>
date Sun, 06 Nov 2011 21:43:29 +0100
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1 /* glpini02.c */
2
3 /***********************************************************************
4 * This code is part of GLPK (GNU Linear Programming Kit).
5 *
6 * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
7 * 2009, 2010, 2011 Andrew Makhorin, Department for Applied Informatics,
8 * Moscow Aviation Institute, Moscow, Russia. All rights reserved.
9 * E-mail: <mao@gnu.org>.
10 *
11 * GLPK is free software: you can redistribute it and/or modify it
12 * under the terms of the GNU General Public License as published by
13 * the Free Software Foundation, either version 3 of the License, or
14 * (at your option) any later version.
15 *
16 * GLPK is distributed in the hope that it will be useful, but WITHOUT
17 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18 * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
19 * License for more details.
20 *
21 * You should have received a copy of the GNU General Public License
22 * along with GLPK. If not, see <http://www.gnu.org/licenses/>.
23 ***********************************************************************/
24
25 #include "glpapi.h"
26
27 struct var
28 { /* structural variable */
29 int j;
30 /* ordinal number */
31 double q;
32 /* penalty value */
33 };
34
35 static int fcmp(const void *ptr1, const void *ptr2)
36 { /* this routine is passed to the qsort() function */
37 struct var *col1 = (void *)ptr1, *col2 = (void *)ptr2;
38 if (col1->q < col2->q) return -1;
39 if (col1->q > col2->q) return +1;
40 return 0;
41 }
42
43 static int get_column(glp_prob *lp, int j, int ind[], double val[])
44 { /* Bixby's algorithm assumes that the constraint matrix is scaled
45 such that the maximum absolute value in every non-zero row and
46 column is 1 */
47 int k, len;
48 double big;
49 len = glp_get_mat_col(lp, j, ind, val);
50 big = 0.0;
51 for (k = 1; k <= len; k++)
52 if (big < fabs(val[k])) big = fabs(val[k]);
53 if (big == 0.0) big = 1.0;
54 for (k = 1; k <= len; k++) val[k] /= big;
55 return len;
56 }
57
58 static void cpx_basis(glp_prob *lp)
59 { /* main routine */
60 struct var *C, *C2, *C3, *C4;
61 int m, n, i, j, jk, k, l, ll, t, n2, n3, n4, type, len, *I, *r,
62 *ind;
63 double alpha, gamma, cmax, temp, *v, *val;
64 xprintf("Constructing initial basis...\n");
65 /* determine the number of rows and columns */
66 m = glp_get_num_rows(lp);
67 n = glp_get_num_cols(lp);
68 /* allocate working arrays */
69 C = xcalloc(1+n, sizeof(struct var));
70 I = xcalloc(1+m, sizeof(int));
71 r = xcalloc(1+m, sizeof(int));
72 v = xcalloc(1+m, sizeof(double));
73 ind = xcalloc(1+m, sizeof(int));
74 val = xcalloc(1+m, sizeof(double));
75 /* make all auxiliary variables non-basic */
76 for (i = 1; i <= m; i++)
77 { if (glp_get_row_type(lp, i) != GLP_DB)
78 glp_set_row_stat(lp, i, GLP_NS);
79 else if (fabs(glp_get_row_lb(lp, i)) <=
80 fabs(glp_get_row_ub(lp, i)))
81 glp_set_row_stat(lp, i, GLP_NL);
82 else
83 glp_set_row_stat(lp, i, GLP_NU);
84 }
85 /* make all structural variables non-basic */
86 for (j = 1; j <= n; j++)
87 { if (glp_get_col_type(lp, j) != GLP_DB)
88 glp_set_col_stat(lp, j, GLP_NS);
89 else if (fabs(glp_get_col_lb(lp, j)) <=
90 fabs(glp_get_col_ub(lp, j)))
91 glp_set_col_stat(lp, j, GLP_NL);
92 else
93 glp_set_col_stat(lp, j, GLP_NU);
94 }
95 /* C2 is a set of free structural variables */
96 n2 = 0, C2 = C + 0;
97 for (j = 1; j <= n; j++)
98 { type = glp_get_col_type(lp, j);
99 if (type == GLP_FR)
100 { n2++;
101 C2[n2].j = j;
102 C2[n2].q = 0.0;
103 }
104 }
105 /* C3 is a set of structural variables having excatly one (lower
106 or upper) bound */
107 n3 = 0, C3 = C2 + n2;
108 for (j = 1; j <= n; j++)
109 { type = glp_get_col_type(lp, j);
110 if (type == GLP_LO)
111 { n3++;
112 C3[n3].j = j;
113 C3[n3].q = + glp_get_col_lb(lp, j);
114 }
115 else if (type == GLP_UP)
116 { n3++;
117 C3[n3].j = j;
118 C3[n3].q = - glp_get_col_ub(lp, j);
119 }
120 }
121 /* C4 is a set of structural variables having both (lower and
122 upper) bounds */
123 n4 = 0, C4 = C3 + n3;
124 for (j = 1; j <= n; j++)
125 { type = glp_get_col_type(lp, j);
126 if (type == GLP_DB)
127 { n4++;
128 C4[n4].j = j;
129 C4[n4].q = glp_get_col_lb(lp, j) - glp_get_col_ub(lp, j);
130 }
131 }
132 /* compute gamma = max{|c[j]|: 1 <= j <= n} */
133 gamma = 0.0;
134 for (j = 1; j <= n; j++)
135 { temp = fabs(glp_get_obj_coef(lp, j));
136 if (gamma < temp) gamma = temp;
137 }
138 /* compute cmax */
139 cmax = (gamma == 0.0 ? 1.0 : 1000.0 * gamma);
140 /* compute final penalty for all structural variables within sets
141 C2, C3, and C4 */
142 switch (glp_get_obj_dir(lp))
143 { case GLP_MIN: temp = +1.0; break;
144 case GLP_MAX: temp = -1.0; break;
145 default: xassert(lp != lp);
146 }
147 for (k = 1; k <= n2+n3+n4; k++)
148 { j = C[k].j;
149 C[k].q += (temp * glp_get_obj_coef(lp, j)) / cmax;
150 }
151 /* sort structural variables within C2, C3, and C4 in ascending
152 order of penalty value */
153 qsort(C2+1, n2, sizeof(struct var), fcmp);
154 for (k = 1; k < n2; k++) xassert(C2[k].q <= C2[k+1].q);
155 qsort(C3+1, n3, sizeof(struct var), fcmp);
156 for (k = 1; k < n3; k++) xassert(C3[k].q <= C3[k+1].q);
157 qsort(C4+1, n4, sizeof(struct var), fcmp);
158 for (k = 1; k < n4; k++) xassert(C4[k].q <= C4[k+1].q);
159 /*** STEP 1 ***/
160 for (i = 1; i <= m; i++)
161 { type = glp_get_row_type(lp, i);
162 if (type != GLP_FX)
163 { /* row i is either free or inequality constraint */
164 glp_set_row_stat(lp, i, GLP_BS);
165 I[i] = 1;
166 r[i] = 1;
167 }
168 else
169 { /* row i is equality constraint */
170 I[i] = 0;
171 r[i] = 0;
172 }
173 v[i] = +DBL_MAX;
174 }
175 /*** STEP 2 ***/
176 for (k = 1; k <= n2+n3+n4; k++)
177 { jk = C[k].j;
178 len = get_column(lp, jk, ind, val);
179 /* let alpha = max{|A[l,jk]|: r[l] = 0} and let l' be such
180 that alpha = |A[l',jk]| */
181 alpha = 0.0, ll = 0;
182 for (t = 1; t <= len; t++)
183 { l = ind[t];
184 if (r[l] == 0 && alpha < fabs(val[t]))
185 alpha = fabs(val[t]), ll = l;
186 }
187 if (alpha >= 0.99)
188 { /* B := B union {jk} */
189 glp_set_col_stat(lp, jk, GLP_BS);
190 I[ll] = 1;
191 v[ll] = alpha;
192 /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
193 for (t = 1; t <= len; t++)
194 { l = ind[t];
195 if (val[t] != 0.0) r[l]++;
196 }
197 /* continue to the next k */
198 continue;
199 }
200 /* if |A[l,jk]| > 0.01 * v[l] for some l, continue to the
201 next k */
202 for (t = 1; t <= len; t++)
203 { l = ind[t];
204 if (fabs(val[t]) > 0.01 * v[l]) break;
205 }
206 if (t <= len) continue;
207 /* otherwise, let alpha = max{|A[l,jk]|: I[l] = 0} and let l'
208 be such that alpha = |A[l',jk]| */
209 alpha = 0.0, ll = 0;
210 for (t = 1; t <= len; t++)
211 { l = ind[t];
212 if (I[l] == 0 && alpha < fabs(val[t]))
213 alpha = fabs(val[t]), ll = l;
214 }
215 /* if alpha = 0, continue to the next k */
216 if (alpha == 0.0) continue;
217 /* B := B union {jk} */
218 glp_set_col_stat(lp, jk, GLP_BS);
219 I[ll] = 1;
220 v[ll] = alpha;
221 /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
222 for (t = 1; t <= len; t++)
223 { l = ind[t];
224 if (val[t] != 0.0) r[l]++;
225 }
226 }
227 /*** STEP 3 ***/
228 /* add an artificial variable (auxiliary variable for equality
229 constraint) to cover each remaining uncovered row */
230 for (i = 1; i <= m; i++)
231 if (I[i] == 0) glp_set_row_stat(lp, i, GLP_BS);
232 /* free working arrays */
233 xfree(C);
234 xfree(I);
235 xfree(r);
236 xfree(v);
237 xfree(ind);
238 xfree(val);
239 return;
240 }
241
242 /***********************************************************************
243 * NAME
244 *
245 * glp_cpx_basis - construct Bixby's initial LP basis
246 *
247 * SYNOPSIS
248 *
249 * void glp_cpx_basis(glp_prob *lp);
250 *
251 * DESCRIPTION
252 *
253 * The routine glp_cpx_basis constructs an advanced initial basis for
254 * the specified problem object.
255 *
256 * The routine is based on Bixby's algorithm described in the paper:
257 *
258 * Robert E. Bixby. Implementing the Simplex Method: The Initial Basis.
259 * ORSA Journal on Computing, Vol. 4, No. 3, 1992, pp. 267-84. */
260
261 void glp_cpx_basis(glp_prob *lp)
262 { if (lp->m == 0 || lp->n == 0)
263 glp_std_basis(lp);
264 else
265 cpx_basis(lp);
266 return;
267 }
268
269 /* eof */