lemon-project-template-glpk
view deps/glpk/src/glplpf.h @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* glplpf.h (LP basis factorization, Schur complement version) */
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 ***********************************************************************/
25 #ifndef GLPLPF_H
26 #define GLPLPF_H
28 #include "glpscf.h"
29 #include "glpluf.h"
31 /***********************************************************************
32 * The structure LPF defines the factorization of the basis mxm matrix
33 * B, where m is the number of rows in corresponding problem instance.
34 *
35 * This factorization is the following septet:
36 *
37 * [B] = (L0, U0, R, S, C, P, Q), (1)
38 *
39 * and is based on the following main equality:
40 *
41 * ( B F^) ( B0 F ) ( L0 0 ) ( U0 R )
42 * ( ) = P ( ) Q = P ( ) ( ) Q, (2)
43 * ( G^ H^) ( G H ) ( S I ) ( 0 C )
44 *
45 * where:
46 *
47 * B is the current basis matrix (not stored);
48 *
49 * F^, G^, H^ are some additional matrices (not stored);
50 *
51 * B0 is some initial basis matrix (not stored);
52 *
53 * F, G, H are some additional matrices (not stored);
54 *
55 * P, Q are permutation matrices (stored in both row- and column-like
56 * formats);
57 *
58 * L0, U0 are some matrices that defines a factorization of the initial
59 * basis matrix B0 = L0 * U0 (stored in an invertable form);
60 *
61 * R is a matrix defined from L0 * R = F, so R = inv(L0) * F (stored in
62 * a column-wise sparse format);
63 *
64 * S is a matrix defined from S * U0 = G, so S = G * inv(U0) (stored in
65 * a row-wise sparse format);
66 *
67 * C is the Schur complement for matrix (B0 F G H). It is defined from
68 * S * R + C = H, so C = H - S * R = H - G * inv(U0) * inv(L0) * F =
69 * = H - G * inv(B0) * F. Matrix C is stored in an invertable form.
70 *
71 * REFERENCES
72 *
73 * 1. M.A.Saunders, "LUSOL: A basis package for constrained optimiza-
74 * tion," SCCM, Stanford University, 2006.
75 *
76 * 2. M.A.Saunders, "Notes 5: Basis Updates," CME 318, Stanford Univer-
77 * sity, Spring 2006.
78 *
79 * 3. M.A.Saunders, "Notes 6: LUSOL---a Basis Factorization Package,"
80 * ibid. */
82 typedef struct LPF LPF;
84 struct LPF
85 { /* LP basis factorization */
86 int valid;
87 /* the factorization is valid only if this flag is set */
88 /*--------------------------------------------------------------*/
89 /* initial basis matrix B0 */
90 int m0_max;
91 /* maximal value of m0 (increased automatically, if necessary) */
92 int m0;
93 /* the order of B0 */
94 LUF *luf;
95 /* LU-factorization of B0 */
96 /*--------------------------------------------------------------*/
97 /* current basis matrix B */
98 int m;
99 /* the order of B */
100 double *B; /* double B[1+m*m]; */
101 /* B in dense format stored by rows and used only for debugging;
102 normally this array is not allocated */
103 /*--------------------------------------------------------------*/
104 /* augmented matrix (B0 F G H) of the order m0+n */
105 int n_max;
106 /* maximal number of additional rows and columns */
107 int n;
108 /* current number of additional rows and columns */
109 /*--------------------------------------------------------------*/
110 /* m0xn matrix R in column-wise format */
111 int *R_ptr; /* int R_ptr[1+n_max]; */
112 /* R_ptr[j], 1 <= j <= n, is a pointer to j-th column */
113 int *R_len; /* int R_len[1+n_max]; */
114 /* R_len[j], 1 <= j <= n, is the length of j-th column */
115 /*--------------------------------------------------------------*/
116 /* nxm0 matrix S in row-wise format */
117 int *S_ptr; /* int S_ptr[1+n_max]; */
118 /* S_ptr[i], 1 <= i <= n, is a pointer to i-th row */
119 int *S_len; /* int S_len[1+n_max]; */
120 /* S_len[i], 1 <= i <= n, is the length of i-th row */
121 /*--------------------------------------------------------------*/
122 /* Schur complement C of the order n */
123 SCF *scf; /* SCF scf[1:n_max]; */
124 /* factorization of the Schur complement */
125 /*--------------------------------------------------------------*/
126 /* matrix P of the order m0+n */
127 int *P_row; /* int P_row[1+m0_max+n_max]; */
128 /* P_row[i] = j means that P[i,j] = 1 */
129 int *P_col; /* int P_col[1+m0_max+n_max]; */
130 /* P_col[j] = i means that P[i,j] = 1 */
131 /*--------------------------------------------------------------*/
132 /* matrix Q of the order m0+n */
133 int *Q_row; /* int Q_row[1+m0_max+n_max]; */
134 /* Q_row[i] = j means that Q[i,j] = 1 */
135 int *Q_col; /* int Q_col[1+m0_max+n_max]; */
136 /* Q_col[j] = i means that Q[i,j] = 1 */
137 /*--------------------------------------------------------------*/
138 /* Sparse Vector Area (SVA) is a set of locations intended to
139 store sparse vectors which represent columns of matrix R and
140 rows of matrix S; each location is a doublet (ind, val), where
141 ind is an index, val is a numerical value of a sparse vector
142 element; in the whole each sparse vector is a set of adjacent
143 locations defined by a pointer to its first element and its
144 length, i.e. the number of its elements */
145 int v_size;
146 /* the SVA size, in locations; locations are numbered by integers
147 1, 2, ..., v_size, and location 0 is not used */
148 int v_ptr;
149 /* pointer to the first available location */
150 int *v_ind; /* int v_ind[1+v_size]; */
151 /* v_ind[k], 1 <= k <= v_size, is the index field of location k */
152 double *v_val; /* double v_val[1+v_size]; */
153 /* v_val[k], 1 <= k <= v_size, is the value field of location k */
154 /*--------------------------------------------------------------*/
155 double *work1; /* double work1[1+m0+n_max]; */
156 /* working array */
157 double *work2; /* double work2[1+m0+n_max]; */
158 /* working array */
159 };
161 /* return codes: */
162 #define LPF_ESING 1 /* singular matrix */
163 #define LPF_ECOND 2 /* ill-conditioned matrix */
164 #define LPF_ELIMIT 3 /* update limit reached */
166 #define lpf_create_it _glp_lpf_create_it
167 LPF *lpf_create_it(void);
168 /* create LP basis factorization */
170 #define lpf_factorize _glp_lpf_factorize
171 int lpf_factorize(LPF *lpf, int m, const int bh[], int (*col)
172 (void *info, int j, int ind[], double val[]), void *info);
173 /* compute LP basis factorization */
175 #define lpf_ftran _glp_lpf_ftran
176 void lpf_ftran(LPF *lpf, double x[]);
177 /* perform forward transformation (solve system B*x = b) */
179 #define lpf_btran _glp_lpf_btran
180 void lpf_btran(LPF *lpf, double x[]);
181 /* perform backward transformation (solve system B'*x = b) */
183 #define lpf_update_it _glp_lpf_update_it
184 int lpf_update_it(LPF *lpf, int j, int bh, int len, const int ind[],
185 const double val[]);
186 /* update LP basis factorization */
188 #define lpf_delete_it _glp_lpf_delete_it
189 void lpf_delete_it(LPF *lpf);
190 /* delete LP basis factorization */
192 #endif
194 /* eof */