COIN-OR::LEMON - Graph Library

source: glpk-cmake/src/glplux.h @ 1:c445c931472f

Last change on this file since 1:c445c931472f was 1:c445c931472f, checked in by Alpar Juttner <alpar@…>, 10 years ago

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1/* glplux.h (LU-factorization, bignum arithmetic) */
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 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#ifndef GLPLUX_H
26#define GLPLUX_H
27
28#include "glpdmp.h"
29#include "glpgmp.h"
30
31/*----------------------------------------------------------------------
32// The structure LUX defines LU-factorization of a square matrix A,
33// which is the following quartet:
34//
35//    [A] = (F, V, P, Q),                                            (1)
36//
37// where F and V are such matrices that
38//
39//    A = F * V,                                                     (2)
40//
41// and P and Q are such permutation matrices that the matrix
42//
43//    L = P * F * inv(P)                                             (3)
44//
45// is lower triangular with unity diagonal, and the matrix
46//
47//    U = P * V * Q                                                  (4)
48//
49// is upper triangular. All the matrices have the order n.
50//
51// The matrices F and V are stored in row/column-wise sparse format as
52// row and column linked lists of non-zero elements. Unity elements on
53// the main diagonal of the matrix F are not stored. Pivot elements of
54// the matrix V (that correspond to diagonal elements of the matrix U)
55// are also missing from the row and column lists and stored separately
56// in an ordinary array.
57//
58// The permutation matrices P and Q are stored as ordinary arrays using
59// both row- and column-like formats.
60//
61// The matrices L and U being completely defined by the matrices F, V,
62// P, and Q are not stored explicitly.
63//
64// It is easy to show that the factorization (1)-(3) is some version of
65// LU-factorization. Indeed, from (3) and (4) it follows that:
66//
67//    F = inv(P) * L * P,
68//
69//    V = inv(P) * U * inv(Q),
70//
71// and substitution into (2) gives:
72//
73//    A = F * V = inv(P) * L * U * inv(Q).
74//
75// For more details see the program documentation. */
76
77typedef struct LUX LUX;
78typedef struct LUXELM LUXELM;
79typedef struct LUXWKA LUXWKA;
80
81struct LUX
82{     /* LU-factorization of a square matrix */
83      int n;
84      /* the order of matrices A, F, V, P, Q */
85      DMP *pool;
86      /* memory pool for elements of matrices F and V */
87      LUXELM **F_row; /* LUXELM *F_row[1+n]; */
88      /* F_row[0] is not used;
89         F_row[i], 1 <= i <= n, is a pointer to the list of elements in
90         i-th row of matrix F (diagonal elements are not stored) */
91      LUXELM **F_col; /* LUXELM *F_col[1+n]; */
92      /* F_col[0] is not used;
93         F_col[j], 1 <= j <= n, is a pointer to the list of elements in
94         j-th column of matrix F (diagonal elements are not stored) */
95      mpq_t *V_piv; /* mpq_t V_piv[1+n]; */
96      /* V_piv[0] is not used;
97         V_piv[p], 1 <= p <= n, is a pivot element v[p,q] corresponding
98         to a diagonal element u[k,k] of matrix U = P*V*Q (used on k-th
99         elimination step, k = 1, 2, ..., n) */
100      LUXELM **V_row; /* LUXELM *V_row[1+n]; */
101      /* V_row[0] is not used;
102         V_row[i], 1 <= i <= n, is a pointer to the list of elements in
103         i-th row of matrix V (except pivot elements) */
104      LUXELM **V_col; /* LUXELM *V_col[1+n]; */
105      /* V_col[0] is not used;
106         V_col[j], 1 <= j <= n, is a pointer to the list of elements in
107         j-th column of matrix V (except pivot elements) */
108      int *P_row; /* int P_row[1+n]; */
109      /* P_row[0] is not used;
110         P_row[i] = j means that p[i,j] = 1, where p[i,j] is an element
111         of permutation matrix P */
112      int *P_col; /* int P_col[1+n]; */
113      /* P_col[0] is not used;
114         P_col[j] = i means that p[i,j] = 1, where p[i,j] is an element
115         of permutation matrix P */
116      /* if i-th row or column of matrix F is i'-th row or column of
117         matrix L = P*F*inv(P), or if i-th row of matrix V is i'-th row
118         of matrix U = P*V*Q, then P_row[i'] = i and P_col[i] = i' */
119      int *Q_row; /* int Q_row[1+n]; */
120      /* Q_row[0] is not used;
121         Q_row[i] = j means that q[i,j] = 1, where q[i,j] is an element
122         of permutation matrix Q */
123      int *Q_col; /* int Q_col[1+n]; */
124      /* Q_col[0] is not used;
125         Q_col[j] = i means that q[i,j] = 1, where q[i,j] is an element
126         of permutation matrix Q */
127      /* if j-th column of matrix V is j'-th column of matrix U = P*V*Q,
128         then Q_row[j] = j' and Q_col[j'] = j */
129      int rank;
130      /* the (exact) rank of matrices A and V */
131};
132
133struct LUXELM
134{     /* element of matrix F or V */
135      int i;
136      /* row index, 1 <= i <= m */
137      int j;
138      /* column index, 1 <= j <= n */
139      mpq_t val;
140      /* numeric (non-zero) element value */
141      LUXELM *r_prev;
142      /* pointer to previous element in the same row */
143      LUXELM *r_next;
144      /* pointer to next element in the same row */
145      LUXELM *c_prev;
146      /* pointer to previous element in the same column */
147      LUXELM *c_next;
148      /* pointer to next element in the same column */
149};
150
151struct LUXWKA
152{     /* working area (used only during factorization) */
153      /* in order to efficiently implement Markowitz strategy and Duff
154         search technique there are two families {R[0], R[1], ..., R[n]}
155         and {C[0], C[1], ..., C[n]}; member R[k] is a set of active
156         rows of matrix V having k non-zeros, and member C[k] is a set
157         of active columns of matrix V having k non-zeros (in the active
158         submatrix); each set R[k] and C[k] is implemented as a separate
159         doubly linked list */
160      int *R_len; /* int R_len[1+n]; */
161      /* R_len[0] is not used;
162         R_len[i], 1 <= i <= n, is the number of non-zero elements in
163         i-th row of matrix V (that is the length of i-th row) */
164      int *R_head; /* int R_head[1+n]; */
165      /* R_head[k], 0 <= k <= n, is the number of a first row, which is
166         active and whose length is k */
167      int *R_prev; /* int R_prev[1+n]; */
168      /* R_prev[0] is not used;
169         R_prev[i], 1 <= i <= n, is the number of a previous row, which
170         is active and has the same length as i-th row */
171      int *R_next; /* int R_next[1+n]; */
172      /* R_prev[0] is not used;
173         R_prev[i], 1 <= i <= n, is the number of a next row, which is
174         active and has the same length as i-th row */
175      int *C_len; /* int C_len[1+n]; */
176      /* C_len[0] is not used;
177         C_len[j], 1 <= j <= n, is the number of non-zero elements in
178         j-th column of the active submatrix of matrix V (that is the
179         length of j-th column in the active submatrix) */
180      int *C_head; /* int C_head[1+n]; */
181      /* C_head[k], 0 <= k <= n, is the number of a first column, which
182         is active and whose length is k */
183      int *C_prev; /* int C_prev[1+n]; */
184      /* C_prev[0] is not used;
185         C_prev[j], 1 <= j <= n, is the number of a previous column,
186         which is active and has the same length as j-th column */
187      int *C_next; /* int C_next[1+n]; */
188      /* C_next[0] is not used;
189         C_next[j], 1 <= j <= n, is the number of a next column, which
190         is active and has the same length as j-th column */
191};
192
193#define lux_create            _glp_lux_create
194#define lux_decomp            _glp_lux_decomp
195#define lux_f_solve           _glp_lux_f_solve
196#define lux_v_solve           _glp_lux_v_solve
197#define lux_solve             _glp_lux_solve
198#define lux_delete            _glp_lux_delete
199
200LUX *lux_create(int n);
201/* create LU-factorization */
202
203int lux_decomp(LUX *lux, int (*col)(void *info, int j, int ind[],
204      mpq_t val[]), void *info);
205/* compute LU-factorization */
206
207void lux_f_solve(LUX *lux, int tr, mpq_t x[]);
208/* solve system F*x = b or F'*x = b */
209
210void lux_v_solve(LUX *lux, int tr, mpq_t x[]);
211/* solve system V*x = b or V'*x = b */
212
213void lux_solve(LUX *lux, int tr, mpq_t x[]);
214/* solve system A*x = b or A'*x = b */
215
216void lux_delete(LUX *lux);
217/* delete LU-factorization */
218
219#endif
220
221/* eof */
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