1 /* glplpf.h (LP basis factorization, Schur complement version) */ 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 GLPLPF_H 26 #define GLPLPF_H 27 28 #include "glpscf.h" 29 #include "glpluf.h" AMD_preprocess(Int n,const Int Ap[],const Int Ai[],Int Rp[],Int Ri[],Int W[],Int Flag[])30 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. */ 81 82 typedef struct LPF LPF; 83 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 }; 160 161 /* 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 */ 165 166 #define lpf_create_it _glp_lpf_create_it 167 LPF *lpf_create_it(void); 168 /* create LP basis factorization */ 169 170 #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 */ 174 175 #define lpf_ftran _glp_lpf_ftran 176 void lpf_ftran(LPF *lpf, double x[]); 177 /* perform forward transformation (solve system B*x = b) */ 178 179 #define lpf_btran _glp_lpf_btran 180 void lpf_btran(LPF *lpf, double x[]); 181 /* perform backward transformation (solve system B'*x = b) */ 182 183 #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 */ 187 188 #define lpf_delete_it _glp_lpf_delete_it 189 void lpf_delete_it(LPF *lpf); 190 /* delete LP basis factorization */ 191 192 #endif 193 194 /* eof */ 195