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1 /* glplpf.h (LP basis factorization, Schur complement version) */ |
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2 |
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3 /*********************************************************************** |
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4 * This code is part of GLPK (GNU Linear Programming Kit). |
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5 * |
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6 * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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7 * 2009, 2010 Andrew Makhorin, Department for Applied Informatics, |
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8 * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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9 * E-mail: <mao@gnu.org>. |
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10 * |
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11 * GLPK is free software: you can redistribute it and/or modify it |
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12 * under the terms of the GNU General Public License as published by |
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13 * the Free Software Foundation, either version 3 of the License, or |
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14 * (at your option) any later version. |
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15 * |
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16 * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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17 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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18 * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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19 * License for more details. |
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20 * |
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21 * You should have received a copy of the GNU General Public License |
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22 * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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23 ***********************************************************************/ |
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24 |
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25 #ifndef GLPLPF_H |
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26 #define GLPLPF_H |
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27 |
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28 #include "glpscf.h" |
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29 #include "glpluf.h" |
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30 |
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31 /*********************************************************************** |
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32 * The structure LPF defines the factorization of the basis mxm matrix |
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33 * B, where m is the number of rows in corresponding problem instance. |
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34 * |
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35 * This factorization is the following septet: |
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36 * |
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37 * [B] = (L0, U0, R, S, C, P, Q), (1) |
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38 * |
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39 * and is based on the following main equality: |
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40 * |
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41 * ( B F^) ( B0 F ) ( L0 0 ) ( U0 R ) |
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42 * ( ) = P ( ) Q = P ( ) ( ) Q, (2) |
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43 * ( G^ H^) ( G H ) ( S I ) ( 0 C ) |
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44 * |
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45 * where: |
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46 * |
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47 * B is the current basis matrix (not stored); |
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48 * |
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49 * F^, G^, H^ are some additional matrices (not stored); |
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50 * |
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51 * B0 is some initial basis matrix (not stored); |
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52 * |
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53 * F, G, H are some additional matrices (not stored); |
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54 * |
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55 * P, Q are permutation matrices (stored in both row- and column-like |
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56 * formats); |
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57 * |
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58 * L0, U0 are some matrices that defines a factorization of the initial |
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59 * basis matrix B0 = L0 * U0 (stored in an invertable form); |
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60 * |
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61 * R is a matrix defined from L0 * R = F, so R = inv(L0) * F (stored in |
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62 * a column-wise sparse format); |
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63 * |
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64 * S is a matrix defined from S * U0 = G, so S = G * inv(U0) (stored in |
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65 * a row-wise sparse format); |
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66 * |
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67 * C is the Schur complement for matrix (B0 F G H). It is defined from |
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68 * S * R + C = H, so C = H - S * R = H - G * inv(U0) * inv(L0) * F = |
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69 * = H - G * inv(B0) * F. Matrix C is stored in an invertable form. |
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70 * |
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71 * REFERENCES |
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72 * |
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73 * 1. M.A.Saunders, "LUSOL: A basis package for constrained optimiza- |
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74 * tion," SCCM, Stanford University, 2006. |
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75 * |
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76 * 2. M.A.Saunders, "Notes 5: Basis Updates," CME 318, Stanford Univer- |
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77 * sity, Spring 2006. |
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78 * |
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79 * 3. M.A.Saunders, "Notes 6: LUSOL---a Basis Factorization Package," |
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80 * ibid. */ |
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81 |
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82 typedef struct LPF LPF; |
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83 |
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84 struct LPF |
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85 { /* LP basis factorization */ |
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86 int valid; |
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87 /* the factorization is valid only if this flag is set */ |
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88 /*--------------------------------------------------------------*/ |
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89 /* initial basis matrix B0 */ |
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90 int m0_max; |
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91 /* maximal value of m0 (increased automatically, if necessary) */ |
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92 int m0; |
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93 /* the order of B0 */ |
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94 LUF *luf; |
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95 /* LU-factorization of B0 */ |
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96 /*--------------------------------------------------------------*/ |
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97 /* current basis matrix B */ |
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98 int m; |
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99 /* the order of B */ |
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100 double *B; /* double B[1+m*m]; */ |
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101 /* B in dense format stored by rows and used only for debugging; |
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102 normally this array is not allocated */ |
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103 /*--------------------------------------------------------------*/ |
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104 /* augmented matrix (B0 F G H) of the order m0+n */ |
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105 int n_max; |
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106 /* maximal number of additional rows and columns */ |
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107 int n; |
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108 /* current number of additional rows and columns */ |
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109 /*--------------------------------------------------------------*/ |
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110 /* m0xn matrix R in column-wise format */ |
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111 int *R_ptr; /* int R_ptr[1+n_max]; */ |
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112 /* R_ptr[j], 1 <= j <= n, is a pointer to j-th column */ |
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113 int *R_len; /* int R_len[1+n_max]; */ |
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114 /* R_len[j], 1 <= j <= n, is the length of j-th column */ |
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115 /*--------------------------------------------------------------*/ |
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116 /* nxm0 matrix S in row-wise format */ |
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117 int *S_ptr; /* int S_ptr[1+n_max]; */ |
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118 /* S_ptr[i], 1 <= i <= n, is a pointer to i-th row */ |
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119 int *S_len; /* int S_len[1+n_max]; */ |
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120 /* S_len[i], 1 <= i <= n, is the length of i-th row */ |
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121 /*--------------------------------------------------------------*/ |
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122 /* Schur complement C of the order n */ |
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123 SCF *scf; /* SCF scf[1:n_max]; */ |
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124 /* factorization of the Schur complement */ |
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125 /*--------------------------------------------------------------*/ |
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126 /* matrix P of the order m0+n */ |
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127 int *P_row; /* int P_row[1+m0_max+n_max]; */ |
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128 /* P_row[i] = j means that P[i,j] = 1 */ |
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129 int *P_col; /* int P_col[1+m0_max+n_max]; */ |
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130 /* P_col[j] = i means that P[i,j] = 1 */ |
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131 /*--------------------------------------------------------------*/ |
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132 /* matrix Q of the order m0+n */ |
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133 int *Q_row; /* int Q_row[1+m0_max+n_max]; */ |
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134 /* Q_row[i] = j means that Q[i,j] = 1 */ |
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135 int *Q_col; /* int Q_col[1+m0_max+n_max]; */ |
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136 /* Q_col[j] = i means that Q[i,j] = 1 */ |
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137 /*--------------------------------------------------------------*/ |
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138 /* Sparse Vector Area (SVA) is a set of locations intended to |
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139 store sparse vectors which represent columns of matrix R and |
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140 rows of matrix S; each location is a doublet (ind, val), where |
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141 ind is an index, val is a numerical value of a sparse vector |
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142 element; in the whole each sparse vector is a set of adjacent |
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143 locations defined by a pointer to its first element and its |
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144 length, i.e. the number of its elements */ |
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145 int v_size; |
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146 /* the SVA size, in locations; locations are numbered by integers |
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147 1, 2, ..., v_size, and location 0 is not used */ |
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148 int v_ptr; |
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149 /* pointer to the first available location */ |
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150 int *v_ind; /* int v_ind[1+v_size]; */ |
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151 /* v_ind[k], 1 <= k <= v_size, is the index field of location k */ |
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152 double *v_val; /* double v_val[1+v_size]; */ |
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153 /* v_val[k], 1 <= k <= v_size, is the value field of location k */ |
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154 /*--------------------------------------------------------------*/ |
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155 double *work1; /* double work1[1+m0+n_max]; */ |
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156 /* working array */ |
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157 double *work2; /* double work2[1+m0+n_max]; */ |
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158 /* working array */ |
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159 }; |
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160 |
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161 /* return codes: */ |
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162 #define LPF_ESING 1 /* singular matrix */ |
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163 #define LPF_ECOND 2 /* ill-conditioned matrix */ |
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164 #define LPF_ELIMIT 3 /* update limit reached */ |
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165 |
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166 #define lpf_create_it _glp_lpf_create_it |
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167 LPF *lpf_create_it(void); |
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168 /* create LP basis factorization */ |
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169 |
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170 #define lpf_factorize _glp_lpf_factorize |
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171 int lpf_factorize(LPF *lpf, int m, const int bh[], int (*col) |
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172 (void *info, int j, int ind[], double val[]), void *info); |
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173 /* compute LP basis factorization */ |
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174 |
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175 #define lpf_ftran _glp_lpf_ftran |
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176 void lpf_ftran(LPF *lpf, double x[]); |
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177 /* perform forward transformation (solve system B*x = b) */ |
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178 |
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179 #define lpf_btran _glp_lpf_btran |
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180 void lpf_btran(LPF *lpf, double x[]); |
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181 /* perform backward transformation (solve system B'*x = b) */ |
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182 |
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183 #define lpf_update_it _glp_lpf_update_it |
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184 int lpf_update_it(LPF *lpf, int j, int bh, int len, const int ind[], |
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185 const double val[]); |
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186 /* update LP basis factorization */ |
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187 |
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188 #define lpf_delete_it _glp_lpf_delete_it |
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189 void lpf_delete_it(LPF *lpf); |
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190 /* delete LP basis factorization */ |
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191 |
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192 #endif |
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193 |
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194 /* eof */ |