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 */ |
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