[9] | 1 | /* glpfhv.h (LP basis factorization, FHV eta file 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, 2011 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 GLPFHV_H |
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| 26 | #define GLPFHV_H |
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| 27 | |
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| 28 | #include "glpluf.h" |
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| 29 | |
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| 30 | /*********************************************************************** |
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| 31 | * The structure FHV defines the factorization of the basis mxm-matrix |
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| 32 | * B, where m is the number of rows in corresponding problem instance. |
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| 33 | * |
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| 34 | * This factorization is the following sextet: |
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| 35 | * |
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| 36 | * [B] = (F, H, V, P0, P, Q), (1) |
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| 37 | * |
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| 38 | * where F, H, and V are such matrices that |
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| 39 | * |
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| 40 | * B = F * H * V, (2) |
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| 41 | * |
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| 42 | * and P0, P, and Q are such permutation matrices that the matrix |
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| 43 | * |
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| 44 | * L = P0 * F * inv(P0) (3) |
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| 45 | * |
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| 46 | * is lower triangular with unity diagonal, and the matrix |
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| 47 | * |
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| 48 | * U = P * V * Q (4) |
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| 49 | * |
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| 50 | * is upper triangular. All the matrices have the same order m, which |
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| 51 | * is the order of the basis matrix B. |
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| 52 | * |
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| 53 | * The matrices F, V, P, and Q are stored in the structure LUF (see the |
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| 54 | * module GLPLUF), which is a member of the structure FHV. |
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| 55 | * |
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| 56 | * The matrix H is stored in the form of eta file using row-like format |
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| 57 | * as follows: |
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| 58 | * |
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| 59 | * H = H[1] * H[2] * ... * H[nfs], (5) |
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| 60 | * |
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| 61 | * where H[k], k = 1, 2, ..., nfs, is a row-like factor, which differs |
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| 62 | * from the unity matrix only by one row, nfs is current number of row- |
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| 63 | * like factors. After the factorization has been built for some given |
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| 64 | * basis matrix B the matrix H has no factors and thus it is the unity |
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| 65 | * matrix. Then each time when the factorization is recomputed for an |
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| 66 | * adjacent basis matrix, the next factor H[k], k = 1, 2, ... is built |
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| 67 | * and added to the end of the eta file H. |
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| 68 | * |
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| 69 | * Being sparse vectors non-trivial rows of the factors H[k] are stored |
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| 70 | * in the right part of the sparse vector area (SVA) in the same manner |
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| 71 | * as rows and columns of the matrix F. |
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| 72 | * |
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| 73 | * For more details see the program documentation. */ |
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| 74 | |
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| 75 | typedef struct FHV FHV; |
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| 76 | |
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| 77 | struct FHV |
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| 78 | { /* LP basis factorization */ |
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| 79 | int m_max; |
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| 80 | /* maximal value of m (increased automatically, if necessary) */ |
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| 81 | int m; |
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| 82 | /* the order of matrices B, F, H, V, P0, P, Q */ |
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| 83 | int valid; |
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| 84 | /* the factorization is valid only if this flag is set */ |
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| 85 | LUF *luf; |
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| 86 | /* LU-factorization (contains the matrices F, V, P, Q) */ |
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| 87 | /*--------------------------------------------------------------*/ |
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| 88 | /* matrix H in the form of eta file */ |
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| 89 | int hh_max; |
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| 90 | /* maximal number of row-like factors (which limits the number of |
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| 91 | updates of the factorization) */ |
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| 92 | int hh_nfs; |
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| 93 | /* current number of row-like factors (0 <= hh_nfs <= hh_max) */ |
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| 94 | int *hh_ind; /* int hh_ind[1+hh_max]; */ |
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| 95 | /* hh_ind[k], k = 1, ..., nfs, is the number of a non-trivial row |
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| 96 | of factor H[k] */ |
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| 97 | int *hh_ptr; /* int hh_ptr[1+hh_max]; */ |
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| 98 | /* hh_ptr[k], k = 1, ..., nfs, is a pointer to the first element |
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| 99 | of the non-trivial row of factor H[k] in the SVA */ |
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| 100 | int *hh_len; /* int hh_len[1+hh_max]; */ |
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| 101 | /* hh_len[k], k = 1, ..., nfs, is the number of non-zero elements |
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| 102 | in the non-trivial row of factor H[k] */ |
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| 103 | /*--------------------------------------------------------------*/ |
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| 104 | /* matrix P0 */ |
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| 105 | int *p0_row; /* int p0_row[1+m_max]; */ |
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| 106 | /* p0_row[i] = j means that p0[i,j] = 1 */ |
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| 107 | int *p0_col; /* int p0_col[1+m_max]; */ |
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| 108 | /* p0_col[j] = i means that p0[i,j] = 1 */ |
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| 109 | /* if i-th row or column of the matrix F corresponds to i'-th row |
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| 110 | or column of the matrix L = P0*F*inv(P0), then p0_row[i'] = i |
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| 111 | and p0_col[i] = i' */ |
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| 112 | /*--------------------------------------------------------------*/ |
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| 113 | /* working arrays */ |
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| 114 | int *cc_ind; /* int cc_ind[1+m_max]; */ |
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| 115 | /* integer working array */ |
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| 116 | double *cc_val; /* double cc_val[1+m_max]; */ |
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| 117 | /* floating-point working array */ |
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| 118 | /*--------------------------------------------------------------*/ |
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| 119 | /* control parameters */ |
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| 120 | double upd_tol; |
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| 121 | /* update tolerance; if after updating the factorization absolute |
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| 122 | value of some diagonal element u[k,k] of matrix U = P*V*Q is |
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| 123 | less than upd_tol * max(|u[k,*]|, |u[*,k]|), the factorization |
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| 124 | is considered as inaccurate */ |
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| 125 | /*--------------------------------------------------------------*/ |
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| 126 | /* some statistics */ |
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| 127 | int nnz_h; |
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| 128 | /* current number of non-zeros in all factors of matrix H */ |
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| 129 | }; |
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| 130 | |
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| 131 | /* return codes: */ |
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| 132 | #define FHV_ESING 1 /* singular matrix */ |
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| 133 | #define FHV_ECOND 2 /* ill-conditioned matrix */ |
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| 134 | #define FHV_ECHECK 3 /* insufficient accuracy */ |
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| 135 | #define FHV_ELIMIT 4 /* update limit reached */ |
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| 136 | #define FHV_EROOM 5 /* SVA overflow */ |
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| 137 | |
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| 138 | #define fhv_create_it _glp_fhv_create_it |
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| 139 | FHV *fhv_create_it(void); |
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| 140 | /* create LP basis factorization */ |
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| 141 | |
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| 142 | #define fhv_factorize _glp_fhv_factorize |
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| 143 | int fhv_factorize(FHV *fhv, int m, int (*col)(void *info, int j, |
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| 144 | int ind[], double val[]), void *info); |
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| 145 | /* compute LP basis factorization */ |
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| 146 | |
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| 147 | #define fhv_h_solve _glp_fhv_h_solve |
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| 148 | void fhv_h_solve(FHV *fhv, int tr, double x[]); |
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| 149 | /* solve system H*x = b or H'*x = b */ |
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| 150 | |
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| 151 | #define fhv_ftran _glp_fhv_ftran |
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| 152 | void fhv_ftran(FHV *fhv, double x[]); |
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| 153 | /* perform forward transformation (solve system B*x = b) */ |
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| 154 | |
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| 155 | #define fhv_btran _glp_fhv_btran |
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| 156 | void fhv_btran(FHV *fhv, double x[]); |
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| 157 | /* perform backward transformation (solve system B'*x = b) */ |
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| 158 | |
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| 159 | #define fhv_update_it _glp_fhv_update_it |
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| 160 | int fhv_update_it(FHV *fhv, int j, int len, const int ind[], |
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| 161 | const double val[]); |
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| 162 | /* update LP basis factorization */ |
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| 163 | |
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| 164 | #define fhv_delete_it _glp_fhv_delete_it |
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| 165 | void fhv_delete_it(FHV *fhv); |
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| 166 | /* delete LP basis factorization */ |
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| 167 | |
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| 168 | #endif |
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| 169 | |
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| 170 | /* eof */ |
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