|
|
/* glplpf.h (LP basis factorization, Schur complement version) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).** Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,* 2009, 2010, 2011, 2013 Andrew Makhorin, Department for Applied* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights* reserved. E-mail: <mao@gnu.org>.** GLPK is free software: you can redistribute it and/or modify it* under the terms of the GNU General Public License as published by* the Free Software Foundation, either version 3 of the License, or* (at your option) any later version.** GLPK is distributed in the hope that it will be useful, but WITHOUT* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public* License for more details.** You should have received a copy of the GNU General Public License* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#ifndef GLPLPF_H
#define GLPLPF_H
#if 0 /* 11/VIII-2013 */
#include "glpscf.h"
#else
#include "ifu.h"
#endif
#if 0 /* 06/VI-2013 */
#include "glpluf.h"
#else
#include "lufint.h"
#endif
/***********************************************************************
* The structure LPF defines the factorization of the basis mxm matrix* B, where m is the number of rows in corresponding problem instance.** This factorization is the following septet:** [B] = (L0, U0, R, S, C, P, Q), (1)** and is based on the following main equality:** ( B F^) ( B0 F ) ( L0 0 ) ( U0 R )* ( ) = P ( ) Q = P ( ) ( ) Q, (2)* ( G^ H^) ( G H ) ( S I ) ( 0 C )** where:** B is the current basis matrix (not stored);** F^, G^, H^ are some additional matrices (not stored);** B0 is some initial basis matrix (not stored);** F, G, H are some additional matrices (not stored);** P, Q are permutation matrices (stored in both row- and column-like* formats);** L0, U0 are some matrices that defines a factorization of the initial* basis matrix B0 = L0 * U0 (stored in an invertable form);** R is a matrix defined from L0 * R = F, so R = inv(L0) * F (stored in* a column-wise sparse format);** S is a matrix defined from S * U0 = G, so S = G * inv(U0) (stored in* a row-wise sparse format);** C is the Schur complement for matrix (B0 F G H). It is defined from* S * R + C = H, so C = H - S * R = H - G * inv(U0) * inv(L0) * F =* = H - G * inv(B0) * F. Matrix C is stored in an invertable form.** REFERENCES** 1. M.A.Saunders, "LUSOL: A basis package for constrained optimiza-* tion," SCCM, Stanford University, 2006.** 2. M.A.Saunders, "Notes 5: Basis Updates," CME 318, Stanford Univer-* sity, Spring 2006.** 3. M.A.Saunders, "Notes 6: LUSOL---a Basis Factorization Package,"* ibid. */
typedef struct LPF LPF;
struct LPF{ /* LP basis factorization */ int valid; /* the factorization is valid only if this flag is set */ /*--------------------------------------------------------------*/ /* initial basis matrix B0 */ int m0_max; /* maximal value of m0 (increased automatically, if necessary) */ int m0; /* the order of B0 */#if 0 /* 06/VI-2013 */
LUF *luf;#else
LUFINT *lufint;#endif
/* LU-factorization of B0 */ /*--------------------------------------------------------------*/ /* current basis matrix B */ int m; /* the order of B */ double *B; /* double B[1+m*m]; */ /* B in dense format stored by rows and used only for debugging;
normally this array is not allocated */ /*--------------------------------------------------------------*/ /* augmented matrix (B0 F G H) of the order m0+n */ int n_max; /* maximal number of additional rows and columns */ int n; /* current number of additional rows and columns */ /*--------------------------------------------------------------*/ /* m0xn matrix R in column-wise format */ int *R_ptr; /* int R_ptr[1+n_max]; */ /* R_ptr[j], 1 <= j <= n, is a pointer to j-th column */ int *R_len; /* int R_len[1+n_max]; */ /* R_len[j], 1 <= j <= n, is the length of j-th column */ /*--------------------------------------------------------------*/ /* nxm0 matrix S in row-wise format */ int *S_ptr; /* int S_ptr[1+n_max]; */ /* S_ptr[i], 1 <= i <= n, is a pointer to i-th row */ int *S_len; /* int S_len[1+n_max]; */ /* S_len[i], 1 <= i <= n, is the length of i-th row */ /*--------------------------------------------------------------*/ /* Schur complement C of the order n */#if 0 /* 11/VIII-2013 */
SCF *scf; /* SCF scf[1:n_max]; */ /* factorization of the Schur complement */#else
IFU ifu; /* IFU-factorization of the Schur complement */ int t_opt; /* type of transformation used to restore triangular structure of
matrix U: */#define SCF_TBG 1 /* Bartels-Golub elimination */
#define SCF_TGR 2 /* Givens plane rotations */
#endif
/*--------------------------------------------------------------*/ /* matrix P of the order m0+n */ int *P_row; /* int P_row[1+m0_max+n_max]; */ /* P_row[i] = j means that P[i,j] = 1 */ int *P_col; /* int P_col[1+m0_max+n_max]; */ /* P_col[j] = i means that P[i,j] = 1 */ /*--------------------------------------------------------------*/ /* matrix Q of the order m0+n */ int *Q_row; /* int Q_row[1+m0_max+n_max]; */ /* Q_row[i] = j means that Q[i,j] = 1 */ int *Q_col; /* int Q_col[1+m0_max+n_max]; */ /* Q_col[j] = i means that Q[i,j] = 1 */ /*--------------------------------------------------------------*/ /* Sparse Vector Area (SVA) is a set of locations intended to
store sparse vectors which represent columns of matrix R and rows of matrix S; each location is a doublet (ind, val), where ind is an index, val is a numerical value of a sparse vector element; in the whole each sparse vector is a set of adjacent locations defined by a pointer to its first element and its length, i.e. the number of its elements */ int v_size; /* the SVA size, in locations; locations are numbered by integers
1, 2, ..., v_size, and location 0 is not used */ int v_ptr; /* pointer to the first available location */ int *v_ind; /* int v_ind[1+v_size]; */ /* v_ind[k], 1 <= k <= v_size, is the index field of location k */ double *v_val; /* double v_val[1+v_size]; */ /* v_val[k], 1 <= k <= v_size, is the value field of location k */ /*--------------------------------------------------------------*/ double *work1; /* double work1[1+m0+n_max]; */ /* working array */ double *work2; /* double work2[1+m0+n_max]; */ /* working array */};
/* return codes: */#define LPF_ESING 1 /* singular matrix */
#define LPF_ECOND 2 /* ill-conditioned matrix */
#define LPF_ELIMIT 3 /* update limit reached */
#define lpf_create_it _glp_lpf_create_it
LPF *lpf_create_it(void);/* create LP basis factorization */
#define lpf_factorize _glp_lpf_factorize
int lpf_factorize(LPF *lpf, int m, const int bh[], int (*col) (void *info, int j, int ind[], double val[]), void *info);/* compute LP basis factorization */
#define lpf_ftran _glp_lpf_ftran
void lpf_ftran(LPF *lpf, double x[]);/* perform forward transformation (solve system B*x = b) */
#define lpf_btran _glp_lpf_btran
void lpf_btran(LPF *lpf, double x[]);/* perform backward transformation (solve system B'*x = b) */
#define lpf_update_it _glp_lpf_update_it
int lpf_update_it(LPF *lpf, int j, int bh, int len, const int ind[], const double val[]);/* update LP basis factorization */
#define lpf_delete_it _glp_lpf_delete_it
void lpf_delete_it(LPF *lpf);/* delete LP basis factorization */
#endif
/* eof */
|
