diff -r d59bea55db9b -r c445c931472f src/glplpf.h --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/glplpf.h Mon Dec 06 13:09:21 2010 +0100 @@ -0,0 +1,194 @@ +/* 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 Andrew Makhorin, Department for Applied Informatics, +* Moscow Aviation Institute, Moscow, Russia. All rights reserved. +* E-mail: . +* +* 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 . +***********************************************************************/ + +#ifndef GLPLPF_H +#define GLPLPF_H + +#include "glpscf.h" +#include "glpluf.h" + +/*********************************************************************** +* 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 */ + LUF *luf; + /* 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 */ + SCF *scf; /* SCF scf[1:n_max]; */ + /* factorization of the Schur complement */ + /*--------------------------------------------------------------*/ + /* 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 */