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/* ifu.h (dense updatable IFU-factorization) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
* Copyright (C) 2012-2013 Free Software Foundation, Inc.
* Written by Andrew Makhorin <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 IFU_H
#define IFU_H
/***********************************************************************
* The structure IFU describes dense updatable IFU-factorization.
*
* The IFU-factorization has the following format:
*
* A = inv(F) * U, (1)
*
* where A is a given (unsymmetric) nxn square matrix, F is a square
* matrix, U is an upper triangular matrix. Obviously, the equality (1)
* is equivalent to the following equality:
*
* F * A = U. (2)
*
* It is assumed that matrix A is small and dense, so matrices F and U
* are stored by rows in dense format as follows:
*
* 1 n n_max 1 n n_max
* 1 * * * * * * x x x x 1 * * * * * * x x x x
* * * * * * * x x x x ? * * * * * x x x x
* * * * * * * x x x x ? ? * * * * x x x x
* * * * * * * x x x x ? ? ? * * * x x x x
* * * * * * * x x x x ? ? ? ? * * x x x x
* n * * * * * * x x x x n ? ? ? ? ? * x x x x
* x x x x x x x x x x x x x x x x x x x x
* x x x x x x x x x x x x x x x x x x x x
* x x x x x x x x x x x x x x x x x x x x
* n_max x x x x x x x x x x n_max x x x x x x x x x x
*
* matrix F matrix U
*
* where '*' are matrix elements, '?' are unused locations, 'x' are
* reserved locations. */
typedef struct IFU IFU;
struct IFU
{ /* IFU-factorization */
int n_max;
/* maximal order of matrices A, F, U; n_max >= 1 */
int n;
/* current order of matrices A, F, U; 0 <= n <= n_max */
double *f; /* double f[n_max*n_max]; */
/* matrix F stored by rows */
double *u; /* double u[n_max*n_max]; */
/* matrix U stored by rows */
};
#define ifu_expand _glp_ifu_expand
void ifu_expand(IFU *ifu, double c[/*1+n*/], double r[/*1+n*/],
double d);
/* expand IFU-factorization */
#define ifu_bg_update _glp_ifu_bg_update
int ifu_bg_update(IFU *ifu, double c[/*1+n*/], double r[/*1+n*/],
double d);
/* update IFU-factorization (Bartels-Golub) */
#define ifu_gr_update _glp_ifu_gr_update
int ifu_gr_update(IFU *ifu, double c[/*1+n*/], double r[/*1+n*/],
double d);
/* update IFU-factorization (Givens rotations) */
#define ifu_a_solve _glp_ifu_a_solve
void ifu_a_solve(IFU *ifu, double x[/*1+n*/], double w[/*1+n*/]);
/* solve system A * x = b */
#define ifu_at_solve _glp_ifu_at_solve
void ifu_at_solve(IFU *ifu, double x[/*1+n*/], double w[/*1+n*/]);
/* solve system A'* x = b */
#endif
/* eof */
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