alpar@1: /* glpscf.h (Schur complement factorization) */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #ifndef GLPSCF_H
alpar@1: #define GLPSCF_H
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  The structure SCF defines the following factorization of a square
alpar@1: *  nxn matrix C (which is the Schur complement):
alpar@1: *
alpar@1: *     F * C = U * P,
alpar@1: *
alpar@1: *  where F is a square transforming matrix, U is an upper triangular
alpar@1: *  matrix, P is a permutation matrix.
alpar@1: *
alpar@1: *  It is assumed that matrix C is small and dense, so matrices F and U
alpar@1: *  are stored in the dense format by rows as follows:
alpar@1: *
alpar@1: *        1         n       n_max    1         n       n_max
alpar@1: *      1 * * * * * * x x x x      1 * * * * * * x x x x
alpar@1: *        * * * * * * x x x x        . * * * * * x x x x
alpar@1: *        * * * * * * x x x x        . . * * * * x x x x
alpar@1: *        * * * * * * x x x x        . . . * * * x x x x
alpar@1: *        * * * * * * x x x x        . . . . * * x x x x
alpar@1: *      n * * * * * * x x x x      n . . . . . * x x x x
alpar@1: *        x x x x x x x x x x        . . . . . . x x x x
alpar@1: *        x x x x x x x x x x        . . . . . . . x x x
alpar@1: *        x x x x x x x x x x        . . . . . . . . x x
alpar@1: *  n_max x x x x x x x x x x  n_max . . . . . . . . . x
alpar@1: *
alpar@1: *             matrix F                   matrix U
alpar@1: *
alpar@1: *  where '*' are matrix elements, 'x' are reserved locations.
alpar@1: *
alpar@1: *  Permutation matrix P is stored in row-like format.
alpar@1: *
alpar@1: *  Matrix C normally is not stored.
alpar@1: *
alpar@1: *  REFERENCES
alpar@1: *
alpar@1: *  1. M.A.Saunders, "LUSOL: A basis package for constrained optimiza-
alpar@1: *     tion," SCCM, Stanford University, 2006.
alpar@1: *
alpar@1: *  2. M.A.Saunders, "Notes 5: Basis Updates," CME 318, Stanford Univer-
alpar@1: *     sity, Spring 2006.
alpar@1: *
alpar@1: *  3. M.A.Saunders, "Notes 6: LUSOL---a Basis Factorization Package,"
alpar@1: *     ibid. */
alpar@1: 
alpar@1: typedef struct SCF SCF;
alpar@1: 
alpar@1: struct SCF
alpar@1: {     /* Schur complement factorization */
alpar@1:       int n_max;
alpar@1:       /* maximal order of matrices C, F, U, P; n_max >= 1 */
alpar@1:       int n;
alpar@1:       /* current order of matrices C, F, U, P; n >= 0 */
alpar@1:       double *f; /* double f[1+n_max*n_max]; */
alpar@1:       /* matrix F stored by rows */
alpar@1:       double *u; /* double u[1+n_max*(n_max+1)/2]; */
alpar@1:       /* upper triangle of matrix U stored by rows */
alpar@1:       int *p; /* int p[1+n_max]; */
alpar@1:       /* matrix P; p[i] = j means that P[i,j] = 1 */
alpar@1:       int t_opt;
alpar@1:       /* type of transformation used to restore triangular structure of
alpar@1:          matrix U: */
alpar@1: #define SCF_TBG      1  /* Bartels-Golub elimination */
alpar@1: #define SCF_TGR      2  /* Givens plane rotation */
alpar@1:       int rank;
alpar@1:       /* estimated rank of matrices C and U */
alpar@1:       double *c; /* double c[1+n_max*n_max]; */
alpar@1:       /* matrix C stored in the same format as matrix F and used only
alpar@1:          for debugging; normally this array is not allocated */
alpar@1:       double *w; /* double w[1+n_max]; */
alpar@1:       /* working array */
alpar@1: };
alpar@1: 
alpar@1: /* return codes: */
alpar@1: #define SCF_ESING    1  /* singular matrix */
alpar@1: #define SCF_ELIMIT   2  /* update limit reached */
alpar@1: 
alpar@1: #define scf_create_it _glp_scf_create_it
alpar@1: SCF *scf_create_it(int n_max);
alpar@1: /* create Schur complement factorization */
alpar@1: 
alpar@1: #define scf_update_exp _glp_scf_update_exp
alpar@1: int scf_update_exp(SCF *scf, const double x[], const double y[],
alpar@1:       double z);
alpar@1: /* update factorization on expanding C */
alpar@1: 
alpar@1: #define scf_solve_it _glp_scf_solve_it
alpar@1: void scf_solve_it(SCF *scf, int tr, double x[]);
alpar@1: /* solve either system C * x = b or C' * x = b */
alpar@1: 
alpar@1: #define scf_reset_it _glp_scf_reset_it
alpar@1: void scf_reset_it(SCF *scf);
alpar@1: /* reset factorization for empty matrix C */
alpar@1: 
alpar@1: #define scf_delete_it _glp_scf_delete_it
alpar@1: void scf_delete_it(SCF *scf);
alpar@1: /* delete Schur complement factorization */
alpar@1: 
alpar@1: #endif
alpar@1: 
alpar@1: /* eof */