/* 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: <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

#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 */