zgsrfs.c File Reference

Improves computed solution to a system of inear equations. More...

`#include <math.h>`
`#include "slu_zdefs.h"`
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## Macros

#define | ITMAX 5

## Functions

void | zgsrfs (trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U, int *perm_c, int *perm_r, char *equed, double *R, double *C, SuperMatrix *B, SuperMatrix *X, double *ferr, double *berr, SuperLUStat_t *stat, int *info)

## Detailed Description

Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)

All rights reserved.

The source code is distributed under BSD license, see the file License.txt at the top-level directory.

    – SuperLU routine (version 5.1) –
    Univ. of California Berkeley, Xerox Palo Alto Research Center,
    and Lawrence Berkeley National Lab.
    October 15, 2003

    Modified from lapack routine ZGERFS
    Last modified: December 3, 2015

## Macro Definition Documentation

#define ITMAX 5

## Function Documentation

void zgsrfs | ( | trans_t | trans,
|  | SuperMatrix * | A,
|  | SuperMatrix * | L,
|  | SuperMatrix * | U,
|  | int * | perm_c,
|  | int * | perm_r,
|  | char * | equed,
|  | double * | R,
|  | double * | C,
|  | SuperMatrix * | B,
|  | SuperMatrix * | X,
|  | double * | ferr,
|  | double * | berr,
|  | SuperLUStat_t * | stat,
|  | int * | info
| ) |  |

#

    Purpose

      ZGSRFS improves the computed solution to a system of linear
      equations and provides error bounds and backward error estimates for
      the solution.

      If equilibration was performed, the system becomes:
              (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.

      See supermatrix.h for the definition of 'SuperMatrix' structure.

#

    Arguments

    trans   (input) trans_t
             Specifies the form of the system of equations:
             = NOTRANS: A * X = B  (No transpose)
             = TRANS:   A'* X = B  (Transpose)
             = CONJ:    A**H * X = B  (Conjugate transpose)

      A       (input) SuperMatrix*
              The original matrix A in the system, or the scaled A if
              equilibration was done. The type of A can be:
              Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_GE.

      L       (input) SuperMatrix*
              The factor L from the factorization Pr*A*Pc=L*U. Use
              compressed row subscripts storage for supernodes,
              i.e., L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.

      U       (input) SuperMatrix*
              The factor U from the factorization Pr*A*Pc=L*U as computed by
              zgstrf(). Use column-wise storage scheme,
              i.e., U has types: Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.

      perm_c  (input) int*, dimension (A->ncol)
              Column permutation vector, which defines the
              permutation matrix Pc; perm_c[i] = j means column i of A is
              in position j in A*Pc.

      perm_r  (input) int*, dimension (A->nrow)
              Row permutation vector, which defines the permutation matrix Pr;
              perm_r[i] = j means row i of A is in position j in Pr*A.

      equed   (input) Specifies the form of equilibration that was done.
              = 'N': No equilibration.
              = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
              = 'C': Column equilibration, i.e., A was postmultiplied by
                     diag(C).
              = 'B': Both row and column equilibration, i.e., A was replaced
                     by diag(R)*A*diag(C).

      R       (input) double*, dimension (A->nrow)
              The row scale factors for A.
              If equed = 'R' or 'B', A is premultiplied by diag(R).
              If equed = 'N' or 'C', R is not accessed.

      C       (input) double*, dimension (A->ncol)
              The column scale factors for A.
              If equed = 'C' or 'B', A is postmultiplied by diag(C).
              If equed = 'N' or 'R', C is not accessed.

      B       (input) SuperMatrix*
              B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
              The right hand side matrix B.
              if equed = 'R' or 'B', B is premultiplied by diag(R).

      X       (input/output) SuperMatrix*
              X has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
              On entry, the solution matrix X, as computed by zgstrs().
              On exit, the improved solution matrix X.
              if *equed = 'C' or 'B', X should be premultiplied by diag(C)
                  in order to obtain the solution to the original system.

      FERR    (output) double*, dimension (B->ncol)
              The estimated forward error bound for each solution vector
              X(j) (the j-th column of the solution matrix X).
              If XTRUE is the true solution corresponding to X(j), FERR(j)
              is an estimated upper bound for the magnitude of the largest
              element in (X(j) - XTRUE) divided by the magnitude of the
              largest element in X(j).  The estimate is as reliable as
              the estimate for RCOND, and is almost always a slight
              overestimate of the true error.

      BERR    (output) double*, dimension (B->ncol)
              The componentwise relative backward error of each solution
              vector X(j) (i.e., the smallest relative change in
              any element of A or B that makes X(j) an exact solution).

      stat     (output) SuperLUStat_t*
               Record the statistics on runtime and floating-point operation count.
               See util.h for the definition of 'SuperLUStat_t'.

      info    (output) int*
              = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value

#

    Internal Parameters

       ITMAX is the maximum number of steps of iterative refinement.

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