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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