SRC/cgsrfs.c File Reference

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

#include <math.h>
#include "slu_cdefs.h"

Defines
#define	ITMAX   5
Functions
void	cgsrfs (trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U, int *perm_c, int *perm_r, char *equed, float *R, float *C, SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr, SuperLUStat_t *stat, int *info)

---

Detailed Description

 -- SuperLU routine (version 3.0) --
 Univ. of California Berkeley, Xerox Palo Alto Research Center,
 and Lawrence Berkeley National Lab.
 October 15, 2003

 Modified from lapack routine CGERFS
 

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Define Documentation

#define ITMAX   5

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Function Documentation

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

   Purpose   
   =======

   CGSRFS 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_C, 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_C, Mtype = SLU_TRLU.

   U       (input) SuperMatrix*
           The factor U from the factorization Pr*A*Pc=L*U as computed by
           cgstrf(). Use column-wise storage scheme, 
           i.e., U has types: Stype = SLU_NC, Dtype = SLU_C, 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) float*, 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) float*, 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_C, 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_C, Mtype = SLU_GE.
           On entry, the solution matrix X, as computed by cgstrs().
           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) float*, 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) float*, 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.