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<title>SuperLU: SRC/sgsrfs.c File Reference</title>
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    SRC/sgsrfs.c File Reference

    Improves computed solution to a system of inear equations. More...
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    #include <math.h>
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    #include "slu_sdefs.h"
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    Defines

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    #define ITMAX   5
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    Functions

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    void sgsrfs (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)
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    Detailed Description

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

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     Modified from lapack routine SGERFS
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    Define Documentation

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              #define ITMAX   5          
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    Function Documentation

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

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

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

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

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       Arguments   
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       =========

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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        Internal Parameters   
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        ===================

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        ITMAX is the maximum number of steps of iterative refinement.

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    <address style="text-align: right;"><small>Generated on Mon Nov 22 10:23:48 2010 for SuperLU by </small></address>
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