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<title>SuperLU: SRC/sgsrfs.c File Reference</title>
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<link href="doxygen.css" rel="stylesheet" type="text/css">
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Main Page
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Data Structures
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Files
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SRC/sgsrfs.c File ReferenceImproves 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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 1.5.5
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