sgerfs(3F)

NAME
     SGERFS - improve the computed solution to a system of linear equations
     and provides error bounds and backward error estimates for the solution

SYNOPSIS
     SUBROUTINE SGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
                        LDX, FERR, BERR, WORK, IWORK, INFO )

         CHARACTER      TRANS

         INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS

         INTEGER        IPIV( * ), IWORK( * )

         REAL           A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
                        FERR( * ), WORK( * ), X( LDX, * )

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


ARGUMENTS
     TRANS   (input) CHARACTER*1
             Specifies the form of the system of equations:
             = 'N':  A * X = B     (No transpose)
             = 'T':  A**T * X = B  (Transpose)
             = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrices B and X.  NRHS >= 0.

     A       (input) REAL array, dimension (LDA,N)
             The original N-by-N matrix A.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,N).

     AF      (input) REAL array, dimension (LDAF,N)
             The factors L and U from the factorization A = P*L*U as computed
             by SGETRF.

     LDAF    (input) INTEGER
             The leading dimension of the array AF.  LDAF >= max(1,N).

     IPIV    (input) INTEGER array, dimension (N)
             The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix
             was interchanged with row IPIV(i).
     B       (input) REAL array, dimension (LDB,NRHS)
             The right hand side matrix B.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     X       (input/output) REAL array, dimension (LDX,NRHS)
             On entry, the solution matrix X, as computed by SGETRS.  On exit,
             the improved solution matrix X.

     LDX     (input) INTEGER
             The leading dimension of the array X.  LDX >= max(1,N).

     FERR    (output) REAL array, dimension (NRHS)
             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) REAL array, dimension (NRHS)
             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).

     WORK    (workspace) REAL array, dimension (3*N)

     IWORK   (workspace) INTEGER array, dimension (N)

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

PARAMETERS
     ITMAX is the maximum number of steps of iterative refinement.