SGERFS (3lapack)

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.