DTRRFS (3lapack)

provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix

SYNOPSIS

  SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
                     FERR, BERR, WORK, IWORK, INFO )

      CHARACTER      DIAG, TRANS, UPLO

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

      INTEGER        IWORK( * )

      DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR( *
                     ), WORK( * ), X( LDX, * )

PURPOSE

  DTRRFS provides error bounds and backward error estimates for the solution
  to a system of linear equations with a triangular coefficient matrix.

  The solution matrix X must be computed by DTRTRS or some other means before
  entering this routine.  DTRRFS does not do iterative refinement because
  doing so cannot improve the backward error.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

  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)

  DIAG    (input) CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

  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) DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper
          triangular part of the array A contains the upper triangular
          matrix, and the strictly lower triangular part of A is not
          referenced.  If UPLO = 'L', the leading N-by-N lower triangular
          part of the array A contains the lower triangular matrix, and the
          strictly upper triangular part of A is not referenced.  If DIAG =
          'U', the diagonal elements of A are also not referenced and are
          assumed to be 1.

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

  B       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
          The solution matrix X.

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

  FERR    (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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