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ctrrfs

 NAME
      CTRRFS - provide error bounds and backward error estimates
      for the solution to a system of linear equations with a tri-
      angular coefficient matrix

 SYNOPSIS
      SUBROUTINE CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B,
                         LDB, X, LDX, FERR, BERR, WORK, RWORK,
                         INFO )

          CHARACTER      DIAG, TRANS, UPLO

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

          REAL           BERR( * ), FERR( * ), RWORK( * )

          COMPLEX        A( LDA, * ), B( LDB, * ), WORK( * ), X(
                         LDX, * )

 PURPOSE
      CTRRFS provides error bounds and backward error estimates
      for the solution to a system of linear equations with a tri-
      angular coefficient matrix.

      The solution matrix X must be computed by CTRTRS or some
      other means before entering this routine.  CTRRFS 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)

      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) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
              The 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 bounds for each solution
              vector X(j) (the j-th column of the solution matrix
              X).  If XTRUE is the true solution, FERR(j) bounds
              the magnitude of the largest entry in (X(j) - XTRUE)
              divided by the magnitude of the largest entry in
              X(j).  The quality of the error bound depends on the
              quality of the estimate of norm(inv(A)) computed in
              the code; if the estimate of norm(inv(A)) is accu-
              rate, the error bound is guaranteed.

      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 entry of A or B that makes X(j) an
              exact solution).

      WORK    (workspace) COMPLEX array, dimension (2*N)

      RWORK   (workspace) REAL array, dimension (N)

      INFO    (output) INTEGER
              = 0:  successful exit

              < 0:  if INFO = -i, the i-th argument had an illegal
              value