ctrrfs(3F)

NAME
     CTRRFS - provide error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular 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 triangular 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 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) 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