NAME

       ctrrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ctrrfs (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK,
           RWORK, INFO)
           CTRRFS

Function/Subroutine Documentation

   subroutine ctrrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerNRHS,
       complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB,
       complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( *
       )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
       CTRRFS

       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.

       Parameters:
           UPLO

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

           TRANS

                     TRANS is 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

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

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           NRHS

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

           A

                     A is 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

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

           B

                     B is COMPLEX array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB

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

           X

                     X is COMPLEX array, dimension (LDX,NRHS)
                     The solution matrix X.

           LDX

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

           FERR

                     FERR is 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

                     BERR is 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

                     WORK is COMPLEX array, dimension (2*N)

           RWORK

                     RWORK is REAL array, dimension (N)

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 182 of file ctrrfs.f.

Author

       Generated automatically by Doxygen for LAPACK from the source code.