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


SYNOPSIS

       SUBROUTINE ZTRRFS( 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

           DOUBLE         PRECISION  BERR( * ), FERR( * ), RWORK(
                          * )

           COMPLEX*16     A( LDA, * ), B( LDB, * ), WORK( * ), X(
                          LDX, * )


PURPOSE

       ZTRRFS  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 ZTRTRS or some other means before  entering
       this  routine.   ZTRRFS  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*16 array, dimension (LDA,N)
               The triangular matrix A.  If UPLO = 'U', the lead­
               ing N-by-N upper triangular part of  the  array  A

               strictly lower triangular part of A is not  refer­
               enced.   If  UPLO  = 'L', the leading N-by-N lower
               triangular part of the array A contains the  lower
               triangular matrix, and the strictly upper triangu­
               lar 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*16 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*16 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 solu­
               tion vector X(j) (the j-th column of the  solution
               matrix  X).   If XTRUE is the true solution corre­
               sponding 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 reli­
               able 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) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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