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


SYNOPSIS

       SUBROUTINE ZTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB,
                          X, LDX, FERR, BERR, WORK, RWORK, INFO )

           CHARACTER      DIAG, TRANS, UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

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

           COMPLEX*16     AP( * ), B( LDB, * ),  WORK(  *  ),  X(
                          LDX, * )


PURPOSE

       ZTPRFS  provides error bounds and backward error estimates
       for the solution to a system of linear  equations  with  a
       triangular packed coefficient matrix.  The solution matrix
       X must be computed by ZTPTRS or some  other  means  before
       entering  this  routine.   ZTPRFS  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.

       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
               The upper or lower  triangular  matrix  A,  packed
               columnwise  in a linear array.  The j-th column of

               'U',  AP(i  +  (j-1)*j/2) = A(i,j) for 1<=i<=j; if
               UPLO = 'L', AP(i + (j-1)*(2n-j)/2)  =  A(i,j)  for
               j<=i<=n.   If DIAG = 'U', the diagonal elements of
               A are not referenced and are assumed to be 1.

       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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