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


SYNOPSIS

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

           CHARACTER      DIAG, TRANS, UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

           INTEGER        IWORK( * )

           REAL           AP(  * ), B( LDB, * ), BERR( * ), FERR(
                          * ), WORK( * ), X( LDX, * )


PURPOSE

       STPRFS 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 STPTRS or some other means before
       entering this  routine.   STPRFS  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  =
               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) REAL 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)*(2*n-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) REAL 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) REAL 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  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) 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) REAL array, dimension (3*N)

       IWORK   (workspace) INTEGER 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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