CTPRFS(3)                  MathKeisan LAPACK routine                 CTPRFS(3)



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

SYNOPSIS
       SUBROUTINE CTPRFS( 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

           REAL           BERR( * ), FERR( * ), RWORK( * )

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

PURPOSE
       CTPRFS provides error bounds and backward error estimates for the solu-
       tion  to  a system of linear equations with a triangular packed coeffi-
       cient matrix.

       The solution matrix X must be computed by CTPTRS or  some  other  means
       before  entering this routine.  CTPRFS 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 array, dimension (N*(N+1)/2)
               The  upper or lower triangular matrix A, packed columnwise in a
               linear array.  The j-th column of A is stored in the  array  AP
               as  follows:  if  UPLO  =  '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 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 vec-
               tor  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



 LAPACK routine (version 3.1)    November 2006                       CTPRFS(3)