TESTING/LIN/cpot05.f(3)    Library Functions Manual    TESTING/LIN/cpot05.f(3)

NAME
       TESTING/LIN/cpot05.f

SYNOPSIS
   Functions/Subroutines
       subroutine cpot05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
           ferr, berr, reslts)
           CPOT05

Function/Subroutine Documentation
   subroutine cpot05 (character uplo, integer n, integer nrhs, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
       integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex,
       dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr,
       real, dimension( * ) berr, real, dimension( * ) reslts)
       CPOT05

       Purpose:


            CPOT05 tests the error bounds from iterative refinement for the
            computed solution to a system of equations A*X = B, where A is a
            Hermitian n by n matrix.

            RESLTS(1) = test of the error bound
                      = norm(X - XACT) / ( norm(X) * FERR )

            A large value is returned if this ratio is not less than one.

            RESLTS(2) = residual from the iterative refinement routine
                      = the maximum of BERR / ( (n+1)*EPS + (*) ), where
                        (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     Hermitian matrix A is stored.
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           N

                     N is INTEGER
                     The number of rows of the matrices X, B, and XACT, and the
                     order of the matrix A.  N >= 0.

           NRHS

                     NRHS is INTEGER
                     The number of columns of the matrices X, B, and XACT.
                     NRHS >= 0.

           A

                     A is COMPLEX array, dimension (LDA,N)
                     The Hermitian matrix A.  If UPLO = 'U', the leading n by n
                     upper triangular part of A contains the upper triangular part
                     of the matrix A, and the strictly lower triangular part of A
                     is not referenced.  If UPLO = 'L', the leading n by n lower
                     triangular part of A contains the lower triangular part of
                     the matrix A, and the strictly upper triangular part of A is
                     not referenced.

           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 vectors for the system of linear
                     equations.

           LDB

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

           X

                     X is COMPLEX array, dimension (LDX,NRHS)
                     The computed solution vectors.  Each vector is stored as a
                     column of the matrix X.

           LDX

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

           XACT

                     XACT is COMPLEX array, dimension (LDX,NRHS)
                     The exact solution vectors.  Each vector is stored as a
                     column of the matrix XACT.

           LDXACT

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

           FERR

                     FERR is REAL array, dimension (NRHS)
                     The estimated forward error bounds for each solution vector
                     X.  If XTRUE is the true solution, FERR bounds the magnitude
                     of the largest entry in (X - XTRUE) divided by the magnitude
                     of the largest entry in X.

           BERR

                     BERR is REAL array, dimension (NRHS)
                     The componentwise relative backward error of each solution
                     vector (i.e., the smallest relative change in any entry of A
                     or B that makes X an exact solution).

           RESLTS

                     RESLTS is REAL array, dimension (2)
                     The maximum over the NRHS solution vectors of the ratios:
                     RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
                     RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 163 of file cpot05.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/LIN/cpot05.f(3)