zpot06.f

Go to the documentation of this file.

*> \brief \b ZPOT06
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
*                          RWORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDA, LDB, LDX, N, NRHS
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZPOT06 computes the residual for a solution of a system of linear
*> equations  A*x = b :
*>    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          symmetric matrix A is stored:
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of rows and columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns of B, the matrix of right hand sides.
*>          NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          The original M x N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
*>          The computed solution vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  If TRANS = 'N',
*>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
*>          On entry, the right hand side vectors for the system of
*>          linear equations.
*>          On exit, B is overwritten with the difference B - A*X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  IF TRANS = 'N',
*>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          The maximum over the number of right hand sides of
*>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE zpot06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
     $                   RWORK, RESID )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         CONE, NEGCONE
      parameter( cone = ( 1.0d+0, 0.0d+0 ) )
      parameter( negcone = ( -1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            IFAIL, J
      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
      COMPLEX*16         ZDUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            IZAMAX
      DOUBLE PRECISION   DLAMCH, ZLANSY
      EXTERNAL           lsame, izamax, dlamch, zlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           zhemm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag, max
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function definitions ..
      cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
*     ..
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0
*
      IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = zlansy( 'I', uplo, n, a, lda, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Compute  B - A*X  and store in B.
      ifail=0
*
      CALL zhemm( 'Left', uplo, n, nrhs, negcone, a, lda, x,
     $            ldx, cone, b, ldb )
*
*     Compute the maximum over the number of right hand sides of
*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
*
      resid = zero
      DO 10 j = 1, nrhs
         bnorm = cabs1(b(izamax( n, b( 1, j ), 1 ),j))
         xnorm = cabs1(x(izamax( n, x( 1, j ), 1 ),j))
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
         END IF
   10 CONTINUE
*
      RETURN
*
*     End of ZPOT06
*
      END