dpot06.f

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*> \brief \b DPOT06
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPOT06( 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   A( LDA, * ), B( LDB, * ), RWORK( * ),
*      $                   X( LDX, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPOT06 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. 
*
*> \date November 2011
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dpot06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
     $                   rwork, resid )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            lda, ldb, ldx, n, nrhs
      DOUBLE PRECISION   resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( lda, * ), b( ldb, * ), rwork( * ),
     $                   x( ldx, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one, negone
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      parameter( negone = -1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            ifail, j
      DOUBLE PRECISION   anorm, bnorm, eps, xnorm
*     ..
*     .. External Functions ..
      INTEGER            idamax
      DOUBLE PRECISION   dlamch, dlansy
      EXTERNAL           idamax, dlamch, dlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           dsymm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, abs
*     ..
*     .. 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 = dlansy( '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 dsymm( 'Left', uplo, n, nrhs, negone, a, lda, x,
     $            ldx, one, 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 = abs(b(idamax( n, b( 1, j ), 1 ),j))
         xnorm = abs(x(idamax( 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 DPOT06
*
      END