spot03.f

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*> \brief \b SPOT03
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
*                          RWORK, RCOND, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDA, LDAINV, LDWORK, N
*       REAL               RCOND, RESID
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
*      $                   WORK( LDWORK, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SPOT03 computes the residual for a symmetric matrix times its
*> inverse:
*>    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * 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] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          The original symmetric matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N)
*> \endverbatim
*>
*> \param[in,out] AINV
*> \verbatim
*>          AINV is REAL array, dimension (LDAINV,N)
*>          On entry, the inverse of the matrix A, stored as a symmetric
*>          matrix in the same format as A.
*>          In this version, AINV is expanded into a full matrix and
*>          multiplied by A, so the opposing triangle of AINV will be
*>          changed; i.e., if the upper triangular part of AINV is
*>          stored, the lower triangular part will be used as work space.
*> \endverbatim
*>
*> \param[in] LDAINV
*> \verbatim
*>          LDAINV is INTEGER
*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LDWORK,N)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*>          LDWORK is INTEGER
*>          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is REAL
*>          The reciprocal of the condition number of A, computed as
*>          ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is REAL
*>          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE spot03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
     $                   RWORK, RCOND, 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, LDAINV, LDWORK, N
      REAL               RCOND, RESID
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
     $                   work( ldwork, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      REAL               AINVNM, ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH, SLANGE, SLANSY
      EXTERNAL           lsame, slamch, slange, slansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           ssymm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          real
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( n.LE.0 ) THEN
         rcond = one
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = slansy( '1', uplo, n, a, lda, rwork )
      ainvnm = slansy( '1', uplo, n, ainv, ldainv, rwork )
      IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
         rcond = zero
         resid = one / eps
         RETURN
      END IF
      rcond = ( one / anorm ) / ainvnm
*
*     Expand AINV into a full matrix and call SSYMM to multiply
*     AINV on the left by A.
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 20 j = 1, n
            DO 10 i = 1, j - 1
               ainv( j, i ) = ainv( i, j )
   10       CONTINUE
   20    CONTINUE
      ELSE
         DO 40 j = 1, n
            DO 30 i = j + 1, n
               ainv( j, i ) = ainv( i, j )
   30       CONTINUE
   40    CONTINUE
      END IF
      CALL ssymm( 'Left', uplo, n, n, -one, a, lda, ainv, ldainv, zero,
     $            work, ldwork )
*
*     Add the identity matrix to WORK .
*
      DO 50 i = 1, n
         work( i, i ) = work( i, i ) + one
   50 CONTINUE
*
*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = slange( '1', n, n, work, ldwork, rwork )
*
      resid = ( ( resid*rcond ) / eps ) / real( n )
*
      RETURN
*
*     End of SPOT03
*
      END