zpot03.f

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      SUBROUTINE zpot03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
     $                   rwork, rcond, resid )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            lda, ldainv, ldwork, n
      DOUBLE PRECISION   rcond, resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   rwork( * )
      COMPLEX*16         a( lda, * ), ainv( ldainv, * ),
     $                   work( ldwork, * )
*     ..
*
*  Purpose
*  =======
*
*  ZPOT03 computes the residual for a Hermitian matrix times its
*  inverse:
*     norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*  where EPS is the machine epsilon.
*
*  Arguments
*  ==========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The number of rows and columns of the matrix A.  N >= 0.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          The original Hermitian matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N)
*
*  AINV    (input/output) COMPLEX*16 array, dimension (LDAINV,N)
*          On entry, the inverse of the matrix A, stored as a Hermitian
*          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.
*
*  LDAINV  (input) INTEGER
*          The leading dimension of the array AINV.  LDAINV >= max(1,N).
*
*  WORK    (workspace) COMPLEX*16 array, dimension (LDWORK,N)
*
*  LDWORK  (input) INTEGER
*          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
*
*  RCOND   (output) DOUBLE PRECISION
*          The reciprocal of the condition number of A, computed as
*          ( 1/norm(A) ) / norm(AINV).
*
*  RESID   (output) DOUBLE PRECISION
*          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         czero, cone
      parameter( czero = ( 0.0d+0, 0.0d+0 ),
     $                   cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j
      DOUBLE PRECISION   ainvnm, anorm, eps
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      DOUBLE PRECISION   dlamch, zlange, zlanhe
      EXTERNAL           lsame, dlamch, zlange, zlanhe
*     ..
*     .. External Subroutines ..
      EXTERNAL           zhemm
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, dconjg
*     ..
*     .. 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 = dlamch( 'Epsilon' )
      anorm = zlanhe( '1', uplo, n, a, lda, rwork )
      ainvnm = zlanhe( '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 ZHEMM 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 ) = dconjg( ainv( i, j ) )
   10       continue
   20    continue
      ELSE
         DO 40 j = 1, n
            DO 30 i = j + 1, n
               ainv( j, i ) = dconjg( ainv( i, j ) )
   30       continue
   40    continue
      END IF
      CALL zhemm( 'Left', uplo, n, n, -cone, a, lda, ainv, ldainv,
     $            czero, work, ldwork )
*
*     Add the identity matrix to WORK .
*
      DO 50 i = 1, n
         work( i, i ) = work( i, i ) + cone
   50 continue
*
*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = zlange( '1', n, n, work, ldwork, rwork )
*
      resid = ( ( resid*rcond ) / eps ) / dble( n )
*
      return
*
*     End of ZPOT03
*
      END