zpot01.f

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*> \brief \b ZPOT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDA, LDAFAC, N
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZPOT01 reconstructs a Hermitian positive definite matrix  A  from
*> its L*L' or U'*U factorization and computes the residual
*>    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*>    norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of L,
*> and U' is the conjugate transpose of U.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          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
*> \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 COMPLEX*16 array, dimension (LDA,N)
*>          The original Hermitian 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] AFAC
*> \verbatim
*>          AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
*>          On entry, the factor L or U from the L*L' or U'*U
*>          factorization of A.
*>          Overwritten with the reconstructed matrix, and then with the
*>          difference L*L' - A (or U'*U - A).
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*>          LDAFAC is INTEGER
*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE zpot01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, LDAFAC, N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, K
      DOUBLE PRECISION   ANORM, EPS, TR
      COMPLEX*16         TC
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, ZLANHE
      COMPLEX*16         ZDOTC
      EXTERNAL           lsame, dlamch, zlanhe, zdotc
*     ..
*     .. External Subroutines ..
      EXTERNAL           zher, zscal, ztrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, dimag
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( n.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = zlanhe( '1', uplo, n, a, lda, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Check the imaginary parts of the diagonal elements and return with
*     an error code if any are nonzero.
*
      DO 10 j = 1, n
         IF( dimag( afac( j, j ) ).NE.zero ) THEN
            resid = one / eps
            RETURN
         END IF
   10 CONTINUE
*
*     Compute the product U'*U, overwriting U.
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 20 k = n, 1, -1
*
*           Compute the (K,K) element of the result.
*
            tr = zdotc( k, afac( 1, k ), 1, afac( 1, k ), 1 )
            afac( k, k ) = tr
*
*           Compute the rest of column K.
*
            CALL ztrmv( 'Upper', 'Conjugate', 'Non-unit', k-1, afac,
     $                  ldafac, afac( 1, k ), 1 )
*
   20    CONTINUE
*
*     Compute the product L*L', overwriting L.
*
      ELSE
         DO 30 k = n, 1, -1
*
*           Add a multiple of column K of the factor L to each of
*           columns K+1 through N.
*
            IF( k+1.LE.n )
     $         CALL zher( 'Lower', n-k, one, afac( k+1, k ), 1,
     $                    afac( k+1, k+1 ), ldafac )
*
*           Scale column K by the diagonal element.
*
            tc = afac( k, k )
            CALL zscal( n-k+1, tc, afac( k, k ), 1 )
*
   30    CONTINUE
      END IF
*
*     Compute the difference  L*L' - A (or U'*U - A).
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 50 j = 1, n
            DO 40 i = 1, j - 1
               afac( i, j ) = afac( i, j ) - a( i, j )
   40       CONTINUE
            afac( j, j ) = afac( j, j ) - dble( a( j, j ) )
   50    CONTINUE
      ELSE
         DO 70 j = 1, n
            afac( j, j ) = afac( j, j ) - dble( a( j, j ) )
            DO 60 i = j + 1, n
               afac( i, j ) = afac( i, j ) - a( i, j )
   60       CONTINUE
   70    CONTINUE
      END IF
*
*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
      resid = zlanhe( '1', uplo, n, afac, ldafac, rwork )
*
      resid = ( ( resid / dble( n ) ) / anorm ) / eps
*
      RETURN
*
*     End of ZPOT01
*
      END