244 lines
6.5 KiB
Fortran
244 lines
6.5 KiB
Fortran
*> \brief \b ZHPT01
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDC, N
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* DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its
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*> block L*D*L' or U*D*U' factorization and computes the residual
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*> norm( C - A ) / ( N * norm(A) * EPS ),
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*> where C is the reconstructed matrix, EPS is the machine epsilon,
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*> L' is the conjugate transpose of L, and U' is the conjugate transpose
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*> of U.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix A is stored:
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (N*(N+1)/2)
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*> The original Hermitian matrix A, stored as a packed
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*> triangular matrix.
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*> \endverbatim
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*>
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*> \param[in] AFAC
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*> \verbatim
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*> AFAC is COMPLEX*16 array, dimension (N*(N+1)/2)
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*> The factored form of the matrix A, stored as a packed
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*> triangular matrix. AFAC contains the block diagonal matrix D
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*> and the multipliers used to obtain the factor L or U from the
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*> block L*D*L' or U*D*U' factorization as computed by ZHPTRF.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from ZHPTRF.
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*> \endverbatim
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*>
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*> \param[out] C
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*> \verbatim
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*> C is COMPLEX*16 array, dimension (LDC,N)
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
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*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDC, N
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J, JC
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DOUBLE PRECISION ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, ZLANHE, ZLANHP
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EXTERNAL LSAME, DLAMCH, ZLANHE, ZLANHP
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLASET, ZLAVHP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DIMAG
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Determine EPS and the norm of A.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
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*
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* Check the imaginary parts of the diagonal elements and return with
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* an error code if any are nonzero.
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*
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JC = 1
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 10 J = 1, N
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IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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JC = JC + J + 1
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10 CONTINUE
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ELSE
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DO 20 J = 1, N
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IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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JC = JC + N - J + 1
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20 CONTINUE
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END IF
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*
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* Initialize C to the identity matrix.
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*
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CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
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*
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* Call ZLAVHP to form the product D * U' (or D * L' ).
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*
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CALL ZLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C,
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$ LDC, INFO )
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*
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* Call ZLAVHP again to multiply by U ( or L ).
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*
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CALL ZLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
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$ LDC, INFO )
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*
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* Compute the difference C - A .
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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JC = 0
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DO 40 J = 1, N
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DO 30 I = 1, J - 1
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C( I, J ) = C( I, J ) - A( JC+I )
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30 CONTINUE
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C( J, J ) = C( J, J ) - DBLE( A( JC+J ) )
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JC = JC + J
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40 CONTINUE
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ELSE
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JC = 1
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DO 60 J = 1, N
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C( J, J ) = C( J, J ) - DBLE( A( JC ) )
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DO 50 I = J + 1, N
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C( I, J ) = C( I, J ) - A( JC+I-J )
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50 CONTINUE
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JC = JC + N - J + 1
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60 CONTINUE
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END IF
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*
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* Compute norm( C - A ) / ( N * norm(A) * EPS )
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*
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RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK )
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*
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IF( ANORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
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END IF
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*
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RETURN
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*
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* End of ZHPT01
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*
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END
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