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261 lines
7.2 KiB
261 lines
7.2 KiB
*> \brief \b ZSYT01
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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 ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
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* RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDA, LDAFAC, 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( LDA, * ), AFAC( LDAFAC, * ), 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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*> ZSYT01 reconstructs a hermitian indefinite 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 and EPS is the machine epsilon.
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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 (LDA,N)
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*> The original hermitian matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N)
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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 (LDAFAC,N)
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*> The factored form of the matrix A. AFAC contains the block
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*> diagonal matrix D and the multipliers used to obtain the
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*> factor L or U from the block L*D*L' or U*D*U' factorization
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*> as computed by ZSYTRF.
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*> \endverbatim
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*>
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*> \param[in] LDAFAC
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*> \verbatim
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*> LDAFAC is INTEGER
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*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
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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 ZSYTRF.
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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 COMPLEX*16 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 COMPLEX*16
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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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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
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$ LDC, RWORK, RESID )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDA, LDAFAC, 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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COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
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DOUBLE PRECISION RWORK( * )
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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, J
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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, ZLANSY
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EXTERNAL LSAME, DLAMCH, ZLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLASET, ZLAVSY
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE
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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 = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
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*
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* Initialize C to the tridiagonal matrix T.
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*
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CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC )
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CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
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IF( N.GT.1 ) THEN
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IF( LSAME( UPLO, 'U' ) ) THEN
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CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
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$ LDC+1 )
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CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
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$ LDC+1 )
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ELSE
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CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
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$ LDC+1 )
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CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
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$ LDC+1 )
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ENDIF
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*
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* Call ZTRMM to form the product U' * D (or L * D ).
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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CALL ZTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
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$ CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
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ELSE
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CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
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$ CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
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END IF
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*
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* Call ZTRMM again to multiply by U (or L ).
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
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$ CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
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ELSE
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CALL ZTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
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$ CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
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END IF
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ENDIF
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*
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* Apply symmetric pivots
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*
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DO J = N, 1, -1
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I = IPIV( J )
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IF( I.NE.J )
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$ CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
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END DO
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DO J = N, 1, -1
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I = IPIV( J )
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IF( I.NE.J )
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$ CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
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END DO
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*
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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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DO J = 1, N
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DO I = 1, J
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C( I, J ) = C( I, J ) - A( I, J )
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END DO
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END DO
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ELSE
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DO J = 1, N
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DO I = J, N
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C( I, J ) = C( I, J ) - A( I, J )
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END DO
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END DO
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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 = ZLANSY( '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 ZSYT01_AA
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*
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END
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