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version 1.9, 2011/11/21 20:43:11	version 1.20, 2023/08/07 08:39:23
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*> \brief \b ZHEGS2	*> \brief \b ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).
*	*
* =========== DOCUMENTATION ===========	* =========== DOCUMENTATION ===========
*	*
* Online html documentation available at	* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/	* http://www.netlib.org/lapack/explore-html/
*	*
*> \htmlonly	*> \htmlonly
*> Download ZHEGS2 + dependencies	*> Download ZHEGS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegs2.f">	*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegs2.f">
*> [TGZ]</a>	*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegs2.f">	*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegs2.f">
*> [ZIP]</a>	*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegs2.f">	*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegs2.f">
*> [TXT]</a>	*> [TXT]</a>
*> \endhtmlonly	*> \endhtmlonly
*	*
* Definition:	* Definition:
* ===========	* ===========
*	*
* SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )	* SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*	*
* .. Scalar Arguments ..	* .. Scalar Arguments ..
* CHARACTER UPLO	* CHARACTER UPLO
* INTEGER INFO, ITYPE, LDA, LDB, N	* INTEGER INFO, ITYPE, LDA, LDB, N
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* .. Array Arguments ..	* .. Array Arguments ..
* COMPLEX16 A( LDA, ), B( LDB, * )	* COMPLEX16 A( LDA, ), B( LDB, * )
* ..	* ..
*	*
*	*
*> \par Purpose:	*> \par Purpose:
* =============	* =============
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*> The leading dimension of the array A. LDA >= max(1,N).	*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim	*> \endverbatim
*>	*>
*> \param[in] B	*> \param[in,out] B
*> \verbatim	*> \verbatim
> B is COMPLEX16 array, dimension (LDB,N)	> B is COMPLEX16 array, dimension (LDB,N)
*> The triangular factor from the Cholesky factorization of B,	*> The triangular factor from the Cholesky factorization of B,
*> as returned by ZPOTRF.	*> as returned by ZPOTRF.
	*> B is modified by the routine but restored on exit.
*> \endverbatim	*> \endverbatim
*>	*>
*> \param[in] LDB	*> \param[in] LDB
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* Authors:	* Authors:
* ========	* ========
*	*
*> \author Univ. of Tennessee	*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley	*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver	*> \author Univ. of Colorado Denver
*> \author NAG Ltd.	*> \author NAG Ltd.
*
*> \date November 2011
*	*
*> \ingroup complex16HEcomputational	*> \ingroup complex16HEcomputational
*	*
* =====================================================================	* =====================================================================
SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )	SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*	*
* -- LAPACK computational routine (version 3.4.0) --	* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --	* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--	* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*	*
* .. Scalar Arguments ..	* .. Scalar Arguments ..
CHARACTER UPLO	CHARACTER UPLO
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*	*
* Update the upper triangle of A(k:n,k:n)	* Update the upper triangle of A(k:n,k:n)
*	*
AKK = A( K, K )	AKK = DBLE( A( K, K ) )
BKK = B( K, K )	BKK = DBLE( B( K, K ) )
AKK = AKK / BKK**2	AKK = AKK / BKK**2
A( K, K ) = AKK	A( K, K ) = AKK
IF( K.LT.N ) THEN	IF( K.LT.N ) THEN
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*	*
* Update the lower triangle of A(k:n,k:n)	* Update the lower triangle of A(k:n,k:n)
*	*
AKK = A( K, K )	AKK = DBLE( A( K, K ) )
BKK = B( K, K )	BKK = DBLE( B( K, K ) )
AKK = AKK / BKK**2	AKK = AKK / BKK**2
A( K, K ) = AKK	A( K, K ) = AKK
IF( K.LT.N ) THEN	IF( K.LT.N ) THEN
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*	*
* Update the upper triangle of A(1:k,1:k)	* Update the upper triangle of A(1:k,1:k)
*	*
AKK = A( K, K )	AKK = DBLE( A( K, K ) )
BKK = B( K, K )	BKK = DBLE( B( K, K ) )
CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,	CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
$ LDB, A( 1, K ), 1 )	$ LDB, A( 1, K ), 1 )
CT = HALF*AKK	CT = HALF*AKK
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*	*
* Update the lower triangle of A(1:k,1:k)	* Update the lower triangle of A(1:k,1:k)
*	*
AKK = A( K, K )	AKK = DBLE( A( K, K ) )
BKK = B( K, K )	BKK = DBLE( B( K, K ) )
CALL ZLACGV( K-1, A( K, 1 ), LDA )	CALL ZLACGV( K-1, A( K, 1 ), LDA )
CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,	CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,
$ B, LDB, A( K, 1 ), LDA )	$ B, LDB, A( K, 1 ), LDA )

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