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*> \brief \b CLAQHE scales a Hermitian matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLAQHE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claqhe.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claqhe.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claqhe.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* .. Scalar Arguments ..
* CHARACTER EQUED, UPLO
* INTEGER LDA, N
* REAL AMAX, SCOND
* ..
* .. Array Arguments ..
* REAL S( * )
* COMPLEX A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLAQHE equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
*> \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 order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
*> n by n upper triangular part of A contains the upper
*> triangular part of the matrix A, and the strictly lower
*> triangular part of A is not referenced. If UPLO = 'L', the
*> leading n by n lower triangular part of A contains the lower
*> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced.
*>
*> On exit, if EQUED = 'Y', the equilibrated matrix:
*> diag(S) * A * diag(S).
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(N,1).
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is REAL array, dimension (N)
*> The scale factors for A.
*> \endverbatim
*>
*> \param[in] SCOND
*> \verbatim
*> SCOND is REAL
*> Ratio of the smallest S(i) to the largest S(i).
*> \endverbatim
*>
*> \param[in] AMAX
*> \verbatim
*> AMAX is REAL
*> Absolute value of largest matrix entry.
*> \endverbatim
*>
*> \param[out] EQUED
*> \verbatim
*> EQUED is CHARACTER*1
*> Specifies whether or not equilibration was done.
*> = 'N': No equilibration.
*> = 'Y': Equilibration was done, i.e., A has been replaced by
*> diag(S) * A * diag(S).
*> \endverbatim
*
*> \par Internal Parameters:
* =========================
*>
*> \verbatim
*> THRESH is a threshold value used to decide if scaling should be done
*> based on the ratio of the scaling factors. If SCOND < THRESH,
*> scaling is done.
*>
*> LARGE and SMALL are threshold values used to decide if scaling should
*> be done based on the absolute size of the largest matrix element.
*> If AMAX > LARGE or AMAX < SMALL, scaling is done.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexHEauxiliary
*
* =====================================================================
SUBROUTINE CLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
* -- LAPACK auxiliary 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 EQUED, UPLO
INTEGER LDA, N
REAL AMAX, SCOND
* ..
* .. Array Arguments ..
REAL S( * )
COMPLEX A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, THRESH
PARAMETER ( ONE = 1.0E+0, THRESH = 0.1E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
REAL CJ, LARGE, SMALL
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH
EXTERNAL LSAME, SLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
*
* No equilibration
*
EQUED = 'N'
ELSE
*
* Replace A by diag(S) * A * diag(S).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangle of A is stored.
*
DO 20 J = 1, N
CJ = S( J )
DO 10 I = 1, J - 1
A( I, J ) = CJ*S( I )*A( I, J )
10 CONTINUE
A( J, J ) = CJ*CJ*REAL( A( J, J ) )
20 CONTINUE
ELSE
*
* Lower triangle of A is stored.
*
DO 40 J = 1, N
CJ = S( J )
A( J, J ) = CJ*CJ*REAL( A( J, J ) )
DO 30 I = J + 1, N
A( I, J ) = CJ*S( I )*A( I, J )
30 CONTINUE
40 CONTINUE
END IF
EQUED = 'Y'
END IF
*
RETURN
*
* End of CLAQHE
*
END
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