221 lines
5.9 KiB
Fortran
221 lines
5.9 KiB
Fortran
*> \brief \b ZLAQHE scales a Hermitian matrix.
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download ZLAQHE + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqhe.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqhe.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqhe.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER EQUED, UPLO
|
|
* INTEGER LDA, N
|
|
* DOUBLE PRECISION AMAX, SCOND
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION S( * )
|
|
* COMPLEX*16 A( LDA, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZLAQHE 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*16 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 DOUBLE PRECISION array, dimension (N)
|
|
*> The scale factors for A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] SCOND
|
|
*> \verbatim
|
|
*> SCOND is DOUBLE PRECISION
|
|
*> Ratio of the smallest S(i) to the largest S(i).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] AMAX
|
|
*> \verbatim
|
|
*> AMAX is DOUBLE PRECISION
|
|
*> 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.
|
|
*
|
|
*> \ingroup complex16HEauxiliary
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
|
|
*
|
|
* -- LAPACK auxiliary routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER EQUED, UPLO
|
|
INTEGER LDA, N
|
|
DOUBLE PRECISION AMAX, SCOND
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION S( * )
|
|
COMPLEX*16 A( LDA, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE, THRESH
|
|
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, J
|
|
DOUBLE PRECISION CJ, LARGE, SMALL
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
DOUBLE PRECISION DLAMCH
|
|
EXTERNAL LSAME, DLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DBLE
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.LE.0 ) THEN
|
|
EQUED = 'N'
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Initialize LARGE and SMALL.
|
|
*
|
|
SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( '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*DBLE( 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*DBLE( 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 ZLAQHE
|
|
*
|
|
END
|