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*> \brief <b> ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, UPLO
* INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RWORK( * ), W( * )
* COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
*> complex Hermitian matrix in packed storage.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] JOBZ
*> \verbatim
*> JOBZ is CHARACTER*1
*> = 'N': Compute eigenvalues only;
*> = 'V': Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*> On entry, the upper or lower triangle of the Hermitian matrix
*> A, packed columnwise in a linear array. The j-th column of A
*> is stored in the array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
*> \endverbatim
*> \verbatim
*> On exit, AP is overwritten by values generated during the
*> reduction to tridiagonal form. If UPLO = 'U', the diagonal
*> and first superdiagonal of the tridiagonal matrix T overwrite
*> the corresponding elements of A, and if UPLO = 'L', the
*> diagonal and first subdiagonal of T overwrite the
*> corresponding elements of A.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*> W is DOUBLE PRECISION array, dimension (N)
*> If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is COMPLEX*16 array, dimension (LDZ, N)
*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
*> eigenvectors of the matrix A, with the i-th column of Z
*> holding the eigenvector associated with W(i).
*> If JOBZ = 'N', then Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1, and if
*> JOBZ = 'V', LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, the algorithm failed to converge; i
*> off-diagonal elements of an intermediate tridiagonal
*> form did not converge to zero.
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16OTHEReigen
*
* =====================================================================
SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
$ INFO )
*
* -- LAPACK eigen routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
LOGICAL WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
$ ISCALE
DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANHP
EXTERNAL LSAME, DLAMCH, ZLANHP
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEQR,
$ ZUPGTR
* ..
* .. Intrinsic Functions ..
INTRINSIC SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
$ THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -7
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHPEV ', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
W( 1 ) = AP( 1 )
RWORK( 1 ) = 1
IF( WANTZ )
$ Z( 1, 1 ) = ONE
RETURN
END IF
*
* Get machine constants.
*
SAFMIN = DLAMCH( 'Safe minimum' )
EPS = DLAMCH( 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = SQRT( BIGNUM )
*
* Scale matrix to allowable range, if necessary.
*
ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
ISCALE = 0
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / ANRM
ELSE IF( ANRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / ANRM
END IF
IF( ISCALE.EQ.1 ) THEN
CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
END IF
*
* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
*
INDE = 1
INDTAU = 1
CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
$ IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, first call
* ZUPGTR to generate the orthogonal matrix, then call ZSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, RWORK( INDE ), INFO )
ELSE
INDWRK = INDTAU + N
CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
$ WORK( INDWRK ), IINFO )
INDRWK = INDE + N
CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
$ RWORK( INDRWK ), INFO )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = N
ELSE
IMAX = INFO - 1
END IF
CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
RETURN
*
* End of ZHPEV
*
END
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