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389 lines
12 KiB
389 lines
12 KiB
*> \brief <b> CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
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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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*> \htmlonly
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*> Download CHEEVD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevd.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevd.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevd.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
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* LRWORK, IWORK, LIWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ, UPLO
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* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* REAL RWORK( * ), W( * )
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* COMPLEX A( LDA, * ), WORK( * )
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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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*> CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
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*> complex Hermitian matrix A. If eigenvectors are desired, it uses a
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*> divide and conquer algorithm.
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*>
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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] JOBZ
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*> \verbatim
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*> JOBZ is CHARACTER*1
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*> = 'N': Compute eigenvalues only;
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*> = 'V': Compute eigenvalues and eigenvectors.
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*> \endverbatim
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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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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is stored.
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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 order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA, N)
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*> On entry, the Hermitian matrix A. If UPLO = 'U', the
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*> leading N-by-N upper triangular part of A contains the
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*> upper triangular part of the matrix A. If UPLO = 'L',
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*> the leading N-by-N lower triangular part of A contains
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*> the lower triangular part of the matrix A.
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*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
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*> orthonormal eigenvectors of the matrix A.
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*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
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*> or the upper triangle (if UPLO='U') of A, including the
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*> diagonal, is destroyed.
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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[out] W
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*> \verbatim
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*> W is REAL array, dimension (N)
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*> If INFO = 0, the eigenvalues in ascending order.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK.
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*> If N <= 1, LWORK must be at least 1.
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*> If JOBZ = 'N' and N > 1, LWORK must be at least N + 1.
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*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal sizes of the WORK, RWORK and
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*> IWORK arrays, returns these values as the first entries of
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*> the WORK, RWORK and IWORK arrays, and no error message
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*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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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 REAL array,
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*> dimension (LRWORK)
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*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
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*> \endverbatim
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*>
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*> \param[in] LRWORK
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*> \verbatim
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*> LRWORK is INTEGER
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*> The dimension of the array RWORK.
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*> If N <= 1, LRWORK must be at least 1.
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*> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
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*> If JOBZ = 'V' and N > 1, LRWORK must be at least
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*> 1 + 5*N + 2*N**2.
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*>
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*> If LRWORK = -1, then a workspace query is assumed; the
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*> routine only calculates the optimal sizes of the WORK, RWORK
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*> and IWORK arrays, returns these values as the first entries
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*> of the WORK, RWORK and IWORK arrays, and no error message
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*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
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*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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*> \endverbatim
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*>
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*> \param[in] LIWORK
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*> \verbatim
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*> LIWORK is INTEGER
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*> The dimension of the array IWORK.
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*> If N <= 1, LIWORK must be at least 1.
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*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
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*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
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*>
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*> If LIWORK = -1, then a workspace query is assumed; the
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*> routine only calculates the optimal sizes of the WORK, RWORK
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*> and IWORK arrays, returns these values as the first entries
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*> of the WORK, RWORK and IWORK arrays, and no error message
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*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
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*> to converge; i off-diagonal elements of an intermediate
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*> tridiagonal form did not converge to zero;
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*> if INFO = i and JOBZ = 'V', then the algorithm failed
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*> to compute an eigenvalue while working on the submatrix
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*> lying in rows and columns INFO/(N+1) through
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*> mod(INFO,N+1).
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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 complexHEeigen
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*
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*> \par Further Details:
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* =====================
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*>
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*> Modified description of INFO. Sven, 16 Feb 05.
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*
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*> \par Contributors:
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* ==================
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*>
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*> Jeff Rutter, Computer Science Division, University of California
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*> at Berkeley, USA
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*>
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* =====================================================================
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SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
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$ LRWORK, IWORK, LIWORK, INFO )
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*
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* -- LAPACK driver 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 JOBZ, UPLO
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INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL RWORK( * ), W( * )
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COMPLEX A( LDA, * ), WORK( * )
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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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, LQUERY, WANTZ
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INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
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$ INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK,
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$ LLWRK2, LOPT, LROPT, LRWMIN, LWMIN
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REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
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$ SMLNUM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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REAL CLANHE, SLAMCH
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EXTERNAL ILAENV, LSAME, CLANHE, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CHETRD, CLACPY, CLASCL, CSTEDC, CUNMTR, SSCAL,
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$ SSTERF, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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WANTZ = LSAME( JOBZ, 'V' )
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LOWER = LSAME( UPLO, 'L' )
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LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
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*
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INFO = 0
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IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -1
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ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( N.LE.1 ) THEN
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LWMIN = 1
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LRWMIN = 1
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LIWMIN = 1
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LOPT = LWMIN
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LROPT = LRWMIN
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LIOPT = LIWMIN
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ELSE
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IF( WANTZ ) THEN
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LWMIN = 2*N + N*N
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LRWMIN = 1 + 5*N + 2*N**2
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LIWMIN = 3 + 5*N
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ELSE
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LWMIN = N + 1
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LRWMIN = N
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LIWMIN = 1
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END IF
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LOPT = MAX( LWMIN, N +
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$ N*ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) )
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LROPT = LRWMIN
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LIOPT = LIWMIN
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END IF
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WORK( 1 ) = LOPT
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RWORK( 1 ) = LROPT
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IWORK( 1 ) = LIOPT
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*
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -8
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ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -10
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -12
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END IF
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CHEEVD', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( N.EQ.1 ) THEN
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W( 1 ) = REAL( A( 1, 1 ) )
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IF( WANTZ )
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$ A( 1, 1 ) = CONE
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RETURN
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END IF
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*
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* Get machine constants.
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*
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SAFMIN = SLAMCH( 'Safe minimum' )
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EPS = SLAMCH( 'Precision' )
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SMLNUM = SAFMIN / EPS
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BIGNUM = ONE / SMLNUM
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RMIN = SQRT( SMLNUM )
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RMAX = SQRT( BIGNUM )
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*
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* Scale matrix to allowable range, if necessary.
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*
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ANRM = CLANHE( 'M', UPLO, N, A, LDA, RWORK )
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ISCALE = 0
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IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
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ISCALE = 1
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SIGMA = RMIN / ANRM
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ELSE IF( ANRM.GT.RMAX ) THEN
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ISCALE = 1
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SIGMA = RMAX / ANRM
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END IF
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IF( ISCALE.EQ.1 )
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$ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
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*
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* Call CHETRD to reduce Hermitian matrix to tridiagonal form.
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*
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INDE = 1
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INDTAU = 1
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INDWRK = INDTAU + N
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INDRWK = INDE + N
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INDWK2 = INDWRK + N*N
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LLWORK = LWORK - INDWRK + 1
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LLWRK2 = LWORK - INDWK2 + 1
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LLRWK = LRWORK - INDRWK + 1
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CALL CHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
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$ WORK( INDWRK ), LLWORK, IINFO )
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*
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* For eigenvalues only, call SSTERF. For eigenvectors, first call
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* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
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* tridiagonal matrix, then call CUNMTR to multiply it to the
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* Householder transformations represented as Householder vectors in
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* A.
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*
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IF( .NOT.WANTZ ) THEN
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CALL SSTERF( N, W, RWORK( INDE ), INFO )
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ELSE
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CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N,
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$ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK,
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$ IWORK, LIWORK, INFO )
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CALL CUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
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$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
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CALL CLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
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END IF
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*
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* If matrix was scaled, then rescale eigenvalues appropriately.
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*
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IF( ISCALE.EQ.1 ) THEN
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IF( INFO.EQ.0 ) THEN
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IMAX = N
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ELSE
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IMAX = INFO - 1
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END IF
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CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
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END IF
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*
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WORK( 1 ) = LOPT
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RWORK( 1 ) = LROPT
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IWORK( 1 ) = LIOPT
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*
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RETURN
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*
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* End of CHEEVD
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*
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END
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