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403 lines
13 KiB
403 lines
13 KiB
*> \brief \b CHEGVD
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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 CHEGVD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chegvd.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/chegvd.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/chegvd.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 CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
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* LWORK, RWORK, 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, ITYPE, LDA, LDB, 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, * ), B( LDB, * ), 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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*> CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
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*> of a complex generalized Hermitian-definite eigenproblem, of the form
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*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
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*> B are assumed to be Hermitian and B is also positive definite.
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*> If eigenvectors are desired, it uses a 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] ITYPE
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*> \verbatim
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*> ITYPE is INTEGER
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*> Specifies the problem type to be solved:
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*> = 1: A*x = (lambda)*B*x
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*> = 2: A*B*x = (lambda)*x
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*> = 3: B*A*x = (lambda)*x
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*> \endverbatim
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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 triangles of A and B are stored;
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*> = 'L': Lower triangles of A and B are 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 matrices A and B. 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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*>
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*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
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*> matrix Z of eigenvectors. The eigenvectors are normalized
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*> as follows:
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*> if ITYPE = 1 or 2, Z**H*B*Z = I;
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*> if ITYPE = 3, Z**H*inv(B)*Z = I.
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*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
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*> or the lower triangle (if UPLO='L') 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[in,out] B
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*> \verbatim
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*> B is COMPLEX array, dimension (LDB, N)
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*> On entry, the Hermitian matrix B. If UPLO = 'U', the
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*> leading N-by-N upper triangular part of B contains the
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*> upper triangular part of the matrix B. If UPLO = 'L',
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*> the leading N-by-N lower triangular part of B contains
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*> the lower triangular part of the matrix B.
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*>
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*> On exit, if INFO <= N, the part of B containing the matrix is
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*> overwritten by the triangular factor U or L from the Cholesky
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*> factorization B = U**H*U or B = L*L**H.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= 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 >= 1.
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*> If JOBZ = 'N' and N > 1, LWORK >= N + 1.
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*> If JOBZ = 'V' and N > 1, LWORK >= 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, dimension (MAX(1,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 >= 1.
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*> If JOBZ = 'N' and N > 1, LRWORK >= N.
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*> If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
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*> If JOBZ = 'N' and N > 1, LIWORK >= 1.
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*> If JOBZ = 'V' and N > 1, LIWORK >= 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: CPOTRF or CHEEVD returned an error code:
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*> <= N: if INFO = i and JOBZ = 'N', then the algorithm
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*> failed to converge; i off-diagonal elements of an
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*> intermediate tridiagonal form did not converge to
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*> zero;
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*> if INFO = i and JOBZ = 'V', then the algorithm
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*> failed to compute an eigenvalue while working on
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*> the submatrix lying in rows and columns INFO/(N+1)
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*> through mod(INFO,N+1);
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*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
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*> principal minor of order i of B is not positive.
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*> The factorization of B could not be completed and
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*> no eigenvalues or eigenvectors were computed.
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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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*> \verbatim
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*>
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*> Modified so that no backsubstitution is performed if CHEEVD fails to
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*> converge (NEIG in old code could be greater than N causing out of
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*> bounds reference to A - reported by Ralf Meyer). Also corrected the
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*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
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*> \endverbatim
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*
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*> \par Contributors:
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* ==================
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*>
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*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
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*>
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* =====================================================================
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SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
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$ LWORK, RWORK, 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, ITYPE, LDA, LDB, 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, * ), B( LDB, * ), 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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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER, WANTZ
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CHARACTER TRANS
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INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CHEEVD, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, REAL
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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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UPPER = LSAME( UPLO, 'U' )
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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( 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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ELSE IF( WANTZ ) THEN
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LWMIN = 2*N + N*N
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LRWMIN = 1 + 5*N + 2*N*N
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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 = LWMIN
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LROPT = LRWMIN
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LIOPT = LIWMIN
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IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
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INFO = -1
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ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -2
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ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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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 = -11
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ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -13
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -15
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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( 'CHEGVD', -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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* Form a Cholesky factorization of B.
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*
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CALL CPOTRF( UPLO, N, B, LDB, INFO )
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IF( INFO.NE.0 ) THEN
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INFO = N + INFO
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RETURN
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END IF
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*
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* Transform problem to standard eigenvalue problem and solve.
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*
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CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
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CALL CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
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$ IWORK, LIWORK, INFO )
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LOPT = INT( MAX( REAL( LOPT ), REAL( WORK( 1 ) ) ) )
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LROPT = INT( MAX( REAL( LROPT ), REAL( RWORK( 1 ) ) ) )
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LIOPT = INT( MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) ) )
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*
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IF( WANTZ .AND. INFO.EQ.0 ) THEN
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*
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* Backtransform eigenvectors to the original problem.
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*
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IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
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*
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* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
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* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
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*
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IF( UPPER ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'C'
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END IF
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*
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CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
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$ B, LDB, A, LDA )
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*
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ELSE IF( ITYPE.EQ.3 ) THEN
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*
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* For B*A*x=(lambda)*x;
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* backtransform eigenvectors: x = L*y or U**H *y
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*
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IF( UPPER ) THEN
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TRANS = 'C'
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ELSE
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TRANS = 'N'
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END IF
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*
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CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
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$ B, LDB, A, LDA )
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END IF
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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 CHEGVD
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*
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END
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