version 1.2, 2010/04/21 13:45:31
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version 1.16, 2017/06/17 10:54:15
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*> \brief \b ZHEGV |
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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 ZHEGV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegv.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/zhegv.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/zhegv.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 ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
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* LWORK, RWORK, 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, LWORK, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION RWORK( * ), W( * ) |
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* COMPLEX*16 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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*> ZHEGV 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. |
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*> Here A and B are assumed to be Hermitian and B is also |
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*> positive definite. |
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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*16 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*16 array, dimension (LDB, N) |
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*> On entry, the Hermitian positive definite matrix B. |
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*> If UPLO = 'U', the leading N-by-N upper triangular part of B |
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*> contains the upper triangular part of the matrix B. |
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*> If UPLO = 'L', the leading N-by-N lower triangular part of B |
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*> contains 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 DOUBLE PRECISION 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*16 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. LWORK >= max(1,2*N-1). |
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*> For optimal efficiency, LWORK >= (NB+1)*N, |
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*> where NB is the blocksize for ZHETRD returned by ILAENV. |
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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 size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK 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 DOUBLE PRECISION array, dimension (max(1, 3*N-2)) |
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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: ZPOTRF or ZHEEV returned an error code: |
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*> <= N: if INFO = i, ZHEEV failed to converge; |
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*> i off-diagonal elements of an intermediate |
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*> tridiagonal form did not converge to zero; |
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*> > N: if INFO = N + i, for 1 <= i <= N, then the leading |
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*> minor of order i of B is not positive definite. |
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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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*> \date December 2016 |
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* |
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*> \ingroup complex16HEeigen |
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* |
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* ===================================================================== |
SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, |
$ LWORK, RWORK, INFO ) |
$ LWORK, RWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
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COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHEGV 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. |
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* Here A and B are assumed to be Hermitian and B is also |
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* positive definite. |
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* |
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* Arguments |
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* ========= |
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* |
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* ITYPE (input) 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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* |
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* JOBZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only; |
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* = 'V': Compute eigenvalues and eigenvectors. |
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* |
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* UPLO (input) 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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* |
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* N (input) INTEGER |
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* The order of the matrices A and B. N >= 0. |
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* |
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* A (input/output) COMPLEX*16 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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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB, N) |
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* On entry, the Hermitian positive definite matrix B. |
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* If UPLO = 'U', the leading N-by-N upper triangular part of B |
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* contains the upper triangular part of the matrix B. |
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* If UPLO = 'L', the leading N-by-N lower triangular part of B |
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* contains 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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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* W (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, the eigenvalues in ascending order. |
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* |
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* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The length of the array WORK. LWORK >= max(1,2*N-1). |
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* For optimal efficiency, LWORK >= (NB+1)*N, |
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* where NB is the blocksize for ZHETRD returned by ILAENV. |
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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 size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) |
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* |
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* INFO (output) 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: ZPOTRF or ZHEEV returned an error code: |
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* <= N: if INFO = i, ZHEEV failed to converge; |
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* i off-diagonal elements of an intermediate |
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* tridiagonal form did not converge to zero; |
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* > N: if INFO = N + i, for 1 <= i <= N, then the leading |
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* minor of order i of B is not positive definite. |
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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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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN |
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN |
* |
* |
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; |
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; |
* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y |
* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y |
* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
TRANS = 'N' |
TRANS = 'N' |
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ELSE IF( ITYPE.EQ.3 ) THEN |
ELSE IF( ITYPE.EQ.3 ) THEN |
* |
* |
* For B*A*x=(lambda)*x; |
* For B*A*x=(lambda)*x; |
* backtransform eigenvectors: x = L*y or U'*y |
* backtransform eigenvectors: x = L*y or U**H *y |
* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
TRANS = 'C' |
TRANS = 'C' |