version 1.5, 2010/08/07 13:22:33
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version 1.8, 2011/11/21 20:43:11
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*> \brief <b> ZHEEV 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 ZHEEV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheev.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/zheev.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/zheev.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 ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, |
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* 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, 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, * ), 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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*> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a |
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*> complex Hermitian matrix A. |
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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*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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*> 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 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: if INFO = i, the algorithm failed to converge; i |
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*> off-diagonal elements of an intermediate tridiagonal |
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*> form did not converge to zero. |
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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 November 2011 |
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* |
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*> \ingroup complex16HEeigen |
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* |
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* ===================================================================== |
SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, |
SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
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COMPLEX*16 A( LDA, * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHEEV computes all eigenvalues and, optionally, eigenvectors of a |
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* complex Hermitian matrix A. |
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* |
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* Arguments |
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* ========= |
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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 triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. 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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* 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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* |
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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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* 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: if INFO = i, the algorithm failed to converge; i |
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* off-diagonal elements of an intermediate tridiagonal |
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* form did not converge to zero. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |