version 1.4, 2010/08/06 15:32:41
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version 1.11, 2012/12/14 14:22:46
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*> \brief <b> ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 ZHBEV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbev.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/zhbev.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/zhbev.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 ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
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* 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, KD, LDAB, LDZ, 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 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
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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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*> ZHBEV computes all the eigenvalues and, optionally, eigenvectors of |
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*> a complex Hermitian band 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] KD |
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*> \verbatim |
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*> KD is INTEGER |
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*> The number of superdiagonals of the matrix A if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AB |
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*> \verbatim |
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*> AB is COMPLEX*16 array, dimension (LDAB, N) |
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*> On entry, the upper or lower triangle of the Hermitian band |
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*> matrix A, stored in the first KD+1 rows of the array. The |
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*> j-th column of A is stored in the j-th column of the array AB |
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*> as follows: |
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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*> |
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*> On exit, AB is overwritten by values generated during the |
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*> reduction to tridiagonal form. If UPLO = 'U', the first |
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*> superdiagonal and the diagonal of the tridiagonal matrix T |
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*> are returned in rows KD and KD+1 of AB, and if UPLO = 'L', |
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*> the diagonal and first subdiagonal of T are returned in the |
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*> first two rows of AB. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDAB >= KD + 1. |
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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] Z |
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*> \verbatim |
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*> Z is COMPLEX*16 array, dimension (LDZ, N) |
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*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal |
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*> eigenvectors of the matrix A, with the i-th column of Z |
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*> holding the eigenvector associated with W(i). |
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*> If JOBZ = 'N', then Z is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDZ >= 1, and if |
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*> JOBZ = 'V', LDZ >= max(1,N). |
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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 (N) |
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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 complex16OTHEReigen |
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* |
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* ===================================================================== |
SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
$ RWORK, INFO ) |
$ RWORK, 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 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHBEV computes all the eigenvalues and, optionally, eigenvectors of |
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* a complex Hermitian band 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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* KD (input) INTEGER |
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* The number of superdiagonals of the matrix A if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
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* |
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* AB (input/output) COMPLEX*16 array, dimension (LDAB, N) |
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* On entry, the upper or lower triangle of the Hermitian band |
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* matrix A, stored in the first KD+1 rows of the array. The |
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* j-th column of A is stored in the j-th column of the array AB |
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* as follows: |
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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* |
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* On exit, AB is overwritten by values generated during the |
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* reduction to tridiagonal form. If UPLO = 'U', the first |
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* superdiagonal and the diagonal of the tridiagonal matrix T |
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* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', |
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* the diagonal and first subdiagonal of T are returned in the |
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* first two rows of AB. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KD + 1. |
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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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* Z (output) COMPLEX*16 array, dimension (LDZ, N) |
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* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal |
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* eigenvectors of the matrix A, with the i-th column of Z |
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* holding the eigenvector associated with W(i). |
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* If JOBZ = 'N', then Z is not referenced. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1, and if |
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* JOBZ = 'V', LDZ >= max(1,N). |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (N) |
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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 .. |