version 1.7, 2010/12/21 13:53:55
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version 1.8, 2011/11/21 20:43:21
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*> \brief \b ZSTEQR |
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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 ZSTEQR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsteqr.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/zsteqr.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/zsteqr.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 ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER COMPZ |
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* INTEGER INFO, LDZ, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION D( * ), E( * ), WORK( * ) |
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* COMPLEX*16 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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*> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a |
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*> symmetric tridiagonal matrix using the implicit QL or QR method. |
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*> The eigenvectors of a full or band complex Hermitian matrix can also |
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*> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this |
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*> matrix to tridiagonal form. |
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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] COMPZ |
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*> \verbatim |
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*> COMPZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only. |
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*> = 'V': Compute eigenvalues and eigenvectors of the original |
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*> Hermitian matrix. On entry, Z must contain the |
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*> unitary matrix used to reduce the original matrix |
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*> to tridiagonal form. |
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*> = 'I': Compute eigenvalues and eigenvectors of the |
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*> tridiagonal matrix. Z is initialized to the identity |
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*> matrix. |
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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. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> On entry, the diagonal elements of the tridiagonal matrix. |
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*> On exit, if INFO = 0, the eigenvalues in ascending order. |
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*> \endverbatim |
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*> |
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*> \param[in,out] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> On entry, the (n-1) subdiagonal elements of the tridiagonal |
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*> matrix. |
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*> On exit, E has been destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Z |
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*> \verbatim |
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*> Z is COMPLEX*16 array, dimension (LDZ, N) |
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*> On entry, if COMPZ = 'V', then Z contains the unitary |
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*> matrix used in the reduction to tridiagonal form. |
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*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the |
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*> orthonormal eigenvectors of the original Hermitian matrix, |
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*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors |
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*> of the symmetric tridiagonal matrix. |
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*> If COMPZ = '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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*> eigenvectors are desired, then 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 DOUBLE PRECISION array, dimension (max(1,2*N-2)) |
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*> If COMPZ = 'N', then WORK is not referenced. |
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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: the algorithm has failed to find all the eigenvalues in |
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*> a total of 30*N iterations; if INFO = i, then i |
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*> elements of E have not converged to zero; on exit, D |
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*> and E contain the elements of a symmetric tridiagonal |
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*> matrix which is unitarily similar to the original |
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*> matrix. |
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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 complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) |
SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational 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 COMPZ |
CHARACTER COMPZ |
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COMPLEX*16 Z( LDZ, * ) |
COMPLEX*16 Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a |
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* symmetric tridiagonal matrix using the implicit QL or QR method. |
|
* The eigenvectors of a full or band complex Hermitian matrix can also |
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* be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this |
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* matrix to tridiagonal form. |
|
* |
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* Arguments |
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* ========= |
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* |
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* COMPZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only. |
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* = 'V': Compute eigenvalues and eigenvectors of the original |
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* Hermitian matrix. On entry, Z must contain the |
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* unitary matrix used to reduce the original matrix |
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* to tridiagonal form. |
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* = 'I': Compute eigenvalues and eigenvectors of the |
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* tridiagonal matrix. Z is initialized to the identity |
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* matrix. |
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* |
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* N (input) INTEGER |
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* The order of the matrix. N >= 0. |
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* |
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* D (input/output) DOUBLE PRECISION array, dimension (N) |
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* On entry, the diagonal elements of the tridiagonal matrix. |
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* On exit, if INFO = 0, the eigenvalues in ascending order. |
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* |
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* E (input/output) DOUBLE PRECISION array, dimension (N-1) |
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* On entry, the (n-1) subdiagonal elements of the tridiagonal |
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* matrix. |
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* On exit, E has been destroyed. |
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* |
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* Z (input/output) COMPLEX*16 array, dimension (LDZ, N) |
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* On entry, if COMPZ = 'V', then Z contains the unitary |
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* matrix used in the reduction to tridiagonal form. |
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* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the |
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* orthonormal eigenvectors of the original Hermitian matrix, |
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* and if COMPZ = 'I', Z contains the orthonormal eigenvectors |
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* of the symmetric tridiagonal matrix. |
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* If COMPZ = '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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* eigenvectors are desired, then LDZ >= max(1,N). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2)) |
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* If COMPZ = 'N', then WORK is not referenced. |
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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: the algorithm has failed to find all the eigenvalues in |
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* a total of 30*N iterations; if INFO = i, then i |
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* elements of E have not converged to zero; on exit, D |
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* and E contain the elements of a symmetric tridiagonal |
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* matrix which is unitarily similar to the original |
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* matrix. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |