version 1.6, 2010/08/13 21:03:58
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version 1.8, 2011/11/21 20:43:04
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*> \brief \b DSTEGR |
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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 DSTEGR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstegr.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/dstegr.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/dstegr.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 DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
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* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, |
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* LIWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, RANGE |
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* INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N |
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* DOUBLE PRECISION ABSTOL, VL, VU |
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* .. |
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* .. Array Arguments .. |
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* INTEGER ISUPPZ( * ), IWORK( * ) |
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* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) |
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* DOUBLE PRECISION 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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*> DSTEGR computes selected eigenvalues and, optionally, eigenvectors |
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*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has |
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*> a well defined set of pairwise different real eigenvalues, the corresponding |
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*> real eigenvectors are pairwise orthogonal. |
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*> |
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*> The spectrum may be computed either completely or partially by specifying |
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*> either an interval (VL,VU] or a range of indices IL:IU for the desired |
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*> eigenvalues. |
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*> |
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*> DSTEGR is a compatability wrapper around the improved DSTEMR routine. |
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*> See DSTEMR for further details. |
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*> |
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*> One important change is that the ABSTOL parameter no longer provides any |
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*> benefit and hence is no longer used. |
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*> |
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*> Note : DSTEGR and DSTEMR work only on machines which follow |
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*> IEEE-754 floating-point standard in their handling of infinities and |
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*> NaNs. Normal execution may create these exceptiona values and hence |
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*> may abort due to a floating point exception in environments which |
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*> do not conform to the IEEE-754 standard. |
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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] RANGE |
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*> \verbatim |
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*> RANGE is CHARACTER*1 |
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*> = 'A': all eigenvalues will be found. |
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*> = 'V': all eigenvalues in the half-open interval (VL,VU] |
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*> will be found. |
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*> = 'I': the IL-th through IU-th eigenvalues will be found. |
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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 N diagonal elements of the tridiagonal matrix |
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*> T. On exit, D is overwritten. |
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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) |
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*> On entry, the (N-1) subdiagonal elements of the tridiagonal |
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*> matrix T in elements 1 to N-1 of E. E(N) need not be set on |
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*> input, but is used internally as workspace. |
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*> On exit, E is overwritten. |
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*> \endverbatim |
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*> |
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*> \param[in] VL |
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*> \verbatim |
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*> VL is DOUBLE PRECISION |
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*> \endverbatim |
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*> |
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*> \param[in] VU |
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*> \verbatim |
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*> VU is DOUBLE PRECISION |
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*> |
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*> If RANGE='V', the lower and upper bounds of the interval to |
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*> be searched for eigenvalues. VL < VU. |
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*> Not referenced if RANGE = 'A' or 'I'. |
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*> \endverbatim |
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*> |
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*> \param[in] IL |
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*> \verbatim |
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*> IL is INTEGER |
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*> \endverbatim |
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*> |
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*> \param[in] IU |
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*> \verbatim |
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*> IU is INTEGER |
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*> |
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*> If RANGE='I', the indices (in ascending order) of the |
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*> smallest and largest eigenvalues to be returned. |
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*> 1 <= IL <= IU <= N, if N > 0. |
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*> Not referenced if RANGE = 'A' or 'V'. |
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*> \endverbatim |
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*> |
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*> \param[in] ABSTOL |
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*> \verbatim |
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*> ABSTOL is DOUBLE PRECISION |
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*> Unused. Was the absolute error tolerance for the |
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*> eigenvalues/eigenvectors in previous versions. |
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*> \endverbatim |
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*> |
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*> \param[out] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The total number of eigenvalues found. 0 <= M <= N. |
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*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+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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*> The first M elements contain the selected eigenvalues in |
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*> 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 DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) |
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*> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z |
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*> contain the orthonormal eigenvectors of the matrix T |
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*> corresponding to the selected eigenvalues, with the i-th |
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*> column of Z holding the eigenvector associated with W(i). |
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*> If JOBZ = 'N', then Z is not referenced. |
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*> Note: the user must ensure that at least max(1,M) columns are |
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*> supplied in the array Z; if RANGE = 'V', the exact value of M |
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*> is not known in advance and an upper bound must be used. |
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*> Supplying N columns is always safe. |
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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', then LDZ >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] ISUPPZ |
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*> \verbatim |
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*> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) ) |
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*> The support of the eigenvectors in Z, i.e., the indices |
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*> indicating the nonzero elements in Z. The i-th computed eigenvector |
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*> is nonzero only in elements ISUPPZ( 2*i-1 ) through |
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*> ISUPPZ( 2*i ). This is relevant in the case when the matrix |
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*> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. |
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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 (LWORK) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal |
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*> (and minimal) 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 dimension of the array WORK. LWORK >= max(1,18*N) |
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*> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. |
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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] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER array, dimension (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. LIWORK >= max(1,10*N) |
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*> if the eigenvectors are desired, and LIWORK >= max(1,8*N) |
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*> if only the eigenvalues are to be computed. |
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*> If LIWORK = -1, then a workspace query is assumed; the |
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*> routine only calculates the optimal size of the IWORK array, |
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*> returns this value as the first entry of the IWORK array, and |
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*> no error message related to 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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*> On exit, INFO |
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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 = 1X, internal error in DLARRE, |
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*> if INFO = 2X, internal error in DLARRV. |
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*> Here, the digit X = ABS( IINFO ) < 10, where IINFO is |
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*> the nonzero error code returned by DLARRE or |
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*> DLARRV, respectively. |
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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 doubleOTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Inderjit Dhillon, IBM Almaden, USA \n |
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*> Osni Marques, LBNL/NERSC, USA \n |
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*> Christof Voemel, LBNL/NERSC, USA \n |
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* |
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* ===================================================================== |
SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, |
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, |
$ LIWORK, INFO ) |
$ LIWORK, INFO ) |
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IMPLICIT NONE |
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* |
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* |
* |
* -- LAPACK computational 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 JOBZ, RANGE |
CHARACTER JOBZ, RANGE |
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DOUBLE PRECISION Z( LDZ, * ) |
DOUBLE PRECISION Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
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* DSTEGR computes selected eigenvalues and, optionally, eigenvectors |
|
* of a real symmetric tridiagonal matrix T. Any such unreduced matrix has |
|
* a well defined set of pairwise different real eigenvalues, the corresponding |
|
* real eigenvectors are pairwise orthogonal. |
|
* |
|
* The spectrum may be computed either completely or partially by specifying |
|
* either an interval (VL,VU] or a range of indices IL:IU for the desired |
|
* eigenvalues. |
|
* |
|
* DSTEGR is a compatability wrapper around the improved DSTEMR routine. |
|
* See DSTEMR for further details. |
|
* |
|
* One important change is that the ABSTOL parameter no longer provides any |
|
* benefit and hence is no longer used. |
|
* |
|
* Note : DSTEGR and DSTEMR work only on machines which follow |
|
* IEEE-754 floating-point standard in their handling of infinities and |
|
* NaNs. Normal execution may create these exceptiona values and hence |
|
* may abort due to a floating point exception in environments which |
|
* do not conform to the IEEE-754 standard. |
|
* |
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* Arguments |
|
* ========= |
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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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* RANGE (input) CHARACTER*1 |
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* = 'A': all eigenvalues will be found. |
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* = 'V': all eigenvalues in the half-open interval (VL,VU] |
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* will be found. |
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* = 'I': the IL-th through IU-th eigenvalues will be found. |
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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 N diagonal elements of the tridiagonal matrix |
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* T. On exit, D is overwritten. |
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* |
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* E (input/output) DOUBLE PRECISION array, dimension (N) |
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* On entry, the (N-1) subdiagonal elements of the tridiagonal |
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* matrix T in elements 1 to N-1 of E. E(N) need not be set on |
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* input, but is used internally as workspace. |
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* On exit, E is overwritten. |
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* |
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* VL (input) DOUBLE PRECISION |
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* VU (input) DOUBLE PRECISION |
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* If RANGE='V', the lower and upper bounds of the interval to |
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* be searched for eigenvalues. VL < VU. |
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* Not referenced if RANGE = 'A' or 'I'. |
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* |
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* IL (input) INTEGER |
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* IU (input) INTEGER |
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* If RANGE='I', the indices (in ascending order) of the |
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* smallest and largest eigenvalues to be returned. |
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* 1 <= IL <= IU <= N, if N > 0. |
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* Not referenced if RANGE = 'A' or 'V'. |
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* |
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* ABSTOL (input) DOUBLE PRECISION |
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* Unused. Was the absolute error tolerance for the |
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* eigenvalues/eigenvectors in previous versions. |
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* |
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* M (output) INTEGER |
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* The total number of eigenvalues found. 0 <= M <= N. |
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* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. |
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* |
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* W (output) DOUBLE PRECISION array, dimension (N) |
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* The first M elements contain the selected eigenvalues in |
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* ascending order. |
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* |
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* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) |
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* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z |
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* contain the orthonormal eigenvectors of the matrix T |
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* corresponding to the selected eigenvalues, with the i-th |
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* column of Z holding the eigenvector associated with W(i). |
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* If JOBZ = 'N', then Z is not referenced. |
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* Note: the user must ensure that at least max(1,M) columns are |
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* supplied in the array Z; if RANGE = 'V', the exact value of M |
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* is not known in advance and an upper bound must be used. |
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* Supplying N columns is always safe. |
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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', then LDZ >= max(1,N). |
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* |
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* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) ) |
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* The support of the eigenvectors in Z, i.e., the indices |
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* indicating the nonzero elements in Z. The i-th computed eigenvector |
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* is nonzero only in elements ISUPPZ( 2*i-1 ) through |
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* ISUPPZ( 2*i ). This is relevant in the case when the matrix |
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* is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. |
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* |
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) |
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* On exit, if INFO = 0, WORK(1) returns the optimal |
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* (and minimal) LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. LWORK >= max(1,18*N) |
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* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. |
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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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* IWORK (workspace/output) INTEGER array, dimension (LIWORK) |
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* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
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* |
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* LIWORK (input) INTEGER |
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* The dimension of the array IWORK. LIWORK >= max(1,10*N) |
|
* if the eigenvectors are desired, and LIWORK >= max(1,8*N) |
|
* if only the eigenvalues are to be computed. |
|
* If LIWORK = -1, then a workspace query is assumed; the |
|
* routine only calculates the optimal size of the IWORK array, |
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* returns this value as the first entry of the IWORK array, and |
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* no error message related to LIWORK is issued by XERBLA. |
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* |
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* INFO (output) INTEGER |
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* On exit, INFO |
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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 = 1X, internal error in DLARRE, |
|
* if INFO = 2X, internal error in DLARRV. |
|
* Here, the digit X = ABS( IINFO ) < 10, where IINFO is |
|
* the nonzero error code returned by DLARRE or |
|
* DLARRV, respectively. |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* Based on contributions by |
|
* Inderjit Dhillon, IBM Almaden, USA |
|
* Osni Marques, LBNL/NERSC, USA |
|
* Christof Voemel, LBNL/NERSC, USA |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |