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 ZSTEMR |
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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 ZSTEMR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zstemr.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/zstemr.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/zstemr.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 ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
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* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, |
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* IWORK, LIWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, RANGE |
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* LOGICAL TRYRAC |
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* INTEGER IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N |
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* DOUBLE PRECISION 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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* 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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*> ZSTEMR 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 |
|
*> 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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*> Depending on the number of desired eigenvalues, these are computed either |
|
*> by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are |
|
*> computed by the use of various suitable L D L^T factorizations near clusters |
|
*> of close eigenvalues (referred to as RRRs, Relatively Robust |
|
*> Representations). An informal sketch of the algorithm follows. |
|
*> |
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*> For each unreduced block (submatrix) of T, |
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*> (a) Compute T - sigma I = L D L^T, so that L and D |
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*> define all the wanted eigenvalues to high relative accuracy. |
|
*> This means that small relative changes in the entries of D and L |
|
*> cause only small relative changes in the eigenvalues and |
|
*> eigenvectors. The standard (unfactored) representation of the |
|
*> tridiagonal matrix T does not have this property in general. |
|
*> (b) Compute the eigenvalues to suitable accuracy. |
|
*> If the eigenvectors are desired, the algorithm attains full |
|
*> accuracy of the computed eigenvalues only right before |
|
*> the corresponding vectors have to be computed, see steps c) and d). |
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*> (c) For each cluster of close eigenvalues, select a new |
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*> shift close to the cluster, find a new factorization, and refine |
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*> the shifted eigenvalues to suitable accuracy. |
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*> (d) For each eigenvalue with a large enough relative separation compute |
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*> the corresponding eigenvector by forming a rank revealing twisted |
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*> factorization. Go back to (c) for any clusters that remain. |
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*> |
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*> For more details, see: |
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*> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations |
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*> to compute orthogonal eigenvectors of symmetric tridiagonal matrices," |
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*> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. |
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*> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and |
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*> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, |
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*> 2004. Also LAPACK Working Note 154. |
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*> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric |
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*> tridiagonal eigenvalue/eigenvector problem", |
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*> Computer Science Division Technical Report No. UCB/CSD-97-971, |
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*> UC Berkeley, May 1997. |
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*> |
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*> Further Details |
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*> 1.ZSTEMR works only on machines which follow IEEE-754 |
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*> floating-point standard in their handling of infinities and NaNs. |
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*> This permits the use of efficient inner loops avoiding a check for |
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*> zero divisors. |
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*> |
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*> 2. LAPACK routines can be used to reduce a complex Hermitean matrix to |
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*> real symmetric tridiagonal form. |
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*> |
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*> (Any complex Hermitean tridiagonal matrix has real values on its diagonal |
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*> and potentially complex numbers on its off-diagonals. By applying a |
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*> similarity transform with an appropriate diagonal matrix |
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*> diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean |
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*> matrix can be transformed into a real symmetric matrix and complex |
|
*> arithmetic can be entirely avoided.) |
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*> |
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*> While the eigenvectors of the real symmetric tridiagonal matrix are real, |
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*> the eigenvectors of original complex Hermitean matrix have complex entries |
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*> in general. |
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*> Since LAPACK drivers overwrite the matrix data with the eigenvectors, |
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*> ZSTEMR accepts complex workspace to facilitate interoperability |
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*> with ZUNMTR or ZUPMTR. |
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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[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 COMPLEX*16 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 can be computed with a workspace |
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*> query by setting NZC = -1, see below. |
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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[in] NZC |
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*> \verbatim |
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*> NZC is INTEGER |
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*> The number of eigenvectors to be held in the array Z. |
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*> If RANGE = 'A', then NZC >= max(1,N). |
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*> If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU]. |
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*> If RANGE = 'I', then NZC >= IU-IL+1. |
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*> If NZC = -1, then a workspace query is assumed; the |
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*> routine calculates the number of columns of the array Z that |
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*> are needed to hold the eigenvectors. |
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*> This value is returned as the first entry of the Z array, and |
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*> no error message related to NZC is issued by XERBLA. |
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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[in,out] TRYRAC |
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*> \verbatim |
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*> TRYRAC is LOGICAL |
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*> If TRYRAC.EQ..TRUE., indicates that the code should check whether |
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*> the tridiagonal matrix defines its eigenvalues to high relative |
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*> accuracy. If so, the code uses relative-accuracy preserving |
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*> algorithms that might be (a bit) slower depending on the matrix. |
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*> If the matrix does not define its eigenvalues to high relative |
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*> accuracy, the code can uses possibly faster algorithms. |
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*> If TRYRAC.EQ..FALSE., the code is not required to guarantee |
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*> relatively accurate eigenvalues and can use the fastest possible |
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*> techniques. |
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*> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix |
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*> does not define its eigenvalues to high relative accuracy. |
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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 ZLARRV. |
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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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*> ZLARRV, 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 complex16OTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Beresford Parlett, University of California, Berkeley, USA \n |
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*> Jim Demmel, University of California, Berkeley, USA \n |
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*> Inderjit Dhillon, University of Texas, Austin, USA \n |
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*> Osni Marques, LBNL/NERSC, USA \n |
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*> Christof Voemel, University of California, Berkeley, USA \n |
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* |
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* ===================================================================== |
SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, |
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, |
$ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, |
$ IWORK, LIWORK, INFO ) |
$ IWORK, LIWORK, INFO ) |
IMPLICIT NONE |
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* |
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* -- LAPACK computational routine (version 3.2.1) -- |
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* |
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* -- April 2009 -- |
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* |
* |
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* -- 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..-- |
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* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, RANGE |
CHARACTER JOBZ, RANGE |
Line 22
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Line 346
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COMPLEX*16 Z( LDZ, * ) |
COMPLEX*16 Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZSTEMR 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. |
|
* |
|
* Depending on the number of desired eigenvalues, these are computed either |
|
* by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are |
|
* computed by the use of various suitable L D L^T factorizations near clusters |
|
* of close eigenvalues (referred to as RRRs, Relatively Robust |
|
* Representations). An informal sketch of the algorithm follows. |
|
* |
|
* For each unreduced block (submatrix) of T, |
|
* (a) Compute T - sigma I = L D L^T, so that L and D |
|
* define all the wanted eigenvalues to high relative accuracy. |
|
* This means that small relative changes in the entries of D and L |
|
* cause only small relative changes in the eigenvalues and |
|
* eigenvectors. The standard (unfactored) representation of the |
|
* tridiagonal matrix T does not have this property in general. |
|
* (b) Compute the eigenvalues to suitable accuracy. |
|
* If the eigenvectors are desired, the algorithm attains full |
|
* accuracy of the computed eigenvalues only right before |
|
* the corresponding vectors have to be computed, see steps c) and d). |
|
* (c) For each cluster of close eigenvalues, select a new |
|
* shift close to the cluster, find a new factorization, and refine |
|
* the shifted eigenvalues to suitable accuracy. |
|
* (d) For each eigenvalue with a large enough relative separation compute |
|
* the corresponding eigenvector by forming a rank revealing twisted |
|
* factorization. Go back to (c) for any clusters that remain. |
|
* |
|
* For more details, see: |
|
* - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations |
|
* to compute orthogonal eigenvectors of symmetric tridiagonal matrices," |
|
* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. |
|
* - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and |
|
* Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, |
|
* 2004. Also LAPACK Working Note 154. |
|
* - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric |
|
* tridiagonal eigenvalue/eigenvector problem", |
|
* Computer Science Division Technical Report No. UCB/CSD-97-971, |
|
* UC Berkeley, May 1997. |
|
* |
|
* Further Details |
|
* 1.ZSTEMR works only on machines which follow IEEE-754 |
|
* floating-point standard in their handling of infinities and NaNs. |
|
* This permits the use of efficient inner loops avoiding a check for |
|
* zero divisors. |
|
* |
|
* 2. LAPACK routines can be used to reduce a complex Hermitean matrix to |
|
* real symmetric tridiagonal form. |
|
* |
|
* (Any complex Hermitean tridiagonal matrix has real values on its diagonal |
|
* and potentially complex numbers on its off-diagonals. By applying a |
|
* similarity transform with an appropriate diagonal matrix |
|
* diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean |
|
* matrix can be transformed into a real symmetric matrix and complex |
|
* arithmetic can be entirely avoided.) |
|
* |
|
* While the eigenvectors of the real symmetric tridiagonal matrix are real, |
|
* the eigenvectors of original complex Hermitean matrix have complex entries |
|
* in general. |
|
* Since LAPACK drivers overwrite the matrix data with the eigenvectors, |
|
* ZSTEMR accepts complex workspace to facilitate interoperability |
|
* with ZUNMTR or ZUPMTR. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOBZ (input) CHARACTER*1 |
|
* = 'N': Compute eigenvalues only; |
|
* = 'V': Compute eigenvalues and eigenvectors. |
|
* |
|
* RANGE (input) CHARACTER*1 |
|
* = 'A': all eigenvalues will be found. |
|
* = 'V': all eigenvalues in the half-open interval (VL,VU] |
|
* will be found. |
|
* = 'I': the IL-th through IU-th eigenvalues will be found. |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrix. N >= 0. |
|
* |
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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 |
|
* T. On exit, D is overwritten. |
|
* |
|
* E (input/output) DOUBLE PRECISION array, dimension (N) |
|
* On entry, the (N-1) subdiagonal elements of the tridiagonal |
|
* matrix T in elements 1 to N-1 of E. E(N) need not be set on |
|
* input, but is used internally as workspace. |
|
* On exit, E is overwritten. |
|
* |
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* VL (input) DOUBLE PRECISION |
|
* VU (input) DOUBLE PRECISION |
|
* If RANGE='V', the lower and upper bounds of the interval to |
|
* be searched for eigenvalues. VL < VU. |
|
* Not referenced if RANGE = 'A' or 'I'. |
|
* |
|
* IL (input) INTEGER |
|
* IU (input) INTEGER |
|
* If RANGE='I', the indices (in ascending order) of the |
|
* smallest and largest eigenvalues to be returned. |
|
* 1 <= IL <= IU <= N, if N > 0. |
|
* Not referenced if RANGE = 'A' or 'V'. |
|
* |
|
* M (output) INTEGER |
|
* 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. |
|
* |
|
* W (output) DOUBLE PRECISION array, dimension (N) |
|
* The first M elements contain the selected eigenvalues in |
|
* ascending order. |
|
* |
|
* Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) ) |
|
* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z |
|
* contain the orthonormal eigenvectors of the matrix T |
|
* corresponding to the selected eigenvalues, with the i-th |
|
* column of Z holding the eigenvector associated with W(i). |
|
* If JOBZ = 'N', then Z is not referenced. |
|
* Note: the user must ensure that at least max(1,M) columns are |
|
* supplied in the array Z; if RANGE = 'V', the exact value of M |
|
* is not known in advance and can be computed with a workspace |
|
* query by setting NZC = -1, see below. |
|
* |
|
* LDZ (input) INTEGER |
|
* The leading dimension of the array Z. LDZ >= 1, and if |
|
* JOBZ = 'V', then LDZ >= max(1,N). |
|
* |
|
* NZC (input) INTEGER |
|
* The number of eigenvectors to be held in the array Z. |
|
* If RANGE = 'A', then NZC >= max(1,N). |
|
* If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU]. |
|
* If RANGE = 'I', then NZC >= IU-IL+1. |
|
* If NZC = -1, then a workspace query is assumed; the |
|
* routine calculates the number of columns of the array Z that |
|
* are needed to hold the eigenvectors. |
|
* This value is returned as the first entry of the Z array, and |
|
* no error message related to NZC is issued by XERBLA. |
|
* |
|
* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) ) |
|
* The support of the eigenvectors in Z, i.e., the indices |
|
* indicating the nonzero elements in Z. The i-th computed eigenvector |
|
* 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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* TRYRAC (input/output) LOGICAL |
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* If TRYRAC.EQ..TRUE., indicates that the code should check whether |
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* the tridiagonal matrix defines its eigenvalues to high relative |
|
* accuracy. If so, the code uses relative-accuracy preserving |
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* algorithms that might be (a bit) slower depending on the matrix. |
|
* If the matrix does not define its eigenvalues to high relative |
|
* accuracy, the code can uses possibly faster algorithms. |
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* If TRYRAC.EQ..FALSE., the code is not required to guarantee |
|
* relatively accurate eigenvalues and can use the fastest possible |
|
* techniques. |
|
* On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix |
|
* does not define its eigenvalues to high relative accuracy. |
|
* |
|
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) |
|
* On exit, if INFO = 0, WORK(1) returns the optimal |
|
* (and minimal) LWORK. |
|
* |
|
* LWORK (input) INTEGER |
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* The dimension of the array WORK. LWORK >= max(1,18*N) |
|
* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. |
|
* If LWORK = -1, then a workspace query is assumed; the routine |
|
* only calculates the optimal size of the WORK array, returns |
|
* this value as the first entry of the WORK array, and no error |
|
* message related to LWORK is issued by XERBLA. |
|
* |
|
* IWORK (workspace/output) INTEGER array, dimension (LIWORK) |
|
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
|
* |
|
* LIWORK (input) INTEGER |
|
* 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, |
|
* returns this value as the first entry of the IWORK array, and |
|
* no error message related to LIWORK is issued by XERBLA. |
|
* |
|
* INFO (output) INTEGER |
|
* On exit, INFO |
|
* = 0: successful exit |
|
* < 0: if INFO = -i, the i-th argument had an illegal value |
|
* > 0: if INFO = 1X, internal error in DLARRE, |
|
* if INFO = 2X, internal error in ZLARRV. |
|
* Here, the digit X = ABS( IINFO ) < 10, where IINFO is |
|
* the nonzero error code returned by DLARRE or |
|
* ZLARRV, respectively. |
|
* |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* Based on contributions by |
|
* Beresford Parlett, University of California, Berkeley, USA |
|
* Jim Demmel, University of California, Berkeley, USA |
|
* Inderjit Dhillon, University of Texas, Austin, USA |
|
* Osni Marques, LBNL/NERSC, USA |
|
* Christof Voemel, University of California, Berkeley, USA |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |