version 1.6, 2010/08/13 21:03:58
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version 1.10, 2012/08/22 09:48:25
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*> \brief \b DSTEIN |
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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 DSTEIN + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstein.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/dstein.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/dstein.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 DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, |
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* IWORK, IFAIL, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDZ, M, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), |
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* $ IWORK( * ) |
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* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DSTEIN computes the eigenvectors of a real symmetric tridiagonal |
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*> matrix T corresponding to specified eigenvalues, using inverse |
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*> iteration. |
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*> |
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*> The maximum number of iterations allowed for each eigenvector is |
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*> specified by an internal parameter MAXITS (currently set to 5). |
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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] 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] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> The n diagonal elements of the tridiagonal matrix T. |
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*> \endverbatim |
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*> |
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*> \param[in] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) subdiagonal elements of the tridiagonal matrix |
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*> T, in elements 1 to N-1. |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of eigenvectors to be found. 0 <= M <= N. |
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*> \endverbatim |
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*> |
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*> \param[in] 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 of W contain the eigenvalues for |
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*> which eigenvectors are to be computed. The eigenvalues |
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*> should be grouped by split-off block and ordered from |
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*> smallest to largest within the block. ( The output array |
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*> W from DSTEBZ with ORDER = 'B' is expected here. ) |
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*> \endverbatim |
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*> |
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*> \param[in] IBLOCK |
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*> \verbatim |
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*> IBLOCK is INTEGER array, dimension (N) |
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*> The submatrix indices associated with the corresponding |
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*> eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to |
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*> the first submatrix from the top, =2 if W(i) belongs to |
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*> the second submatrix, etc. ( The output array IBLOCK |
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*> from DSTEBZ is expected here. ) |
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*> \endverbatim |
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*> |
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*> \param[in] ISPLIT |
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*> \verbatim |
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*> ISPLIT is INTEGER array, dimension (N) |
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*> The splitting points, at which T breaks up into submatrices. |
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*> The first submatrix consists of rows/columns 1 to |
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*> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 |
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*> through ISPLIT( 2 ), etc. |
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*> ( The output array ISPLIT from DSTEBZ is expected here. ) |
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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, M) |
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*> The computed eigenvectors. The eigenvector associated |
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*> with the eigenvalue W(i) is stored in the i-th column of |
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*> Z. Any vector which fails to converge is set to its current |
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*> iterate after MAXITS iterations. |
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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 >= 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 (5*N) |
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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 (N) |
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*> \endverbatim |
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*> |
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*> \param[out] IFAIL |
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*> \verbatim |
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*> IFAIL is INTEGER array, dimension (M) |
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*> On normal exit, all elements of IFAIL are zero. |
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*> If one or more eigenvectors fail to converge after |
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*> MAXITS iterations, then their indices are stored in |
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*> array IFAIL. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit. |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, then i eigenvectors failed to converge |
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*> in MAXITS iterations. Their indices are stored in |
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*> array IFAIL. |
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*> \endverbatim |
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* |
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*> \par Internal Parameters: |
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* ========================= |
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*> |
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*> \verbatim |
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*> MAXITS INTEGER, default = 5 |
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*> The maximum number of iterations performed. |
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*> |
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*> EXTRA INTEGER, default = 2 |
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*> The number of iterations performed after norm growth |
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*> criterion is satisfied, should be at least 1. |
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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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* ===================================================================== |
SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, |
SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, |
$ IWORK, IFAIL, INFO ) |
$ IWORK, IFAIL, 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 .. |
INTEGER INFO, LDZ, M, N |
INTEGER INFO, LDZ, M, N |
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DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) |
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
|
* DSTEIN computes the eigenvectors of a real symmetric tridiagonal |
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* matrix T corresponding to specified eigenvalues, using inverse |
|
* iteration. |
|
* |
|
* The maximum number of iterations allowed for each eigenvector is |
|
* specified by an internal parameter MAXITS (currently set to 5). |
|
* |
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* Arguments |
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* ========= |
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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) DOUBLE PRECISION array, dimension (N) |
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* The n diagonal elements of the tridiagonal matrix T. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) subdiagonal elements of the tridiagonal matrix |
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* T, in elements 1 to N-1. |
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* |
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* M (input) INTEGER |
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* The number of eigenvectors to be found. 0 <= M <= N. |
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* |
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* W (input) DOUBLE PRECISION array, dimension (N) |
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* The first M elements of W contain the eigenvalues for |
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* which eigenvectors are to be computed. The eigenvalues |
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* should be grouped by split-off block and ordered from |
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* smallest to largest within the block. ( The output array |
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* W from DSTEBZ with ORDER = 'B' is expected here. ) |
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* |
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* IBLOCK (input) INTEGER array, dimension (N) |
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* The submatrix indices associated with the corresponding |
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* eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to |
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* the first submatrix from the top, =2 if W(i) belongs to |
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* the second submatrix, etc. ( The output array IBLOCK |
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* from DSTEBZ is expected here. ) |
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* |
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* ISPLIT (input) INTEGER array, dimension (N) |
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* The splitting points, at which T breaks up into submatrices. |
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* The first submatrix consists of rows/columns 1 to |
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* ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 |
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* through ISPLIT( 2 ), etc. |
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* ( The output array ISPLIT from DSTEBZ is expected here. ) |
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* |
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* Z (output) DOUBLE PRECISION array, dimension (LDZ, M) |
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* The computed eigenvectors. The eigenvector associated |
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* with the eigenvalue W(i) is stored in the i-th column of |
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* Z. Any vector which fails to converge is set to its current |
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* iterate after MAXITS iterations. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= max(1,N). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (5*N) |
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* |
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* IWORK (workspace) INTEGER array, dimension (N) |
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* |
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* IFAIL (output) INTEGER array, dimension (M) |
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* On normal exit, all elements of IFAIL are zero. |
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* If one or more eigenvectors fail to converge after |
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* MAXITS iterations, then their indices are stored in |
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* array IFAIL. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit. |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i, then i eigenvectors failed to converge |
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* in MAXITS iterations. Their indices are stored in |
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* array IFAIL. |
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* |
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* Internal Parameters |
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* =================== |
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* |
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* MAXITS INTEGER, default = 5 |
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* The maximum number of iterations performed. |
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* |
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* EXTRA INTEGER, default = 2 |
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* The number of iterations performed after norm growth |
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* criterion is satisfied, should be at least 1. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |