version 1.11, 2011/11/21 22:19:34
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version 1.24, 2023/08/07 08:38:58
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*> \brief \b DLARRV |
*> \brief \b DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download DLARRV + dependencies |
*> Download DLARRV + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrv.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrv.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrv.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrv.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrv.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrv.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
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* RTOL1, RTOL2, W, WERR, WGAP, |
* RTOL1, RTOL2, W, WERR, WGAP, |
* IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, |
* IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, |
* WORK, IWORK, INFO ) |
* WORK, IWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER DOL, DOU, INFO, LDZ, M, N |
* INTEGER DOL, DOU, INFO, LDZ, M, N |
* DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU |
* DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU |
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* $ WGAP( * ), WORK( * ) |
* $ WGAP( * ), WORK( * ) |
* DOUBLE PRECISION Z( LDZ, * ) |
* DOUBLE PRECISION Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> \param[in] VL |
*> \param[in] VL |
*> \verbatim |
*> \verbatim |
*> VL is DOUBLE PRECISION |
*> VL is DOUBLE PRECISION |
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*> Lower bound of the interval that contains the desired |
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*> eigenvalues. VL < VU. Needed to compute gaps on the left or right |
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*> end of the extremal eigenvalues in the desired RANGE. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] VU |
*> \param[in] VU |
*> \verbatim |
*> \verbatim |
*> VU is DOUBLE PRECISION |
*> VU is DOUBLE PRECISION |
*> Lower and upper bounds of the interval that contains the desired |
*> Upper bound of the interval that contains the desired |
*> eigenvalues. VL < VU. Needed to compute gaps on the left or right |
*> eigenvalues. VL < VU. |
*> end of the extremal eigenvalues in the desired RANGE. |
*> Note: VU is currently not used by this implementation of DLARRV, VU is |
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*> passed to DLARRV because it could be used compute gaps on the right end |
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*> of the extremal eigenvalues. However, with not much initial accuracy in |
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*> LAMBDA and VU, the formula can lead to an overestimation of the right gap |
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*> and thus to inadequately early RQI 'convergence'. This is currently |
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*> prevented this by forcing a small right gap. And so it turns out that VU |
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*> is currently not used by this implementation of DLARRV. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] D |
*> \param[in,out] D |
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*> L is DOUBLE PRECISION array, dimension (N) |
*> L is DOUBLE PRECISION array, dimension (N) |
*> On entry, the (N-1) subdiagonal elements of the unit |
*> On entry, the (N-1) subdiagonal elements of the unit |
*> bidiagonal matrix L are in elements 1 to N-1 of L |
*> bidiagonal matrix L are in elements 1 to N-1 of L |
*> (if the matrix is not splitted.) At the end of each block |
*> (if the matrix is not split.) At the end of each block |
*> is stored the corresponding shift as given by DLARRE. |
*> is stored the corresponding shift as given by DLARRE. |
*> On exit, L is overwritten. |
*> On exit, L is overwritten. |
*> \endverbatim |
*> \endverbatim |
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*> RTOL2 is DOUBLE PRECISION |
*> RTOL2 is DOUBLE PRECISION |
*> Parameters for bisection. |
*> Parameters for bisection. |
*> An interval [LEFT,RIGHT] has converged if |
*> An interval [LEFT,RIGHT] has converged if |
*> RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) |
*> RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] W |
*> \param[in,out] W |
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*> INFO is INTEGER |
*> INFO is INTEGER |
*> = 0: successful exit |
*> = 0: successful exit |
*> |
*> |
*> > 0: A problem occured in DLARRV. |
*> > 0: A problem occurred in DLARRV. |
*> < 0: One of the called subroutines signaled an internal problem. |
*> < 0: One of the called subroutines signaled an internal problem. |
*> Needs inspection of the corresponding parameter IINFO |
*> Needs inspection of the corresponding parameter IINFO |
*> for further information. |
*> for further information. |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
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*> \date November 2011 |
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* |
* |
*> \ingroup doubleOTHERauxiliary |
*> \ingroup doubleOTHERauxiliary |
* |
* |
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$ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, |
$ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, |
$ WORK, IWORK, INFO ) |
$ WORK, IWORK, INFO ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK auxiliary routine -- |
* -- 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 2011 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER DOL, DOU, INFO, LDZ, M, N |
INTEGER DOL, DOU, INFO, LDZ, M, N |
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* .. Executable Statements .. |
* .. Executable Statements .. |
* .. |
* .. |
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INFO = 0 |
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* |
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* Quick return if possible |
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* |
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IF( (N.LE.0).OR.(M.LE.0) ) THEN |
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RETURN |
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END IF |
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* |
* The first N entries of WORK are reserved for the eigenvalues |
* The first N entries of WORK are reserved for the eigenvalues |
INDLD = N+1 |
INDLD = N+1 |
INDLLD= 2*N+1 |
INDLLD= 2*N+1 |