version 1.3, 2010/08/06 15:28:43
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version 1.12, 2012/12/14 14:22:35
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*> \brief \b DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. |
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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 DLASD5 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd5.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/dlasd5.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/dlasd5.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 DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER I |
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* DOUBLE PRECISION DSIGMA, RHO |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) |
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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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*> This subroutine computes the square root of the I-th eigenvalue |
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*> of a positive symmetric rank-one modification of a 2-by-2 diagonal |
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*> matrix |
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*> |
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*> diag( D ) * diag( D ) + RHO * Z * transpose(Z) . |
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*> |
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*> The diagonal entries in the array D are assumed to satisfy |
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*> |
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*> 0 <= D(i) < D(j) for i < j . |
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*> |
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*> We also assume RHO > 0 and that the Euclidean norm of the vector |
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*> Z is one. |
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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] I |
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*> \verbatim |
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*> I is INTEGER |
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*> The index of the eigenvalue to be computed. I = 1 or I = 2. |
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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 ( 2 ) |
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*> The original eigenvalues. We assume 0 <= D(1) < D(2). |
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*> \endverbatim |
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*> |
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*> \param[in] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension ( 2 ) |
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*> The components of the updating vector. |
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*> \endverbatim |
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*> |
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*> \param[out] DELTA |
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*> \verbatim |
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*> DELTA is DOUBLE PRECISION array, dimension ( 2 ) |
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*> Contains (D(j) - sigma_I) in its j-th component. |
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*> The vector DELTA contains the information necessary |
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*> to construct the eigenvectors. |
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*> \endverbatim |
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*> |
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*> \param[in] RHO |
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*> \verbatim |
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*> RHO is DOUBLE PRECISION |
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*> The scalar in the symmetric updating formula. |
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*> \endverbatim |
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*> |
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*> \param[out] DSIGMA |
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*> \verbatim |
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*> DSIGMA is DOUBLE PRECISION |
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*> The computed sigma_I, the I-th updated eigenvalue. |
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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 ( 2 ) |
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*> WORK contains (D(j) + sigma_I) in its j-th component. |
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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 September 2012 |
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* |
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*> \ingroup auxOTHERauxiliary |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Ren-Cang Li, Computer Science Division, University of California |
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*> at Berkeley, USA |
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*> |
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* ===================================================================== |
SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) |
SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER I |
INTEGER I |
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DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) |
DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* This subroutine computes the square root of the I-th eigenvalue |
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* of a positive symmetric rank-one modification of a 2-by-2 diagonal |
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* matrix |
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* |
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* diag( D ) * diag( D ) + RHO * Z * transpose(Z) . |
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* |
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* The diagonal entries in the array D are assumed to satisfy |
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* |
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* 0 <= D(i) < D(j) for i < j . |
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* |
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* We also assume RHO > 0 and that the Euclidean norm of the vector |
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* Z is one. |
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* |
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* Arguments |
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* ========= |
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* |
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* I (input) INTEGER |
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* The index of the eigenvalue to be computed. I = 1 or I = 2. |
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* |
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* D (input) DOUBLE PRECISION array, dimension ( 2 ) |
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* The original eigenvalues. We assume 0 <= D(1) < D(2). |
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* |
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* Z (input) DOUBLE PRECISION array, dimension ( 2 ) |
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* The components of the updating vector. |
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* |
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* DELTA (output) DOUBLE PRECISION array, dimension ( 2 ) |
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* Contains (D(j) - sigma_I) in its j-th component. |
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* The vector DELTA contains the information necessary |
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* to construct the eigenvectors. |
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* |
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* RHO (input) DOUBLE PRECISION |
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* The scalar in the symmetric updating formula. |
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* |
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* DSIGMA (output) DOUBLE PRECISION |
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* The computed sigma_I, the I-th updated eigenvalue. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension ( 2 ) |
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* WORK contains (D(j) + sigma_I) in its j-th component. |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Ren-Cang Li, Computer Science Division, University of California |
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* at Berkeley, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |