version 1.3, 2011/07/22 07:38:07
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version 1.9, 2014/01/27 09:28:22
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SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN ) |
*> \brief \b DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. |
IMPLICIT NONE |
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* |
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* -- LAPACK routine (version 3.3.0) -- |
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* |
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* -- Contributed by Brian Sutton of the Randolph-Macon College -- |
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* -- November 2010 |
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* |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* |
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* .. Scalar Arguments .. |
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DOUBLE PRECISION CS, SIGMA, SN, X, Y |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
* |
* DLARTGS generates a plane rotation designed to introduce a bulge in |
* =========== DOCUMENTATION =========== |
* Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD |
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* problem. X and Y are the top-row entries, and SIGMA is the shift. |
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* The computed CS and SN define a plane rotation satisfying |
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* |
* |
* [ CS SN ] . [ X^2 - SIGMA ] = [ R ], |
* Online html documentation available at |
* [ -SN CS ] [ X * Y ] [ 0 ] |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the |
*> \htmlonly |
* rotation is by PI/2. |
*> Download DLARTGS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlartgs.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/dlartgs.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/dlartgs.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 DLARTGS( X, Y, SIGMA, CS, SN ) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION CS, SIGMA, SN, X, Y |
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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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*> DLARTGS generates a plane rotation designed to introduce a bulge in |
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*> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD |
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*> problem. X and Y are the top-row entries, and SIGMA is the shift. |
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*> The computed CS and SN define a plane rotation satisfying |
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*> |
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*> [ CS SN ] . [ X^2 - SIGMA ] = [ R ], |
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*> [ -SN CS ] [ X * Y ] [ 0 ] |
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*> |
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*> with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the |
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*> rotation is by PI/2. |
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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] X |
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*> \verbatim |
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*> X is DOUBLE PRECISION |
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*> The (1,1) entry of an upper bidiagonal matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] Y |
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*> \verbatim |
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*> Y is DOUBLE PRECISION |
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*> The (1,2) entry of an upper bidiagonal matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] SIGMA |
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*> \verbatim |
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*> SIGMA is DOUBLE PRECISION |
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*> The shift. |
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*> \endverbatim |
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*> |
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*> \param[out] CS |
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*> \verbatim |
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*> CS is DOUBLE PRECISION |
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*> The cosine of the rotation. |
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*> \endverbatim |
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*> |
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*> \param[out] SN |
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*> \verbatim |
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*> SN is DOUBLE PRECISION |
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*> The sine of the rotation. |
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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. |
* |
* |
* Arguments |
*> \date September 2012 |
* ========= |
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* |
* |
* X (input) DOUBLE PRECISION |
*> \ingroup auxOTHERcomputational |
* The (1,1) entry of an upper bidiagonal matrix. |
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* |
* |
* Y (input) DOUBLE PRECISION |
* ===================================================================== |
* The (1,2) entry of an upper bidiagonal matrix. |
SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN ) |
* |
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* SIGMA (input) DOUBLE PRECISION |
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* The shift. |
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* |
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* CS (output) DOUBLE PRECISION |
* -- LAPACK computational routine (version 3.4.2) -- |
* The cosine of the rotation. |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* September 2012 |
* |
* |
* SN (output) DOUBLE PRECISION |
* .. Scalar Arguments .. |
* The sine of the rotation. |
DOUBLE PRECISION CS, SIGMA, SN, X, Y |
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* .. |
* |
* |
* =================================================================== |
* =================================================================== |
* |
* |