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version 1.13, 2014/01/27 09:28:22
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*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. |
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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 DLAS2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.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/dlas2.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/dlas2.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 DLAS2( F, G, H, SSMIN, SSMAX ) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION F, G, H, SSMAX, SSMIN |
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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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*> DLAS2 computes the singular values of the 2-by-2 matrix |
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*> [ F G ] |
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*> [ 0 H ]. |
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*> On return, SSMIN is the smaller singular value and SSMAX is the |
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*> larger singular value. |
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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] F |
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*> \verbatim |
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*> F is DOUBLE PRECISION |
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*> The (1,1) element of the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] G |
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*> \verbatim |
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*> G is DOUBLE PRECISION |
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*> The (1,2) element of the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] H |
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*> \verbatim |
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*> H is DOUBLE PRECISION |
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*> The (2,2) element of the 2-by-2 matrix. |
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*> \endverbatim |
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*> |
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*> \param[out] SSMIN |
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*> \verbatim |
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*> SSMIN is DOUBLE PRECISION |
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*> The smaller singular value. |
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*> \endverbatim |
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*> |
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*> \param[out] SSMAX |
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*> \verbatim |
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*> SSMAX is DOUBLE PRECISION |
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*> The larger singular value. |
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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 Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Barring over/underflow, all output quantities are correct to within |
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*> a few units in the last place (ulps), even in the absence of a guard |
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*> digit in addition/subtraction. |
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*> |
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*> In IEEE arithmetic, the code works correctly if one matrix element is |
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*> infinite. |
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*> |
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*> Overflow will not occur unless the largest singular value itself |
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*> overflows, or is within a few ulps of overflow. (On machines with |
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*> partial overflow, like the Cray, overflow may occur if the largest |
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*> singular value is within a factor of 2 of overflow.) |
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*> |
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*> Underflow is harmless if underflow is gradual. Otherwise, results |
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*> may correspond to a matrix modified by perturbations of size near |
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*> the underflow threshold. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) |
SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) |
* |
* |
* -- 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 .. |
DOUBLE PRECISION F, G, H, SSMAX, SSMIN |
DOUBLE PRECISION F, G, H, SSMAX, SSMIN |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLAS2 computes the singular values of the 2-by-2 matrix |
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* [ F G ] |
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* [ 0 H ]. |
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* On return, SSMIN is the smaller singular value and SSMAX is the |
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* larger singular value. |
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* |
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* Arguments |
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* ========= |
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* |
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* F (input) DOUBLE PRECISION |
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* The (1,1) element of the 2-by-2 matrix. |
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* |
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* G (input) DOUBLE PRECISION |
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* The (1,2) element of the 2-by-2 matrix. |
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* |
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* H (input) DOUBLE PRECISION |
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* The (2,2) element of the 2-by-2 matrix. |
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* |
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* SSMIN (output) DOUBLE PRECISION |
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* The smaller singular value. |
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* |
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* SSMAX (output) DOUBLE PRECISION |
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* The larger singular value. |
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* |
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* Further Details |
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* =============== |
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* |
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* Barring over/underflow, all output quantities are correct to within |
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* a few units in the last place (ulps), even in the absence of a guard |
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* digit in addition/subtraction. |
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* |
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* In IEEE arithmetic, the code works correctly if one matrix element is |
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* infinite. |
|
* |
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* Overflow will not occur unless the largest singular value itself |
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* overflows, or is within a few ulps of overflow. (On machines with |
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* partial overflow, like the Cray, overflow may occur if the largest |
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* singular value is within a factor of 2 of overflow.) |
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* |
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* Underflow is harmless if underflow is gradual. Otherwise, results |
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* may correspond to a matrix modified by perturbations of size near |
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* the underflow threshold. |
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* |
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* ==================================================================== |
* ==================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |