--- rpl/lapack/lapack/dlas2.f 2010/12/21 13:53:32 1.7 +++ rpl/lapack/lapack/dlas2.f 2018/05/29 07:18:00 1.17 @@ -1,60 +1,121 @@ +*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAS2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION F, G, H, SSMAX, SSMIN +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAS2 computes the singular values of the 2-by-2 matrix +*> [ F G ] +*> [ 0 H ]. +*> On return, SSMIN is the smaller singular value and SSMAX is the +*> larger singular value. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] F +*> \verbatim +*> F is DOUBLE PRECISION +*> The (1,1) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] G +*> \verbatim +*> G is DOUBLE PRECISION +*> The (1,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] H +*> \verbatim +*> H is DOUBLE PRECISION +*> The (2,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[out] SSMIN +*> \verbatim +*> SSMIN is DOUBLE PRECISION +*> The smaller singular value. +*> \endverbatim +*> +*> \param[out] SSMAX +*> \verbatim +*> SSMAX is DOUBLE PRECISION +*> The larger singular value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date December 2016 +* +*> \ingroup OTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Barring over/underflow, all output quantities are correct to within +*> a few units in the last place (ulps), even in the absence of a guard +*> digit in addition/subtraction. +*> +*> In IEEE arithmetic, the code works correctly if one matrix element is +*> infinite. +*> +*> Overflow will not occur unless the largest singular value itself +*> overflows, or is within a few ulps of overflow. (On machines with +*> partial overflow, like the Cray, overflow may occur if the largest +*> singular value is within a factor of 2 of overflow.) +*> +*> Underflow is harmless if underflow is gradual. Otherwise, results +*> may correspond to a matrix modified by perturbations of size near +*> the underflow threshold. +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION F, G, H, SSMAX, SSMIN * .. * -* Purpose -* ======= -* -* DLAS2 computes the singular values of the 2-by-2 matrix -* [ F G ] -* [ 0 H ]. -* On return, SSMIN is the smaller singular value and SSMAX is the -* larger singular value. -* -* Arguments -* ========= -* -* F (input) DOUBLE PRECISION -* The (1,1) element of the 2-by-2 matrix. -* -* G (input) DOUBLE PRECISION -* The (1,2) element of the 2-by-2 matrix. -* -* H (input) DOUBLE PRECISION -* The (2,2) element of the 2-by-2 matrix. -* -* SSMIN (output) DOUBLE PRECISION -* The smaller singular value. -* -* SSMAX (output) DOUBLE PRECISION -* The larger singular value. -* -* Further Details -* =============== -* -* Barring over/underflow, all output quantities are correct to within -* a few units in the last place (ulps), even in the absence of a guard -* digit in addition/subtraction. -* -* In IEEE arithmetic, the code works correctly if one matrix element is -* infinite. -* -* Overflow will not occur unless the largest singular value itself -* overflows, or is within a few ulps of overflow. (On machines with -* partial overflow, like the Cray, overflow may occur if the largest -* singular value is within a factor of 2 of overflow.) -* -* Underflow is harmless if underflow is gradual. Otherwise, results -* may correspond to a matrix modified by perturbations of size near -* the underflow threshold. -* * ==================================================================== * * .. Parameters ..