--- rpl/lapack/lapack/dlae2.f 2010/12/21 13:53:28 1.7 +++ rpl/lapack/lapack/dlae2.f 2011/11/21 20:42:54 1.8 @@ -1,55 +1,116 @@ +*> \brief \b DLAE2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAE2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, RT1, RT2 +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix +*> [ A B ] +*> [ B C ]. +*> On return, RT1 is the eigenvalue of larger absolute value, and RT2 +*> is the eigenvalue of smaller absolute value. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION +*> The (1,1) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION +*> The (1,2) and (2,1) elements of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> The (2,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[out] RT1 +*> \verbatim +*> RT1 is DOUBLE PRECISION +*> The eigenvalue of larger absolute value. +*> \endverbatim +*> +*> \param[out] RT2 +*> \verbatim +*> RT2 is DOUBLE PRECISION +*> The eigenvalue of smaller absolute value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> RT1 is accurate to a few ulps barring over/underflow. +*> +*> RT2 may be inaccurate if there is massive cancellation in the +*> determinant A*C-B*B; higher precision or correctly rounded or +*> correctly truncated arithmetic would be needed to compute RT2 +*> accurately in all cases. +*> +*> Overflow is possible only if RT1 is within a factor of 5 of overflow. +*> Underflow is harmless if the input data is 0 or exceeds +*> underflow_threshold / macheps. +*> \endverbatim +*> +* ===================================================================== SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, RT1, RT2 * .. * -* Purpose -* ======= -* -* DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix -* [ A B ] -* [ B C ]. -* On return, RT1 is the eigenvalue of larger absolute value, and RT2 -* is the eigenvalue of smaller absolute value. -* -* Arguments -* ========= -* -* A (input) DOUBLE PRECISION -* The (1,1) element of the 2-by-2 matrix. -* -* B (input) DOUBLE PRECISION -* The (1,2) and (2,1) elements of the 2-by-2 matrix. -* -* C (input) DOUBLE PRECISION -* The (2,2) element of the 2-by-2 matrix. -* -* RT1 (output) DOUBLE PRECISION -* The eigenvalue of larger absolute value. -* -* RT2 (output) DOUBLE PRECISION -* The eigenvalue of smaller absolute value. -* -* Further Details -* =============== -* -* RT1 is accurate to a few ulps barring over/underflow. -* -* RT2 may be inaccurate if there is massive cancellation in the -* determinant A*C-B*B; higher precision or correctly rounded or -* correctly truncated arithmetic would be needed to compute RT2 -* accurately in all cases. -* -* Overflow is possible only if RT1 is within a factor of 5 of overflow. -* Underflow is harmless if the input data is 0 or exceeds -* underflow_threshold / macheps. -* * ===================================================================== * * .. Parameters ..