\brief \b ESMF_DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. \htmlonly Download ESMF_DLAE2 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:
\verbatim
ESMF_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 \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 \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
RT1 is accurate to a few ulps barring over/underflow.
RT2 may be inaccurate if there is massive cancellation in the determinant AC-BB; 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
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| double precision | :: | A | ||||
| double precision | :: | B | ||||
| double precision | :: | C | ||||
| double precision | :: | RT1 | ||||
| double precision | :: | RT2 |