+++ /dev/null
-*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
-*
-* =========== DOCUMENTATION ===========
-*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
-*
-*> \htmlonly
-*> Download DLAE2 + dependencies
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.f">
-*> [TGZ]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlae2.f">
-*> [ZIP]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlae2.f">
-*> [TXT]</a>
-*> \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 September 2012
-*
-*> \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 3.4.2) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
-*
-* .. Scalar Arguments ..
- DOUBLE PRECISION A, B, C, RT1, RT2
-* ..
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE
- PARAMETER ( ONE = 1.0D0 )
- DOUBLE PRECISION TWO
- PARAMETER ( TWO = 2.0D0 )
- DOUBLE PRECISION ZERO
- PARAMETER ( ZERO = 0.0D0 )
- DOUBLE PRECISION HALF
- PARAMETER ( HALF = 0.5D0 )
-* ..
-* .. Local Scalars ..
- DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, SQRT
-* ..
-* .. Executable Statements ..
-*
-* Compute the eigenvalues
-*
- SM = A + C
- DF = A - C
- ADF = ABS( DF )
- TB = B + B
- AB = ABS( TB )
- IF( ABS( A ).GT.ABS( C ) ) THEN
- ACMX = A
- ACMN = C
- ELSE
- ACMX = C
- ACMN = A
- END IF
- IF( ADF.GT.AB ) THEN
- RT = ADF*SQRT( ONE+( AB / ADF )**2 )
- ELSE IF( ADF.LT.AB ) THEN
- RT = AB*SQRT( ONE+( ADF / AB )**2 )
- ELSE
-*
-* Includes case AB=ADF=0
-*
- RT = AB*SQRT( TWO )
- END IF
- IF( SM.LT.ZERO ) THEN
- RT1 = HALF*( SM-RT )
-*
-* Order of execution important.
-* To get fully accurate smaller eigenvalue,
-* next line needs to be executed in higher precision.
-*
- RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
- ELSE IF( SM.GT.ZERO ) THEN
- RT1 = HALF*( SM+RT )
-*
-* Order of execution important.
-* To get fully accurate smaller eigenvalue,
-* next line needs to be executed in higher precision.
-*
- RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
- ELSE
-*
-* Includes case RT1 = RT2 = 0
-*
- RT1 = HALF*RT
- RT2 = -HALF*RT
- END IF
- RETURN
-*
-* End of DLAE2
-*
- END