183 lines
4.6 KiB
Fortran
183 lines
4.6 KiB
Fortran
*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric 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 DLAE2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.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/dlae2.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/dlae2.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 DLAE2( A, B, C, RT1, RT2 )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION A, B, C, RT1, RT2
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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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*> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
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*> [ A B ]
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*> [ B C ].
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*> On return, RT1 is the eigenvalue of larger absolute value, and RT2
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*> is the eigenvalue of smaller absolute 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] A
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*> \verbatim
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*> A 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] B
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*> \verbatim
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*> B is DOUBLE PRECISION
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*> The (1,2) and (2,1) elements of the 2-by-2 matrix.
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C 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] RT1
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*> \verbatim
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*> RT1 is DOUBLE PRECISION
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*> The eigenvalue of larger absolute value.
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*> \endverbatim
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*>
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*> \param[out] RT2
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*> \verbatim
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*> RT2 is DOUBLE PRECISION
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*> The eigenvalue of smaller absolute 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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*> \ingroup OTHERauxiliary
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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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*> RT1 is accurate to a few ulps barring over/underflow.
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*>
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*> RT2 may be inaccurate if there is massive cancellation in the
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*> determinant A*C-B*B; higher precision or correctly rounded or
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*> correctly truncated arithmetic would be needed to compute RT2
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*> accurately in all cases.
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*>
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*> Overflow is possible only if RT1 is within a factor of 5 of overflow.
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*> Underflow is harmless if the input data is 0 or exceeds
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*> underflow_threshold / macheps.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION A, B, C, RT1, RT2
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D0 )
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DOUBLE PRECISION TWO
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PARAMETER ( TWO = 2.0D0 )
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D0 )
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DOUBLE PRECISION HALF
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PARAMETER ( HALF = 0.5D0 )
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Compute the eigenvalues
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*
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SM = A + C
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DF = A - C
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ADF = ABS( DF )
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TB = B + B
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AB = ABS( TB )
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IF( ABS( A ).GT.ABS( C ) ) THEN
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ACMX = A
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ACMN = C
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ELSE
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ACMX = C
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ACMN = A
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END IF
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IF( ADF.GT.AB ) THEN
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RT = ADF*SQRT( ONE+( AB / ADF )**2 )
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ELSE IF( ADF.LT.AB ) THEN
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RT = AB*SQRT( ONE+( ADF / AB )**2 )
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ELSE
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*
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* Includes case AB=ADF=0
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*
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RT = AB*SQRT( TWO )
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END IF
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IF( SM.LT.ZERO ) THEN
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RT1 = HALF*( SM-RT )
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*
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* Order of execution important.
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* To get fully accurate smaller eigenvalue,
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* next line needs to be executed in higher precision.
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*
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RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
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ELSE IF( SM.GT.ZERO ) THEN
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RT1 = HALF*( SM+RT )
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*
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* Order of execution important.
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* To get fully accurate smaller eigenvalue,
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* next line needs to be executed in higher precision.
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*
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RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
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ELSE
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*
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* Includes case RT1 = RT2 = 0
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*
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RT1 = HALF*RT
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RT2 = -HALF*RT
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END IF
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RETURN
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*
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* End of DLAE2
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*
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END
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