| *> \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 |