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dlae2
C DLAE2     SOURCE    BP208322  18/07/10    21:15:06     9872           *> \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*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlae2.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlae2.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DLAE2( A, B, C, RT1, RT2 )**       .. Scalar Arguments ..*       REAL*8   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 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 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 3.7.0) --*  -- LAPACK is a software package provided by Univ. of Tennessee,    --*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--*     December 2016**     .. Scalar Arguments ..      REAL*8   A, B, C, RT1, RT2*     ..** =====================================================================**     .. Parameters ..      REAL*8   ONE      PARAMETER          ( ONE = 1.0D0 )      REAL*8   TWO      PARAMETER          ( TWO = 2.0D0 )      REAL*8   ZERO      PARAMETER          ( ZERO = 0.0D0 )      REAL*8   HALF      PARAMETER          ( HALF = 0.5D0 )*     ..*     .. Local Scalars ..      REAL*8   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   

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