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C DLAEV2    SOURCE    BP208322  18/07/10    21:15:07     9872           *> \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download DLAEV2 + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaev2.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaev2.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaev2.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )**       .. Scalar Arguments ..*       REAL*8   A, B, C, CS1, RT1, RT2, SN1*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix*>    [  A   B  ]*>    [  B   C  ].*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right*> eigenvector for RT1, giving the decomposition*>*>    [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]*>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].*> \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) element and the conjugate of the (2,1) element 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*>*> \param[out] CS1*> \verbatim*>          CS1 is DOUBLE PRECISION*> \endverbatim*>*> \param[out] SN1*> \verbatim*>          SN1 is DOUBLE PRECISION*>          The vector (CS1, SN1) is a unit right eigenvector for RT1.*> \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.*>*>  CS1 and SN1 are accurate to a few ulps barring over/underflow.*>*>  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 DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )**  -- 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, CS1, RT1, RT2, SN1*     ..** =====================================================================**     .. 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 ..      INTEGER            SGN1, SGN2      REAL*8   AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM,     \$                   TB, TN*     ..**     .. 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 )         SGN1 = -1**        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 )         SGN1 = 1**        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         SGN1 = 1      END IF**     Compute the eigenvector*      IF( DF.GE.ZERO ) THEN         CS = DF + RT         SGN2 = 1      ELSE         CS = DF - RT         SGN2 = -1      END IF      ACS = ABS( CS )      IF( ACS.GT.AB ) THEN         CT = -TB / CS         SN1 = ONE / SQRT( ONE+CT*CT )         CS1 = CT*SN1      ELSE         IF( AB.EQ.ZERO ) THEN            CS1 = ONE            SN1 = ZERO         ELSE            TN = -CS / TB            CS1 = ONE / SQRT( ONE+TN*TN )            SN1 = TN*CS1         END IF      END IF      IF( SGN1.EQ.SGN2 ) THEN         TN = CS1         CS1 = -SN1         SN1 = TN      END IF      RETURN**     End of DLAEV2*      END

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