*> \brief \b CLAEV2 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 CLAEV2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * .. Scalar Arguments .. * REAL CS1, RT1, RT2 * COMPLEX A, B, C, SN1 * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix *> [ A B ] *> [ CONJG(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 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] *> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. *> \endverbatim * * Arguments: * ========== * *> \param[in] A *> \verbatim *> A is COMPLEX *> The (1,1) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX *> 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 COMPLEX *> The (2,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[out] RT1 *> \verbatim *> RT1 is REAL *> The eigenvalue of larger absolute value. *> \endverbatim *> *> \param[out] RT2 *> \verbatim *> RT2 is REAL *> The eigenvalue of smaller absolute value. *> \endverbatim *> *> \param[out] CS1 *> \verbatim *> CS1 is REAL *> \endverbatim *> *> \param[out] SN1 *> \verbatim *> SN1 is COMPLEX *> 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. * *> \ingroup complexOTHERauxiliary * *> \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 CLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL CS1, RT1, RT2 COMPLEX A, B, C, SN1 * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) REAL ONE PARAMETER ( ONE = 1.0E0 ) * .. * .. Local Scalars .. REAL T COMPLEX W * .. * .. External Subroutines .. EXTERNAL SLAEV2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, REAL * .. * .. Executable Statements .. * IF( ABS( B ).EQ.ZERO ) THEN W = ONE ELSE W = CONJG( B ) / ABS( B ) END IF CALL SLAEV2( REAL( A ), ABS( B ), REAL( C ), RT1, RT2, CS1, T ) SN1 = W*T RETURN * * End of CLAEV2 * END