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163 lines
4.3 KiB
163 lines
4.3 KiB
2 years ago
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*> \brief \b CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian 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 CLAEV2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claev2.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/claev2.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/claev2.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 CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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*
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* .. Scalar Arguments ..
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* REAL CS1, RT1, RT2
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* COMPLEX A, B, C, SN1
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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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*> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
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*> [ A B ]
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*> [ CONJG(B) C ].
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*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
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*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
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*> eigenvector for RT1, giving the decomposition
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*>
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*> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
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*> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
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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 COMPLEX
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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 COMPLEX
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*> The (1,2) element and the conjugate of the (2,1) element of
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*> 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 COMPLEX
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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 REAL
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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 REAL
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*> The eigenvalue of smaller absolute value.
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*> \endverbatim
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*>
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*> \param[out] CS1
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*> \verbatim
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*> CS1 is REAL
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*> \endverbatim
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*>
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*> \param[out] SN1
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*> \verbatim
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*> SN1 is COMPLEX
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*> The vector (CS1, SN1) is a unit right eigenvector for RT1.
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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 complexOTHERauxiliary
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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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*> CS1 and SN1 are accurate to a few ulps barring over/underflow.
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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 CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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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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REAL CS1, RT1, RT2
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COMPLEX A, B, C, SN1
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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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REAL ZERO
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PARAMETER ( ZERO = 0.0E0 )
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REAL ONE
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PARAMETER ( ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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REAL T
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COMPLEX W
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* ..
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* .. External Subroutines ..
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EXTERNAL SLAEV2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, CONJG, REAL
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* ..
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* .. Executable Statements ..
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*
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IF( ABS( B ).EQ.ZERO ) THEN
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W = ONE
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ELSE
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W = CONJG( B ) / ABS( B )
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END IF
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CALL SLAEV2( REAL( A ), ABS( B ), REAL( C ), RT1, RT2, CS1, T )
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SN1 = W*T
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RETURN
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*
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* End of CLAEV2
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*
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END
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