julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
97 lines
2.7 KiB
FortranFixed
97 lines
2.7 KiB
FortranFixed
SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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*
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* -- LAPACK auxiliary routine (version 3.2) --
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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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* November 2006
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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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* Purpose
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* =======
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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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*
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* Arguments
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* =========
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*
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* A (input) COMPLEX
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* The (1,1) element of the 2-by-2 matrix.
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*
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* B (input) 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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*
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* C (input) COMPLEX
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* The (2,2) element of the 2-by-2 matrix.
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*
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* RT1 (output) REAL
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* The eigenvalue of larger absolute value.
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*
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* RT2 (output) REAL
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* The eigenvalue of smaller absolute value.
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*
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* CS1 (output) REAL
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* SN1 (output) COMPLEX
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* The vector (CS1, SN1) is a unit right eigenvector for RT1.
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*
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* Further Details
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* ===============
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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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*
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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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