96 lines
2.7 KiB
FortranFixed
96 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 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley 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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