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SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1992
*
* .. Scalar Arguments ..
DOUBLE PRECISION CS1, RT1, RT2
COMPLEX*16 A, B, C, SN1
* ..
*
* Purpose
* =======
*
* ZLAEV2 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 ].
*
* Arguments
* =========
*
* A (input) COMPLEX*16
* The (1,1) element of the 2-by-2 matrix.
*
* B (input) COMPLEX*16
* The (1,2) element and the conjugate of the (2,1) element of
* the 2-by-2 matrix.
*
* C (input) COMPLEX*16
* The (2,2) element of the 2-by-2 matrix.
*
* RT1 (output) DOUBLE PRECISION
* The eigenvalue of larger absolute value.
*
* RT2 (output) DOUBLE PRECISION
* The eigenvalue of smaller absolute value.
*
* CS1 (output) DOUBLE PRECISION
* SN1 (output) COMPLEX*16
* The vector (CS1, SN1) is a unit right eigenvector for RT1.
*
* Further Details
* ===============
*
* 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.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION T
COMPLEX*16 W
* ..
* .. External Subroutines ..
EXTERNAL DLAEV2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCONJG
* ..
* .. Executable Statements ..
*
IF( ABS( B ).EQ.ZERO ) THEN
W = ONE
ELSE
W = DCONJG( B ) / ABS( B )
END IF
CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
SN1 = W*T
RETURN
*
* End of ZLAEV2
*
END
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