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SUBROUTINE <a name="CLAEV2.1"></a><a href="claev2.f.html#CLAEV2.1">CLAEV2</a>( A, B, C, RT1, RT2, CS1, SN1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> REAL CS1, RT1, RT2
COMPLEX A, B, C, SN1
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLAEV2.15"></a><a href="claev2.f.html#CLAEV2.1">CLAEV2</a> computes the eigendecomposition of a 2-by-2 Hermitian matrix
</span><span class="comment">*</span><span class="comment"> [ A B ]
</span><span class="comment">*</span><span class="comment"> [ CONJG(B) C ].
</span><span class="comment">*</span><span class="comment"> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
</span><span class="comment">*</span><span class="comment"> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
</span><span class="comment">*</span><span class="comment"> eigenvector for RT1, giving the decomposition
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
</span><span class="comment">*</span><span class="comment"> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input) COMPLEX
</span><span class="comment">*</span><span class="comment"> The (1,1) element of the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) COMPLEX
</span><span class="comment">*</span><span class="comment"> The (1,2) element and the conjugate of the (2,1) element of
</span><span class="comment">*</span><span class="comment"> the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input) COMPLEX
</span><span class="comment">*</span><span class="comment"> The (2,2) element of the 2-by-2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RT1 (output) REAL
</span><span class="comment">*</span><span class="comment"> The eigenvalue of larger absolute value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RT2 (output) REAL
</span><span class="comment">*</span><span class="comment"> The eigenvalue of smaller absolute value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CS1 (output) REAL
</span><span class="comment">*</span><span class="comment"> SN1 (output) COMPLEX
</span><span class="comment">*</span><span class="comment"> The vector (CS1, SN1) is a unit right eigenvector for RT1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RT1 is accurate to a few ulps barring over/underflow.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RT2 may be inaccurate if there is massive cancellation in the
</span><span class="comment">*</span><span class="comment"> determinant A*C-B*B; higher precision or correctly rounded or
</span><span class="comment">*</span><span class="comment"> correctly truncated arithmetic would be needed to compute RT2
</span><span class="comment">*</span><span class="comment"> accurately in all cases.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> CS1 and SN1 are accurate to a few ulps barring over/underflow.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Overflow is possible only if RT1 is within a factor of 5 of overflow.
</span><span class="comment">*</span><span class="comment"> Underflow is harmless if the input data is 0 or exceeds
</span><span class="comment">*</span><span class="comment"> underflow_threshold / macheps.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO
PARAMETER ( ZERO = 0.0E0 )
REAL ONE
PARAMETER ( ONE = 1.0E0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> REAL T
COMPLEX W
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLAEV2.77"></a><a href="slaev2.f.html#SLAEV2.1">SLAEV2</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, CONJG, REAL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> IF( ABS( B ).EQ.ZERO ) THEN
W = ONE
ELSE
W = CONJG( B ) / ABS( B )
END IF
CALL <a name="SLAEV2.89"></a><a href="slaev2.f.html#SLAEV2.1">SLAEV2</a>( REAL( A ), ABS( B ), REAL( C ), RT1, RT2, CS1, T )
SN1 = W*T
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="CLAEV2.93"></a><a href="claev2.f.html#CLAEV2.1">CLAEV2</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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