ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermi
tian matrix [ A B ] [ CONJG(B) C ]
SYNOPSIS
SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
DOUBLE PRECISION CS1, RT1, RT2
COMPLEX*16 A, B, C, SN1
PURPOSE
ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermi
tian 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/under
flow.
of overflow. Underflow is harmless if the input data is 0
or exceeds
underflow_threshold / macheps.
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