SLAEV2 - compute the eigendecomposition of a 2-by-2 sym
metric matrix [ A B ] [ B C ]
SYNOPSIS
SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
REAL A, B, C, CS1, RT1, RT2, SN1
PURPOSE
SLAEV2 computes the eigendecomposition of a 2-by-2 symmet
ric matrix [ A B ] [ B C ]. On return, RT1 is the eigen
value 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 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
[-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
ARGUMENTS
A (input) REAL
The (1,1) element of the 2-by-2 matrix.
B (input) REAL
The (1,2) element and the conjugate of the (2,1)
element of the 2-by-2 matrix.
C (input) REAL
The (2,2) element of the 2-by-2 matrix.
RT1 (output) REAL
The eigenvalue of larger absolute value.
RT2 (output) REAL
The eigenvalue of smaller absolute value.
CS1 (output) REAL
SN1 (output) REAL 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.
Overflow is possible only if RT1 is within a factor of 5
of overflow. Underflow is harmless if the input data is 0
underflow_threshold / macheps.
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