CLAEV2(l) ) CLAEV2(l)NAME
CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [
A B ] [ CONJG(B) C ]
SYNOPSIS
SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
REAL CS1, RT1, RT2
COMPLEX A, B, C, SN1
PURPOSE
CLAEV2 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
The (1,1) element of the 2-by-2 matrix.
B (input) COMPLEX
The (1,2) element and the conjugate of the (2,1) element of the
2-by-2 matrix.
C (input) COMPLEX
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) COMPLEX 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 determi‐
nant A*C-B*B; higher precision or correctly rounded or correctly trun‐
cated 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.
LAPACK version 3.0 15 June 2000 CLAEV2(l)
