zlaev2(3)

NAME

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 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 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 ac

curately 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 or ex

ceeds

underflow_threshold / macheps.

LAPACK version 3.0 15 June 2000

ZLAEV2(3)