CLAESY(3) computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value

## SYNOPSIS

SUBROUTINE CLAESY(
A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

COMPLEX A, B, C, CS1, EVSCAL, RT1, RT2, SN1

## PURPOSE

CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value. RT1 is the eigenvalue of larger absolute value, and RT2 of smaller absolute value. If the eigenvectors are computed, then on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ] [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]

## ARGUMENTS

A (input) COMPLEX
The ( 1, 1 ) element of input matrix.
B (input) COMPLEX
The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element is also given by B, since the 2-by-2 matrix is symmetric.
C (input) COMPLEX
The ( 2, 2 ) element of input matrix.
RT1 (output) COMPLEX
The eigenvalue of larger modulus.
RT2 (output) COMPLEX
The eigenvalue of smaller modulus.
EVSCAL (output) COMPLEX
The complex value by which the eigenvector matrix was scaled to make it orthonormal. If EVSCAL is zero, the eigenvectors were not computed. This means one of two things: the 2-by-2 matrix could not be diagonalized, or the norm of the matrix of eigenvectors before scaling was larger than the threshold value THRESH (set below).
CS1 (output) COMPLEX
SN1 (output) COMPLEX If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector for RT1.