ZLAESY - compute the eigendecomposition of a 2-by-2 sym
metric matrix ( ( A, B );( B, C ) ) provided the norm of
the matrix of eigenvectors is larger than some threshold
value
SYNOPSIS
SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
COMPLEX*16 A, B, C, CS1, EVSCAL, RT1, RT2, SN1
PURPOSE
ZLAESY computes the eigendecomposition of a 2-by-2 symmet
ric 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*16
The ( 1, 1 ) element of input matrix.
B (input) COMPLEX*16
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*16
The ( 2, 2 ) element of input matrix.
RT1 (output) COMPLEX*16
The eigenvalue of larger modulus.
RT2 (output) COMPLEX*16
The eigenvalue of smaller modulus.
EVSCAL (output) COMPLEX*16
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*16
SN1 (output) COMPLEX*16 If EVSCAL .NE. 0, (
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