zlaesy(3F)

NAME
     ZLAESY - compute 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 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 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*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,  ( CS1, SN1 ) is
             the unit right eigenvector for RT1.