ZLAESY(3)      LAPACK routine of NEC Numeric Library Collection      ZLAESY(3)



NAME
       ZLAESY

SYNOPSIS
       SUBROUTINE ZLAESY (A, B, C, RT1, RT2, EVSCAL, CS1, 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)
                     A is COMPLEX*16
                     The ( 1, 1 ) element of input matrix.

           B         (input)
                     B is 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)
                     C is COMPLEX*16
                     The ( 2, 2 ) element of input matrix.

           RT1       (output)
                     RT1 is COMPLEX*16
                     The eigenvalue of larger modulus.

           RT2       (output)
                     RT2 is COMPLEX*16
                     The eigenvalue of smaller modulus.

           EVSCAL    (output)
                     EVSCAL is 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)
                     CS1 is COMPLEX*16

           SN1       (output)
                     SN1 is COMPLEX*16
                     If EVSCAL .NE. 0,  ( CS1, SN1 ) is the unit right eigenvector
                     for RT1.



LAPACK routine                  31 October 2017                      ZLAESY(3)