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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