ZLAESY (3lapack)

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.