LAESY - 5.2 English - 68552

LAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

Purpose:

   LAESY 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 ]

Parameters:

• A – [in]

  A is COMPLEX

  The (1, 1) element of input matrix.

• B – [in]

  B is COMPLEX

  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 – [in]

  C is COMPLEX

  The (2, 2) element of input matrix.

• RT1 – [out]

  RT1 is COMPLEX

  The eigenvalue of larger modulus.

• RT2 – [out]

  RT2 is COMPLEX

  The eigenvalue of smaller modulus.

• EVSCAL – [out]

  EVSCAL is COMPLEX

  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 – [out] CS1 is COMPLEX

• SN1 – [out]

  SN1 is COMPLEX

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