SLAE2 (3lapack)

compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]

SYNOPSIS

  SUBROUTINE SLAE2( A, B, C, RT1, RT2 )

      REAL          A, B, C, RT1, RT2

PURPOSE

  SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
     [  A   B  ]
     [  B   C  ].  On return, RT1 is the eigenvalue of larger absolute value,
  and RT2 is the eigenvalue of smaller absolute value.

ARGUMENTS

  A       (input) REAL
          The (1,1) element of the 2-by-2 matrix.

  B       (input) REAL
          The (1,2) and (2,1) elements of the 2-by-2 matrix.

  C       (input) REAL
          The (2,2) element of the 2-by-2 matrix.

  RT1     (output) REAL
          The eigenvalue of larger absolute value.

  RT2     (output) REAL
          The eigenvalue of smaller absolute value.

FURTHER DETAILS

  RT1 is accurate to a few ulps barring over/underflow.

  RT2 may be inaccurate if there is massive cancellation in the determinant
  A*C-B*B; higher precision or correctly rounded or correctly truncated
  arithmetic would be needed to compute RT2 accurately in all cases.

  Overflow is possible only if RT1 is within a factor of 5 of overflow.
  Underflow is harmless if the input data is 0 or exceeds
     underflow_threshold / macheps.