DLAEV2 (3lapack)

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

SYNOPSIS

  SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

      DOUBLE         PRECISION A, B, C, CS1, RT1, RT2, SN1

PURPOSE

  DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
     [  A   B  ]
     [  B   C  ].  On return, RT1 is the eigenvalue of larger absolute value,
  RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit
  right eigenvector for RT1, giving the decomposition

     [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
     [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].

ARGUMENTS

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

  B       (input) DOUBLE PRECISION
          The (1,2) element and the conjugate of the (2,1) element of the 2-
          by-2 matrix.

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

  RT1     (output) DOUBLE PRECISION
          The eigenvalue of larger absolute value.

  RT2     (output) DOUBLE PRECISION
          The eigenvalue of smaller absolute value.

  CS1     (output) DOUBLE PRECISION
          SN1     (output) DOUBLE PRECISION The vector (CS1, SN1) is a unit
          right eigenvector for RT1.

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.

  CS1 and SN1 are accurate to a few ulps barring over/underflow.

  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.