claev2.f

          SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          REAL               CS1, RT1, RT2
          COMPLEX            A, B, C, SN1
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
    *     [  A         B  ]
    *     [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
    *  [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
    *
    *  Arguments
    *  =========
    *
    *  A      (input) COMPLEX
    *         The (1,1) element of the 2-by-2 matrix.
    *
    *  B      (input) COMPLEX
    *         The (1,2) element and the conjugate of the (2,1) element of
    *         the 2-by-2 matrix.
    *
    *  C      (input) COMPLEX
    *         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.
    *
    *  CS1    (output) REAL
    *  SN1    (output) COMPLEX
    *         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.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO
          PARAMETER          ( ZERO = 0.0E0 )
          REAL               ONE
          PARAMETER          ( ONE = 1.0E0 )
    *     ..
    *     .. Local Scalars ..
          REAL               T
          COMPLEX            W
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SLAEV2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, CONJG, REAL
    *     ..
    *     .. Executable Statements ..
    *
          IF( ABS( B ).EQ.ZERO ) THEN
             W = ONE
          ELSE
             W = CONJG( B ) / ABS( B )
          END IF
          CALL SLAEV2( REAL( A ), ABS( B ), REAL( C ), RT1, RT2, CS1, T )
          SN1 = W*T
          RETURN
    *
    *     End of CLAEV2
    *
          END