CXML
        	    
LAPACK version 3.0
claev2(3)

PURPOSE
  CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B
  ] [ CONJG(B) C ]

SYNTAX
  SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

      REAL	     CS1, RT1, RT2

      COMPLEX	     A, B, C, SN1

DESCRIPTION
  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.