zlaev2()

subroutine zlaev2	(	complex*16	A,
		complex*16	B,
		complex*16	C,
		double precision	RT1,
		double precision	RT2,
		double precision	CS1,
		complex*16	SN1
	)

ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Download ZLAEV2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 ZLAEV2 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 ].

Parameters

[in]	A	A is COMPLEX*16 The (1,1) element of the 2-by-2 matrix.
[in]	B	B is COMPLEX*16 The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
[in]	C	C is COMPLEX*16 The (2,2) element of the 2-by-2 matrix.
[out]	RT1	RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.
[out]	RT2	RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value.
[out]	CS1	CS1 is DOUBLE PRECISION
[out]	SN1	SN1 is COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.