slaev2()

subroutine slaev2	(	real	A,
		real	B,
		real	C,
		real	RT1,
		real	RT2,
		real	CS1,
		real	SN1
	)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

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Purpose:

 SLAEV2 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 ].

Parameters

[in]	A	A is REAL The (1,1) element of the 2-by-2 matrix.
[in]	B	B is REAL The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
[in]	C	C is REAL The (2,2) element of the 2-by-2 matrix.
[out]	RT1	RT1 is REAL The eigenvalue of larger absolute value.
[out]	RT2	RT2 is REAL The eigenvalue of smaller absolute value.
[out]	CS1	CS1 is REAL
[out]	SN1	SN1 is REAL 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.