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 ].

A

          A is REAL


          The (1,1) element of the 2-by-2 matrix.

B

          B is REAL


          The (1,2) element and the conjugate of the (2,1) element of


          the 2-by-2 matrix.

C

          C is REAL


          The (2,2) element of the 2-by-2 matrix.

RT1

          RT1 is REAL


          The eigenvalue of larger absolute value.

RT2

          RT2 is REAL


          The eigenvalue of smaller absolute value.

CS1

          CS1 is REAL

SN1

          SN1 is REAL


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  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.