SLAEV2(3)      LAPACK routine of NEC Numeric Library Collection      SLAEV2(3)



NAME
       SLAEV2

SYNOPSIS
       SUBROUTINE SLAEV2 (A, B, C, RT1, RT2, CS1, SN1)



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 ].




ARGUMENTS
           A         (input)
                     A is REAL
                     The (1,1) element of the 2-by-2 matrix.

           B         (input)
                     B is REAL
                     The (1,2) element and the conjugate of the (2,1) element of
                     the 2-by-2 matrix.

           C         (input)
                     C is REAL
                     The (2,2) element of the 2-by-2 matrix.

           RT1       (output)
                     RT1 is REAL
                     The eigenvalue of larger absolute value.

           RT2       (output)
                     RT2 is REAL
                     The eigenvalue of smaller absolute value.

           CS1       (output)
                     CS1 is REAL

           SN1       (output)
                     SN1 is REAL
                     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.



LAPACK routine                  31 October 2017                      SLAEV2(3)