SRC/dlaev2.f(3)            Library Functions Manual            SRC/dlaev2.f(3)

NAME
       SRC/dlaev2.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlaev2 (a, b, c, rt1, rt2, cs1, sn1)
           DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2
           symmetric/Hermitian matrix.

Function/Subroutine Documentation
   subroutine dlaev2 (double precision a, double precision b, double precision
       c, double precision rt1, double precision rt2, double precision cs1,
       double precision sn1)
       DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2
       symmetric/Hermitian matrix.

       Purpose:


            DLAEV2 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
           A

                     A is DOUBLE PRECISION
                     The (1,1) element of the 2-by-2 matrix.

           B

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

           C

                     C is DOUBLE PRECISION
                     The (2,2) element of the 2-by-2 matrix.

           RT1

                     RT1 is DOUBLE PRECISION
                     The eigenvalue of larger absolute value.

           RT2

                     RT2 is DOUBLE PRECISION
                     The eigenvalue of smaller absolute value.

           CS1

                     CS1 is DOUBLE PRECISION

           SN1

                     SN1 is DOUBLE PRECISION
                     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.

       Definition at line 119 of file dlaev2.f.

Author
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LAPACK                          Version 3.12.0                 SRC/dlaev2.f(3)