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[Marie Rognes <meg@xxxxxxxxxxx>]

We would like to evaluate the degrees of freedom on a given function in 
ffc. In order to do that with relative easy, it would be very handy if 
we could extend the current information about the dual bases in FIAT.

We were thinking that if we could represent functionals in terms of 
three attributes, 'points', 'components' and 'weights', then it would be 
very easy to generate code for the evaluation of these in ffc.

Some examples for the motivation for the choice of representation

   Example 1: L = Point evaluation at component k:

      weights = [1]
      components = [k]
      points = [p_0]

   Then given a function f, we want

      L(f) = 1*f[k](p_0)

   Example 2: L = Normal component at diagonal edge:

      weights = [1, 1]
      components = [0, 1]
      points  = [p]

   Then

      L(f) = [1, 1]*(f[0](p), f[1](p)) = 1*f[0](p) + 1*f[1](p)

   Example 3: L = Integral over interior of component k:

      weights, points = make_quadrature(...)
      components = [k]

      L(f) = [w_0, ... w_m] (f[k](p_0), .... ,f[k](p_m))
           = sum_j w_j f[k](p_j)


Maybe the finite elements/dual bases in FIAT could supply this 
information in addition to the 'entity_ids'?

I was thinking something along the lines of letting the Functional class 
have the additional attributes, and initializing these when constructing 
the dual bases.

If there are some attributes that don't apply (such as weights and 
component for scalar Lagrange elements), these could of course be left 
empty.

How does this sound?

--
Marie E. Rognes
Ph.D Fellow, 
Centre of Mathematics for Applications, 
University of Oslo
http://folk.uio.no/meg