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[Anders Logg <logg@xxxxxxxxx>]

On Tue, Mar 03, 2009 at 09:10:50PM +0100, Martin Sandve Alnæs wrote:
> On Tue, Mar 3, 2009 at 12:18 AM, Anders Logg <logg@xxxxxxxxx> wrote:
> > Is there a way to transform an expression to remove ListTensor from
> > the tree? I'm struggling with the monomial transformation.
> >
> > Take for example the following expression:
> >
> >  inner(as_tensor([v[0], v[1]]), as_tensor([u[0], u[0].dx(1)]))
> >
> > This might be rewritten as
> >
> >  a = v[0]*u[0] + v[1]*u[0].dx(1)
> >
> > This I can handle, but not the version containing ListTensor.
> 
> You have something similar in FFC, right?
> vec and mat or something?
> How do you handle those?
> 
> Martin

The corresponding thing in FFC is regular Python lists. For example,
here's the grad() operator:

def grad(v):
    "Return gradient of given function."
    # Get shape dimension
    d = __cell_dimension(v)
    # Check if we have a vector
    if value_rank(v) == 1:
        return [[D(v[i], j) for j in range(d)] for i in range(len(v))]
    # Otherwise assume we have a scalar
    return [D(v, i) for i in range(d)]

At some later point, the list will appear as an argument of a dot
product or it might be indexed (with a fixed index). The result of
both operations will remove the list and return a scalar expression.

So when a form has been defined correctly, the resulting expression is
always a scalar which does not contain any lists. What makes this
simpler in FFC might be that only fixed indices (ints) are allowed as
indices in a list, whereas UFL allows general indices to be used.

In particular, the following is not allowed in FFC:

  a = grad(v)[i]*grad(u)[i]*dx

One must write one of the following:

  a = dot(grad(v), grad(u))*dx
  a = v.dx(i)*u.dx(i)*dx

The important point here is that dot() will pick out the elements in
the list one by one and return something that is not a list.

I don't know if it would be a too severe restriction to disallow
general indices in a ListTensor.

-- 
Anders

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