ufl team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Wed, Mar 04, 2009 at 08:15:53AM +0100, Martin Sandve Alnæs wrote:
> On Wed, Mar 4, 2009 at 12:31 AM, Kristian Oelgaard
> <k.b.oelgaard@xxxxxxxxxx> wrote:
> > Quoting 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.
> >
> > If I understood it correctly, it should be
> > 'general indices OF a ListTensor' ??
> >
> > Kristian
> 
> That's what I think he meant too. And if I understand this
> correctly, arbitrary limitations like that is not an option in UFL.
> Any tensor _valued_ expression can be indexed, and that's
> the way it should be. That's also the whole point of the ListTensor,
> to make subexpressions into a tensor valued expression.
> The alternative is an inconsistent language and special cases
> all over the place. The limitations of the tensor representation
> is one of the reasons I got into this in the first place :-P

Would it help to expand IndexSum into a sum of terms, adding more Sum
nodes to the tree, each one with a fixed index value? This should (at
least in some simple cases with limited nesting) result in Indexed
nodes with children that are ListTensor and FixedIndex, which would
make it possible to just pick out the correct item and remove
ListTensor from the tree.

-- 
Anders

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