Getting values from UFL operators

In short, I don't think that you can.

When you say you want "to get the value of the dot product", what do you expect to get? With f as a finite element function in a space V, dot(f, f) would be a function in some other space W. However, UFL is a language for working with forms, and so the "value" in the UFL sense is indeed Dot(...) and so on.

If you want to evaluate the function g = dot(f, f) at certain points, you can project this onto some other appropriately defined finite element space, and then evaluate the resulting function at those points.

Technically, UFL has functionality for computing the value of
expressions at a point x, but that requires the user to provide
code for computing the value of coefficients and their derivatives.
Thus you could achieve this by writing some ufl/dolfin integration
code. This is really cumbersome though.

It should be possible to make this more usable in the future,
though it will always be an expensive operation.

Martin

On 7 August 2011 15:21, Marie Rognes
<email address hidden> wrote:
> Question #166754 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/166754
>
>    Status: Open => Answered
>
> Marie Rognes proposed the following answer:
>
> In short, I don't think that you can.
>
> When you say you want "to get the value of the dot product", what do you
> expect to get?  With f as a finite element function in a space V, dot(f,
> f) would be a function in some other space W.  However, UFL is a
> language for working with forms, and so the "value" in the UFL sense is
> indeed Dot(...) and so on.
>
> If you want to evaluate the function g = dot(f, f) at certain points,
> you can project this onto some other appropriately defined finite
> element space, and then evaluate the resulting function at those points.
>
> --
> You received this question notification because you are a member of
> DOLFIN Team, which is an answer contact for DOLFIN.
>

Hi,

On Sun, Aug 7, 2011 at 3:21 PM, Marie Rognes
<email address hidden> wrote:
> Question #166754 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/166754
>
>    Status: Open => Answered
>
> Marie Rognes proposed the following answer:
>
> In short, I don't think that you can.
>
> When you say you want "to get the value of the dot product", what do you
> expect to get?  With f as a finite element function in a space V, dot(f,
> f) would be a function in some other space W.  However, UFL is a
> language for working with forms, and so the "value" in the UFL sense is
> indeed Dot(...) and so on.

I ran into a similar issue when trying to do a fairly complicated
postprocessing functional. I set up Expression() objects for various
vector quantities, then used dot() and cross() on that. This is before
involving any function spaces. At that point it would be nice to be
able to numerically evaluate the combination of Expression objects and
dot/cross operators to ascertain the correctness of the Expressions.
The expressions I implemented would not be exactly representable by
any standard FEM function space, which means you can't test their
exact correctness by first projecting onto a function space. I hope
this makes sense :)

This is related to my question here:
https://answers.launchpad.net/dolfin/+question/162499

Cheers
Neilen

With the latest dev versions of ufl and dolfin, you should be able to do this.

Runnable example:

from dolfin import *
mesh = UnitCube(20, 20, 20)
f = Expression(["sin(6.28*x[0])", "cos(6.28*x[1])", "0.0"])
g = Expression(["cos(6.28*x[0])", "-sin(6.28*x[1])", "0.0"])
plot(f, title='f', mesh=mesh)
plot(g, title='g', mesh=mesh)
plot(cross(f, g), title='f x g', mesh=mesh)
interactive()