ufl team mailing list archive

[Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>]

Quoting Martin Sandve Alnæs <martinal@xxxxxxxxx>:

> On Mon, Feb 23, 2009 at 11:44 AM, Kristian Oelgaard
> <k.b.oelgaard@xxxxxxxxxx> wrote:
> > Quoting Martin Sandve Alnæs <martinal@xxxxxxxxx>:
> >
> >> On Mon, Feb 23, 2009 at 11:23 AM, Kristian Oelgaard
> >> <k.b.oelgaard@xxxxxxxxxx> wrote:
> >> > Quoting Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>:
> >> >
> >> >> Quoting Anders Logg <logg@xxxxxxxxx>:
> >> >>
> >> >> > I thought about it some more and I think I might be able to generate
> >> >> > the indices on the fly as part of the monomial extraction so it
> might
> >> >> > not be necessary.
> >> >> >
> >> >> > So if it's not needed for quadrature it can be part of the monomial
> >> >> > extraction. Otherwise, it seems pretty simple to make a transformer
> >> >> > for index renumbering.
> >> >>
> >> >> I don't think index renumbering is needed for quadrature. A thing that
> is
> >> >> needed, however, is the component number of functions/basisfunctions
> but
> >> is
> >> >> this
> >> >> alway represented by index?
> >> >
> >> > Sorry, 'index' should be Indexed in the above.
> >> >
> >> > Kristian
> >>
> >> This question is too inaccurate for me to know what to say... But I'll
> try.
> >>
> >> A (basis) function never _has_ an index, but expressions
> >> may refer to a component of a function using Indexed.
> >> However, you can also have e.g. sums of Functions
> >> on vector elements, and Indexed outside that.
> >
> > Does this means that for
> >
> > a = V[0].dx(1)*dx
> >
> > one will have to return something like [V[0].dx(1), V[1].dx(1)] from
> > BasisFunction and then let Indexed pick the correct value? This looks very
> > inefficient and it makes it more complicated to know which variable names
> are
> > going to be used in the code.
> 
> I'm not sure, but if I understand you right, you're talking about using
> the transformer framework. As I've suggested before, state can be
> kept on a stack, updated by Indexed and SpatialDerivative, and
> then basis_function can simply return the current component (0)
> and derivative (1).

Yes, and I get all that. I just wanted to be sure that Indexed always referred
to components of basisfunctions. But I see now that Indexed is also used for the
components of ComponentTensor but in this case a second mapping of index values
is needed.

E.g.,

a = inner(grad(V), grad(U))*dx

IndexSum                         
(                                
  IndexSum                     
  (                            
    Product                  
    (                        
      Indexed              
      (                    
        ComponentTensor  
        (                
          Indexed      
          (            
            SpatialDerivative
            (                
              BasisFunction(VectorElement('Lagrange',1, 2), -2)
              MultiIndex((Index(16),))
            )
            MultiIndex((Index(17),))
          )
          MultiIndex((Index(16), Index(17)))
        )
        MultiIndex((Index(18), Index(19)))
      )
[snip]

Here the first Indexed will set the values of index18 and index19, which
ComponentTensor should use to map the values of index16 and index17 such that
BasisFunction can generate the correct component V[index17].dx(index16)

correct?
 
> But as I've said before, I intend to use linearized computational
> graphs as an intermediate step for quadrature code generation.
> I'm soon getting to updating the graph tools since differentiation
> seems to work ok now. (I plan to get back to improving differentiation
> later with better algorithms (reverse mode AD), but want to get
> something up and running first!)

OK, that's understandable.

Kristian
 
> > BTW index renumbering breaks for
> >
> > V[0]*V[1]*dx
> 
> Fixed. (not tested)
> 
> Martin
>