ufl team mailing list archive

[Martin Sandve Alnæs <martinal@xxxxxxxxx>]

On Mon, Feb 23, 2009 at 5:42 PM, Anders Logg <logg@xxxxxxxxx> wrote:
> - Show quoted text -
> On Mon, Feb 23, 2009 at 12:59:33PM +0100, Martin Sandve Alnæs wrote:
>> On Mon, Feb 23, 2009 at 12:37 PM, Kristian Oelgaard
>> <k.b.oelgaard@xxxxxxxxxx> wrote:
>> > 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.
>>
>> I think you've got it right, but just to be sure: It's a bit more
>> general than this.
>>
>> Indexed represents components of <any tensor-valued expression>,
>> which can also be for example a Sum of other tensor-valued expressions,
>> a ComponentTensor, or a ListTensor.
>>
>> ComponentTensor represents a tensor-valued expression
>> with components given by a scalar expression with free indices
>> that are "bound" to tensor axes.
>>
>> In a sense ComponentTensor and Indexed are opposite operations,
>> Indexed mapping from tensor valued to scalar valued with free indices,
>> and ComponentTensor mapping from scalar valued with free indices to
>> tensor valued.
>
> So why then are both needed in the current example? I would imagine
> Indexed applied to ComponentTensor would cancel out so that we can get
>
>  IndexSum
>  (
>  IndexSum
>  (
>    Product
>    (
>      Indexed
>        (
>        SpatialDerivative
>        (
>          BasisFunction(VectorElement('Lagrange',1, 2), -2)
>          MultiIndex((Index(16),))
>        )
>        MultiIndex((Index(17),))

It's generally a good idea to not modify
input expressions to any operators.
Doing so may have side effects in other
algorithms, and can be done at a later
stage anyway. This is also related to the
index renumbering I mentioned eariler
today, so I guess I'll get back to this later.

Martin