[Dune] Question regarding the size() function of functionspacebases in dune-functions

[Carsten Gräser]

Hello,

Am 17.10.18 um 16:34 schrieb Felix Mueller:
> /basis.size()/ returns 8 as is expected (since each basis includes one
> Q1 element with 4 DoFs).
> 
> Intuitively I would assume /basis.size({0})/ would return 4, yet it
> returns 0.
there's a misconception on what basis.size(prefix) is doing.
In principle dune-functions supports multi-indices that
need not to be consistent with the product space structure.
The basis.size(prefix) method exists for exploring the
set of not necessarily flat multi-indices.

For M=basis.size(prefix) the number M is the maximal one,
such that there's a multi-index (prefix,M-1,...). If you
consider the multi-indices as leaves in a tree, then any
prefix addresses a node in this tree and M is the number
of direct children of this node. For more details have a
look at the manual: https://arxiv.org/abs/1806.09545

Since you selected plain indices {(0),(1), ..., (7)}
the prefix (0) addresses a leave and the number of children
is 0. Currently there's no method returning the number of basis
functions in a subspace basis, since there's hardly any practical
use for this. Notice that the indices of a subspacebasis
are still the same as for the whole basis such that you
can use them to access a full vector. By using flat interleaved
indices, the indices of the subspaceBasis(basis,0) would be
{0, 2, 4, 6} while the ones for subspaceBasis(basis,1) would
be {1, 3, 5, 7}.

Best,
Carsten



> 
> The problem also occurs when using a composite basis.
> 
> I am using *dune-functions*, *dune-common* and *dune-grid v2.6.0*. My
> test is included below and was compiled with *g++7.2.0* using a new
> module generated with *duneproject*.
> 
> _Is this the proper behaviour or did I encounter a bug?
> 
> If this is indeed correct _behaviour_, what function yields the result I
> am looking for?_
> 
> 
> Thanks for your help and have a good day,
> 
> Felix Müller
> 
> 
> /#include <dune/common/filledarray.hh>
> #include <dune/grid/yaspgrid.hh>
> #include <dune/functions/functionspacebases/compositebasis.hh>
> #include <dune/functions/functionspacebases/powerbasis.hh>
> #include <dune/functions/functionspacebases/lagrangebasis.hh>
> 
> using namespace Dune::Functions::BasisFactory;
> 
> int main()
> {
>   // create grid
>   Dune::FieldVector<double, 2> L;
>   L = 1.0;
>   auto s = Dune::filledArray<2>(1);
>   Dune::YaspGrid<2> grid(L, s);
> 
>   // create taylorHood
>   auto taylorHood = makeBasis(grid.leafGridView(),
>                          composite(power<2>(lagrange<2>(),
> flatInterleaved()), lagrange<1>(), flatLexicographic()));
>   auto L1xL1 = makeBasis(grid.leafGridView(), power<2>(lagrange<1>(),
> flatInterleaved()));
> 
>   std::cout << "taylorHood.size(): " << taylorHood.size({})          // = 22
>             << "\ntaylorHood.size({0}):" << taylorHood.size({0})     //
> =  0 (expected 18)
>   //        << "\ntaylorHood.size({0,0}):" << taylorHood.size({0,0}) //
> assertion failed (expected 9)
>             << "\ntaylorHood.size({1}):" << taylorHood.size({1})     //
> =  0 (expected 4)
>             << "\n";
>   std::cout << "L1xL1.size(): " << L1xL1.size({})      // = 8
>             << "\nL1xL1.size({0}):" << L1xL1.size({0}) // = 0 (expected 4)
>             << "\nL1xL1.size({1}):" << L1xL1.size({1}) // = 0 (expected 4)
>             << "\n";
> }/
> 
> 
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-- 
Prof. Dr. Carsten Gräser
Freie Universität Berlin
Institut für Mathematik
Arnimallee 6
14195 Berlin, Germany
phone: +49 30 838 72637
fax  : +49 30 838 472637
email: graeser at mi.fu-berlin.de
URL  : http://page.mi.fu-berlin.de/graeser

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