Re: [eigen] [RFC] Tensor module: class hierarchy

[Ralf Denzer <ralf.denzer@xxxxxxxxxxxxxx>]

Hello Christian,

just a comment concerning your TODO-list:

* generic expressions with index placeholders, such has result(_1, _2, 
_3) = tensor1(_1, _, _) * tensor2(_, _2, _3) or similar (need to define 
a nice API for this)

I don't know if you know about FTensor library from Walter Landry:

http://www.wlandry.net/Projects/FTensor

He can do the following code:

FTensor::Index<'i', 3> i;
FTensor::Index<'j', 3> j;
FTensor::Index<'k', 3> k;
FTensor::Index<'l', 3> l;

FTensor::Tensor2<double, 3,3> cauchy;
FTensor::Tensor2<double, 3,3> P;
FTensor::Tensor2<double, 3,3> f;
double JF;

    ...

// single contraction with 'j'
// so, he has Einstein summation convention!
P(i, k) = JF * cauchy(j, i) * f(k, j);

    ...

FTensor::Tensor4<double, 3,3,3,3> C4;
FTensor::Tensor4<double, 3,3,3,3> IdydI;

    ...

// dyadic products of 2nd order tensor
// additionally with some transpositions

C4(i, j, k, l) =    IdydI(i, k, j, l)
                 +  f(j, i) * f(l, k)
                 -  f(l, i) * f(j, k);

Personally, I like his notation very much,
because it's very close to the usual
index notation for tensors.
Thus, he defines a lot of operator*,
operator+ etc. for all kinds of contractions
and other tensor products ... and he defines
some special tensors of different order
with symmetries ...

A similar library is
https://code.google.com/p/ltensor/

Best

Ralf





On 06/08/2014 01:26 PM, Christian Seiler wrote:
> Hi there,
>
> I am currently working on the tensor module to try to make it more
> useful. (In case you are not familiar with it: I put some introductory
> words in the wiki: [1])
>
> The current state is: it basically only stores data for now.
>
> My goal for the immediate future is to implement a class hierarchy
> similar to that which Eigen uses itself. This will then allow me to
> introduce some basic expressions such as adding two tensors etc, which
> will immediately make the tensor module quite a bit more useful than
> beforehand.
>
> My problem here is that I have some conceptual questions I'd like to
> discuss before proceeding. I've documented the details under:
> http://eigen.tuxfamily.org/index.php?title=Working_notes_-_Tensor_module
>
> Basically I have three immediate things I'd like to have feedback on:
>
> 1. the names of the new class hierarchy: do you agree or do you have
>     better ideas?
>
> 2. packet access for tensors: should I just deviate from Eigen by
>     changing the argument order of writePacket for tensors or should
>     writePacket() for tensors only accept std::array for index
>     specification? (see wiki page for an explanation)
>
> 3. expression template names: is it possible to somehow reuse the
>     CwiseBinaryOp etc. names for tensors (obviously with a different
>     implementation behind it) or do I have to go the way of
>     TensorCwiseBinaryOp?
>
> Any other general comments / ideas / suggestions are of course also welcome.
>
> Thank you!
>
> Regards,
> Christian
>
> [1] http://eigen.tuxfamily.org/index.php?title=Tensor_support