Hi Cem,

thanks for sending this out !

On 2018-09-13 11:34 AM, Cem Bassoy via ublas wrote:

The GSOC 2018 project with the title "Adding tensor support " has been succefully completed. Boost.uBlas may support tensors in future. The code, project and documentation can be found here and here.

The tensor template class is parametrized in terms of data type, storage format (first- or last-order), storage type (e.g. std::vector or std::array):

(Minor nit-pick: it's a class template. There is no such thing as "template classes" in C++ :-). I know the existing ublas docs are full of that spelling...)

template<class T, class F=first_order, class A=std::vector<T,std::allocator<T>>>

class tensor;

An instance of a tensor template class has dynamic rank (number of dimensions) and  dimensions using a shape class that holds the data. It is a adaptor of std::vector where the rank is the size of it:

// {3,4,2} could be runtime variables of an integer type.

auto A = tensor<float>{make_shape(3,4,2)};

---------------------
---------------------

I am thinking to redesign the tensor template class where  the rank is a compile time parameter:

template<class T, std::size_t N, class F=first_order<N>, class A=std::vector<T,std::allocator<T>>>
class tensor;

An instance of a tensor template class could be generated as follows:

// {3,4,2} could be runtime variables of an integer type.
auto A = tensor<float,3>(make_shape(3,4,2));

This instantiation could be definitely improved. However, having a static rank has the following advantages and disadvantages:

-------------

Advantages:

1. improving runtime behavior about 30% to 5 % of basic tensor operations ( depends according to my findings on the length of the inner most loop ).
2. ability to statically distinguish between different tensor types at compile time. tensor<float,3> is a different type than tensor<float,4>. If so, why not setting matrix as an alias:

template <class type, class format, class storage>

using matrix = tensor<type,2,format,storage>.

We would only need to specify and implement one data structure ' tensor ' and if needed  provide optimized functions for matrices. This simplifies the maintenance.

A big advantage (which has been my main motivation for pushing for this solution) is that such a scenario would be fully in line with the existing Boost.uBLAS API, so your work becomes a natural extension of what we already have.

Alternatively, if you keep the rank a runtime parameter, you are basically proposing an entirely new API, which means that Boost.uBLAS users will have to decide whether to use the old or the new API, which I'm afraid will result in a fragmentation of the community. Likewise, many existing operations only support existing vector and matrix types, so maintainers will have more work to do to support both APIs.

That, to me as library maintainer, is a very high cost, so I'm reluctant to such a change, even if the proposed API with runtime ranks is otherwise sound.

Also there might be advantages in terms of subtensor and iterator support. However implementing them will be harder. 

---------

Disadvantages:

1. The implementations become more complicated especially for tensor multiplications and tensor reshaping.

I have worked on a BLAS library with compile-time constant ranks. And while capturing parameters such as ranks in the type system itself can indeed be a bit of a challenge, I think it's definitely doable, and may even lead to clearer code down the road.

1. With static rank the interfaces are harder to use (setting the rank as a template parameter).

That depends on the use case. It simply means that you have to think about the rank slightly differently, while writing code.

(It could simply mean that you have to drag along an additional template parameter, if you want to write generic code. But as I mentioned above, this could arguably lead to clearer code, so I consider this a feature, not a bug. :-) )

1. The number of contracted dimensions must be known at compile time. Therefore, implementing some tensor algorithms would only be possible with template specialization instead of simple for loops. Making algorithms becomes more difficult.
   

Right.

Although Eigen and Boost.MultiArray decided  for compile time, it might be a critical point for uBLAS.

I am working on this right now and also I am trying to suppprt p! number of linear storage formats as a compile time parameter if p is the rank of the tensor. Actually unit-testing becomes very hard as I am not able to use fixtures so easily. Supporting static and dynamic rank will be a maintenance nightmare.

Yeah, the parameter space to cover grows exponentially. But that is true no matter whether the rank is determined at compile-time or at runtime. The difference is only in whether you use normal functions or meta-functions to compute derived ranks, storage formats, et al.