Generic tensor contraction

[ivan-pi]

The FortranCon 2020 presentation from Patrick Seewald on "Generic Programming Techniques by example of a tensor contraction" contains an excellent demonstration of a generic tensor class which would be difficult to write without a preprocessor.

Full code examples can be found in the fortran-einsum-example GitHub repository.

As Patrick notes at the end of his presentation, the biggest limitations of the current approach are:

• all templates are explicitly instantiated, leading to large binary sizes and long compilation times
• the mixture of Fortran and preprocessor syntax is hard to read and debug

Here are some einsum reference pages:

• np.einsum (NumPy)
• tf.einsum (TensorFlow)
• Einsum.jl (Julia)
• OMEinsum.jl (Julia)

And here are two blog posts with explanations:

• Einstein Summation in Numpy by Olexa Bilaniuk
• A basic introduction to NumPy's einsum by Alex Riley

[arjenmarkus]

Slightly abusing this ticket: I experimented a bit with Kronecker products, My intention was to create a concise routine that can be extended to any number of dimensions. The code I attach here is limited to two-dimensional arrays leading to a four-dimensional array, but with the help of assumed-rank arrays I can make it "dimension-agnostic".
kronecker_general.f90.txt