In this example we describe the usage of TensorMul.tensordot. First let's load the package.

import TensorMul

Let's define the dimensions of the problem.

N = (3,7)
M = (2,3)
B = 16

We will assume our data consists of B batch examples, where each example consists of matrices X of size N, and matrices Y of size M.

X = randn(N..., B)
Y = randn(M..., B)

These datasets are combined via some weight tensor of corresponding dimensions:

W = randn(N..., M...)

Now we want to form a contraction of X and Y with W. More precisely, we want to compute the quantity:

C = [
    sum(
        X[i,b] * W[i,μ] * Y[μ,b]
        for i in CartesianIndices(N),
            μ in CartesianIndices(M)
    ) for b in 1:B
]

Here C is a vector with B elements.

The downside with the above approach is that we have to know which dimensions to reduce, what dimensions correspond to batches, and dimensions of X correspond to those of W, etc. That's what TensorMul.tensordot computes. In the following line, it will compute the same quantity C, but automatically figuring out which dimensions to reduce.

TensorMul.tensordot(X, W, Y) ≈ C

true

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