einsum

Efficiently calculates tensor contraction in any dimension. It uses MATLAB's matrix multiplication so it's parallelized and optimized.

Usage: einsum(A,B,s)
einsum(A,B,iA,iB)

Calculates the contraction of A and B which are n-dimensional tensors.
The contraction is specified either by s, in Einstein notation, or by two
vectors, iA and iB which list the indices to contract on for each tensor.

Example:
A=rand(7,4,5);
B=rand(5,7);
To contract the 1st dimension of A with the 2nd dimension of B, use
einsum(A, B, 'ijk,li->jkl') OR einsum(A, B, 1, 2)
The result will be of size [4,5,5].

To contract the 3rd dimension of A with the 1st dimension of B, use
einsum(A, B, 'ijk,kl->ijl') OR einsum(A, B, 3, 1)
The result will be of size [7,4,7].

To do both contractions at once, use
einsum(A,B,'ijk,ki->j') OR einsum(A, B, [1 3], [2 1])

Using the iA, iB it is not possible to specify the order of dimensions
in the output, they're just in the same order as the input, with the
contracted dimensions omitted.

Author: Yohai Bar-Sinai