Einstein summation

@einsum (i,j...) -> expr
@einsum expr

Conducts tensor computation based on Einstein summation convention. The arguments of the anonymous function are regard as free indices. If arguments are not given, they are guessed based on the order that indices appears from left to right.

Examples

julia> A = rand(Mat{3,3})
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 0.325977  0.894245  0.953125
 0.549051  0.353112  0.795547
 0.218587  0.394255  0.49425

julia> B = rand(Mat{3,3})
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 0.748415  0.00744801  0.682533
 0.578232  0.199377    0.956741
 0.727935  0.439243    0.647855

julia> @einsum (i,j) -> A[i,k] * B[k,j]
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 1.45486   0.599373  1.69554
 1.19421   0.42393   1.22798
 0.751346  0.297329  0.846595

julia> @einsum A[i,k] * B[k,j] # same as above
3×3 Tensor{Tuple{3, 3}, Float64, 2, 9}:
 1.45486   0.599373  1.69554
 1.19421   0.42393   1.22798
 0.751346  0.297329  0.846595

julia> @einsum A[i,j] * B[i,j]
2.7026716125808266