`tensorprod`

Tensor product and contraction of arrays along chosen dimensions.

Category: Language Fundamentals > Operators and Elementary Operations

Syntax

C = tensorprod(A, B)

Outer (tensor) product: every element of A times every element of B. The result has ndims(A) + ndims(B) dimensions.

C = tensorprod(A, B, dimA, dimB)

Contracts: multiplies and sums over dimension dimA of A and dimB of B.

C = tensorprod(A, B, 'all')

Contracts over all dimensions, which gives the full inner product as a scalar.

Description

Without contraction dimensions, tensorprod builds the outer product, so two vectors of lengths 3 and 3 give a result of size 1x3x1x3. Contracting one pair of dimensions generalizes matrix multiplication: tensorprod(A, B, 2, 1) equals A*B for matrices. Contracting [1 2] with [1 2] sums the products of all matching elements.

It is the general tool behind dot products, matrix products and Einstein-summation style contractions.

Input arguments

A, B: Numeric arrays.
dimA, dimB: Dimensions to contract. They must have equal sizes in A and B and the same number of entries.

Output arguments

C: The result. The remaining dimensions of A come first, followed by those of B.

Example

a = [1 2 3];
b = [4 5 6];
size(tensorprod(a, b))
tensorprod(a, b, 'all')
A = [1 2; 3 4];
tensorprod(A, A, 2, 1)

Output

ans = 1×4

     1     3     1     3
ans = 32
ans = 2×2

     7    10
    15    22

tensorprod