What does the kron function do in MATLAB / RunMat?

kron(A, B) forms the Kronecker (tensor) product of arrays A and B. Every element of A scales a copy of B, yielding a block-structured array whose size is size(A) .* size(B) when interpreted with MATLAB's column-major ordering.

How does the kron function behave in MATLAB / RunMat?

• Works with scalars, vectors, matrices, and higher-rank tensors; trailing singleton dimensions are honoured.
• If either input is complex, the output is complex and uses MATLAB's complex arithmetic rules.
• Logical and char inputs are promoted to double precision before multiplication.
• Scalar arguments act as uniform scalars (kron(a, B) behaves like a * B).
• Empty dimensions propagate; if any replicated dimension is zero, the result is empty along that axis.
• Invalid inputs (non-numeric/non-logical, or values that would overflow the maximum size) raise descriptive MATLAB-style errors.

kron Function GPU Execution Behaviour

When a GPU provider is active, RunMat first consults the provider's kron hook so the operation can run entirely on the device. Providers that have not implemented this hook fall back to a safe path: the runtime gathers both operands to host memory, performs the Kronecker product in Rust, and then attempts to upload the result back to the originating device so downstream GPU work can continue without additional copies.

Examples of using the kron function in MATLAB / RunMat

Computing the Kronecker product of two matrices

A = [1 2; 3 4];
B = [0 5; 6 7];
C = kron(A, B);

Expected output:

C =
     0     5     0    10
     6     7    12    14
     0    15     0    20
    18    21    24    28

Kronecker product with row and column vectors

row = [1 2 3];
col = (1:3)';
K = kron(row, col);
size(K)

Expected output:

ans =
     3     9

Scaling a matrix with a scalar using kron

A = [1 2; 3 4];
S = kron(2, A);

Expected output:

S =
     2     4
     6     8

Building block-diagonal systems with kron

I = eye(3);
M = [1 0; 0 -1];
blockDiag = kron(I, M);

Expected output: blockDiag is a 6-by-6 matrix with M along the block diagonal.

Kronecker product of complex matrices

A = [1+2i 0; 0 3-1i];
B = [0 1; 2 3i];
C = kron(A, B);

Expected behaviour: complex arithmetic propagates, with each block carrying the complex scaling.

Using kron with logical masks

mask = logical([1 0; 0 1]);
tile = kron(mask, ones(2));

Expected output: tile is a numeric 4-by-4 array whose diagonal 2-by-2 blocks are all ones.

Running kron on GPU-resident tensors

G = gpuArray(rand(2));
H = gpuArray([1 -1; -1 1]);
K = kron(G, H);
isgpuarray(K)

Expected output:

ans = logical 1

GPU residency in RunMat (Do I need gpuArray?)

You usually do not need to call gpuArray explicitly. RunMat's planner keeps values resident on the GPU whenever it is profitable. Explicit gpuArray calls remain supported for MATLAB compatibility and for users who want direct control over residency.

FAQ

When should I use kron instead of standard matrix multiplication?

Use kron when you need block matrices built from every combination of two operands. Matrix multiplication collapses dimensions, while kron expands them.

Does kron preserve sparsity?

The current dense runtime converts inputs to dense double or complex tensors. Sparse fidelity is on the roadmap; today, sparse inputs are first densified.

Can I mix real and complex inputs?

Yes. If either operand is complex, the output is complex, with MATLAB-compatible real/imaginary components.

What happens with logical or boolean inputs?

Logical arrays are converted to doubles (0 and 1) before the Kronecker product, mirroring MATLAB's behaviour.

Are character arrays supported?

Yes. Character arrays are converted to their Unicode code points (double precision) before forming the product.

How big can the result be?

kron checks for overflow when multiplying dimension sizes. If the result would exceed the maximum addressable size, the builtin raises a descriptive error before allocating memory.

Does the GPU path always stay on-device?

When the provider supplies a kron hook, execution stays on-device. Otherwise RunMat gathers to the host, computes the product, and re-uploads the result when a provider is available.

See Also

repmat, reshape, sum, matmul, gpuArray, gather

Source & Feedback

• Implementation: crates/runmat-runtime/src/builtins/array/shape/kron.rs
• Found an issue? Please open an issue with a minimal reproduction.