FastTWD: A MATLAB package for matrix-free CPU/GPU tensor wheel decomposition

Tensor wheel (TW) decomposition is an emerging tensor-network format for compact representation of multidimensional data. Owing to its wheel topology, TW connects several important tensor formats, including CP, Tucker, tensor-train, and tensor-ring models, and has strong potential in multilinear data modelling, tensor completion, and high-dimensional data analysis. However, practical use of TW decomposition requires efficient and reproducible software, especially for testing different rank configurations and larger multiway arrays. FastTWD is a MATLAB package for matrix-free CPU/GPU TW decomposition. It implements a contraction-based reformulation of the proximal alternating minimization (PAM) algorithm, preserving the TW-PAM update structure while reducing memory demand and runtime. The package provides CPU and GPU solvers, reconstruction utilities, and benchmark scripts. Numerical experiments show lower runtime and peak memory usage with comparable reconstruction accuracy relative to the reference TW baseline.