TensorRSVD

Tensor-free randomized Higher-Order SVD (Tucker decomposition).

TensorRSVD computes Tucker decompositions of high-dimensional tensors that are defined as Python functions without ever forming the dense tensor in memory. It uses randomized linear algebra (Halko et al. 2011) to approximate the dominant factor matrices mode-by-mode, scaling to tensors that would be impossible to store explicitly.

Installation

pip install tensorrsvd

Optional backends for GPU or JIT-compiled acceleration:

pip install "tensorrsvd[jax]"          # JAX (CPU / GPU / TPU)
pip install "tensorrsvd[jaxcuda12]"    # JAX with CUDA 12
pip install "tensorrsvd[jaxcuda13]"    # JAX with CUDA 13
pip install "tensorrsvd[cupy]"         # CuPy (NVIDIA GPU, CUDA required)

Note: CuPy wheels are CUDA-version-specific. If the above does not match your CUDA installation, install CuPy manually following the CuPy installation guide.

Quick start

import numpy as np
from tensorrsvd import ho_rsvd

# Define your tensor as a callable
def my_tensor(x0, x1, x2):
    return x0 - x1 + x2

# Compute the randomized Tucker factors
U_list, S_list = ho_rsvd(
    tensor=my_tensor,
    tensor_shape=(64, 64, 64),
    dtype=np.float64,
    rank=4,
    num_oversamples=10,
    num_idxs=3,
)

# U_list[i] has shape (n_i, rank_i) with orthonormal columns
# S_list[i] has shape (rank_i,) (descending singular values)
print([U.shape for U in U_list])   # [(64, 4), (64, 4), (64, 4)]

Switch to a JAX or CuPy backend by passing backend="jax" or backend="cupy".

Documentation

Full documentation (installation, user guide, theory, and API reference, etc.) is available at tensorrsvd.readthedocs.io.

References

• N. Halko, P. G. Martinsson, and J. A. Tropp, Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions, SIAM Review, 53(2):217–288, 2011. doi:10.1137/090771806

• L. De Lathauwer, B. De Moor, and J. Vandewalle, A Multilinear Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000. doi:10.1137/S0895479896305696

License

MIT (see LICENSE)