TensorLy

Warnings

• breaking In version 0.5.1, `Kruskal-tensors` were renamed to `cp_tensors` and `Matrix-product-state` was renamed to `tensor-train` for API consistency. The old names (`kruskal_tensor`, `mps_tensor`) were deprecated and later removed.
  Fix: Update imports and class instantiations from `tensorly.kruskal_tensor` to `tensorly.cp_tensor` and from `tensorly.mps_tensor` to `tensorly.tt_tensor`.
• deprecated The MXNet backend was deprecated in version 0.8.0.
  Fix: Migrate to another supported backend such as PyTorch, JAX, TensorFlow, CuPy, or PaddlePaddle.
• gotcha TensorLy's `unfold` function uses 0-indexed modes, meaning `tl.unfold(tensor, 0)` unfolds along the *first* dimension. This can differ from conventions in some classical tensor literature.
  Fix: Always remember that TensorLy's mode indexing starts from 0, consistent with Python's array indexing.
• gotcha While TensorLy transparently supports `einsum` operations since 0.8.0, and `tenalg.set_backend('einsum')` can dispatch all tensor algebraic operations to the backend's `einsum`, this might change performance characteristics or require adjustments if you previously relied on TensorLy's 'hand-crafted' implementations. Plugins like `use_opt_einsum` further modify `einsum` behavior.
  Fix: If encountering unexpected behavior or performance, be aware of the `tensorly.tenalg.set_backend` and `tensorly.plugins` functions (`use_opt_einsum`, `use_cuquantum`, `use_default_einsum`) which control `einsum` dispatching and optimization.

Install

• pip install -U tensorly Recommended installation via pip

Imports

• tensorly

  import tensorly as tl

  Standard alias for core TensorLy functionalities.
• decomposition modules

  from tensorly.decomposition import parafac, tucker

  Import specific decomposition algorithms from the decomposition module.
• tl.tensor

  tensor = tl.tensor(numpy_array)

  Always create tensors using `tl.tensor` or `tl.random.random_tensor` to ensure compatibility with the active backend, rather than native backend array constructors.
• Backend functions

  tl.mean(tensor)

  To maintain backend transparency, always use TensorLy's dispatched functions (e.g., `tl.mean`, `tl.dot`) instead of directly calling functions from the native backend (e.g., `numpy.mean`).
• Index assignment

  tensor = tl.index_update(tensor, (indices), values)

  Direct NumPy-style index assignment (`tensor[indices] = values`) is not universally supported across all backends. Use `tl.index_update` for cross-backend compatibility.

Quickstart

This quickstart demonstrates how to initialize TensorLy, create a tensor, optionally set a backend, perform a CANDECOMP/PARAFAC (CP) decomposition, and reconstruct the tensor from the learned factors.

import tensorly as tl
import numpy as np
from tensorly.decomposition import parafac

# Set the backend (optional, defaults to numpy)
tl.set_backend('numpy') # Or 'pytorch', 'jax', 'tensorflow', 'cupy', 'paddle'

# Create a random tensor
# tensor = tl.random.random_tensor((3, 4, 2))
# Create a tensor from a NumPy array
tensor = tl.tensor(np.arange(24).reshape((3, 4, 2)), dtype=tl.float64)

print(f"Original tensor shape: {tensor.shape}")

# Perform CP decomposition
rank = 2
factors = parafac(tensor, rank=rank)

# Reconstruct the tensor from factors
reconstructed_tensor = tl.cp_to_tensor(factors)

print(f"Reconstructed tensor shape: {reconstructed_tensor.shape}")
print(f"Reconstruction error: {tl.norm(tensor - reconstructed_tensor) / tl.norm(tensor):.4f}")