pysiglib.linear_sig

pysiglib.linear_sig#

Added in version v3.0.0.

linear_sig(displacement, dimension, degree, *, scalar_term=False, n_jobs=1)[source]#

Computes the truncated signature of a single linear segment defined by a displacement vector. Given a displacement vector \(v \in \mathbb{R}^d\), this computes the signature of the linear path from \(0\) to \(v\),

\[S(v) = \left(1, v, \frac{v^{\otimes 2}}{2!}, \ldots, \frac{v^{\otimes N}}{N!}\right).\]
Parameters:

  • displacement (numpy.ndarray | torch.tensor) – The displacement vector or batch of displacement vectors. For a single displacement, this must be of shape (dimension,). For a batch, this must be of shape (batch_size, dimension).

  • dimension (int) – Dimension of the underlying space, \(d\).

  • degree (int) – Truncation level of the signature, \(N\).

  • scalar_term (bool) – If True, the output includes the leading constant 1 at index 0 (the empty-word term). If False (default), this leading element is stripped from the output.

  • n_jobs (int) – Number of threads to run in parallel. If n_jobs = 1, the computation is run serially. If set to -1, all available threads are used. For n_jobs below -1, (max_threads + 1 + n_jobs) threads are used. For example if n_jobs = -2, all threads but one are used.

Returns:

Truncated signature of the linear segment, or a batch of truncated signatures.

Return type:

numpy.ndarray | torch.tensor

Example:#

import pysiglib
import numpy as np

dimension = 5
degree = 3

displacement = np.random.uniform(size=(dimension,))
lsig = pysiglib.linear_sig(displacement, dimension, degree)

# Batch version
batch_size = 32
displacements = np.random.uniform(size=(batch_size, dimension))
lsigs = pysiglib.linear_sig(displacements, dimension, degree, n_jobs=-1)

Citation#

If you found this library useful in your research, please consider citing the paper:

@article{shmelev2025pysiglib,
  title={pySigLib-Fast Signature-Based Computations on CPU and GPU},
  author={Shmelev, Daniil and Salvi, Cristopher},
  journal={arXiv preprint arXiv:2509.10613},
  year={2025}
}
Contents