pysiglib.signature

pysiglib.signature#

signature(path, degree, time_aug=False, lead_lag=False, end_time=1.0, horner=True, n_jobs=1)[source]#

Computes the truncated signature of single path or a batch of paths. For a single path \(x\), the signature is given by

\[S(x)_{[s,t]} := \left( 1, S(x)^{(1)}_{[s,t]}, \ldots, S(x)^{(N)}_{[s,t]}\right) \in T((\mathbb{R}^d)),\]
\[S(x)^{(k)}_{[s,t]} := \int_{s < t_1 < \cdots < t_k < t} dx_{t_1} \otimes dx_{t_2} \otimes \cdots \otimes dx_{t_k} \in \left(\mathbb{R}^d\right)^{\otimes k}.\]
Parameters:

  • path (numpy.ndarray | torch.tensor) – The underlying path or batch of paths, given as a numpy.ndarray or torch.tensor. For a single path, this must be of shape (length, dimension). For a batch of paths, this must be of shape (batch_size, length, dimension).

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

  • time_aug (bool) – If set to True, will compute the signature of the time-augmented path, \(\hat{x}_t := (t, x_t)\), defined as the original path with an extra channel set to time, \(t\). This channel spans \([0, t_L]\), where \(t_L\) is given by the parameter end_time.

  • lead_lag (bool) – If set to True, will compute the signature of the path after applying the lead-lag transformation.

  • end_time (float) – End time for time-augmentation, \(t_L\).

  • horner (bool) – If True, will use Horner’s algorithm for polynomial multiplication.

  • 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, or a batch of truncated signatures.

Return type:

numpy.ndarray | torch.tensor

Note

Ideally, any array passed to pysiglib.signature should be both contiguous and own its data. If this is not the case, pysiglib.signature will internally create a contiguous copy, which may be inefficient.


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}
}
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