pysiglib.log_sig_join

pysiglib.log_sig_join#

Added in version v3.0.0.

log_sig_join(log_sig, displacement, dimension, degree, *, n_jobs=1)[source]#

Extends a truncated log-signature by a single displacement vector using the Baker-Campbell-Hausdorff (BCH) formula. This is the log-signature analogue of sig_join.

Given a log-signature \(L(x)\) and a displacement \(v\), this computes

\[L(x * v) = \text{BCH}(L(x), v),\]

where \(v\) is embedded as a degree-1 element of the free Lie algebra.

Note

log_sig is expected in the Lyndon bracket basis (method=2 output). You must call pysiglib.prepare_log_sig(dimension, degree, method=2) before using this function. This precomputes the Lyndon basis and BCH coefficients needed internally.

Parameters:

  • log_sig (numpy.ndarray | torch.tensor) – The existing truncated log-signature, of shape (..., log_sig_length).

  • displacement (numpy.ndarray | torch.tensor) – The displacement vector, of shape (..., dimension). Leading batch dimensions must match those of log_sig.

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

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

  • 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:

Extended log-signature, \(L(x * v)\).

Return type:

numpy.ndarray | torch.tensor

Example:#

import pysiglib
import numpy as np

dimension = 5
degree = 3
pysiglib.prepare_log_sig(dimension, degree, method=2)

path = np.random.uniform(size=(100, dimension))
ls = pysiglib.log_sig(path, degree, method=2)

displacement = np.random.uniform(size=(dimension,))
extended_ls = pysiglib.log_sig_join(ls, displacement, dimension, degree)

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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