pysiglib.log_sig_length

Added in version v1.0.0.

log_sig_length(dimension, degree, *, time_aug=False, lead_lag=False)

Returns the length of a truncated log signature,

\[\sum_{i=0}^N \frac{1}{i} \sum_{x | i} \mu\left(\frac{i}{x}\right) d^x,\]

where \(d\) is the dimension of the underlying path, \(N\) is the truncation level of the log signature and \(\mu\) is the Mobius function.

Parameters:

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

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

• time_aug (bool) – Whether time augmentation is applied before computing the signature. This flag is provided for convenience, and is equivalent to calling sig_length(dimension + 1, degree).

• lead_lag (bool) – Whether the lead lag transformation is applied before computing the signature. This flag is provided for convenience, and is equivalent to calling sig_length(2 * dimension, degree).

Returns:

Length of a truncated log signature

Return type:

int

Example:

import pysiglib

# Length of a truncated log signature for a 3-dimensional path at degree 4
length = pysiglib.log_sig_length(3, 4)
print(length) # 32

# Log signature length with time augmentation and lead-lag
import pysiglib

length = pysiglib.log_sig_length(3, 4, time_aug=True, lead_lag=True)
print(length) # 728

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}
}