pysiglib.sig_combine

pysiglib.sig_combine#

sig_combine(sig1, sig2, dimension, degree, *, time_aug=False, lead_lag=False, n_jobs=1)[source]#

Combines two truncated signatures of the same degree and dimension into one signature. In particular, let \(x_1, x_2\) be two paths such that the first point of \(x_2\) is the last point of \(x_1\). Let \(S(x_1), S(x_2)\) be the truncated signatures of \(x_1, x_2\) respectively. Then calling this function on \(S(x_1), S(x_2)\) returns the truncated signature of the concatenated path,

\[S(x_1 * x_2) = S(x_1) \otimes S(x_2),\]

where \(x_1 * x_2\) is the concatenation of the two paths \(x_1, x_2\).

Parameters:

  • sig1 (numpy.ndarray | torch.tensor) – The first truncated signature

  • sig2 (numpy.ndarray | torch.tensor) – The second truncated signature. Must have the same degree and dimension as the first.

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

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

  • time_aug (bool) – Whether time augmentation was applied before computing the signature.

  • lead_lag (bool) – Whether the lead lag transformation was applied before computing the signature.

  • 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:

Combined signature, \(S(x_1 * x_2)\), in the same scalar-term format as the inputs.

Return type:

numpy.ndarray | torch.tensor

Example usage:

import pysiglib
import numpy as np

batch_size = 32
length = 100
dimension = 5
degree = 3

X1 = np.random.uniform(size=(batch_size, length, dimension))
X2 = np.random.uniform(size=(batch_size, length, dimension))
X_concat = np.concatenate((X1, X2), axis=1)

X2 = np.concatenate((X1[:, [-1], :], X2), axis=1) # Make sure first pt of X2 is last pt of X1
sig1 = pysiglib.sig(X1, degree)
sig2 = pysiglib.sig(X2, degree)

# The tensor product...
sig_mult = pysiglib.sig_combine(sig1, sig2, dimension, degree)

# ... is the same as the signature of the concatenated path:
sig = pysiglib.sig(X_concat, 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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