pysiglib.idx_to_tree

pysiglib.idx_to_tree#

idx_to_tree(idx, dimension, degree, *, tree_order='canonical', planar=False, scalar_term=False)[source]#

Inverse of tree_to_idx(). Given a flat index in the branched-signature coefficient vector, returns the corresponding decorated rooted tree.

With scalar_term=True, index 0 maps to the empty tree (None). With scalar_term=False (default), all indices shift down by 1 (index 0 maps to the first non-empty tree) and the empty tree is unreachable.

Parameters:

  • idx (int) – Flat index in the branched signature vector.

  • dimension (int) – Path dimension (alphabet size).

  • degree (int) – Maximum number of nodes (same as degree in branched_sig()).

  • tree_order (str) – Tree ordering convention. "canonical" (default) matches branched_sig(..., tree_order="canonical"). "recursive" matches branched_sig(..., tree_order="recursive") (the default).

  • planar (bool) – If True, interpret idx in the planar (ordered) enumeration matching branched_sig(..., planar=True).

  • scalar_term (bool) – Whether the source branched signature includes the leading scalar 1 at index 0. Must match the format of the bsig the index was taken from. Default False.

Returns:

Decorated rooted tree (None for empty tree when scalar_term=True, tuple otherwise).

Return type:

tuple or None

Example:#

import pysiglib

tree = pysiglib.idx_to_tree(3, dimension=2, degree=3)
print(tree)

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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