lzcomplexity 2.0.0

lzcomplexity computes information-theoretic measures of symbolic sequences using Lempel–Ziv 76 (LZ76) factorization [1]. The LZ76 complexity c(S) is the minimum number of factors needed to represent a sequence, where each factor is either a new symbol or the longest previously-seen substring. From c(S) you get a non-parametric entropy-rate estimator — h ≈ c(S)·log_k(n)/n — that converges to the true entropy rate of ergodic sources [2].

The library ships two things:

1. A Python library (import lzcomplexity) built on a Rust core via PyO3.
2. Two standalone command-line tools — lzcomplexity and lzdistance.

The core is implemented in Rust; the two front-ends share it. Common applications: neuroscience time-series, DNA analysis, anomaly detection, structural pattern analysis.

This is the Rust implementation, the current production backend. The original C++/nanobind implementation lives on the main branch. Numerical outputs are equivalent up to deterministic shuffle seeding (see Differences from the C++ version).

Spectral analysis (psd, spectral entropy, semc) has been removed from this library and now lives in a separate package.

Python library

Install

You need Python ≥ 3.9. From PyPI:

pip install lzcomplexity

Or from a clone of this repository (requires a Rust toolchain):

pip install .

pip invokes maturin, which compiles the Rust workspace, produces a wheel, and installs it. No CMake, no submodules, no C++ toolchain.

Development install

python3 -m venv .venv
source .venv/bin/activate
pip install maturin
maturin develop --release

Re-run maturin develop --release after Rust changes.

Quick start

import lzcomplexity as lz

# Complexity + factor boundaries — factor i spans [factors[i], factors[i+1])
complexity, factors = lz.factorization("banana")
# → (3, [0, 1, 2, 3, 7])

# Normalised entropy density / entropy-rate estimator — `h`
lz.h("01010101")
# → 0.75

# Effective measure complexity: the value and the terms that sum to it
emc_value, summands = lz.emc("01001010101101010101110101010101010000100101011")

# Everything in one call (returns a dict)
full = lz.lz76("ABRACADABRA")
full["complexity"], full["h"], full["factors"]
full["emc"]     # {"value", "summands", "max_block_size", "multi_information"}
full["extras"]  # {"rajski_distance", "redundancy", "fh_uncertainty", ...}

# Normalized information distance (NID) between two sequences
lz.nid("ABRACADABRA", "ABRACADABRZ")     # → small, similar
lz.nid("ABRACADABRA", "ZYXWVUTSRQP")     # → large, dissimilar

Public API

lz.lz76(...) returns a dict with keys: complexity, h, factors, emc (a nested dict), epsilon, factors_stddev, normal_error, poison_error, extras (a nested dict).

Common keyword arguments:

• partitions (int, default 1) — suffix-array partition count; performance knob, no effect on results.
• alphabet (int | None, default None) — auto-detect (distinct symbols, min 2) when None.
• log_base (int | None, default None) — matches alphabet when None (normalised entropy in units of symbols); pass 2 for bits.
• max_block_size (int, default −1) — shuffle block-size cap for emc/lz76; −1 auto-selects.
• jobs (int, default 0) — reserved; currently ignored (rayon manages its pool).

Run help(lzcomplexity.<name>) for full per-function docs. Type stubs (__init__.pyi) ship with the package.

Accepted input types

Every sequence-accepting function accepts any of:

• str — symbols taken from the string bytes directly.
• bytes — raw byte sequence.
• list[str] — concatenated as-is (e.g. ["A","C","G","T"]).
• list[int] — each element becomes its decimal string, concatenated, so [0, 1, 10] → "0110".
• Any iterable of ints — covers NumPy arrays; same conversion as list[int].

Standalone binaries

Two command-line tools are built from the same Rust core.

Build them from a clone:

cargo build --release
# → target/release/lzcomplexity   and   target/release/lzdistance

Prebuilt binaries for Linux/macOS/Windows are attached to each GitHub release.

lzcomplexity

Reads a sequence file and writes a JSON report with the LZ76 complexity, entropy density, and random-shuffle effective measure complexity.

lzcomplexity input.txt                 # → input.lz76.json
lzcomplexity input.txt -m -d           # multi-line + distance between consecutive lines
lzcomplexity input.txt -n              # entropy density only
lzcomplexity input.txt -a 4 -l 2       # explicit alphabet / log base

Key flags: -a/--alphabet, -l/--log-base, -p/--partitions, -m/--multi-line, -d/--dlz, -n/--entropy-density, -f/--factors <file>, -F/--format <fmt>, -o/--output, -v/--verbose, -V/--version.

lzdistance

Computes pairwise information-distance and shuffle-distance matrices between one or two data sources (files or directories).

lzdistance sequences.txt               # self-distance matrix (first_dim × first_dim)
lzdistance A.txt B.txt                  # cross matrix
lzdistance genomes/ -a                  # a directory of files, DNA complement-aware
lzdistance A.txt B.txt -g 5             # also emit the directed graph

Key flags: -a/--adn (DNA), -b/--binary, -r/--reverse, -y/--trajectory, -g/--get-direction [threshold], -I/--first-format, -S/--second-format, -i/--first #:#, -s/--second #:#, -p/--partitions, -o/--output, -L/--logs, -v/--version.

Input formats

Both tools auto-detect the format (or accept -F/-I/-S): raw text and binary, CSV/TSV, PBM/PGM images (P1/P2/P4/P5), and FASTA/DNA/RNA (including .gz). Use -m (or a directory) to treat each line/file as a separate sequence.

Contributing & releases

This repo uses Conventional Commits together with release-please so that versioning and PyPI publishing happen automatically — you never bump a version or push a tag by hand.

How to commit

Prefix every commit title with a type:

Add ! after the type (e.g. feat!:) or a BREAKING CHANGE: footer to force a major bump (1.x → 2.0.0). Before 1.0 a breaking change only bumped the minor; that is no longer the case.

Keep commit messages ASCII-only. release-please failed to parse a message containing Unicode maths symbols and silently dropped it from the changelog.

feat: add spectral-free NID batch mode
fix: correct off-by-one in PGM reader
docs: document the lzdistance directed graph

What happens automatically

The Python package is released from the rust-backend branch; the C++ main branch is kept only as a verification reference and is not published.

1. You merge conventional commits into rust-backend.
2. release-please opens (and keeps updating) a "release PR" that bumps the version in Cargo.toml and pyproject.toml, and updates CHANGELOG.md.
3. When you merge that release PR, release-please tags the release (vX.Y.Z) and creates a GitHub release.
4. The Release workflow then builds the wheels with maturin, publishes them to PyPI via OIDC trusted publishing (no token needed), and attaches the standalone binaries to the GitHub release.

So the entire flow is: write conventional commits → merge the release PR → PyPI updates itself.

One-time setup on PyPI: the trusted publisher for the lzcomplexity project (Settings → Publishing) is keyed on the repository and the workflow filename (plus an optional environment) — not on a branch. Point its Workflow name at release.yml (the previous C++ setup used wheels.yml). No API token or secret is stored in the repo.

CI

Every push and PR runs CI: cargo fmt --check, cargo clippy -D warnings, cargo test, a smoke test of both standalone binaries, and a wheel build + Python API smoke test on Linux/macOS/Windows.

Repository layout

crates/
├── lzcomplexity-core/   Rust crate: algorithms (LZ76, suffix array, LPF,
│                        shuffle, metrics). No Python or CLI types.
├── lzcomplexity-py/     PyO3 bindings → the `lzcomplexity` Python extension.
└── lzcomplexity-cli/    The `lzcomplexity` and `lzdistance` binaries.
python/lzcomplexity/     Python package skin: __init__.py, __init__.pyi, py.typed.
pyproject.toml           Maturin build config.

cargo test --workspace exercises the algorithmic core.

Differences from the C++ version

Same input ⇒ same outputs across Rust and C++ within float tolerance for the deterministic measures (factorization, factors, entropy density, information distance) — verified by differential testing. Shuffle-based metrics (emc) differ only in that Rust is reproducible run-to-run.

References

1. Lempel, A., & Ziv, J. (1976). On the complexity of finite sequences. IEEE Transactions on Information Theory, 22(1), 75–81.
2. Kontoyiannis, I., Algoet, P. H., Suhov, Y. M., & Wyner, A. J. (1998). Nonparametric entropy estimation for stationary processes and random fields. IEEE Transactions on Information Theory, 44(3), 1319–1327.

Authors

• Efrén Aragón Pérez — principal author and creator of lzcomplexity. The library exists because of him; he wrote the original implementation this work descends from.
• Daniel Estévez Moya — the Rust rewrite that is the current production backend.
• Ernesto Estévez Rams — from the research lineage of the original C++ implementation.

Citation

@software{lzcomplexity_2026,
  title   = {lzcomplexity: LZ76 complexity, entropy rate and information distance
             for symbolic sequences},
  author  = {Arag{\'o}n P{\'e}rez, Efr{\'e}n and
             Est{\'e}vez Moya, Daniel and
             Est{\'e}vez Rams, Ernesto},
  url     = {https://github.com/pleros-ai/lzcomplexity},
  version = {1.0.0},
  year    = {2026}
}

License

MIT — see LICENSE.