Wavelet Matrix

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High-performance Wavelet Matrix implementation powered by Rust,
supporting fast rank / select / range queries over indexed sequences

Features:

  • Fast rank, select, quantile
  • Rich range queries (freq / sum / top-k / min / max)
  • Optional disk-backed storage for static WaveletMatrix (on_disk=True)
  • Optional dynamic updates (insert / remove / update)

Installation

pip install wavelet-matrix

WaveletMatrix

WaveletMatrix indexes a static sequence of integers,
enabling fast queries where runtime depends on bit-width, not data size.

from wavelet_matrix import WaveletMatrix

data = [5, 4, 5, 5, 2, 1, 5, 6, 1, 3, 5, 0]
wm = WaveletMatrix(data)

WaveletMatrix also supports disk-backed storage for large static sequences.
Set on_disk=True to keep its internal data on disk instead of holding it all in memory.

wm = WaveletMatrix(data, on_disk=True)

Frequency Queries

Count occurrences (rank)

wm.rank(value=5, end=9)
# 4

Find position (select)

wm.select(value=5, kth=4)
# 6

Order Statistics

k-th smallest value (quantile)

wm.quantile(start=2, end=12, kth=8)
# 5

Range Aggregation

Sum values (range_sum)

wm.range_sum(start=2, end=8)
# 24

Count values in [lower, upper) (range_freq)

wm.range_freq(start=1, end=9, lower=4, upper=6)
# 4

List values with counts (range_list)

wm.range_list(start=1, end=9, lower=4, upper=6)
# [{'value': 4, 'count': 1}, {'value': 5, 'count': 3}]

Top-K Queries

Most frequent values (topk)

wm.topk(start=1, end=10, k=2)
# [{'value': 5, 'count': 3}, {'value': 1, 'count': 2}]

Extreme values (range_maxk / range_mink)

wm.range_maxk(start=1, end=9, k=2)
# [{'value': 6, 'count': 1}, {'value': 5, 'count': 3}]
wm.range_mink(start=1, end=9, k=2)
# [{'value': 1, 'count': 2}, {'value': 2, 'count': 1}]

Boundary Queries

wm.prev_value(start=1, end=9, upper=7)
# 6
wm.next_value(start=1, end=9, lower=4)
# 4

DynamicWaveletMatrix

DynamicWaveletMatrix supports mutable sequences with insert/remove/update.

Trade-off:

  • Higher overhead
  • Values must fit within max_bit
from wavelet_matrix import DynamicWaveletMatrix

dwm = DynamicWaveletMatrix(data, max_bit=4)

Insert

dwm.insert(index=4, value=8)

Remove

dwm.remove(index=4)

Update

dwm.update(index=4, value=5)
# or dwm[4] = 5

Development

Running Tests

pip install -e ".[test]"
cargo test --all --release
pytest

Formating Code

pip install -e ".[dev]"
cargo fmt
ruff format

Generating Docs

pdoc wavelet_matrix \
      --output-directory docs \
      --no-search \
      --docformat markdown \
      --template-directory pdoc_templates

References

  • Francisco Claude, Gonzalo Navarro, Alberto Ordóñez,
    The wavelet matrix: An efficient wavelet tree for large alphabets,
    Information Systems,
    Volume 47,
    2015,
    Pages 15-32,
    ISSN 0306-4379,
    https://doi.org/10.1016/j.is.2014.06.002.

Project links

Data verified by PyPI on
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Newer release available (2.2.6)

1 maintainer

PyPI data
Data sourced directly from PyPI's database.
Avatar for math-hiyoko from gravatar.com math-hiyoko

Credits

Author: Koki Watanabe

GitHub Statistics

Data verified by PyPI on 
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

MIT License

Requires

Python >=3.9

Provides Extra

dev test

Tags

wavelet matrix data structure algorithm sequence index rank select quantile top-k range query dynamic update indexing succinct

Classifiers

Report project as malware

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