Wavelet Matrix
High-performance Wavelet Matrix implementation powered by Rust,
supporting fast rank / select / range queries over indexed sequences
- PyPI: https://pypi.org/project/wavelet-matrix
- Document: https://math-hiyoko.github.io/wavelet-matrix
- Repository: https://github.com/math-hiyoko/wavelet-matrix
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.
1 maintainer
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