https://github.com/biojulia/waveletmatrices.jl

The Wavelet Matrix
https://github.com/biojulia/waveletmatrices.jl

Last synced: about 1 year ago
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The Wavelet Matrix

• Host: GitHub
• URL: https://github.com/biojulia/waveletmatrices.jl
• Owner: BioJulia
• License: other
• Created: 2015-05-30T23:45:36.000Z (about 11 years ago)
• Default Branch: master
• Last Pushed: 2023-04-23T14:25:53.000Z (about 3 years ago)
• Last Synced: 2025-04-15T21:30:28.170Z (about 1 year ago)
• Language: Julia
• Size: 62.5 KB
• Stars: 11
• Watchers: 10
• Forks: 7
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • Contributing: CONTRIBUTING.md
  • License: LICENSE.md
  • Code of conduct: CODE_OF_CONDUCT.md

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README

          
# WaveletMatrices

[![Build Status](https://travis-ci.org/BioJulia/WaveletMatrices.jl.svg?branch=master)](https://travis-ci.org/BioJulia/WaveletMatrices.jl)

[![GitHub latest release](https://img.shields.io/badge/latest-v0.2.0-blue)](https://github.com/BioJulia/WaveletMatrices.jl)

[![GitHub latest release](https://img.shields.io/badge/stable-v0.2.0-green)](https://github.com/BioJulia/WaveletMatrices.jl/releases)

[![Julia versions](https://img.shields.io/badge/julia-1.0+-blue)](https://julialang.org/)

An implementation of "The Wavelet Matrix" (Claude and Navarro) .

The wavelet matrix is a data structure to represent an immutable sequence of

unsigned integers that supports some queries efficiently.

The `WaveletMatrix` type is defined as follows:

```julia

struct WaveletMatrix{w,T<:Unsigned,B<:AbstractBitVector} <: AbstractVector{T}

```

where

* `w`: the number of bits required to encode the unsigned integers (elements)

* `T`: the type of elements

* `B`: the type of bit vectors used to store elements.

To efficiently pack a sequence of unsigned integers, `w` should be as small as possible but enough to encode those integers.

For example, if you want to store integers between 0x00 and 0x03 (i.e. four distinct integers), setting `w = 2 (= ceil(log2(4)))` is the best choice.

The basic operations available on the wavelet matrix are:

* `getindex(wm::WaveletMatrix, i::Integer)`: Return `i`-th element of `wm`.

* `rank(a::Unsigned, wm::WaveletMatrix, i::Integer)`: Count the number of `a`'s occurrences in `wm` between `1:i`.

* `select(a::Unsigned, wm::WaveletMatrix, j::Integer)`: Return the position of the `j`-th occurrence of `a` in `wm`.

## Example

```julia

data = rand(0x00:0x03, 100_000)

wm = WaveletMatrix{2}(data)

wm[129]

rank(0x02, wm, 5555)

partialsort(0x01, wm, 9876)

```