An implementation of "The Wavelet Matrix" (Claude and Navarro) http://www.dcc.uchile.cl/~gnavarro/ps/spire12.4.pdf.

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:

```
immutable 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`

.

```
data = rand(0x00:0x03, 100_000)
wm = WaveletMatrix{2}(data)
wm[129]
rank(0x02, wm, 5555)
select(0x01, wm, 9876)
```

05/30/2015

6 months ago

66 commits