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https://github.com/nin93/alea
Repeatable pseudo-random sampling, CDF over most known probability distributions.
https://github.com/nin93/alea
cdf crystal crystal-lang cumulative-distribution-function prng random random-draw random-generation random-number-generators
Last synced: about 2 months ago
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Repeatable pseudo-random sampling, CDF over most known probability distributions.
- Host: GitHub
- URL: https://github.com/nin93/alea
- Owner: nin93
- License: other
- Created: 2020-04-20T21:55:49.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2022-02-20T15:27:00.000Z (over 2 years ago)
- Last Synced: 2024-04-29T13:56:30.891Z (about 2 months ago)
- Topics: cdf, crystal, crystal-lang, cumulative-distribution-function, prng, random, random-draw, random-generation, random-number-generators
- Language: Crystal
- Homepage: https://nin93.github.io/alea/
- Size: 788 KB
- Stars: 12
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.md
Lists
- awesome-crystal - alea - Repeatable sampling, CDF and other utilities to work with probability distributions (Science and Data analysis)
README
# Alea
[](https://actions-badge.atrox.dev/nin93/alea/goto?ref=master)
[](https://github.com/crystal-lang/crystal)
[](https://crystalshards.org/shards/github/nin93/alea)
[](https://nin93.github.io/alea/)
[](https://github.com/nin93/alea/blob/master/LICENSE.md)
Alea is a collection of utilities to work with most known probability distributions,
written in pure Crystal.
> **Note**: This project is in development state and many distributions are
still missing, as well as cumulative distribution functions, so keep in mind that
breaking changes may occur frequently.
## Why Crystal?
Crystal compiles to really fast native code without sacrificing any of the modern
programming languages standards providing a nice and clean interface.
## Index
* [Features](#features)
+ [Currently Available](#currently-available)
+ [Supported Distributions](#supported-distributions)
+ [Projects](#projects)
* [Installation](#installation)
* [Usage](#usage)
+ [Sampling](#sampling)
+ [Unsafe Methods](#unsafe-methods)
+ [Pseudo Random Number Generators](#prngs)
+ [Custom PRNG](#custom-prng)
+ [Cumulative Distribution Functions](#cumulative-distribution-functions)
+ [Documentation](#documentation)
* [References](#references)
* [Contributing](#contributing)
* [Contributors](#contributors)
## Features
### Currently Available
* PRNGs implementations
* Random sampling (single/double precision)
* Cumulative Distribution Functions (single/double precision)
### Supported Distributions
| Distribution | Sampling (32 / 64)| CDF (32 / 64) |
|:--------------|:-----------------:|:-------------:|
| Beta | Y Y | N N |
| Chi-Square | Y Y | Y Y |
| Exponential | Y Y | Y Y |
| F-Snedecor | Y Y | N N |
| Gamma | Y Y | Y Y |
| Laplace | Y Y | Y Y |
| Log-Normal | Y Y | Y Y |
| Normal | Y Y | Y Y |
| Poisson | N Y | N Y |
| T-Student | Y Y | N N |
| Uniform | Y Y | Y Y |
### Projects
* Distribution and empirical data statistical properties
* Quantile Functions
## Installation
1. Add the dependency to your `shard.yml`:
```yaml
dependencies:
alea:
github: nin93/alea
```
2. Run `shards install`
3. Import the library:
```crystal
require "alea"
```
## Usage
### Sampling
`Random` is the interface provided to perform sampling:
```crystal
random = Alea::Random(Alea::XSR128).new
random.normal # => -0.36790519967553736 : Float64
# Append '32' to call the single-precision version
random.normal32 # => 0.19756398 : Float32
```
It also accepts an initial seed to reproduce the same seemingly random events across runs:
```crystal
seed = 9377
random = Alea::Random(Alea::XSR128).new(seed)
random.exp # => 0.10203669577353723 : Float64
```
#### Unsafe Methods
Plain sampling methods (such as `#normal`, `#gamma32`) performs checks
over arguments passed to prevent bad data generation or inner exceptions.
In order to avoid checks (might be slow in a large data generation) you must use their
unsafe version by prepending `next_` to them:
```crystal
random = Alea::Random(Alea::XSR128).new
random.normal(loc: 0, sigma: 0) # raises Alea::UndefinedError: sigma is 0 or negative.
random.next_normal(loc: 0, sigma: 0) # these might raise internal exceptions.
```
Timings are definitely comparable, though: see the
[benchmarks](https://github.com/nin93/alea/tree/master/benchmarks)
for direct comparisons between these methods.
### PRNGs
`Random` is actually a wrapper over a well defined pseudo-random number generator.
The basic generation of integers and floats comes from the underlying engine, more specifically
from: `#next_u32`, returning a random `UInt32`, and `#next_u64`, returning a random `UInt64`.
Floats are obtained by `ldexp` (load exponent) operations upon generated
unsigned integers; signed integers are obtained by raw cast.
Currently implemented engines:
+ `XSR128` backed by *xoroshiro128++* (32/64 bit)
+ `XSR256` backed by *xoshiro256++* (32/64 bit)
+ `MT19937` backed by *mersenne twister* (32/64 bit)
The digits in the class name stand for the overall period of the PRNG as a power of 2:
`(2^N) - 1`, where `N` is the said number.
`XSR256` and `XSR128` engines are from the [xoshiro](http://prng.di.unimi.it/) (XOR/shift/rotate)
collection, designed by Sebastiano Vigna and David Blackman: really fast generators promising
exquisite statistical properties as well.
`MT19937` engine is an implementation of the famous
[Mersenne Twister](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html), developed by Makoto
Matsumoto and Takuji Nishimura: the most widely used PRNG passing most strict statistical tests.
#### Custom PRNG
All PRNGs in this library inherit from a module: `PRNG`. You are allowed to build
your own custom PRNG by including the module and defining the methods needed by
`Alea::Random` to ensure proper repeatability and sampling, as described in this
[example](https://github.com/nin93/alea/blob/master/custom_prng.cr).
It is worth noting that in these implementations `#next_u32` and `#next_u64`
depend on different states and thus they are independent from each other,
as well as `#next_f32` and `#next_f64` or `#next_i32` and `#next_i64`.
It is still fine, though, if both `#next_u32` and `#next_u64` rely on the same
state, if you want. I choose not to, as it makes state advancements unpredictable.
### Cumulative Distribution Functions
`CDF` is the interface used to calculate the Cumulative Distribution Functions.
Given *X* ~ *D* and a fixed quantile *x*, CDFs are defined as the functions that
associate *x* to the probability that the real-valued random *X* from the
distribution *D* will take a value less or equal to *x*.
Arguments passed to `CDF` methods to shape the distributions are analogous to
those used for sampling:
```crystal
Alea::CDF.normal(0.0) # => 0.5 : Float64
Alea::CDF.normal(2.0, loc: 1.0, sigma: 0.5) # => 0.9772498680518208 : Float64
Alea::CDF.chisq(5.279, df: 5.0) # => 0.6172121213841358 : Float64
Alea::CDF.chisq32(5.279, df: 5.0) # => 0.61721206 : Float32
```
### Documentation
Documentation is hosted on [GitHub Pages](https://nin93.github.io/alea/).
## Into The Wild
Here is a list of the projects including alea:
* [crystal-data/num.cr](https://github.com/crystal-data/num.cr)
## Aknowledgments
Fully listed in [LICENSE.md](https://github.com/nin93/alea/tree/master/LICENSE.md):
* [Crystal](https://github.com/crystal-lang/crystal) `Random` module for uniform sampling
* [NumPy](https://github.com/numpy/numpy) `random` module for pseudo-random sampling methods
* [NumPy](https://github.com/numpy/numpy) `mt19937` prng implementation
* [JuliaLang](https://github.com/JuliaLang/julia) `random` module for ziggurat methods
* [IncGammaBeta.jl](https://github.com/jkovacic/IncGammaBeta.jl) for incomplete gamma functions
## Contributing
1. Fork it ()
2. Create your feature branch (`git checkout -b my-new-feature`)
3. Commit your changes (`git commit -am 'Add some feature'`)
4. Push to the branch (`git push origin my-new-feature`)
5. Create a new Pull Request
## Contributors
- [Elia Franzella](https://github.com/nin93) - creator and maintainer