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https://github.com/qequ/pyrite

A Crystal library for scientific computing - featuring complex numbers, PRNGs, root-finding, statistical distributions, and more. Inspired by SciLua.
https://github.com/qequ/pyrite

complex-numbers crystal-lang mathematics numerical-methods prng root-finding scientific-computing statistics

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A Crystal library for scientific computing - featuring complex numbers, PRNGs, root-finding, statistical distributions, and more. Inspired by SciLua.

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# Pyrite



Pyrite Logo



Pyrite is a Crystal library for scientific computing, heavily inspired by the SciLua library. It provides a range of functionalities including complex numbers, special mathematical functions, pseudorandom number generators (PRNGs), root-finding algorithms, and statistical distributions. Pyrite is designed for applications requiring high performance and accurate computations in scientific and engineering domains.



## Installation



Add this to your application's shard.yml:



```yaml

dependencies:

  pyrite:

    github: qequ/pyrite

```



Then run:



```bash

$ shards install

```



## Usage



### Complex Numbers



```crystal



require "pyrite/complex"



# Creating complex numbers

c1 = ComplexNumbers::Complex.new(2.0, 3.0)

c2 = ComplexNumbers::Complex.new(1.0, 3.0)



# Operations

sum = c1 + c2

difference = c1 - c2

product = c1 * c2

quotient = c1 / c2

magnitude = c1.abs



puts "Sum: #{sum}"

puts "Difference: #{difference}"

puts "Product: #{product}"

puts "Quotient: #{quotient}"

puts "Magnitude of c1: #{magnitude}"



```



### Mathematical Functions

    

```crystal

require "pyrite/math"



# Special functions and constants

puts "Pi: #{Pyrite::Math::PI}"

puts "Absolute value: #{Pyrite::Math.abs(-3.5)}"

puts "Phi function: #{Pyrite::Math.phi(1.0)}"

```



### Pseudorandom Number Generators



```crystal

require "pyrite/prng"



# Kiss99 PRNG

rng = Pyrite::PRNG::Kiss99.new

puts "Random number: #{rng.next_bits}"

```



### Root-finding Algorithms



```crystal

require "pyrite/root"



# Newton method example

f = ->(x : Float64) { x**2 - 2 }

f_prime = ->(x : Float64) { 2*x }

root, _ = Pyrite::Root.newton(f, f_prime, 0.0, 2.0) { false }

puts "Root of x^2 - 2: #{root}"

```



### Statistical Distributions



#### Normal Distribution



```crystal



require "pyrite/stat"



# Normal Distribution with mean 0 and standard deviation 1

normal_dist = Pyrite::Stat::Normal.new(0.0, 1.0)

puts "PDF of normal distribution at 0: #{normal_dist.pdf(0.0)}"

puts "Random sample from normal distribution: #{normal_dist.sample}"



```



#### Exponential Distribution

  

```crystal

# Exponential Distribution with lambda = 1.5

exp_dist = Pyrite::Stat::Exponential.new(1.5)

puts "Mean of exponential distribution: #{exp_dist.mean}"

puts "Random sample from exponential distribution: #{exp_dist.sample}"



```



#### Uniform Distribution



```crystal

# Uniform Distribution between 0 and 1

uniform_dist = Pyrite::Stat::Uniform.new(0.0, 1.0)

puts "PDF of uniform distribution at 0.5: #{uniform_dist.pdf(0.5)}"

puts "Random sample from uniform distribution: #{uniform_dist.sample}"

  

```



#### Gamma Distribution



```crystal



# Gamma Distribution with alpha = 2.0 and beta = 3.0

gamma_dist = Pyrite::Stat::Gamma.new(2.0, 3.0)

puts "Mean of gamma distribution: #{gamma_dist.mean}"

puts "Random sample from gamma distribution: #{gamma_dist.sample}"

  

```



#### Beta Distribution



```crystal

# Beta Distribution with alpha = 2.0 and beta = 5.0

beta_dist = Pyrite::Stat::Beta.new(2.0, 5.0)

puts "PDF of beta distribution at 0.5: #{beta_dist.pdf(0.5)}"

puts "Random sample from beta distribution: #{beta_dist.sample}"



```



#### Log-Normal Distribution

  

```crystal



# Log-Normal Distribution with mu = 0 and sigma = 1

log_normal_dist = Pyrite::Stat::LogNormal.new(0.0, 1.0)

puts "PDF of log-normal distribution at 1: #{log_normal_dist.pdf(1.0)}"

puts "Random sample from log-normal distribution: #{log_normal_dist.sample}"



```



#### Student-t Distribution

  

```crystal

# Student-t Distribution with nu = 10

student_dist = Pyrite::Stat::Student.new(10)

puts "PDF of student-t distribution at 0: #{student_dist.pdf(0.0)}"

puts "Random sample from student-t distribution: #{student_dist.sample}"



```



## Development



After checking out the repo, run shards install to install dependencies. Then, run `crystal spec` to run the tests.



## Roadmap



Pyrite is continuously evolving, and there are several features and enhancements planned for future releases. The following is a list of potential additions to the library:



- Quasi Random Number Generators (QRNGs): Implement advanced random number generators that can produce quasi-random sequences, offering better coverage of the space than standard pseudorandom number generators.



- Differentiation: Include numerical differentiation capabilities to calculate derivatives of functions, which are essential in various scientific computations.



- Interpolation: Develop methods for interpolating data points, useful in data analysis, curve fitting, and creating smoother transitions between discrete data points.



- Matrix and Algebra: Expand the library to include matrix operations and linear algebra functionalities, which are fundamental in many scientific and engineering applications.



- Optimization Algorithms: Integrate optimization algorithms for finding minima/maxima of functions, which are crucial in fields like machine learning, economics, and engineering design.



- Statistical Analysis Tools: Enhance the statistical capabilities of the library with tools for data analysis, hypothesis testing, regression, and other statistical methods.



- Numerical Integration (Quadrature): Add methods for numerical integration to approximate the integral of functions, a common task in many scientific fields.



- Time Series Analysis: Implement functionality for analyzing and manipulating time series data, important in fields such as finance, economics, and meteorology.



- Signal Processing: Include tools for analyzing, modifying, and synthesizing signals, useful in audio processing, telecommunications, and control systems.



- Graphical and Visualization Tools: Develop visualization tools for data exploration and presentation, an important aspect of data analysis and scientific research.



- Expand Statistical Distributions: Add more statistical distributions and enhance existing ones to cover a wider range of applications.



- Parallel and Distributed Computing: Explore opportunities to leverage Crystal's concurrency model for parallel and distributed computing.



These enhancements aim to make Pyrite a more comprehensive toolkit for scientific computing in Crystal, catering to a wide range of applications and user needs.



## 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



- [Alvaro Frias Garay](https://github.com/qequ) - creator and maintainer



This project is based on and inspired by [SciLua](https://github.com/stepelu/lua-sci). The goal of Pyrite is to bring similar capabilities to the Crystal language, leveraging its performance and syntax features.