Pyrite

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:

dependencies:
  pyrite:
    github: qequ/pyrite

Then run:

$ shards install

Usage

Complex Numbers

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

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

require "pyrite/prng"

# Kiss99 PRNG
rng = Pyrite::PRNG::Kiss99.new
puts "Random number: #{rng.next_bits}"

Root-finding Algorithms

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

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

# 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

# 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

# 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

# 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

# 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

# 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 (https://github.com/qequ/pyrite/fork)
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 - creator and maintainer

This project is based on and inspired by SciLua. The goal of Pyrite is to bring similar capabilities to the Crystal language, leveraging its performance and syntax features.