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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.