DiffusionX

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DiffusionX is a multi-threaded high-performance Rust library for random number generation and stochastic process simulation, designed for scientific computing and quantitative finance applications.

Features

• High Performance: Optimized for computational efficiency with multi-threading support via Rayon
• Comprehensive: Extensive collection of random distributions and stochastic processes for scientific computing
• Extensible: Trait-based architecture enabling easy extension with custom processes and distributions
• Well-documented: Detailed API documentation with mathematical background and usage examples
• Type-safe: Leverages Rust's type system for compile-time safety and correctness
• Zero-cost abstractions: Efficient abstractions with minimal runtime overhead

Visualization

DiffusionX provides built-in visualization capabilities using the plotters crate:

• Process Trajectories: Easily visualize continuous process trajectories
• Customizable Plots: Configure plot appearance including colors, dimensions, and line styles
• Multiple Backends: Support for both BitMap and SVG output formats
• Simple API: Intuitive trait-based API for visualizing simulation results

Implemented

Random Number Generation

• Normal distribution - Gaussian random variables with specified mean and variance
• Uniform distribution - Uniform random variables in specified ranges
• Exponential distribution - Exponential waiting times with specified rate
• Poisson distribution - Discrete count distribution with specified mean
• Alpha-stable distribution - Heavy-tailed distributions with specified stability, skewness, scale, and location

Stochastic Processes

• Brownian motion - Standard and generalized with drift and diffusion
• Alpha-stable Lévy process - Non-Gaussian processes with heavy tails
• Subordinator - Time-changed processes
• Inverse subordinator - Processes for modeling waiting times
• Poisson process - Counting processes with independent increments
• Fractional Brownian motion - Long-range dependent processes
• Continuous time random walk - Jump processes with random waiting times
• Ornstein-Uhlenbeck process - Mean-reverting processes
• Langevin equation - Physical models with friction and noise
• Generalized Langevin equation - Extended models with memory effects
• Subordinated Langevin equation - Time-changed Langevin processes
• Lévy walk - Superdiffusive processes with coupled jump lengths and waiting times
• Birth-death process - Discrete-state processes with birth and death rates
• Random walk - Discrete-time random walk
• Brownian bridge - Brownian motion conditioned to hit origin at the end
• Brownian excursion - Brownian motion conditioned to be positive and to take the value 0 at time 1

Installation

Add the following to your Cargo.toml:

[dependencies]
diffusionx = "*"  # Replace with the latest version

Or use the following command to install:

cargo add diffusionx

Usage

Random Number Generation

use diffusionx::random::{normal, uniform, exponential, poisson, stable};

// Normal Distribution
let normal_sample = normal::rand(0.0, 1.0)?; // Generate a normal random number with mean 0.0 and std 1.0
let std_normal_samples = normal::standard_rands(1000); // Generate 1000 standard normal random numbers

// Uniform Distribution
let uniform_sample = uniform::range_rand(0..10)?; // Generate a uniform random number in range [0, 10)
let std_uniform_samples = uniform::standard_rands(1000); // Generate 1000 uniform random numbers in range [0, 1)

// Exponential Distribution
let exp_samples = exponential::rands(1.0, 1000)?; // Generate 1000 exponential random numbers with rate 1.0

// Poisson Distribution
let poisson_samples = poisson::rands(5.0, 1000)?; // Generate 1000 Poisson random numbers with mean 5.0

// α-Stable Distribution
// Standard α-stable distribution (σ=1, μ=0)
let stable_samples = stable::standard_rands(1.5, 0.5, 1000)?; // Generate 1000 standard stable random numbers

// Object-oriented interface for stable distributions
let stable = stable::Stable::new(1.5, 0.5, 1.0, 0.0)?; // Create a stable distribution object
let samples = stable.samples(1000)?; // Generate 1000 samples

Stochastic Process Simulation

use diffusionx::simulation::{prelude::*, continuous::Bm};

// Brownian motion simulation
let bm = Bm::default();  // Create standard Brownian motion object
let traj = bm.duration(1.0)?;  // Create trajectory with duration 1.0
let (times, positions) = traj.simulate(0.01)?;  // Simulate Brownian motion trajectory with time step 0.01

// Monte Carlo simulation of Brownian motion statistics
let mean = traj.raw_moment(1, 1000, 0.01)?;  // First-order raw moment with 1000 particles
let msd = traj.central_moment(2, 1000, 0.01)?;  // Second-order central moment with 1000 particles

// First passage time of Brownian motion
let fpt = bm.fpt(0.01, (-1.0, 1.0), 1000)?; // Calculate FPT with boundaries at -1.0 and 1.0

Visualization Example

use diffusionx::{
    simulation::{continuous::Bm, prelude::*},
    visualize::{PlotConfigBuilder, PlotterBackend, Visualize},
};

// Create Brownian motion trajectory
let bm = Bm::default();
let traj = bm.duration(10.0)?;

// Configure and create visualization
let config = PlotConfigBuilder::default()
    .time_step(0.01)
    .output_path("brownian_motion.png")
    .title("Brownian Motion Trajectory")
    .x_label("Time t")
    .y_label("Position X(t)")
    .size((800, 600))
    .backend(PlotterBackend::BitMap)
    .build()?;

// Generate plot
traj.plot(&config)?;

Architecture and Extensibility

DiffusionX is designed with a trait-based system for high extensibility and performance:

Core Traits

• ContinuousProcess: Base trait for continuous stochastic processes
• PointProcess: Base trait for point processes
• DiscreteProcess: Base trait for discrete stochastic processes
• Moment: Trait for statistical moments calculation, including raw and central moments
• Visualize: Trait for plotting process trajectories

Functional Distribution Simulation

DiffusionX provides powerful functional distribution simulation for stochastic processes:

1. First Passage Time (FPT): Calculate when a process first reaches a specified boundary

   // For a Brownian motion process
   let bm = Bm::default();
   let fpt = bm.fpt(0.01, (-1.0, 1.0), 1000)?; // Calculate FPT for crossing boundaries
   

2. Occupation Time: Measure time spent by a process in a specified region

   // For a Brownian motion process
   let bm = Bm::default();
   let traj = bm.duration(10.0)?;
   let occupation = traj.occupation_time(0.01, (0.0, 2.0))?; // Calculate time spent in region [0.0, 2.0]
   

Extending with Custom Processes

1. Adding a New Continuous Process:

   #[derive(Clone)]
   struct MyProcess {
       // Your parameters
       // Should be `Send + Sync` for parallel computation
   }
   
   impl ContinuousProcess for MyProcess {
       fn simulate(&self, duration: impl Into<f64>, time_step: f64) -> XResult<(Vec<f64>, Vec<f64>)> {
           // Implement your simulation logic
           todo!()
       }
   }
   

2. Automatic Feature Acquisition:

   • Implementing ContinuousProcess trait automatically provides ContinuousTrajectoryTrait functionality
   • ContinuousTrajectory provides access to the Moment trait functionality
   • Built-in support for moment statistics calculation

Example:

let myprocess = MyProcess::default();
let traj = myprocess.duration(10)?;
let mean = traj.raw_moment(1, 1000, 0.01)?; // Calculate mean with 1000 particles

3. Parallel Computing Support:

   • Automatic parallel computation for moment calculations using Rayon
   • Default parallel strategy for statistical calculations
   • Configurable parallelism for optimal performance

4. Visualization Support:

   • Easy trajectory visualization with minimal code
   • Highly customizable plot configuration

Example:

// Visualize a Brownian motion trajectory
use diffusionx::visualize::{PlotConfigBuilder, Visualize};

let bm = Bm::default().duration(10)?;
let config = PlotConfigBuilder::default()
    .title("Brownian Motion")
    .output_path("brownian_motion.png")
    .build()?;

bm.plot(&config)?; // Generates a plot with the specified configuration

Benchmark

The related content can be found in the Benchmark section of py-diffusionx.

License

This project is dual-licensed under:

• MIT License
• Apache License Version 2.0

You can choose to use either license.