19 releases
Uses new Rust 2024
new 0.3.7 | May 6, 2025 |
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0.3.6 |
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0.3.5 | Apr 29, 2025 |
0.3.1 | Mar 31, 2025 |
0.1.4 | Feb 24, 2025 |
#187 in Algorithms
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DiffusionX
English | 简体中文
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
- Cauchy process - Lévy process with stable index 1
- 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
- Brownian meander
- Gamma process - Non-negative process with independent and stationary increments
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, stable};
// Generate a normal random number with mean 0.0 and std 1.0
let normal_sample = normal::rand(0.0, 1.0)?;
// Generate 1000 standard normal random numbers
let std_normal_samples = normal::standard_rands(1000);
// Generate a uniform random number in range [0, 10)
let uniform_sample = uniform::range_rand(0..10)?;
// Generate 1000 uniform random numbers in range [0, 1)
let std_uniform_samples = uniform::standard_rands(1000);
// Generate 1000 standard stable random numbers
let stable_samples = stable::standard_rands(1.5, 0.5, 1000)?;
Stochastic Process Simulation
use diffusionx::simulation::{prelude::*, continuous::Bm};
// Create standard Brownian motion object
let bm = Bm::default();
// Create trajectory with duration 1.0
let traj = bm.duration(1.0)?;
// Simulate Brownian motion trajectory with time step 0.01
let (times, positions) = traj.simulate(0.01)?;
// Calculate first-order raw moment with 1000 particles and time step 0.01
let mean = traj.raw_moment(1, 1000, 0.01)?;
// Calculate second-order central moment with 1000 particles and time step 0.01
let msd = traj.central_moment(2, 1000, 0.01)?;
// Calculate first passage time of Brownian motion with boundaries at -1.0 and 1.0
let fpt = bm.fpt(0.01, (-1.0, 1.0), 1000)?;
Visualization Example
use diffusionx::{
simulation::{continuous::Bm, prelude::*},
};
// 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")
.caption("Brownian Motion Trajectory")
.x_label("t")
.y_label("B")
.legend("bm")
.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 processesPointProcess
: Base trait for point processesDiscreteProcess
: Base trait for discrete stochastic processesMoment
: Trait for statistical moments calculation, including raw and central momentsVisualize
: Trait for plotting process trajectories
Functional Distribution Simulation
DiffusionX provides powerful functional distribution simulation for stochastic processes:
-
First Passage Time (FPT): Calculate when a process first reaches a specified boundary
// For a Brownian motion process let bm = Bm::default(); // Calculate first passage time with time step 0.01, // boundaries at -1.0 and 1.0, and 1000 particles let fpt = bm.fpt(0.01, (-1.0, 1.0), 1000)?;
-
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)?; // Calculate time spent in region [0.0, 2.0] with time step 0.01 let occupation = traj.occupation_time(0.01, (0.0, 2.0))?;
Extending with Custom Processes
-
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!() } }
-
Automatic Feature Acquisition:
- Implementing
ContinuousProcess
trait automatically providesContinuousTrajectoryTrait
functionality ContinuousTrajectory
provides access to theMoment
trait functionality- Built-in support for moment statistics calculation
- Implementing
Example:
let myprocess = MyProcess::default();
let traj = myprocess.duration(10)?;
// Calculate mean with 1000 particles and time step 0.01
let mean = traj.raw_moment(1, 1000, 0.01)?;
-
Parallel Computing Support:
- Automatic parallel computation for moment calculations using Rayon
- Default parallel strategy for statistical calculations
- Configurable parallelism for optimal performance
-
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:
You can choose to use either license.
Dependencies
~5.5–8.5MB
~156K SLoC