diffusionx 0.3.0

A library for random number/stochastic process simulation with high performance.

DiffusionX

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[!NOTE] Development is in progress.

The Python binding of the same-named Rust crate diffusionx, a multi-threaded Rust crate for random number generation and stochastic process simulation, via PyO3.

Usage

Random Number Generation

High-performance parallel random number generation using diffusionx.random.

from diffusionx import random

# Generate standard normal random numbers (10 samples)
x = random.randn(10)

# Generate uniform random numbers (3x3 matrix) in [0, 1)
u = random.uniform((3, 3), low=0.0, high=1.0)

# Generate alpha-stable random numbers (alpha=1.5, beta=0.5)
s = random.stable_rand(alpha=1.5, beta=0.5, size=1000)

Stochastic Process Simulation

Simulate various stochastic processes and calculate functionals using diffusionx.simulation.

from diffusionx.simulation import Bm, FBm, Levy

# --- Brownian Motion ---
bm = Bm(start_position=0.0, diffusion_coefficient=1.0)
# Simulate trajectory
times, positions = bm.simulate(duration=10.0, time_step=0.01)
# Calculate First Passage Time (FPT) for domain (-1, 1)
fpt = bm.fpt(domain=(-1, 1))

# --- Fractional Brownian Motion ---
fbm = FBm(hurst_exponent=0.7)
# Calculate Time-Averaged Mean Squared Displacement (TAMSD)
tamsd = fbm.tamsd(duration=10.0, delta=1.0)

# --- Alpha-Stable Lévy Process ---
levy = Levy(alpha=1.5)
# Calculate Occupation Time in domain (-1, 1)
occ_time = levy.occupation_time(domain=(-1, 1), duration=10.0)

Features

Random Number Generation (diffusionx.random)

• Gaussian: randn
• Uniform: uniform
• Exponential: randexp
• Poisson: poisson
• $\alpha$-Stable: stable_rand, skew_stable_rand
• Bernoulli: bool_rand

Stochastic Processes (diffusionx.simulation)

Diffusions & Lévy Processes

• Brownian Motion (Bm)
• Geometric Brownian Motion (GeometricBm)
• Fractional Brownian Motion (FBm)
• Lévy Process (Levy, AsymmetricLevy)
• Cauchy Process (Cauchy, AsymmetricCauchy)
• Gamma Process (Gamma)
• Ornstein-Uhlenbeck Process (OU)

Subordinators

• Stable Subordinator (Subordinator)
• Inverse Stable Subordinator (InvSubordinator)

Langevin Dynamics

• Langevin Equation (Langevin)
• Generalized Langevin Equation (GeneralizedLangevin)
• Subordinated Langevin Equation (SubordinatedLangevin)

Brownian Functionals

• Brownian Bridge (BrownianBridge)
• Brownian Excursion (BrownianExcursion)
• Brownian Meander (BrownianMeander)

Others

• Continuous Time Random Walk (CTRW)
• Poisson Process (Poisson)
• Lévy Walk (LevyWalk)

Functionals

Support for calculating various functionals across most processes:

• FPT: First Passage Time (and moments)
• Occupation Time: Time spent in a domain (and moments)
• MSD/TAMSD: Mean Squared Displacement metrics

Benchmark

Performance benchmark tests compare the Rust, C++, Julia, and Python implementations, which can be found here.

License

This project is dual-licensed under:

• MIT License
• Apache License Version 2.0

You can choose to use either license.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.