differential-equations 0.6.0

//! Defines system of stochastic differential equations for numerical solvers.
//! The NumericalMethods use this trait to take a input system from the user and solve
//! Includes a stochastic differential equation. Event handling is provided via the separate `Event` trait.

use crate::traits::{DefaultState, Real, State};

/// SDE Trait for Stochastic Differential Equations
///
/// SDE trait defines the stochastic differential equation dY = a(t,Y)dt + b(t,Y)dW for the solver.
/// The stochastic differential equation is used to solve systems with both deterministic and random components.
///
/// # Impl
/// * `drift`     - Deterministic part a(t,Y) of the SDE in form drift(t, &y, &mut dydt).
/// * `diffusion` - Stochastic part b(t,Y) of the SDE in form diffusion(t, &y, &mut dydw).
/// * `noise`     - Generates the random noise increments for the SDE.
pub trait SDE<T = f64, Y = DefaultState<T>>
where
    T: Real,
    Y: State<T>,
{
    /// Drift function a(t,Y) - deterministic part of the SDE
    ///
    /// A stochastic differential equation (SDE) takes an independent variable
    /// which in this case is 't' as it is typically time and a dependent variable
    /// which is a vector of values 'y'. The drift term represents the deterministic
    /// component of the SDE that describes the expected change in the system over time.
    ///
    /// For efficiency and ergonomics the drift is calculated from an argument
    /// of a mutable reference to the drift vector dydt. This allows for
    /// calculations to be done in place which is more efficient as iterative
    /// SDE solvers require this term to be calculated at each step.
    ///
    /// # Arguments
    /// * `t`    - Independent variable point.
    /// * `y`    - Dependent variable point.
    /// * `dydt` - Drift term output.
    ///
    fn drift(&self, t: T, y: &Y, dydt: &mut Y);

    /// Diffusion function b(t,Y) - stochastic part of the SDE
    ///
    /// This represents the random/stochastic component of the SDE that describes
    /// how noise or random fluctuations affect the system. The diffusion term
    /// is multiplied by a Wiener process (dW) in the SDE formulation.
    ///
    /// # Arguments
    /// * `t`    - Independent variable point.
    /// * `y`    - Dependent variable point.
    /// * `dydw` - Diffusion term output.
    ///
    fn diffusion(&self, t: T, y: &Y, dydw: &mut Y);

    /// Noise function - generates random noise increments for the SDE
    ///
    /// This function allows custom control over how noise is generated for the SDE.
    /// Users should implement this to generate appropriate random increments for their SDE.
    /// For standard Wiener process, this is typically normal distribution with mean 0
    /// and standard deviation sqrt(dt).
    ///
    /// Users are responsible for initializing and managing their own random number
    /// generators, allowing full control over seeding for reproducible results.
    ///
    /// # Arguments
    /// * `dt` - Time step size.
    /// * `dw` - Vector to store generated noise increments.
    ///
    fn noise(&mut self, dt: T, dw: &mut Y);
}