Struct Langevin 

pub struct Langevin<D, G, T: FloatExt = f64>
where
    D: Fn(T, T) -> T + Clone + Send + Sync,
    G: Fn(T, T) -> T + Clone + Send + Sync,
{ /* private fields */ }

Langevin equation.

$$dX(t) = f(X(t), t),dt + g(X(t), t),dW(t),\qquad X(0)=x_0.$$

where (W(t)) is the Wiener process, also called Brownian motion.

Implementations

impl<D, G, T: FloatExt> Langevin<D, G, T>

where D: Fn(T, T) -> T + Clone + Send + Sync, G: Fn(T, T) -> T + Clone + Send + Sync,

pub fn new(drift_func: D, diffusion_func: G, start_position: T) -> XResult<Self>

Create a new Langevin

Arguments

• drift_func - The drift function.
• diffusion_func - The diffusion function.
• start_position - The starting position.

Example

use diffusionx::simulation::continuous::Langevin;

let drift = |x: f64, _t: f64| x;
let diffusion = |_x: f64, _t: f64| 1.0;
let start_position = 0.0;
let langevin = Langevin::new(drift, diffusion, start_position).unwrap();

pub fn get_start_position(&self) -> T

Get the starting position

pub fn get_drift_func(&self) -> &D

Get the drift function

pub fn get_diffusion_func(&self) -> &G

Get the diffusion function

Trait Implementations

impl<D, G, T: Clone + FloatExt> Clone for Langevin<D, G, T>

where D: Fn(T, T) -> T + Clone + Send + Sync + Clone, G: Fn(T, T) -> T + Clone + Send + Sync + Clone,

fn clone(&self) -> Langevin<D, G, T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<D, G, T: FloatExt> ContinuousProcess<T> for Langevin<D, G, T>

where D: Fn(T, T) -> T + Clone + Send + Sync, G: Fn(T, T) -> T + Clone + Send + Sync, StandardNormal: Distribution<T>,

fn start(&self) -> T

Get the starting position.

fn simulate(&self, duration: T, time_step: T) -> XResult<(Vec<T>, Vec<T>)>

Simulate the continuous process

fn displacement(&self, duration: T, time_step: T) -> XResult<T>

Get the displacement of the continuous process.

fn end(&self, duration: T, time_step: T) -> XResult<T>

Get the ending position at the requested duration.

fn mean(&self, duration: T, particles: usize, time_step: T) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the mean of the continuous process

fn msd(&self, duration: T, particles: usize, time_step: T) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the mean square displacement of the continuous process

fn raw_moment( &self, duration: T, order: i32, particles: usize, time_step: T, ) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the raw moment of the continuous process

fn central_moment( &self, duration: T, order: i32, particles: usize, time_step: T, ) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the central moment of the continuous process

fn frac_raw_moment( &self, duration: T, order: T, particles: usize, time_step: T, ) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the fractional raw moment of the continuous process

fn frac_central_moment( &self, duration: T, order: T, particles: usize, time_step: T, ) -> XResult<T>

where Self: ContinuousTrajectoryTrait<T>,

Get the fractional central moment of the continuous process

fn fpt( &self, domain: (T, T), max_duration: T, time_step: T, ) -> XResult<Option<T>>

where Self: Sized,

Get the first passage time of the continuous process

fn occupation_time( &self, domain: (T, T), duration: T, time_step: T, ) -> XResult<T>

where Self: Sized,

Get the occupation time of the continuous process

fn tamsd( &self, duration: T, delta: T, time_step: T, quad_order: usize, ) -> XResult<T>

where Self: Sized,

Get the time-averaged mean square displacement of the continuous process.

fn eatamsd( &self, duration: T, delta: T, particles: usize, time_step: T, quad_order: usize, ) -> XResult<T>

where Self: Sized,

Get the ensemble average of the time-averaged mean square displacement of the continuous process.

impl<D, G, T: Debug + FloatExt> Debug for Langevin<D, G, T>

where D: Fn(T, T) -> T + Clone + Send + Sync + Debug, G: Fn(T, T) -> T + Clone + Send + Sync + Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.