Struct RandomWalk 

pub struct RandomWalk<T: FloatExt = f64> { /* private fields */ }

Random walk with heavy-tailed jump lengths.

Mathematical Formulation

The path is represented by

$$X_n = X_0 + \sum_{i=1}^{n} A_i,$$

where the jump lengths (A_i) are sampled from an alpha-stable law and then assigned a sign according to probability.

Implementations

impl<T: FloatExt> RandomWalk<T>

pub fn new(probability: T, alpha: T, start_position: T) -> XResult<Self>

Create a new RandomWalk

Arguments

• probability - The probability of the step in the positive direction
• alpha - The alpha parameter of the stable distribution
• start_position - The starting position

Example

use diffusionx::simulation::discrete::RandomWalk;

let rw = RandomWalk::new(0.5, 1.0, 0.0).unwrap();

pub fn probability(&self) -> T

Get the probability of the step in the positive direction

pub fn alpha(&self) -> T

Get the alpha parameter of the stable distribution

pub fn start_position(&self) -> T

Get the starting position

Trait Implementations

impl<T: Clone + FloatExt> Clone for RandomWalk<T>

fn clone(&self) -> RandomWalk<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug + FloatExt> Debug for RandomWalk<T>

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

Formats the value using the given formatter.

impl<T: FloatExt> Default for RandomWalk<T>

fn default() -> Self

Returns the “default value” for a type.

impl<N: IntExt, X: FloatExt + SampleUniform> DiscreteProcess<N, X> for RandomWalk<X>

where Exp1: Distribution<X>, Range<N>: IntoParallelIterator + IntoIterator,

fn start(&self) -> X

Get the starting position

fn simulate(&self, num_step: N) -> XResult<Vec<X>>

Simulate the discrete process

fn displacement(&self, num_step: N) -> XResult<X>

Get the displacement of the discrete process

fn end(&self, num_step: N) -> XResult<X>

Get the ending position

fn mean(&self, num_step: N, particles: usize) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the mean of the discrete process

fn msd(&self, num_step: N, particles: usize) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the mean square displacement of the discrete process

fn raw_moment(&self, num_step: N, order: i32, particles: usize) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the raw moment of the discrete process

fn central_moment( &self, num_step: N, order: i32, particles: usize, ) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the central moment of the discrete process

fn frac_raw_moment( &self, num_step: N, order: f64, particles: usize, ) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the fractional raw moment of the discrete process

fn frac_central_moment( &self, num_step: N, order: f64, particles: usize, ) -> XResult<f64>

where Self: DiscreteTrajectoryTrait<N, X>,

Get the fractional central moment of the discrete process