Particle sampling

sample!( rng, pg, df, mesh, method)

Sample from a Particle sampler

• rnd : Random generator
• pg : Particle group
• df : Distribution function
• mesh : Domain
• method : weighted or quietstart with weigth = 1

sample_quietsart!( rng, pg, df, mesh)

Sample from a Particle sampler

• rnd : Random generator
• pg : Particle group
• df : Distribution function
• mesh : Domain

Input r is a random number $\in [0,1]$

\[ f(x) = 1 + \alpha cos(k x)\]

on some domain $[0, 2\pi/k]$

Solve the equation $P(x)-r=0$ with Newton’s method

\[ x^{n+1} = x^n – (P(x)-(2\pi r / k)/f(x) \]

with

\[P(x) = \int_0^x (1 + \alpha cos(k y)) dy\]

\[P(x) = x + \frac{\alpha}{k} sin (k x)\]

sample_weighted!( rng, pg, df, mesh)

Sample from a Particle sampler

• rnd : Random generator
• pg : Particle group
• df : Distribution function
• mesh : Domain