Sampling Fibers

Much like simple Monte Carlo depends on appropriately defined ‘random’ points in the domain of a function of interest to estimate an associated integral, FMC estimators take as argument a collection of random line segments (fibers) in an appropriately defined domain. Whereas in SMC the sampling ‘atom’ is a point with no spatial extent, in FMC the atom is a line segment with nonzero but finite spatial extent (length).

We currently support only rectilinear domains, although it would be relatively straightforward to generalize this in many cases. For a rectangular domain which is illustrated pictorially below, we can use sample to sample a collection of fibers.

import jax.numpy as np
import jax.random as npr
from jaxtyping import Array, Float

import fibermc.estimators as estimators

domain_boundary = np.array([
      0., # x0
      0., # y0
      1., # x1
      1.  # y1
      ])
key = npr.PRNGKey(0)
num_fibers: int = 3
fiber_length: float = 1e-02

fibers: Float[Array, "n 2 2"] = estimators.sample(
                                             key,
                                             bounds,
                                             num_fibers,
                                             fiber_length
                                       )