Class reference

class montecarlo.MonteCarloIntegrator(rectangle: list, parallel: bool = False, seed: bool | int = False)

Class to compute a 2D integral using a MonteCarlo method

__init__(rectangle: list, parallel: bool = False, seed: bool | int = False)

Parameters:

rectangle: tuple

with 4 elements (x0, x1, y0, y1) defining the integration rectangle R

parallel: bool

If true, it will use multiprocessing to evaluate each point. Otherwise, single process.

seed: float or False

Seed for the random number generator (repeatability). If False, random.

static _compute_sample(point: tuple, f: Callable, g: Callable) → float | None

Computes the value of the function f in the point x, y. If the point is inside of g, the function returns the value of the function in f. Otherwise, the function returns None.

Parameters:

point: tuple

x, y pair of values

f: function

callable function defining the function to be integrated

g: function

callable function defining the region

Returns:

compute_integral()

Compute integral using the MonteCarlo Method. Each point is computed by the static method _compute_sample(). Then, it applies the theory of the mean-value theorem to compute the area. The return value is stored within the class, and also returned.

Returns:

Value of the integral.

property f

Function of x,y that is to be integrated. Defined as F(x,y) = 0. If 1 is provided, the integration provides the area.

Parameters:

User defined function f

property g

Function that defines the integration region. It should be defined implicitly as G(x,y) = 0.

Returns:

User defined function g

generate_points(n: int = 20)

Function to generate the random points.

Parameters:

n: int

plot(all_random_points: bool = False)

Function to plot the process. In general, it will plot the contour plot filled of f, the domain defined by g with a shadowed area and border, and the montecarlo points. If any of these is not available, it will simply skip it. Uses two auxiliary functions to actually plot.

Parameters:

all_random_points: bool

If True, it will plot all the points. This may be slow if n is large.

Returns:

fig: figure handles

ax: axes handles