Python Monte Carlo Tools

Library with useful functions for numerical mathematics and physics.

Scaled to support x dimensions

Monte Carlo Integration

To use, call mctools.integrate(f, n, lims, **kwargs), where f is a function of x arguments, n is the iteration density, and lims are the limits of the integral (functions or numbers).

List of kwargs

• start is the x-dimensional coordinate for where the integration begins. The algorithm expands around this point until the shape defined by the limits is encapsulated and the integral converges. Is by default at the origin.
• wedge is the segment of the shape which is integrated. For example, wedge=[3,8] means the function will only integrate the 'third eighth' of the shape. This makes multiprocessing easier as the integral job can be spread over several threads. By default, wedge=[1,1], and may be defined as wedge=[segment, total number of segments]. Note that if multiple segments are used, the total integral is sum of the integral of each wedge e.g. full integral = integrate(..., wedge=[1,2]) + integrate(..., wedge=[2,2])
• box_size is by default 1. Details the size of the line/area/volume/... which is processed at once. The number of throws in each box is round(n * box_size).

Numerical differentiation

Numerical multidimensional derivative functions are included as well:

• mctools.partial_diff(f, position, axis, dimensions, delta) gets partial derivative of function f at position along axisth direction, with dimensions total number of dimensions and step-size delta
• mctools.grad(f, position, dimensions, delta) gets grad of function f with similar arguments to partial_diff
• mctools.direct_diff(f, position, dimensions, delta) gets directional derivative of f

Progress bar

Simple console progress bar

• mctools.pbar(iters, total_iters) prints a progress bar with percentage iters/total_iters