How to integrate in R^d¶

ZüNIS integrates over the unit hypercube. In order to integrate functions over the whole real line, it is necessary to perform a variable transformation. The change of variables has to map [0,1] to R. This can be done by using any bijective function with two divergences such as the tangent and the inverse hyperbolic tangent functions.

Here is for example how to compute a gaussian integral in two dimensions.

import torch
import numpy as np
from zunis.integration import Integrator

device = torch.device("cuda")

d = 2

def f(x):
    return torch.exp(-(x).square().sum(axis=1))

def f_wrapped(x):
    return f(torch.tan(np.pi*(x-0.5)))*((np.pi/(torch.cos(np.pi*(x-0.5)).square()))).prod(axis=1)

integrator = Integrator(d=d,f=f_wrapped,device=device)
result, uncertainty, history = integrator.integrate()