VILTRUM: Varied Integration Layouts for arbiTRary integrals in a Unified Manner - A C++17 header-only library that provides a set of numerical integration routines.

viltrum is a header-only library and has no external dependencies, so installation is rather simple (it does not require any compilation process). You just need to download the library in a specific folder:

folder> git clone https://github.com/adolfomunoz/viltrum.git

Then make sure folder is within the included directories (-Ifolder parameter in g++, include_directories("folder") in CMake) and include it from C++.

#include <viltrum/viltrum.h>

That would be enough to use all the features of the library. There are other alternatives that might be more comfortable for you, see them here. There is a CMake-based building system for several example and test executable files that automatically downloads external dependencies and compiles all executables but it is not needed for the libray's usage.

Integrating a function in a specific n-dimensional range is rather simple. You need the following information:

• An integrator, a numerical integration method.
• An integrand, a function to be integrated. It's only parameter has to be a std::array<F,N>, where F is a floating point number and N is the number of dimensions. There are several ways in which such integrand can be defined
• A range, the integration domain, that is composed on two std::array<F,N> marking the limits of the potentially multidimensional integration domain, which can be defined in different ways

Example:

float sphere(const std::array<float,3>& x) {
    return (x[0]*x[0]+x[1]*x[1]+x[2]*x[2])<=1.0f?1.0f:0.0f;
}
int main() {
    unsigned long samples = 1024;
    auto method = viltrum::integrator_monte_carlo_uniform(samples);
    auto range = viltrum::range(std::array<float,3>{-1.0f,-1.0f,-1.0f},std::array<float,3>{1.0f,1.0f,1.0f});
    std::cout<<"Sphere volume = "<<method.integrate(sphere,range)<<std::endl;