Quickstart

This guide provides a quick introduction to using the kakuhen library for multidimensional Monte Carlo integration.

Basic usage

Let’s integrate a simple function, for example, f(x, y) = x^2 + y^2 over a 2D domain.

First, define your function and use the Plain integrator.

#include <kakuhen/integrator/plain.h>

#include <iostream>
#include <vector>

int main() {
  // Define the function to integrate: f(x, y) = x^2 + y^2
  auto func = [](const kakuhen::integrator::Point<>& p) {
    return p.x[0] * p.x[0] + p.x[1] * p.x[1];
  };

  // Create a Plain Monte Carlo integrator for 2 dimensions
  kakuhen::integrator::Plain plain_integrator(2);

  // Set integration parameters
  int num_evaluations = 100000;
  int num_iterations = 10;  // For statistical analysis

  // Perform the integration
  auto result =
      plain_integrator.integrate(func, {.neval = num_evaluations, .niter = num_iterations});

  // Print the result
  std::cout << "Estimated Integral: " << result.value() << std::endl;
  std::cout << "Error: " << result.error() << std::endl;
  std::cout << "Chi2/dof: " << result.chi2dof() << std::endl;

  return 0;
}

Explanation: * We include necessary headers, specifically kakuhen/integrator/plain.h. * We define our integrand function func which takes a Point<> object. The coordinates are accessed via p.x[i]. * We create an instance of kakuhen::integrator::Plain for a 2-dimensional integration. * We define num_evaluations and num_iterations for the Monte Carlo process. * The integrate method performs the integration and returns a Result object. * Finally, we print the estimated integral value, its error, and the chi-squared per degree of freedom.

Build and run

To compile and run this example:

1. Save the code above (from the literalinclude block) as my_integration_app.cpp.

2. Assuming kakuhen is installed and found by CMake, you can compile and link your application using CMake:

   # CMakeLists.txt for your application
   cmake_minimum_required(VERSION 3.18)
   project(MyIntegrationApp LANGUAGES CXX)
   
   set(CMAKE_CXX_STANDARD 20)
   set(CMAKE_CXX_STANDARD_REQUIRED ON)
   
   find_package(kakuhen CONFIG REQUIRED)
   
   add_executable(my_integration_app my_integration_app.cpp)
   target_link_libraries(my_integration_app PRIVATE kakuhen::kakuhen)
   

   Then, from your build directory:

   cmake -S . -B build
   cmake --build build
   

3. Execute the application:

   ./my_integration_app # On Linux/macOS
   .\\my_integration_app.exe # On Windows
   

This should print the estimated integral value and error to the console.

For more advanced usage and different integration algorithms (e.g., Vegas, Basin), refer to the API Reference and other guides.