box_integral.hpp File Reference

N-dimensional box integration with Monte Carlo methods. More...

#include <span>
#include <string>
#include <array>
#include <cstddef>
#include <sstream>
#include <utility>
#include <random>
#include "../algorithms/core/result.hpp"
#include "../methods/methods.hpp"
#include "nodes/binary.hpp"

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Classes
struct	limes::expr::BoxIntegral< E, Dims >
	N-dimensional integral over a rectangular box. More...
struct	limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >
	Box integral with constraint for irregular regions. More...
struct	limes::expr::is_box_integral< T >
struct	limes::expr::is_box_integral< BoxIntegral< E, D > >
struct	limes::expr::is_constrained_box_integral< T >
struct	limes::expr::is_constrained_box_integral< ConstrainedBoxIntegral< E, D, C > >

Namespaces
namespace	limes
namespace	limes::expr
	Expression layer for composable calculus.
namespace	limes::expr::detail

Functions
template<typename E , std::size_t Dims>
constexpr auto	limes::expr::over_box (E expr, std::array< std::pair< typename E::value_type, typename E::value_type >, Dims > bounds)
	Create a box integral from an expression.
template<typename E >
auto	limes::expr::box2d (E expr, typename E::value_type x0, typename E::value_type x1, typename E::value_type y0, typename E::value_type y1)
	Create a 2D box integral (specialization for common case)
template<typename E >
auto	limes::expr::box3d (E expr, typename E::value_type x0, typename E::value_type x1, typename E::value_type y0, typename E::value_type y1, typename E::value_type z0, typename E::value_type z1)
	Create a 3D box integral (specialization for common case)

Variables
template<typename T >
constexpr bool	limes::expr::is_box_integral_v = is_box_integral<T>::value
template<typename T >
constexpr bool	limes::expr::is_constrained_box_integral_v = is_constrained_box_integral<T>::value

Detailed Description

N-dimensional box integration with Monte Carlo methods.

This module provides BoxIntegral for integrating expressions over rectangular N-dimensional regions, and ConstrainedBoxIntegral for irregular regions via rejection sampling.

Usage

using namespace limes::expr;
using namespace limes::methods;
 
auto x = arg<0>;
auto y = arg<1>;
auto z = arg<2>;
 
// 3D integral over unit cube
auto I = integral(x*y*z).over_box({{0,1}, {0,1}, {0,1}});
auto result = I.eval(monte_carlo_method(100000));
 
// Integral with constraint (triangle region y < x)
auto J = integral(x*y)
    .over_box({{0,1}, {0,1}})
    .where([](auto x, auto y) { return y < x; });
auto r2 = J.eval(100000);  // sample count

See also

BoxIntegral For rectangular regions

ConstrainedBoxIntegral For irregular regions

monte_carlo Monte Carlo method object

Definition in file box_integral.hpp.