limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint > Struct Template Reference

Box integral with constraint for irregular regions. More...

#include <box_integral.hpp>

Public Types
using	value_type = typename E::value_type
using	integrand_type = E
using	bounds_type = std::array< std::pair< value_type, value_type >, Dims >

Public Member Functions
constexpr	ConstrainedBoxIntegral (E e, bounds_type b, Constraint c) noexcept
algorithms::integration_result< value_type >	eval (methods::monte_carlo< value_type > const &method) const
	Evaluate using Monte Carlo with rejection sampling.
algorithms::integration_result< value_type >	eval () const
	Evaluate with default Monte Carlo.
algorithms::integration_result< value_type >	eval (std::size_t samples) const
	Evaluate with sample count.
std::string	to_string () const
	String representation.

Public Attributes
E	integrand
bounds_type	bounds
Constraint	constraint

Static Public Attributes
static constexpr std::size_t	dims_v = Dims
static constexpr std::size_t	arity_v = (E::arity_v > Dims) ? (E::arity_v - Dims) : 0

Detailed Description

template<typename E, std::size_t Dims, typename Constraint>
struct limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >

Box integral with constraint for irregular regions.

Uses rejection sampling to integrate over regions defined by a constraint function. Points are sampled from the bounding box and rejected if they don't satisfy the constraint.

Template Parameters

E	Integrand expression type
Dims	Number of dimensions
Constraint	Constraint predicate type

Example: Triangle region

// Integrate over triangle where y < x
auto I = integral(x*y)
    .over_box({{0,1}, {0,1}})
    .where([](auto x, auto y) { return y < x; });
 
auto result = I.eval(100000);  // 100k samples

Example: Circle region

// Integrate over unit disk
auto J = integral(f)
    .over_box({{-1,1}, {-1,1}})
    .where([](auto x, auto y) { return x*x + y*y < 1; });

Note

The acceptance rate affects variance. For regions that are a small fraction of the bounding box, more samples are needed for accuracy.

See also

BoxIntegral::where() Factory method

Definition at line 253 of file box_integral.hpp.

Member Typedef Documentation

bounds_type

template<typename E , std::size_t Dims, typename Constraint >

using limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::bounds_type = std::array<std::pair<value_type, value_type>, Dims>

Definition at line 256 of file box_integral.hpp.

integrand_type

template<typename E , std::size_t Dims, typename Constraint >

using limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::integrand_type = E

Definition at line 255 of file box_integral.hpp.

value_type

template<typename E , std::size_t Dims, typename Constraint >

using limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::value_type = typename E::value_type

Definition at line 254 of file box_integral.hpp.

Constructor & Destructor Documentation

ConstrainedBoxIntegral()

template<typename E , std::size_t Dims, typename Constraint >

constexpr limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::ConstrainedBoxIntegral ( E  e, bounds_type  b, Constraint  c  )

inlineconstexprnoexcept

Definition at line 265 of file box_integral.hpp.

Member Function Documentation

eval() [1/3]

template<typename E , std::size_t Dims, typename Constraint >

algorithms::integration_result< value_type > limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval ( ) const

inline

Evaluate with default Monte Carlo.

Definition at line 311 of file box_integral.hpp.

References limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval().

Referenced by limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval(), and limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval().

eval() [2/3]

template<typename E , std::size_t Dims, typename Constraint >

algorithms::integration_result< value_type > limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval ( methods::monte_carlo< value_type > const &  method ) const

inline

Evaluate using Monte Carlo with rejection sampling.

Definition at line 270 of file box_integral.hpp.

References limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::bounds, limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::integrand, limes::methods::monte_carlo< T >::samples, limes::methods::monte_carlo< T >::seed, limes::expr::sum(), and limes::expr::y.

eval() [3/3]

template<typename E , std::size_t Dims, typename Constraint >

algorithms::integration_result< value_type > limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval ( std::size_t  samples ) const

inline

Evaluate with sample count.

Definition at line 317 of file box_integral.hpp.

References limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval().

to_string()

template<typename E , std::size_t Dims, typename Constraint >

std::string limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::to_string ( ) const

inline

String representation.

Definition at line 322 of file box_integral.hpp.

References limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::bounds, and limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::integrand.

Member Data Documentation

arity_v

template<typename E , std::size_t Dims, typename Constraint >

constexpr std::size_t limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::arity_v = (E::arity_v > Dims) ? (E::arity_v - Dims) : 0

staticconstexpr

Definition at line 259 of file box_integral.hpp.

bounds

template<typename E , std::size_t Dims, typename Constraint >

bounds_type limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::bounds

Definition at line 262 of file box_integral.hpp.

Referenced by limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval(), and limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::to_string().

constraint

template<typename E , std::size_t Dims, typename Constraint >

Constraint limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::constraint

Definition at line 263 of file box_integral.hpp.

dims_v

template<typename E , std::size_t Dims, typename Constraint >

constexpr std::size_t limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::dims_v = Dims

staticconstexpr

Definition at line 258 of file box_integral.hpp.

integrand

template<typename E , std::size_t Dims, typename Constraint >

E limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::integrand

Definition at line 261 of file box_integral.hpp.

Referenced by limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::eval(), and limes::expr::ConstrainedBoxIntegral< E, Dims, Constraint >::to_string().

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The documentation for this struct was generated from the following file:

• include/limes/expr/box_integral.hpp