Definite integral expression node. More...

#include <integral.hpp>

Public Types
using	value_type = typename E::value_type

using	integrand_type = E

using	lower_bound_type = Lo

using	upper_bound_type = Hi

Public Member Functions
constexpr	Integral (E e, Lo lo, Hi hi, value_type tol=value_type(1e-10)) noexcept

algorithms::integration_result< value_type >	eval (std::span< value_type const > args) const

algorithms::integration_result< value_type >	eval () const

template<typename Method > requires methods::is_integration_method_v<Method>
algorithms::integration_result< value_type >	eval (Method const &method, std::span< value_type const > args) const
	Evaluate the integral using a specific integration method.

template<typename Method > requires methods::is_integration_method_v<Method>
algorithms::integration_result< value_type >	eval (Method const &method) const
	Evaluate the integral using a specific method (no outer arguments)

algorithms::integration_result< value_type >	evaluate (std::span< value_type const > args) const

algorithms::integration_result< value_type >	evaluate () const

template<std::size_t NewDim, typename NewLo , typename NewHi >
constexpr auto	over (NewLo lo, NewHi hi) const

template<std::size_t NewDim>
constexpr auto	over (value_type lo, value_type hi) const

std::string	to_string () const

template<std::size_t SplitDim = Dim>
constexpr auto	split (value_type point) const

template<std::size_t D1, std::size_t D2> requires is_integral_v<E>
constexpr auto	swap () const

template<typename Phi , typename Jacobian >
constexpr auto	transform (Phi phi, Jacobian jacobian, value_type new_lower, value_type new_upper) const

constexpr auto	with_tolerance (value_type tol) const
	Set new tolerance for this integral.

Public Attributes
E	integrand

Lo	lower

Hi	upper

value_type	tolerance

Static Public Attributes
static constexpr std::size_t	dim_v = Dim

static constexpr std::size_t	arity_v = (E::arity_v > 0) ? (E::arity_v - 1) : 0

Detailed Description

template<typename E, std::size_t Dim, typename Lo, typename Hi>
struct limes::expr::Integral< E, Dim, Lo, Hi >

Definite integral expression node.

Represents the integral ∫ₐᵇ f(x₀,...,xₙ) dxₐᵢₘ where:

E is the integrand expression
Dim is the dimension being integrated over
Lo and Hi are the bounds (constant or expression-valued)

The arity of the result is one less than the integrand's arity, since dimension Dim is consumed by the integration.

Template Parameters

E	Integrand expression type
Dim	The variable dimension being integrated (0-indexed)
Lo	Lower bound type (ConstBound or ExprBound)
Hi	Upper bound type (ConstBound or ExprBound)

Domain Operations

split(point) — Split integral at a point: [a,b] → [a,c] + [c,b]
swap<D1,D2>() — Swap integration order (Fubini's theorem)
‘transform(φ, φ’, c, d)` — Change of variables

Method-based Evaluation: I.eval(); // Default (adaptive)

I.eval(gauss<7>()); // Gauss-Legendre

I.eval(monte_carlo_method(10000)); // Monte Carlo

See also: IntegralBuilder Fluent builder; integral() Entry point function

Definition at line 210 of file integral.hpp.

Member Typedef Documentation

◆ integrand_type

template<typename E , std::size_t Dim, typename Lo , typename Hi >

using limes::expr::Integral< E, Dim, Lo, Hi >::integrand_type = E

Definition at line 212 of file integral.hpp.

◆ lower_bound_type

template<typename E , std::size_t Dim, typename Lo , typename Hi >

using limes::expr::Integral< E, Dim, Lo, Hi >::lower_bound_type = Lo

Definition at line 213 of file integral.hpp.

◆ upper_bound_type

template<typename E , std::size_t Dim, typename Lo , typename Hi >

using limes::expr::Integral< E, Dim, Lo, Hi >::upper_bound_type = Hi

Definition at line 214 of file integral.hpp.

◆ value_type

template<typename E , std::size_t Dim, typename Lo , typename Hi >

using limes::expr::Integral< E, Dim, Lo, Hi >::value_type = typename E::value_type

Definition at line 211 of file integral.hpp.

Constructor & Destructor Documentation

◆ Integral()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

constexpr limes::expr::Integral< E, Dim, Lo, Hi >::Integral	(	E	e,
		Lo	lo,
		Hi	hi,
		value_type	tol = `value_type(1e-10)`
	)

inlineconstexprnoexcept

Definition at line 224 of file integral.hpp.

Member Function Documentation

◆ eval() [1/4]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::eval ( ) const

inline

Definition at line 239 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::eval().

Referenced by limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::evaluate(), and limes::expr::Integral< E, Dim, Lo, Hi >::evaluate().

◆ eval() [2/4]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<typename Method >
requires methods::is_integration_method_v<Method>

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::eval ( Method const & method ) const

inline

Evaluate the integral using a specific method (no outer arguments)

Definition at line 259 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::eval().

◆ eval() [3/4]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<typename Method >
requires methods::is_integration_method_v<Method>

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::eval	(	Method const &	method,
		std::span< value_type const >	args
	)		const

inline

Evaluate the integral using a specific integration method.

Definition at line 247 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

◆ eval() [4/4]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::eval ( std::span< value_type const > args ) const

inline

Definition at line 229 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, limes::expr::Integral< E, Dim, Lo, Hi >::tolerance, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

◆ evaluate() [1/2]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::evaluate ( ) const

inline

Definition at line 271 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::eval().

◆ evaluate() [2/2]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

algorithms::integration_result< value_type > limes::expr::Integral< E, Dim, Lo, Hi >::evaluate ( std::span< value_type const > args ) const

inline

Definition at line 265 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::eval().

◆ over() [1/2]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<std::size_t NewDim, typename NewLo , typename NewHi >

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::over	(	NewLo	lo,
		NewHi	hi
	)		const

inlineconstexpr

Definition at line 277 of file integral.hpp.

References limes::expr::make_bound(), and limes::expr::Integral< E, Dim, Lo, Hi >::tolerance.

◆ over() [2/2]

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<std::size_t NewDim>

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::over	(	value_type	lo,
		value_type	hi
	)		const

inlineconstexpr

Definition at line 286 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::tolerance.

◆ split()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<std::size_t SplitDim = Dim>

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::split ( value_type point ) const

inlineconstexpr

Split the integration domain at a given point

Returns a pair of integrals: [lower, point] and [point, upper] Invariant: left.evaluate() + right.evaluate() ≈ original.evaluate()

Example: auto I = integral(f).over<0>(0.0, 1.0); auto [left, right] = I.split(0.5); // left integrates from 0 to 0.5 // right integrates from 0.5 to 1

Definition at line 315 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, limes::expr::Integral< E, Dim, Lo, Hi >::tolerance, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

◆ swap()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<std::size_t D1, std::size_t D2>
requires is_integral_v<E>

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::swap ( ) const

inlineconstexpr

Swap integration order for nested integrals (Fubini's theorem)

For a double integral ∫∫ f(x,y) dx dy, swapping gives ∫∫ f(x,y) dy dx Only available when the integrand is itself an Integral

Example: auto I = integral(integral(x*y).over<0>(0,1)).over<1>(0,1); auto J = I.swap<0, 1>(); // Swap x and y integration order // I.evaluate() ≈ J.evaluate()

Definition at line 340 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, limes::expr::Integral< E, Dim, Lo, Hi >::tolerance, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

◆ to_string()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

std::string limes::expr::Integral< E, Dim, Lo, Hi >::to_string ( ) const

inline

Definition at line 293 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

◆ transform()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

template<typename Phi , typename Jacobian >

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::transform	(	Phi	phi,
		Jacobian	jacobian,
		value_type	new_lower,
		value_type	new_upper
	)		const

inlineconstexpr

Apply a change of variables (substitution) to the integral

For ∫[a,b] f(x) dx, using x = φ(t) gives: ∫[c,d] f(φ(t)) |φ'(t)| dt

Example (removing sqrt singularity using x = t²): auto I = integral(1.0 / sqrt(x)).over<0>(0.0, 1.0); auto T = I.transform( [](double t) { return t*t; }, // φ: t → t² [](double t) { return 2*t; }, // φ': t → 2t 0.0, 1.0 // new bounds );

Definition at line 380 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::tolerance.

◆ with_tolerance()

template<typename E , std::size_t Dim, typename Lo , typename Hi >

constexpr auto limes::expr::Integral< E, Dim, Lo, Hi >::with_tolerance ( value_type tol ) const

inlineconstexpr

Set new tolerance for this integral.

Definition at line 392 of file integral.hpp.

References limes::expr::Integral< E, Dim, Lo, Hi >::integrand, limes::expr::Integral< E, Dim, Lo, Hi >::lower, and limes::expr::Integral< E, Dim, Lo, Hi >::upper.

Member Data Documentation

◆ arity_v

template<typename E , std::size_t Dim, typename Lo , typename Hi >

constexpr std::size_t limes::expr::Integral< E, Dim, Lo, Hi >::arity_v = (E::arity_v > 0) ? (E::arity_v - 1) : 0

staticconstexpr

Definition at line 217 of file integral.hpp.

◆ dim_v

template<typename E , std::size_t Dim, typename Lo , typename Hi >

constexpr std::size_t limes::expr::Integral< E, Dim, Lo, Hi >::dim_v = Dim

staticconstexpr

Definition at line 216 of file integral.hpp.

◆ integrand

template<typename E , std::size_t Dim, typename Lo , typename Hi >

E limes::expr::Integral< E, Dim, Lo, Hi >::integrand

Definition at line 219 of file integral.hpp.

Referenced by limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::split(), limes::expr::Integral< E, Dim, Lo, Hi >::swap(), limes::expr::Integral< E, Dim, Lo, Hi >::to_string(), and limes::expr::Integral< E, Dim, Lo, Hi >::with_tolerance().

◆ lower

template<typename E , std::size_t Dim, typename Lo , typename Hi >

Lo limes::expr::Integral< E, Dim, Lo, Hi >::lower

Definition at line 220 of file integral.hpp.

Referenced by limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::split(), limes::expr::Integral< E, Dim, Lo, Hi >::swap(), limes::expr::Integral< E, Dim, Lo, Hi >::to_string(), and limes::expr::Integral< E, Dim, Lo, Hi >::with_tolerance().

◆ tolerance

template<typename E , std::size_t Dim, typename Lo , typename Hi >

value_type limes::expr::Integral< E, Dim, Lo, Hi >::tolerance

Definition at line 222 of file integral.hpp.

Referenced by limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::over(), limes::expr::Integral< E, Dim, Lo, Hi >::over(), limes::expr::Integral< E, Dim, Lo, Hi >::split(), limes::expr::Integral< E, Dim, Lo, Hi >::swap(), and limes::expr::Integral< E, Dim, Lo, Hi >::transform().

◆ upper

template<typename E , std::size_t Dim, typename Lo , typename Hi >

Hi limes::expr::Integral< E, Dim, Lo, Hi >::upper

Definition at line 221 of file integral.hpp.

Referenced by limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::eval(), limes::expr::Integral< E, Dim, Lo, Hi >::split(), limes::expr::Integral< E, Dim, Lo, Hi >::swap(), limes::expr::Integral< E, Dim, Lo, Hi >::to_string(), and limes::expr::Integral< E, Dim, Lo, Hi >::with_tolerance().

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

include/limes/expr/analysis.hpp
include/limes/expr/integral.hpp

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ integrand_type

◆ lower_bound_type

◆ upper_bound_type

◆ value_type

Constructor & Destructor Documentation

◆ Integral()

Member Function Documentation

◆ eval() [1/4]

◆ eval() [2/4]

◆ eval() [3/4]

◆ eval() [4/4]

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ over() [1/2]

◆ over() [2/2]

◆ split()

◆ swap()

◆ to_string()

◆ transform()

◆ with_tolerance()

Member Data Documentation

◆ arity_v

◆ dim_v

◆ integrand

◆ lower

◆ tolerance

◆ upper