limes::expr::ProductIntegral< I1, I2 > Struct Template Reference

Product of two independent integrals. More...

#include <product_integral.hpp>

Public Types
using	value_type = typename I1::value_type

Public Member Functions
constexpr	ProductIntegral (I1 i1, I2 i2) noexcept
algorithms::integration_result< value_type >	eval () const
	Evaluate the product integral (no outer arguments)
template<typename... Args>
algorithms::integration_result< value_type >	eval (Args &&... args) const
	Evaluate with arguments (for integrals with free variables)
std::string	to_string () const
	String representation.
template<typename I3 >
constexpr auto	operator* (I3 const &other) const
	Multiply with another integral (chaining)

Public Attributes
I1	left
I2	right

Detailed Description

template<typename I1, typename I2>
struct limes::expr::ProductIntegral< I1, I2 >

Product of two independent integrals.

For integrals over independent variables:

The product can be computed by evaluating each integral separately and multiplying the results, which is much faster than nested integration.

Template Parameters

I1	First integral type
I2	Second integral type

Independence Requirement

The two integrals must depend on disjoint variable sets. This is verified at compile time using variable_set analysis. If the integrals share variables, a static_assert fires with a descriptive error message.

Error Propagation

Errors are propagated using the product rule:

Example

auto x = arg<0>;
auto y = arg<1>;
 
auto I = integral(sin(x)).over<0>(0.0, pi);
auto J = integral(exp(y)).over<1>(0.0, 1.0);
 
auto IJ = I * J;
auto result = IJ.eval();  // Evaluates I and J separately

See also

operator*(I1, I2) Factory operator

product() Variadic factory function

Definition at line 138 of file product_integral.hpp.

Member Typedef Documentation

value_type

template<typename I1 , typename I2 >

using limes::expr::ProductIntegral< I1, I2 >::value_type = typename I1::value_type

Definition at line 139 of file product_integral.hpp.

Constructor & Destructor Documentation

ProductIntegral()

template<typename I1 , typename I2 >

constexpr limes::expr::ProductIntegral< I1, I2 >::ProductIntegral ( I1  i1, I2  i2  )

inlineconstexprnoexcept

Definition at line 152 of file product_integral.hpp.

Member Function Documentation

eval() [1/2]

template<typename I1 , typename I2 >

algorithms::integration_result< value_type > limes::expr::ProductIntegral< I1, I2 >::eval ( ) const

inline

Evaluate the product integral (no outer arguments)

Definition at line 157 of file product_integral.hpp.

References limes::expr::ProductIntegral< I1, I2 >::left, and limes::expr::ProductIntegral< I1, I2 >::right.

eval() [2/2]

template<typename I1 , typename I2 >

template<typename... Args>

algorithms::integration_result< value_type > limes::expr::ProductIntegral< I1, I2 >::eval ( Args &&...  args ) const

inline

Evaluate with arguments (for integrals with free variables)

Definition at line 164 of file product_integral.hpp.

References limes::expr::ProductIntegral< I1, I2 >::left, and limes::expr::ProductIntegral< I1, I2 >::right.

operator*()

template<typename I1 , typename I2 >

template<typename I3 >

constexpr auto limes::expr::ProductIntegral< I1, I2 >::operator* ( I3 const &  other ) const

inlineconstexpr

Multiply with another integral (chaining)

Definition at line 193 of file product_integral.hpp.

to_string()

template<typename I1 , typename I2 >

std::string limes::expr::ProductIntegral< I1, I2 >::to_string ( ) const

inline

String representation.

Definition at line 187 of file product_integral.hpp.

References limes::expr::ProductIntegral< I1, I2 >::left, and limes::expr::ProductIntegral< I1, I2 >::right.

Member Data Documentation

left

template<typename I1 , typename I2 >

I1 limes::expr::ProductIntegral< I1, I2 >::left

Definition at line 141 of file product_integral.hpp.

Referenced by limes::expr::ProductIntegral< I1, I2 >::eval(), limes::expr::ProductIntegral< I1, I2 >::eval(), and limes::expr::ProductIntegral< I1, I2 >::to_string().

right

template<typename I1 , typename I2 >

I2 limes::expr::ProductIntegral< I1, I2 >::right

Definition at line 142 of file product_integral.hpp.

Referenced by limes::expr::ProductIntegral< I1, I2 >::eval(), limes::expr::ProductIntegral< I1, I2 >::eval(), and limes::expr::ProductIntegral< I1, I2 >::to_string().

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

• include/limes/expr/product_integral.hpp