Namespaces
namespace	commands

Classes
class	d3vctr

struct	delta

Functions
template<typename Type >
constexpr Type	positive_infinity (Type v)

template<typename Type >
constexpr Type	negative_infinity (Type v)

template<typename Type >
constexpr Type	positive_approach (Type value)

template<typename Type >
constexpr Type	negative_approach (Type value)

template<typename ValueType , std::size_t N, typename PairType = std::pair<ValueType, ValueType>, typename ReturnType = std::array<PairType, N>>
constexpr ReturnType	weights_abscissae () noexcept

template<std::size_t WeightCount = 21, typename FunctionType = double(&)(double), typename ValueType = double>
ValueType	gaussian_quadrature (FunctionType &&f, ValueType x1, ValueType x2)

template<std::size_t WeightCount = 12, typename FuncType = double(&)(double), cpt::arithmetic_c BoundType = double>
BoundType	adaptive_gaussian_quadrature (FuncType &&f, BoundType a, BoundType b)

template<typename FuncType , cpt::tuple_flat_c TupleType> requires (cpt::arithmetic_c<FuncType> \|\| requires{ std::apply(func, arg); })
auto	smart_apply (FuncType &&func, TupleType arg)

template<typename FuncType , cpt::arithmetic_c ArgType> requires (cpt::arithmetic_c<FuncType> \|\| std::invocable<FuncType, ArgType>)
auto	evaluate (FuncType &&f, ArgType arg1)

template<typename FuncType , cpt::arithmetic_c ArgType> requires (cpt::arithmetic_c<FuncType> \|\| std::invocable<FuncType, ArgType, ArgType>)
auto	evaluate (FuncType &&f, ArgType arg1, ArgType arg2)

template<typename FuncType , cpt::arithmetic_c ArgType> requires (cpt::arithmetic_c<FuncType> \|\| std::invocable<FuncType, ArgType, ArgType, ArgType>)
auto	evaluate (FuncType &&f, ArgType arg1, ArgType arg2, ArgType arg3)

template<typename FuncType , cpt::arithmetic_c ArgType> requires (cpt::arithmetic_c<FuncType> \|\| std::invocable<FuncType, ArgType, ArgType, ArgType, ArgType>)
auto	evaluate (FuncType &&f, ArgType arg1, ArgType arg2, ArgType arg3, ArgType arg4)

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>
auto	evaluate (std::tuple< FuncType1, FuncType2 > funcs, ArgType arg1)

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>
auto	evaluate (std::tuple< FuncType1, FuncType2 > funcs, ArgType arg1, ArgType arg2)

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>
auto	evaluate (std::tuple< FuncType1, FuncType2 > funcs, ArgType arg1, ArgType arg2, ArgType arg3)

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>
auto	evaluate (std::tuple< FuncType1, FuncType2 > funcs, ArgType arg1, ArgType arg2, ArgType arg3, ArgType arg4)

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename BoundType = double> requires (cpt::arithmetic_c<FuncType> \|\| std::invocable<FuncType, BoundType>)
BoundType	integral (FuncType &&f, std::tuple< BoundType, BoundType > bound)

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double, typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, auto First = 0, auto Second = 1>
std::common_type_t< Lower_0, Upper_0 >	integral (FuncType &&f, std::tuple< Lower_0, Upper_0 > bound_0, std::tuple< Lower_1, Upper_1 > bound_1, cpt::sequence< First, Second >)

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, typename Lower_2 = double, typename Upper_2 = double, auto First = 0, auto Second = 1, auto Third = 2>
std::common_type_t< Lower_0, Upper_0 >	integral (FuncType &&f, std::tuple< Lower_0, Upper_0 > bound_0, std::tuple< Lower_1, Upper_1 > bound_1, std::tuple< Lower_2, Upper_2 > bound_2, cpt::sequence< First, Second, Third >)

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, typename Lower_2 = double, typename Upper_2 = double, typename Lower_3 = double, typename Upper_3 = double, auto First = 0, auto Second = 1, auto Third = 2, auto Fourth = 3>
std::common_type_t< Lower_0, Upper_0 >	integral (FuncType &&f, std::tuple< Lower_0, Upper_0 > bound_0, std::tuple< Lower_1, Upper_1 > bound_1, std::tuple< Lower_2, Upper_2 > bound_2, std::tuple< Lower_3, Upper_2 > bound_3, cpt::sequence< First, Second, Third, Fourth >)

template<auto Order, typename DeltaType >
constexpr auto	get_delta (delta< DeltaType > del) noexcept

template<typename CountType , typename BoundType >
BoundType	compute_delta (CountType count, std::array< BoundType, 2 > &bound) noexcept

template<typename Type >
Type	adjust_integer (auto arg) noexcept

template<typename Type >
Type	adjust_zero (auto arg) noexcept

template<typename SeqType , typename... SeqTypes>
constexpr auto	create_command (SeqType, SeqTypes...) noexcept

template<std::size_t Order, typename FuncType , typename ArgType >
auto	nine_point_stencil (FuncType &&f, ArgType x) noexcept

template<std::size_t Order, typename FuncType , typename ArgType >
auto	seven_point_stencil (FuncType &&f, ArgType x) noexcept

template<std::size_t Order, typename FunctionType , typename ArgType >
ArgType	five_point_stencil (FunctionType &&f, ArgType x) noexcept

template<auto VarIndex, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	fix_variables_other_than_VarIndex_ed (FuncType &&func, ArgTypes... args) noexcept

template<auto VarIndex, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	fix_variables_other_than_VarIndex_ed (FuncType &&func, std::tuple< ArgTypes... > args) noexcept

template<auto VarIndex, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>
auto	fix_variables_other_than_VarIndex_ed (FuncType &&func, std::array< ArgType, N > args) noexcept

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::sequence< VarIndex, Order >, FuncType &&func, ArgTypes... args) noexcept

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::sequence< VarIndex, Order >, FuncType &&func, std::tuple< ArgTypes... > args) noexcept

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>
auto	partial_derivative (cpt::sequence< VarIndex, Order >, FuncType &&func, std::array< ArgType, N > args) noexcept

template<typename VarOdr , typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::type_container< VarOdr >, FuncType &&func, ArgTypes... args) noexcept

template<typename VarOdr , typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::type_container< VarOdr > cmd, FuncType &&func, std::tuple< ArgTypes... > const &args) noexcept

template<typename VarOdr , typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>
auto	partial_derivative (cpt::type_container< VarOdr > cmd, FuncType &&func, std::array< ArgType, N > const &args) noexcept

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::type_container< VarOdr1, VarOdr2, VarOdrs... >, FuncType &&func, ArgTypes... args) noexcept

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c... ArgTypes>
auto	partial_derivative (cpt::type_container< VarOdr1, VarOdr2, VarOdrs... > cmd, FuncType &&func, std::tuple< ArgTypes... > const &args) noexcept

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>
auto	partial_derivative (cpt::type_container< VarOdr1, VarOdr2, VarOdrs... > cmd, FuncType &&func, std::array< ArgType, N > const &args) noexcept

template<typename FuncType , typename... VariableTypes, typename ParamType >
auto	directional_derivative (FuncType &&f, std::tuple< VariableTypes... > const &vars, ParamType param)

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename... ParamTypes>
auto	parametric_derivative (cpt::type_container< CmdTypes... > cmd, FuncType &&f, std::tuple< VariableTypes... > const &vars, ParamTypes... ps)

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename... ParamTypes>
auto	parametric_derivative (cpt::type_container< CmdTypes... > cmd, FuncType &&f, std::tuple< VariableTypes... > const &vars, std::tuple< ParamTypes... > ps)

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename ParamType , std::size_t N>
auto	parametric_derivative (cpt::type_container< CmdTypes... > cmd, FuncType &&f, std::tuple< VariableTypes... > const &vars, std::array< ParamType, N > ps)

template<typename FuncType , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncType, ArgTypes...> )
auto	gradient (FuncType &&function, ArgTypes... args) noexcept

template<typename FuncType , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncType, ArgTypes...> )
auto	gradient (FuncType &&function, const std::tuple< ArgTypes... > &args) noexcept

template<typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>
auto	gradient (FuncType &&function, const std::array< ArgType, N > &args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )
auto	curl (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, ArgTypes... args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )
auto	curl (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, const std::tuple< ArgTypes... > &args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c ArgType, std::size_t N>
auto	curl (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, const std::array< ArgType, N > &args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )
auto	divergence (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, ArgTypes... args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes> requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )
auto	divergence (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, const std::tuple< ArgTypes... > &args) noexcept

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c ArgType, std::size_t N>
auto	divergence (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, const std::array< ArgType, N > &args) noexcept

template<typename FuncType , typename BoundType > requires requires { func(BoundType{}); }
auto	evaluate (FuncType &&func, std::size_t N, std::array< BoundType, 2 > bound)

template<std::size_t VarIndex, typename FuncType , typename BoundType , typename... ArgTypes>
auto	evaluate (FuncType &&func, std::size_t N, std::array< BoundType, 2 > bound, ArgTypes... args)

template<auto VarIndex, auto DerivativeOrder, typename FuncType , typename BoundType > requires requires { func(BoundType{}); }
auto	differentiate (cpt::sequence< VarIndex, DerivativeOrder >, FuncType &&func, std::size_t N, std::array< BoundType, 2 > bound)

template<auto VarIndex, typename IndexType , typename... IndexTypes, typename FuncType , typename BoundType > requires requires { func(args...); }
auto	differentiate (cpt::type_container< IndexType, IndexTypes... > command, FuncType &&func, std::size_t N, std::array< BoundType, 2 > bound, auto... args)

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncType , typename BoundType > requires requires { func( BoundType{}, BoundType{}, BoundType{}); }
auto	gradients (FuncType &&func, std::array< BoundType, 2 > bound_x, std::array< BoundType, 2 > bound_y, std::array< BoundType, 2 > bound_z)

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , typename BoundType > requires requires { func_x( BoundType{}, BoundType{}, BoundType{}); func_y( BoundType{}, BoundType{}, BoundType{}); func_z( BoundType{}, BoundType{}, BoundType{}); }
auto	curls (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, std::array< BoundType, 2 > bound_x, std::array< BoundType, 2 > bound_y, std::array< BoundType, 2 > bound_z)

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , typename BoundType > requires requires { func_x( BoundType{}, BoundType{}, BoundType{}); func_y( BoundType{}, BoundType{}, BoundType{}); func_z( BoundType{}, BoundType{}, BoundType{}); }
auto	divs (FuncTypeX &&func_x, FuncTypeY &&func_y, FuncTypeZ &&func_z, std::array< BoundType, 2 > bound_x, std::array< BoundType, 2 > bound_y, std::array< BoundType, 2 > bound_z)

template<typename FuncType , cpt::arithmetic_c BoundType>
BoundType	simpson_rule (FuncType &&f, BoundType a, BoundType b) noexcept

template<typename FuncType , cpt::arithmetic_c BoundType>
BoundType	adaptive_simpson_quadrature (FuncType &&f, BoundType a, BoundType b)

Variables
template<typename Type >
constexpr Type	positive_zero = std::numeric_limits<Type>::epsilon()

template<typename Type >
constexpr Type	negative_zero = -std::numeric_limits<Type>::epsilon()

Function Documentation

◆ adaptive_gaussian_quadrature()

template<std::size_t WeightCount = 12, typename FuncType = double(&)(double), cpt::arithmetic_c BoundType = double>

BoundType cpg::numerical_analysis::adaptive_gaussian_quadrature	(	FuncType &&	f,
		BoundType	a,
		BoundType	b
	)

Definition at line 572 of file cpg_calculus.hpp.

◆ adaptive_simpson_quadrature()

template<typename FuncType , cpt::arithmetic_c BoundType>

BoundType cpg::numerical_analysis::adaptive_simpson_quadrature	(	FuncType &&	f,
		BoundType	a,
		BoundType	b
	)

Definition at line 2465 of file cpg_calculus.hpp.

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◆ adjust_integer()

template<typename Type >

Type cpg::numerical_analysis::adjust_integer ( auto arg )

noexcept

Definition at line 891 of file cpg_calculus.hpp.

◆ adjust_zero()

template<typename Type >

Type cpg::numerical_analysis::adjust_zero ( auto arg )

noexcept

Definition at line 898 of file cpg_calculus.hpp.

◆ compute_delta()

template<typename CountType , typename BoundType >

BoundType cpg::numerical_analysis::compute_delta	(	CountType	count,
		std::array< BoundType, 2 > &	bound
	)

noexcept

Definition at line 874 of file cpg_calculus.hpp.

◆ create_command()

template<typename SeqType , typename... SeqTypes>

constexpr auto cpg::numerical_analysis::create_command	(	SeqType	,
		SeqTypes...
	)

constexprnoexcept

Definition at line 919 of file cpg_calculus.hpp.

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◆ curl() [1/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )

auto cpg::numerical_analysis::curl	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		ArgTypes...	args
	)

noexcept

Definition at line 1613 of file cpg_calculus.hpp.

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◆ curl() [2/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::curl	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		const std::array< ArgType, N > &	args
	)

noexcept

Definition at line 1654 of file cpg_calculus.hpp.

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◆ curl() [3/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )

auto cpg::numerical_analysis::curl	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		const std::tuple< ArgTypes... > &	args
	)

noexcept

Definition at line 1641 of file cpg_calculus.hpp.

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◆ curls()

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , typename BoundType >
requires requires { func_x( BoundType{}, BoundType{}, BoundType{}); func_y( BoundType{}, BoundType{}, BoundType{}); func_z( BoundType{}, BoundType{}, BoundType{}); }

auto cpg::numerical_analysis::curls	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		std::array< BoundType, 2 >	bound_x,
		std::array< BoundType, 2 >	bound_y,
		std::array< BoundType, 2 >	bound_z
	)

Definition at line 2300 of file cpg_calculus.hpp.

◆ differentiate() [1/2]

template<auto VarIndex, auto DerivativeOrder, typename FuncType , typename BoundType >
requires requires { func(BoundType{}); }

auto cpg::numerical_analysis::differentiate	(	cpt::sequence< VarIndex, DerivativeOrder >	,
		FuncType &&	func,
		std::size_t	N,
		std::array< BoundType, 2 >	bound
	)

Definition at line 2150 of file cpg_calculus.hpp.

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◆ differentiate() [2/2]

template<auto VarIndex, typename IndexType , typename... IndexTypes, typename FuncType , typename BoundType >
requires requires { func(args...); }

auto cpg::numerical_analysis::differentiate	(	cpt::type_container< IndexType, IndexTypes... >	command,
		FuncType &&	func,
		std::size_t	N,
		std::array< BoundType, 2 >	bound,
		auto...	args
	)

Definition at line 2189 of file cpg_calculus.hpp.

◆ directional_derivative()

template<typename FuncType , typename... VariableTypes, typename ParamType >

auto cpg::numerical_analysis::directional_derivative	(	FuncType &&	f,
		std::tuple< VariableTypes... > const &	vars,
		ParamType	param
	)

Definition at line 1480 of file cpg_calculus.hpp.

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◆ divergence() [1/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )

auto cpg::numerical_analysis::divergence	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		ArgTypes...	args
	)

noexcept

Definition at line 1672 of file cpg_calculus.hpp.

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◆ divergence() [2/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::divergence	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		const std::array< ArgType, N > &	args
	)

noexcept

Definition at line 1708 of file cpg_calculus.hpp.

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◆ divergence() [3/3]

template<typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncTypeX, ArgTypes...> && std::is_invocable_v<FuncTypeY, ArgTypes...> && std::is_invocable_v<FuncTypeZ, ArgTypes...> )

auto cpg::numerical_analysis::divergence	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		const std::tuple< ArgTypes... > &	args
	)

noexcept

Definition at line 1695 of file cpg_calculus.hpp.

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◆ divs()

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncTypeX , typename FuncTypeY , typename FuncTypeZ , typename BoundType >
requires requires { func_x( BoundType{}, BoundType{}, BoundType{}); func_y( BoundType{}, BoundType{}, BoundType{}); func_z( BoundType{}, BoundType{}, BoundType{}); }

auto cpg::numerical_analysis::divs	(	FuncTypeX &&	func_x,
		FuncTypeY &&	func_y,
		FuncTypeZ &&	func_z,
		std::array< BoundType, 2 >	bound_x,
		std::array< BoundType, 2 >	bound_y,
		std::array< BoundType, 2 >	bound_z
	)

Definition at line 2370 of file cpg_calculus.hpp.

◆ evaluate() [1/10]

template<typename FuncType , cpt::arithmetic_c ArgType>
requires (cpt::arithmetic_c<FuncType> || std::invocable<FuncType, ArgType>)

auto cpg::numerical_analysis::evaluate	(	FuncType &&	f,
		ArgType	arg1
	)

Definition at line 614 of file cpg_calculus.hpp.

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◆ evaluate() [2/10]

template<typename FuncType , cpt::arithmetic_c ArgType>
requires (cpt::arithmetic_c<FuncType> || std::invocable<FuncType, ArgType, ArgType>)

auto cpg::numerical_analysis::evaluate	(	FuncType &&	f,
		ArgType	arg1,
		ArgType	arg2
	)

Definition at line 627 of file cpg_calculus.hpp.

◆ evaluate() [3/10]

template<typename FuncType , cpt::arithmetic_c ArgType>
requires (cpt::arithmetic_c<FuncType> || std::invocable<FuncType, ArgType, ArgType, ArgType>)

auto cpg::numerical_analysis::evaluate	(	FuncType &&	f,
		ArgType	arg1,
		ArgType	arg2,
		ArgType	arg3
	)

Definition at line 640 of file cpg_calculus.hpp.

◆ evaluate() [4/10]

template<typename FuncType , cpt::arithmetic_c ArgType>
requires (cpt::arithmetic_c<FuncType> || std::invocable<FuncType, ArgType, ArgType, ArgType, ArgType>)

auto cpg::numerical_analysis::evaluate	(	FuncType &&	f,
		ArgType	arg1,
		ArgType	arg2,
		ArgType	arg3,
		ArgType	arg4
	)

Definition at line 653 of file cpg_calculus.hpp.

◆ evaluate() [5/10]

template<typename FuncType , typename BoundType >
requires requires { func(BoundType{}); }

auto cpg::numerical_analysis::evaluate	(	FuncType &&	func,
		std::size_t	N,
		std::array< BoundType, 2 >	bound
	)

Definition at line 2083 of file cpg_calculus.hpp.

◆ evaluate() [6/10]

template<std::size_t VarIndex, typename FuncType , typename BoundType , typename... ArgTypes>

auto cpg::numerical_analysis::evaluate	(	FuncType &&	func,
		std::size_t	N,
		std::array< BoundType, 2 >	bound,
		ArgTypes...	args
	)

Definition at line 2113 of file cpg_calculus.hpp.

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◆ evaluate() [7/10]

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>

auto cpg::numerical_analysis::evaluate	(	std::tuple< FuncType1, FuncType2 >	funcs,
		ArgType	arg1
	)

Definition at line 666 of file cpg_calculus.hpp.

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◆ evaluate() [8/10]

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>

auto cpg::numerical_analysis::evaluate	(	std::tuple< FuncType1, FuncType2 >	funcs,
		ArgType	arg1,
		ArgType	arg2
	)

Definition at line 674 of file cpg_calculus.hpp.

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◆ evaluate() [9/10]

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>

auto cpg::numerical_analysis::evaluate	(	std::tuple< FuncType1, FuncType2 >	funcs,
		ArgType	arg1,
		ArgType	arg2,
		ArgType	arg3
	)

Definition at line 682 of file cpg_calculus.hpp.

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◆ evaluate() [10/10]

template<typename FuncType1 , typename FuncType2 , cpt::arithmetic_c ArgType>

auto cpg::numerical_analysis::evaluate	(	std::tuple< FuncType1, FuncType2 >	funcs,
		ArgType	arg1,
		ArgType	arg2,
		ArgType	arg3,
		ArgType	arg4
	)

Definition at line 690 of file cpg_calculus.hpp.

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◆ five_point_stencil()

template<std::size_t Order, typename FunctionType , typename ArgType >

ArgType cpg::numerical_analysis::five_point_stencil	(	FunctionType &&	f,
		ArgType	x
	)

noexcept

Definition at line 1282 of file cpg_calculus.hpp.

◆ fix_variables_other_than_VarIndex_ed() [1/3]

template<auto VarIndex, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::fix_variables_other_than_VarIndex_ed	(	FuncType &&	func,
		ArgTypes...	args
	)

noexcept

Definition at line 1341 of file cpg_calculus.hpp.

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◆ fix_variables_other_than_VarIndex_ed() [2/3]

template<auto VarIndex, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::fix_variables_other_than_VarIndex_ed	(	FuncType &&	func,
		std::array< ArgType, N >	args
	)

noexcept

Definition at line 1365 of file cpg_calculus.hpp.

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◆ fix_variables_other_than_VarIndex_ed() [3/3]

template<auto VarIndex, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::fix_variables_other_than_VarIndex_ed	(	FuncType &&	func,
		std::tuple< ArgTypes... >	args
	)

noexcept

Definition at line 1354 of file cpg_calculus.hpp.

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◆ gaussian_quadrature()

template<std::size_t WeightCount = 21, typename FunctionType = double(&)(double), typename ValueType = double>

ValueType cpg::numerical_analysis::gaussian_quadrature	(	FunctionType &&	f,
		ValueType	x1,
		ValueType	x2
	)

Definition at line 552 of file cpg_calculus.hpp.

◆ get_delta()

template<auto Order, typename DeltaType >

constexpr auto cpg::numerical_analysis::get_delta ( delta< DeltaType > del )

inlineconstexprnoexcept

Definition at line 849 of file cpg_calculus.hpp.

◆ gradient() [1/3]

template<typename FuncType , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncType, ArgTypes...> )

auto cpg::numerical_analysis::gradient	(	FuncType &&	function,
		ArgTypes...	args
	)

noexcept

Definition at line 1563 of file cpg_calculus.hpp.

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◆ gradient() [2/3]

template<typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::gradient	(	FuncType &&	function,
		const std::array< ArgType, N > &	args
	)

noexcept

Definition at line 1596 of file cpg_calculus.hpp.

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◆ gradient() [3/3]

template<typename FuncType , cpt::arithmetic_c... ArgTypes>
requires ( std::is_invocable_v<FuncType, ArgTypes...> )

auto cpg::numerical_analysis::gradient	(	FuncType &&	function,
		const std::tuple< ArgTypes... > &	args
	)

noexcept

Definition at line 1585 of file cpg_calculus.hpp.

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◆ gradients()

template<std::size_t CountX, std::size_t CountY, std::size_t CountZ, typename FuncType , typename BoundType >
requires requires { func( BoundType{}, BoundType{}, BoundType{}); }

auto cpg::numerical_analysis::gradients	(	FuncType &&	func,
		std::array< BoundType, 2 >	bound_x,
		std::array< BoundType, 2 >	bound_y,
		std::array< BoundType, 2 >	bound_z
	)

Definition at line 2234 of file cpg_calculus.hpp.

◆ integral() [1/4]

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename BoundType = double>
requires (cpt::arithmetic_c<FuncType> || std::invocable<FuncType, BoundType>)

BoundType cpg::numerical_analysis::integral	(	FuncType &&	f,
		std::tuple< BoundType, BoundType >	bound
	)

Definition at line 700 of file cpg_calculus.hpp.

◆ integral() [2/4]

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double, typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, auto First = 0, auto Second = 1>

std::common_type_t< Lower_0, Upper_0 > cpg::numerical_analysis::integral	(	FuncType &&	f,
		std::tuple< Lower_0, Upper_0 >	bound_0,
		std::tuple< Lower_1, Upper_1 >	bound_1,
		cpt::sequence< First, Second >
	)

Definition at line 726 of file cpg_calculus.hpp.

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◆ integral() [3/4]

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, typename Lower_2 = double, typename Upper_2 = double, auto First = 0, auto Second = 1, auto Third = 2>

std::common_type_t< Lower_0, Upper_0 > cpg::numerical_analysis::integral	(	FuncType &&	f,
		std::tuple< Lower_0, Upper_0 >	bound_0,
		std::tuple< Lower_1, Upper_1 >	bound_1,
		std::tuple< Lower_2, Upper_2 >	bound_2,
		cpt::sequence< First, Second, Third >
	)

Definition at line 757 of file cpg_calculus.hpp.

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◆ integral() [4/4]

template<bool UseRecursion = true, std::size_t WeightCount = 31, typename FuncType = double(&)(double), typename Lower_0 = double, typename Upper_0 = double, typename Lower_1 = double, typename Upper_1 = double, typename Lower_2 = double, typename Upper_2 = double, typename Lower_3 = double, typename Upper_3 = double, auto First = 0, auto Second = 1, auto Third = 2, auto Fourth = 3>

std::common_type_t< Lower_0, Upper_0 > cpg::numerical_analysis::integral	(	FuncType &&	f,
		std::tuple< Lower_0, Upper_0 >	bound_0,
		std::tuple< Lower_1, Upper_1 >	bound_1,
		std::tuple< Lower_2, Upper_2 >	bound_2,
		std::tuple< Lower_3, Upper_2 >	bound_3,
		cpt::sequence< First, Second, Third, Fourth >
	)

Definition at line 796 of file cpg_calculus.hpp.

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◆ negative_approach()

template<typename Type >

constexpr Type cpg::numerical_analysis::negative_approach ( Type value )

inlineconstexpr

Definition at line 54 of file cpg_calculus.hpp.

◆ negative_infinity()

template<typename Type >

constexpr Type cpg::numerical_analysis::negative_infinity ( Type v )

inlineconstexpr

Definition at line 40 of file cpg_calculus.hpp.

◆ nine_point_stencil()

template<std::size_t Order, typename FuncType , typename ArgType >

auto cpg::numerical_analysis::nine_point_stencil	(	FuncType &&	f,
		ArgType	x
	)

noexcept

Definition at line 1082 of file cpg_calculus.hpp.

◆ parametric_derivative() [1/3]

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename... ParamTypes>

auto cpg::numerical_analysis::parametric_derivative	(	cpt::type_container< CmdTypes... >	cmd,
		FuncType &&	f,
		std::tuple< VariableTypes... > const &	vars,
		ParamTypes...	ps
	)

Definition at line 1500 of file cpg_calculus.hpp.

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◆ parametric_derivative() [2/3]

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename ParamType , std::size_t N>

auto cpg::numerical_analysis::parametric_derivative	(	cpt::type_container< CmdTypes... >	cmd,
		FuncType &&	f,
		std::tuple< VariableTypes... > const &	vars,
		std::array< ParamType, N >	ps
	)

Definition at line 1540 of file cpg_calculus.hpp.

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◆ parametric_derivative() [3/3]

template<typename... CmdTypes, typename FuncType , typename... VariableTypes, typename... ParamTypes>

auto cpg::numerical_analysis::parametric_derivative	(	cpt::type_container< CmdTypes... >	cmd,
		FuncType &&	f,
		std::tuple< VariableTypes... > const &	vars,
		std::tuple< ParamTypes... >	ps
	)

Definition at line 1520 of file cpg_calculus.hpp.

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◆ partial_derivative() [1/9]

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::sequence< VarIndex, Order >	,
		FuncType &&	func,
		ArgTypes...	args
	)

noexcept

Definition at line 1376 of file cpg_calculus.hpp.

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◆ partial_derivative() [2/9]

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::partial_derivative	(	cpt::sequence< VarIndex, Order >	,
		FuncType &&	func,
		std::array< ArgType, N >	args
	)

noexcept

Definition at line 1395 of file cpg_calculus.hpp.

◆ partial_derivative() [3/9]

template<auto VarIndex, auto Order, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::sequence< VarIndex, Order >	,
		FuncType &&	func,
		std::tuple< ArgTypes... >	args
	)

noexcept

Definition at line 1385 of file cpg_calculus.hpp.

◆ partial_derivative() [4/9]

template<typename VarOdr , typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr >	cmd,
		FuncType &&	func,
		std::array< ArgType, N > const &	args
	)

noexcept

Definition at line 1428 of file cpg_calculus.hpp.

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◆ partial_derivative() [5/9]

template<typename VarOdr , typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr >	cmd,
		FuncType &&	func,
		std::tuple< ArgTypes... > const &	args
	)

noexcept

Definition at line 1416 of file cpg_calculus.hpp.

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◆ partial_derivative() [6/9]

template<typename VarOdr , typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr >	,
		FuncType &&	func,
		ArgTypes...	args
	)

noexcept

Definition at line 1404 of file cpg_calculus.hpp.

◆ partial_derivative() [7/9]

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c ArgType, std::size_t N>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr1, VarOdr2, VarOdrs... >	cmd,
		FuncType &&	func,
		std::array< ArgType, N > const &	args
	)

noexcept

Definition at line 1467 of file cpg_calculus.hpp.

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◆ partial_derivative() [8/9]

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr1, VarOdr2, VarOdrs... >	cmd,
		FuncType &&	func,
		std::tuple< ArgTypes... > const &	args
	)

noexcept

Definition at line 1454 of file cpg_calculus.hpp.

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◆ partial_derivative() [9/9]

template<typename VarOdr1 , typename VarOdr2 , typename... VarOdrs, typename FuncType , cpt::arithmetic_c... ArgTypes>

auto cpg::numerical_analysis::partial_derivative	(	cpt::type_container< VarOdr1, VarOdr2, VarOdrs... >	,
		FuncType &&	func,
		ArgTypes...	args
	)

noexcept

Definition at line 1441 of file cpg_calculus.hpp.

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◆ positive_approach()

template<typename Type >

constexpr Type cpg::numerical_analysis::positive_approach ( Type value )

inlineconstexpr

Definition at line 47 of file cpg_calculus.hpp.

◆ positive_infinity()

template<typename Type >

constexpr Type cpg::numerical_analysis::positive_infinity ( Type v )

inlineconstexpr

Definition at line 34 of file cpg_calculus.hpp.

◆ seven_point_stencil()

template<std::size_t Order, typename FuncType , typename ArgType >

auto cpg::numerical_analysis::seven_point_stencil	(	FuncType &&	f,
		ArgType	x
	)

noexcept

Definition at line 1198 of file cpg_calculus.hpp.

◆ simpson_rule()

template<typename FuncType , cpt::arithmetic_c BoundType>

BoundType cpg::numerical_analysis::simpson_rule	(	FuncType &&	f,
		BoundType	a,
		BoundType	b
	)

noexcept

Definition at line 2436 of file cpg_calculus.hpp.

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◆ smart_apply()

template<typename FuncType , cpt::tuple_flat_c TupleType>
requires (cpt::arithmetic_c<FuncType> || requires{ std::apply(func, arg); })

auto cpg::numerical_analysis::smart_apply	(	FuncType &&	func,
		TupleType	arg
	)

Definition at line 604 of file cpg_calculus.hpp.

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◆ weights_abscissae()

template<typename ValueType , std::size_t N, typename PairType = std::pair<ValueType, ValueType>, typename ReturnType = std::array<PairType, N>>

constexpr ReturnType cpg::numerical_analysis::weights_abscissae ( )

constexprnoexcept

Definition at line 79 of file cpg_calculus.hpp.

Variable Documentation

◆ negative_zero

template<typename Type >

constexpr Type cpg::numerical_analysis::negative_zero = -std::numeric_limits<Type>::epsilon()

constexpr

Definition at line 63 of file cpg_calculus.hpp.

◆ positive_zero

template<typename Type >

constexpr Type cpg::numerical_analysis::positive_zero = std::numeric_limits<Type>::epsilon()

constexpr

Definition at line 60 of file cpg_calculus.hpp.

Namespaces

Classes

Functions

Variables

Function Documentation

◆ adaptive_gaussian_quadrature()

◆ adaptive_simpson_quadrature()

◆ adjust_integer()

◆ adjust_zero()

◆ compute_delta()

◆ create_command()

◆ curl() [1/3]

◆ curl() [2/3]

◆ curl() [3/3]

◆ curls()

◆ differentiate() [1/2]

◆ differentiate() [2/2]

◆ directional_derivative()

◆ divergence() [1/3]

◆ divergence() [2/3]

◆ divergence() [3/3]

◆ divs()

◆ evaluate() [1/10]

◆ evaluate() [2/10]

◆ evaluate() [3/10]

◆ evaluate() [4/10]

◆ evaluate() [5/10]

◆ evaluate() [6/10]

◆ evaluate() [7/10]

◆ evaluate() [8/10]

◆ evaluate() [9/10]

◆ evaluate() [10/10]

◆ five_point_stencil()

◆ fix_variables_other_than_VarIndex_ed() [1/3]

◆ fix_variables_other_than_VarIndex_ed() [2/3]

◆ fix_variables_other_than_VarIndex_ed() [3/3]

◆ gaussian_quadrature()

◆ get_delta()

◆ gradient() [1/3]

◆ gradient() [2/3]

◆ gradient() [3/3]

◆ gradients()

◆ integral() [1/4]

◆ integral() [2/4]

◆ integral() [3/4]

◆ integral() [4/4]

◆ negative_approach()

◆ negative_infinity()

◆ nine_point_stencil()

◆ parametric_derivative() [1/3]

◆ parametric_derivative() [2/3]

◆ parametric_derivative() [3/3]

◆ partial_derivative() [1/9]

◆ partial_derivative() [2/9]

◆ partial_derivative() [3/9]

◆ partial_derivative() [4/9]

◆ partial_derivative() [5/9]

◆ partial_derivative() [6/9]

◆ partial_derivative() [7/9]

◆ partial_derivative() [8/9]

◆ partial_derivative() [9/9]

◆ positive_approach()

◆ positive_infinity()

◆ seven_point_stencil()

◆ simpson_rule()

◆ smart_apply()

◆ weights_abscissae()

Variable Documentation

◆ negative_zero

◆ positive_zero