limes::expr::DerivativeBuilder< E > Struct Template Reference

Fluent builder for computing symbolic derivatives. More...

#include <derivative_builder.hpp>

Public Types
using	value_type = typename E::value_type
using	expr_type = E

Public Member Functions
constexpr	DerivativeBuilder (E e) noexcept
template<std::size_t Dim>
constexpr auto	wrt () const
	Compute ∂/∂x_Dim and return a new builder for chaining.
template<std::size_t D1, std::size_t D2>
constexpr auto	wrt () const
	Compute ∂²/∂x_D1 ∂x_D2 (convenience for second-order mixed partials)
template<std::size_t D1, std::size_t D2, std::size_t D3>
constexpr auto	wrt () const
	Compute ∂³/∂x_D1 ∂x_D2 ∂x_D3 (convenience for third-order mixed partials)
constexpr auto	gradient () const
	Returns tuple<∂f/∂x₀, ∂f/∂x₁, ..., ∂f/∂x_{n-1}>
constexpr E	get () const noexcept
	Allow implicit conversion to the underlying derivative expression.
constexpr value_type	eval (std::span< value_type const > args) const
	Evaluate the derivative expression.
constexpr value_type	evaluate (std::span< value_type const > args) const
	Deprecated: use eval() instead.
std::string	to_string () const
	String representation.
template<std::size_t Dim>
constexpr auto	derivative () const
	Further differentiation through the member function.

Public Attributes
E	expr

Static Public Attributes
static constexpr std::size_t	arity_v = E::arity_v
	Arity of the derivative expression.

Detailed Description

template<typename E>
struct limes::expr::DerivativeBuilder< E >

Fluent builder for computing symbolic derivatives.

DerivativeBuilder wraps an expression and provides chainable methods for computing partial derivatives. Derivatives are computed symbolically at compile time using the chain rule.

Template Parameters

E	The expression type being differentiated

Fluent API

derivative(f).wrt<0>()              // ∂f/∂x₀
derivative(f).wrt<0>().wrt<1>()     // ∂²f/∂x₀∂x₁
derivative(f).wrt<0, 0>()           // ∂²f/∂x₀² (convenience)
derivative(f).gradient()            // all partials as tuple

Evaluation

The result of differentiation is itself an expression that can be evaluated:

auto df = derivative(sin(x*x)).wrt<0>();
double result = df.eval({2.0});  // Evaluate at x=2

See also

derivative() Entry point function

Definition at line 79 of file derivative_builder.hpp.

Member Typedef Documentation

expr_type

template<typename E >

using limes::expr::DerivativeBuilder< E >::expr_type = E

Definition at line 81 of file derivative_builder.hpp.

value_type

template<typename E >

using limes::expr::DerivativeBuilder< E >::value_type = typename E::value_type

Definition at line 80 of file derivative_builder.hpp.

Constructor & Destructor Documentation

DerivativeBuilder()

template<typename E >

constexpr limes::expr::DerivativeBuilder< E >::DerivativeBuilder ( E  e )

inlineconstexprnoexcept

Definition at line 85 of file derivative_builder.hpp.

Member Function Documentation

derivative()

template<typename E >

template<std::size_t Dim>

constexpr auto limes::expr::DerivativeBuilder< E >::derivative ( ) const

inlineconstexpr

Further differentiation through the member function.

Definition at line 147 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::expr.

eval()

template<typename E >

constexpr value_type limes::expr::DerivativeBuilder< E >::eval ( std::span< value_type const >  args ) const

inlineconstexpr

Evaluate the derivative expression.

Definition at line 127 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::expr.

Referenced by limes::expr::DerivativeBuilder< E >::evaluate().

evaluate()

template<typename E >

constexpr value_type limes::expr::DerivativeBuilder< E >::evaluate ( std::span< value_type const >  args ) const

inlineconstexpr

Deprecated: use eval() instead.

Definition at line 133 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::eval().

get()

template<typename E >

constexpr E limes::expr::DerivativeBuilder< E >::get ( ) const

inlineconstexprnoexcept

Allow implicit conversion to the underlying derivative expression.

Definition at line 124 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::expr.

gradient()

template<typename E >

constexpr auto limes::expr::DerivativeBuilder< E >::gradient ( ) const

inlineconstexpr

Returns tuple<∂f/∂x₀, ∂f/∂x₁, ..., ∂f/∂x_{n-1}>

Definition at line 115 of file derivative_builder.hpp.

to_string()

template<typename E >

std::string limes::expr::DerivativeBuilder< E >::to_string ( ) const

inline

String representation.

Definition at line 138 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::expr.

wrt() [1/3]

template<typename E >

template<std::size_t Dim>

constexpr auto limes::expr::DerivativeBuilder< E >::wrt ( ) const

inlineconstexpr

Compute ∂/∂x_Dim and return a new builder for chaining.

Definition at line 93 of file derivative_builder.hpp.

References limes::expr::DerivativeBuilder< E >::expr.

wrt() [2/3]

template<typename E >

template<std::size_t D1, std::size_t D2>

constexpr auto limes::expr::DerivativeBuilder< E >::wrt ( ) const

inlineconstexpr

Compute ∂²/∂x_D1 ∂x_D2 (convenience for second-order mixed partials)

Definition at line 100 of file derivative_builder.hpp.

wrt() [3/3]

template<typename E >

template<std::size_t D1, std::size_t D2, std::size_t D3>

constexpr auto limes::expr::DerivativeBuilder< E >::wrt ( ) const

inlineconstexpr

Compute ∂³/∂x_D1 ∂x_D2 ∂x_D3 (convenience for third-order mixed partials)

Definition at line 106 of file derivative_builder.hpp.

Member Data Documentation

arity_v

template<typename E >

constexpr std::size_t limes::expr::DerivativeBuilder< E >::arity_v = E::arity_v

staticconstexpr

Arity of the derivative expression.

Definition at line 143 of file derivative_builder.hpp.

expr

template<typename E >

E limes::expr::DerivativeBuilder< E >::expr

Definition at line 83 of file derivative_builder.hpp.

Referenced by limes::expr::DerivativeBuilder< E >::derivative(), limes::expr::DerivativeBuilder< E >::eval(), limes::expr::DerivativeBuilder< E >::get(), limes::expr::DerivativeBuilder< E >::to_string(), and limes::expr::DerivativeBuilder< E >::wrt().

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

• include/limes/expr/derivative_builder.hpp