Namespace of backward-mode automatic differentiation. More...

Namespaces
namespace	graph
	Namespace of graphs in backward-mode automatic differentiation.

namespace	impl
	Namespace of internal implementations.

Classes
struct	constant_tag
	Tag class to specify constants. More...

class	variable
	Class of variables in backward-mode automatic differentiation [17]. More...

struct	variable_tag
	Tag class to specify variables. More...

Typedefs
template<base::concepts::real_scalar_dense_vector ValueVector>
using	variable_vector_type
	Get type of vectors of variables.

Functions
template<base::concepts::real_scalar Scalar>
auto	create_diff_variable (const Scalar &value) -> variable< Scalar >
	Create a variable by which functions will be differentiated.

template<base::concepts::real_scalar_dense_vector ValueVector>
auto	create_diff_variable_vector (const Eigen::MatrixBase< ValueVector > &value_vec) -> Eigen::CwiseNullaryOp< impl::create_diff_variable_vector_functor< ValueVector >, typename impl::create_diff_variable_vector_functor< ValueVector >::result_type >
	Create a vector of variables.

template<typename FuncValType , typename ArgType >
auto	differentiate (const Eigen::MatrixBase< FuncValType > &func_value, const Eigen::MatrixBase< ArgType > &arg) -> Eigen::CwiseNullaryOp< impl::differentiate_vector_with_vector_functor< FuncValType, ArgType >, typename impl::differentiate_vector_with_vector_functor< FuncValType, ArgType >::result_type >
	Compute differential coefficients.

template<typename Scalar , typename ArgDerived >
auto	differentiate (const variable< Scalar > &func_value, const Eigen::MatrixBase< ArgDerived > &arg) -> Eigen::CwiseNullaryOp< impl::differentiate_scalar_with_matrix_functor< ArgDerived >, typename impl::differentiate_scalar_with_matrix_functor< ArgDerived >::result_type >
	Compute differential coefficients.

template<typename Scalar >
auto	differentiate (const variable< Scalar > &func_value, const variable< Scalar > &arg) -> Scalar
	Compute a differential coefficient.

template<typename Scalar >
auto	exp (const variable< Scalar > &x) -> variable< Scalar >
	Calculate exponential.

template<typename Scalar >
auto	log (const variable< Scalar > &x) -> variable< Scalar >
	Calculate logarithm.

template<typename Scalar >
auto	operator* (const Scalar &left, const variable< Scalar > &right) -> variable< Scalar >
	Multiply two variables.

template<typename Scalar >
auto	operator* (const variable< Scalar > &left, const Scalar &right) -> variable< Scalar >
	Multiply two variables.

template<typename Scalar >
auto	operator* (const variable< Scalar > &left, const variable< Scalar > &right) -> variable< Scalar >
	Multiply two variables.

template<typename Scalar >
auto	operator+ (const Scalar &left, const variable< Scalar > &right) -> variable< Scalar >
	Add two variables.

template<typename Scalar >
auto	operator+ (const variable< Scalar > &left, const Scalar &right) -> variable< Scalar >
	Add two variables.

template<typename Scalar >
auto	operator+ (const variable< Scalar > &left, const variable< Scalar > &right) -> variable< Scalar >
	Add two variables.

template<typename Scalar >
auto	operator- (const Scalar &left, const variable< Scalar > &right) -> variable< Scalar >
	Subtract a variable from another variable.

template<typename Scalar >
auto	operator- (const variable< Scalar > &left, const Scalar &right) -> variable< Scalar >
	Subtract a variable from another variable.

template<typename Scalar >
auto	operator- (const variable< Scalar > &left, const variable< Scalar > &right) -> variable< Scalar >
	Subtract a variable from another variable.

template<typename Scalar >
auto	operator/ (const Scalar &left, const variable< Scalar > &right) -> variable< Scalar >
	Divide a variable from another variable.

template<typename Scalar >
auto	operator/ (const variable< Scalar > &left, const Scalar &right) -> variable< Scalar >
	Divide a variable from another variable.

template<typename Scalar >
auto	operator/ (const variable< Scalar > &left, const variable< Scalar > &right) -> variable< Scalar >
	Divide a variable from another variable.

template<typename Scalar >
auto	sqrt (const variable< Scalar > &x) -> variable< Scalar >
	Calculate square root.

Detailed Description

Namespace of backward-mode automatic differentiation.

Typedef Documentation

◆ variable_vector_type

template<base::concepts::real_scalar_dense_vector ValueVector>

using num_collect::auto_diff::backward::variable_vector_type

Initial value:

 
    Eigen::Matrix<variable<typename ValueVector::Scalar>,
        ValueVector::RowsAtCompileTime, 1, Eigen::ColMajor,
        ValueVector::MaxRowsAtCompileTime, 1>

Get type of vectors of variables.

Template Parameters

ValueVector Type of vectors of values.

Definition at line 54 of file create_diff_variable.h.

Function Documentation

◆ create_diff_variable()

template<base::concepts::real_scalar Scalar>

auto num_collect::auto_diff::backward::create_diff_variable ( const Scalar & value ) -> variable<Scalar>

inlinenodiscard

Create a variable by which functions will be differentiated.

Template Parameters

Scalar Type of scalars.

Parameters

[in] value Value.

Returns: Variable.

Definition at line 43 of file create_diff_variable.h.

◆ create_diff_variable_vector()

template<base::concepts::real_scalar_dense_vector ValueVector>

auto num_collect::auto_diff::backward::create_diff_variable_vector ( const Eigen::MatrixBase< ValueVector > & value_vec ) -> Eigen::CwiseNullaryOp< impl::create_diff_variable_vector_functor<ValueVector>, typename impl::create_diff_variable_vector_functor< ValueVector>::result_type>

inlinenodiscard

Create a vector of variables.

Template Parameters

ValueVector Type of vectors of values.

Parameters

[in] value_vec Vector of values.

Returns: Vector of variables.

Definition at line 118 of file create_diff_variable.h.

◆ differentiate() [1/3]

template<typename FuncValType , typename ArgType >

auto num_collect::auto_diff::backward::differentiate	(	const Eigen::MatrixBase< FuncValType > &	func_value,
		const Eigen::MatrixBase< ArgType > &	arg ) -> Eigen::CwiseNullaryOp< impl::differentiate_vector_with_vector_functor<FuncValType, ArgType>, typename impl::differentiate_vector_with_vector_functor<FuncValType, ArgType>::result_type>

inlinenodiscard

Compute differential coefficients.

Template Parameters

FuncValType	Type of function values.
ArgType	Type of function arguments.

Parameters

[in]	func_value	Variable of the function value.
[in]	arg	Variable of the argument.

Returns: Expression of differential coefficients.

Definition at line 208 of file differentiate.h.

◆ differentiate() [2/3]

template<typename Scalar , typename ArgDerived >

auto num_collect::auto_diff::backward::differentiate	(	const variable< Scalar > &	func_value,
		const Eigen::MatrixBase< ArgDerived > &	arg ) -> Eigen::CwiseNullaryOp< impl::differentiate_scalar_with_matrix_functor<ArgDerived>, typename impl::differentiate_scalar_with_matrix_functor< ArgDerived>::result_type>

inlinenodiscard

Compute differential coefficients.

Template Parameters

Scalar	Type of scalars.
ArgDerived	Derived class of argument.

Parameters

[in]	func_value	Variable of the function value.
[in]	arg	Variable of the argument.

Returns: Expression of differential coefficients.

Definition at line 119 of file differentiate.h.

◆ differentiate() [3/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::differentiate	(	const variable< Scalar > &	func_value,
		const variable< Scalar > &	arg ) -> Scalar

inlinenodiscard

Compute a differential coefficient.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	func_value	Variable of the function value.
[in]	arg	Variable of the argument.

Returns: Differential coefficient.

Definition at line 48 of file differentiate.h.

◆ exp()

template<typename Scalar >

auto num_collect::auto_diff::backward::exp ( const variable< Scalar > & x ) -> variable<Scalar>

inlinenodiscard

Calculate exponential.

Template Parameters

Scalar Type of scalars.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 60 of file variable_math.h.

◆ log()

template<typename Scalar >

auto num_collect::auto_diff::backward::log ( const variable< Scalar > & x ) -> variable<Scalar>

inlinenodiscard

Calculate logarithm.

Template Parameters

Scalar Type of scalars.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 74 of file variable_math.h.

◆ operator*() [1/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator*	(	const Scalar &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Multiply two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Product.

Definition at line 353 of file variable.h.

◆ operator*() [2/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator*	(	const variable< Scalar > &	left,
		const Scalar &	right ) -> variable<Scalar>

inlinenodiscard

Multiply two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Product.

Definition at line 367 of file variable.h.

◆ operator*() [3/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator*	(	const variable< Scalar > &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Multiply two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Product.

Definition at line 339 of file variable.h.

◆ operator+() [1/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator+	(	const Scalar &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Add two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Sum.

Definition at line 269 of file variable.h.

◆ operator+() [2/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator+	(	const variable< Scalar > &	left,
		const Scalar &	right ) -> variable<Scalar>

inlinenodiscard

Add two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Sum.

Definition at line 283 of file variable.h.

◆ operator+() [3/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator+	(	const variable< Scalar > &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Add two variables.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Sum.

Definition at line 255 of file variable.h.

◆ operator-() [1/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator-	(	const Scalar &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Difference.

Definition at line 311 of file variable.h.

◆ operator-() [2/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator-	(	const variable< Scalar > &	left,
		const Scalar &	right ) -> variable<Scalar>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Difference.

Definition at line 325 of file variable.h.

◆ operator-() [3/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator-	(	const variable< Scalar > &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Difference.

Definition at line 297 of file variable.h.

◆ operator/() [1/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator/	(	const Scalar &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Divide a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Quotient.

Definition at line 395 of file variable.h.

◆ operator/() [2/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator/	(	const variable< Scalar > &	left,
		const Scalar &	right ) -> variable<Scalar>

inlinenodiscard

Divide a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Quotient.

Definition at line 409 of file variable.h.

◆ operator/() [3/3]

template<typename Scalar >

auto num_collect::auto_diff::backward::operator/	(	const variable< Scalar > &	left,
		const variable< Scalar > &	right ) -> variable<Scalar>

inlinenodiscard

Divide a variable from another variable.

Template Parameters

Scalar Type of scalars.

Parameters

[in]	left	Left-hand-side variable.
[in]	right	Right-hand-side variable.

Returns: Quotient.

Definition at line 381 of file variable.h.

◆ sqrt()

template<typename Scalar >

auto num_collect::auto_diff::backward::sqrt ( const variable< Scalar > & x ) -> variable<Scalar>

inlinenodiscard

Calculate square root.

Template Parameters

Scalar Type of scalars.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 88 of file variable_math.h.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ variable_vector_type

Function Documentation

◆ create_diff_variable()

◆ create_diff_variable_vector()

◆ differentiate() [1/3]

◆ differentiate() [2/3]

◆ differentiate() [3/3]

◆ exp()

◆ log()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ sqrt()