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

Namespaces
namespace	impl
	Namespace of internal implementations.

Classes
class	variable
	Class of variables in forward-mode automatic differentiation [17]. 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 Value>
auto	create_diff_variable (const Value &value) -> variable< Value >
	Create a variable by which functions will be differentiated (for scalar differential coefficients).

template<base::concepts::real_scalar Value, base::concepts::real_scalar_dense_vector Diff>
auto	create_diff_variable (const Value &value, index_type size, index_type index) -> variable< Value, Diff >
	Create a variable by which functions will be differentiated (for vector differential coefficients).

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 Value , typename Diff >
auto	exp (const variable< Value, Diff > &x) -> variable< Value, Diff >
	Calculate exponential.

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

template<base::concepts::dense_vector VectorType>
auto	make_jacobian (const Eigen::MatrixBase< VectorType > &vector) -> Eigen::CwiseNullaryOp< impl::make_jacobian_functor< VectorType >, typename impl::make_jacobian_functor< VectorType >::result_type >
	Make Jacobian from a vector of variables.

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

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

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

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

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

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

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

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

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

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

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

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

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

Detailed Description

Namespace of forward-mode automatic differentiation.

Typedef Documentation

◆ variable_vector_type

template<base::concepts::real_scalar_dense_vector ValueVector>

using num_collect::auto_diff::forward::variable_vector_type

Initial value:

 
    Eigen::Matrix<variable<typename ValueVector::Scalar, ValueVector>,
        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 76 of file create_diff_variable.h.

Function Documentation

◆ create_diff_variable() [1/2]

template<base::concepts::real_scalar Value>

auto num_collect::auto_diff::forward::create_diff_variable ( const Value & value ) -> variable<Value>

inlinenodiscard

Create a variable by which functions will be differentiated (for scalar differential coefficients).

This will set the differential coefficient to one.

Template Parameters

Value	Type of the value.
Diff	Type of the differential coefficient.

Parameters

[in] value Value.

Returns: Variable.

Definition at line 47 of file create_diff_variable.h.

◆ create_diff_variable() [2/2]

template<base::concepts::real_scalar Value, base::concepts::real_scalar_dense_vector Diff>

auto num_collect::auto_diff::forward::create_diff_variable	(	const Value &	value,
		index_type	size,
		index_type	index ) -> variable<Value, Diff>

inlinenodiscard

Create a variable by which functions will be differentiated (for vector differential coefficients).

Template Parameters

Value	Type of the value.
Diff	Type of the differential coefficients.

Parameters

[in]	value	Value.
[in]	size	Size of Diff.
[in]	index	Index of the variable.

Returns: Variable.

Definition at line 65 of file create_diff_variable.h.

◆ create_diff_variable_vector()

template<base::concepts::real_scalar_dense_vector ValueVector>

auto num_collect::auto_diff::forward::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 144 of file create_diff_variable.h.

◆ exp()

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::exp ( const variable< Value, Diff > & x ) -> variable<Value, Diff>

inlinenodiscard

Calculate exponential.

Template Parameters

Value	Type of values.
Diff	Type of differential coefficients.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 61 of file variable_math.h.

◆ log()

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::log ( const variable< Value, Diff > & x ) -> variable<Value, Diff>

inlinenodiscard

Calculate logarithm.

Template Parameters

Value	Type of values.
Diff	Type of differential coefficients.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 77 of file variable_math.h.

◆ make_jacobian()

template<base::concepts::dense_vector VectorType>

auto num_collect::auto_diff::forward::make_jacobian ( const Eigen::MatrixBase< VectorType > & vector ) -> Eigen::CwiseNullaryOp<impl::make_jacobian_functor<VectorType>, typename impl::make_jacobian_functor<VectorType>::result_type>

inlinenodiscard

Make Jacobian from a vector of variables.

Template Parameters

VectorType Type of vectors of variables.

Parameters

[in] vector Vector of variables.

Returns: Jacobian.

Definition at line 100 of file make_jacobian.h.

◆ operator*() [1/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator*	(	const Value &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Multiply two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Product.

Definition at line 320 of file variable.h.

◆ operator*() [2/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator*	(	const variable< Value, Diff > &	left,
		const Value &	right ) -> variable<Value, Diff>

inlinenodiscard

Multiply two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Product.

Definition at line 335 of file variable.h.

◆ operator*() [3/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator*	(	const variable< Value, Diff > &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Multiply two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Product.

Definition at line 305 of file variable.h.

◆ operator+() [1/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator+	(	const Value &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Add two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Sum.

Definition at line 230 of file variable.h.

◆ operator+() [2/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator+	(	const variable< Value, Diff > &	left,
		const Value &	right ) -> variable<Value, Diff>

inlinenodiscard

Add two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Sum.

Definition at line 245 of file variable.h.

◆ operator+() [3/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator+	(	const variable< Value, Diff > &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Add two variables.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Sum.

Definition at line 215 of file variable.h.

◆ operator-() [1/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator-	(	const Value &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Difference.

Definition at line 275 of file variable.h.

◆ operator-() [2/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator-	(	const variable< Value, Diff > &	left,
		const Value &	right ) -> variable<Value, Diff>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Difference.

Definition at line 290 of file variable.h.

◆ operator-() [3/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator-	(	const variable< Value, Diff > &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Subtract a variable from another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Difference.

Definition at line 260 of file variable.h.

◆ operator/() [1/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator/	(	const Value &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Divide a variable by another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Quotient.

Definition at line 365 of file variable.h.

◆ operator/() [2/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator/	(	const variable< Value, Diff > &	left,
		const Value &	right ) -> variable<Value, Diff>

inlinenodiscard

Divide a variable by another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Quotient.

Definition at line 380 of file variable.h.

◆ operator/() [3/3]

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::operator/	(	const variable< Value, Diff > &	left,
		const variable< Value, Diff > &	right ) -> variable<Value, Diff>

inlinenodiscard

Divide a variable by another variable.

Template Parameters

Value	Type of value.
Diff	Type of differential coefficients.

Parameters

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

Returns: Quotient.

Definition at line 350 of file variable.h.

◆ sqrt()

template<typename Value , typename Diff >

auto num_collect::auto_diff::forward::sqrt ( const variable< Value, Diff > & x ) -> variable<Value, Diff>

inlinenodiscard

Calculate square root.

Template Parameters

Value	Type of values.
Diff	Type of differential coefficients.

Parameters

[in] x Argument.

Returns: Value.

Definition at line 93 of file variable_math.h.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ variable_vector_type

Function Documentation

◆ create_diff_variable() [1/2]

◆ create_diff_variable() [2/2]

◆ create_diff_variable_vector()

◆ exp()

◆ log()

◆ make_jacobian()

◆ 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()