Crocoddyl: ActivationModelSmooth1NormTpl< _Scalar > Class Template Reference

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Smooth-abs activation. More...

#include <smooth-1norm.hpp>

Inheritance diagram for ActivationModelSmooth1NormTpl< _Scalar >:

Public Types
typedef ActivationDataAbstractTpl< Scalar >	ActivationDataAbstract
typedef ActivationModelAbstractTpl< Scalar >	Base
typedef ActivationDataSmooth1NormTpl< Scalar >	Data
typedef MathBaseTpl< Scalar >	MathBase
typedef MathBase::MatrixXs	MatrixXs
typedef MathBase::VectorXs	VectorXs
Public Types inherited from ActivationModelAbstractTpl< _Scalar >
typedef ActivationDataAbstractTpl< Scalar >	ActivationDataAbstract
typedef MathBaseTpl< Scalar >	MathBase
typedef MathBase::MatrixXs	MatrixXs
typedef MathBase::VectorXs	VectorXs

Public Member Functions
	ActivationModelSmooth1NormTpl (const std::size_t nr, const Scalar delta=Scalar(1.))
	Initialize the smooth-abs activation model.
virtual void	calc (const std::shared_ptr< ActivationDataAbstract > &data, const Eigen::Ref< const VectorXs > &r) override
	Compute the smooth-abs function.
virtual void	calcDiff (const std::shared_ptr< ActivationDataAbstract > &data, const Eigen::Ref< const VectorXs > &r) override
	Compute the derivatives of the smooth-abs function.
template<typename NewScalar>
ActivationModelSmooth1NormTpl< NewScalar >	cast () const
virtual std::shared_ptr< ActivationDataAbstract >	createData () override
	Create the smooth-abs activation data.
Scalar	get_delta () const
virtual void	print (std::ostream &os) const override
	Print relevant information of the smooth-1norm model.
Public Member Functions inherited from ActivationModelAbstractTpl< _Scalar >
	ActivationModelAbstractTpl (const std::size_t nr)
std::size_t	get_nr () const

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar
Public Attributes inherited from ActivationModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Attributes
Scalar	delta_
	< Dimension of the residual vector
std::size_t	nr_
Protected Attributes inherited from ActivationModelAbstractTpl< _Scalar >
std::size_t	nr_

Detailed Description

template<typename _Scalar>
class crocoddyl::ActivationModelSmooth1NormTpl< _Scalar >

Smooth-abs activation.

This activation function describes a smooth representation of the 1-norm of a residual vector:

$\‍[ a(\mathbf{r}) = \sum_{i=0}^{nr-1} \delta^2\left(\sqrt{1 + (r_i/\delta)^2} - 1\right). \‍]$

Here, $\delta > 0$ is the smoothing scale, is a scalar residual, and is the residual dimension. This is the classical pseudo-Huber form, equivalently $\delta\sqrt{\delta^2 + r_i^2} - \delta^2$ . Its local quadratic approximation is for every $\delta$ . The transition to the linear regime occurs around $|r_i| = \delta$ , with asymptotic slope $\delta$ .

The computation of the function and its derivatives are carried out in calc() and calcDiff(), respectively.

See also: calc(), calcDiff(), createData()

Definition at line 42 of file smooth-1norm.hpp.

Member Typedef Documentation

◆ MathBase

template<typename _Scalar>

typedef MathBaseTpl<Scalar> MathBase

Definition at line 49 of file smooth-1norm.hpp.

◆ Base

template<typename _Scalar>

typedef ActivationModelAbstractTpl<Scalar> Base

Definition at line 50 of file smooth-1norm.hpp.

◆ ActivationDataAbstract

template<typename _Scalar>

typedef ActivationDataAbstractTpl<Scalar> ActivationDataAbstract

Definition at line 51 of file smooth-1norm.hpp.

◆ Data

template<typename _Scalar>

typedef ActivationDataSmooth1NormTpl<Scalar> Data

Definition at line 52 of file smooth-1norm.hpp.

◆ VectorXs

template<typename _Scalar>

typedef MathBase::VectorXs VectorXs

Definition at line 53 of file smooth-1norm.hpp.

◆ MatrixXs

template<typename _Scalar>

typedef MathBase::MatrixXs MatrixXs

Definition at line 54 of file smooth-1norm.hpp.

Constructor & Destructor Documentation

◆ ActivationModelSmooth1NormTpl()

template<typename _Scalar>

ActivationModelSmooth1NormTpl	(	const std::size_t	nr,
		const Scalar	delta = Scalar(1.) )

inlineexplicit

Initialize the smooth-abs activation model.

The default delta value is defined as 1.

Parameters

[in]	nr	Dimension of the residual vector
[in]	delta	Strictly positive smoothing scale (default: 1)

Definition at line 64 of file smooth-1norm.hpp.

Member Function Documentation

◆ calc()

template<typename _Scalar>

virtual void calc	(	const std::shared_ptr< ActivationDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	r )

inlineoverridevirtual

Compute the smooth-abs function.

Parameters

[in]	data	Smooth-abs activation data
[in]	r	Residual vector $\mathbf{r}\in\mathbb{R}^{nr}$

Implements ActivationModelAbstractTpl< _Scalar >.

Definition at line 80 of file smooth-1norm.hpp.

◆ calcDiff()

template<typename _Scalar>

virtual void calcDiff	(	const std::shared_ptr< ActivationDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	r )

inlineoverridevirtual

Compute the derivatives of the smooth-abs function.

Parameters

[in]	data	Smooth-abs activation data
[in]	r	Residual vector $\mathbf{r}\in\mathbb{R}^{nr}$

Implements ActivationModelAbstractTpl< _Scalar >.

Definition at line 100 of file smooth-1norm.hpp.

◆ createData()

template<typename _Scalar>

virtual std::shared_ptr< ActivationDataAbstract > createData ( )

inlineoverridevirtual

Create the smooth-abs activation data.

Returns: the activation data

Reimplemented from ActivationModelAbstractTpl< _Scalar >.

Definition at line 121 of file smooth-1norm.hpp.

◆ cast()

template<typename _Scalar>

template<typename NewScalar>

ActivationModelSmooth1NormTpl< NewScalar > cast ( ) const

inline

Definition at line 126 of file smooth-1norm.hpp.

◆ get_delta()

template<typename _Scalar>

Scalar get_delta ( ) const

inline

Definition at line 132 of file smooth-1norm.hpp.

◆ print()

template<typename _Scalar>

virtual void print ( std::ostream & os ) const

inlineoverridevirtual

Print relevant information of the smooth-1norm model.

Parameters

[out] os Output stream object

Reimplemented from ActivationModelAbstractTpl< _Scalar >.

Definition at line 139 of file smooth-1norm.hpp.

Member Data Documentation

◆ Scalar

template<typename _Scalar>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Definition at line 48 of file smooth-1norm.hpp.

◆ delta_

template<typename _Scalar>

Scalar delta_

protected

< Dimension of the residual vector

Smoothing scale

Definition at line 146 of file smooth-1norm.hpp.

◆ nr_

template<typename _Scalar>

std::size_t nr_

protected

Definition at line 68 of file activation-base.hpp.

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

/build/source/include/crocoddyl/core/activations/smooth-1norm.hpp

crocoddyl
ActivationModelSmooth1NormTpl
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