Jacobian using Auto-Diff Codegeneration. More...

#include <DerivativesCppad.h>

Inheritance diagram for ct::core::DerivativesCppad< IN_DIM, OUT_DIM >:

Public Types
typedef Eigen::Matrix< AD_SCALAR, IN_DIM, 1 >	IN_TYPE_AD
	function input vector type More...

typedef Eigen::Matrix< AD_SCALAR, OUT_DIM, 1 >	OUT_TYPE_AD
	function output vector type More...

typedef Eigen::Matrix< double, IN_DIM, 1 >	IN_TYPE_D
	function input vector type double More...

typedef Eigen::Matrix< double, OUT_DIM, 1 >	OUT_TYPE_D
	function output vector type More...

typedef Eigen::Matrix< double, OUT_DIM, IN_DIM >	JAC_TYPE_D
	Jacobian type. More...

typedef Eigen::Matrix< double, OUT_DIM, IN_DIM, Eigen::RowMajor >	JAC_TYPE_ROW_MAJOR
	Jocobian type in row-major format. More...

typedef Eigen::Matrix< double, IN_DIM, IN_DIM >	HES_TYPE_D

typedef Eigen::Matrix< double, IN_DIM, IN_DIM, Eigen::RowMajor >	HES_TYPE_ROW_MAJOR

typedef std::function< OUT_TYPE_AD(const IN_TYPE_AD &)>	FUN_TYPE_AD

typedef Derivatives< IN_DIM, OUT_DIM >	DerivativesBase

Public Types inherited from ct::core::Derivatives< IN_DIM, OUT_DIM, double >
typedef Eigen::Matrix< double, IN_DIM, 1 >	IN_TYPE
	function input vector type More...

typedef Eigen::Matrix< double, OUT_DIM, 1 >	OUT_TYPE
	function output vector type More...

typedef Eigen::Matrix< double, OUT_DIM, IN_DIM >	JAC_TYPE

typedef Eigen::Matrix< double, IN_DIM, IN_DIM >	HES_TYPE

Public Member Functions
	DerivativesCppad (FUN_TYPE_AD &f, int inputDim=IN_DIM, int outputDim=OUT_DIM)
	Constructs the derivatives for autodiff without codegeneration using a FUN_TYPE_AD function. More...

	DerivativesCppad (const DerivativesCppad &arg)
	copy constructor More...

void	update (FUN_TYPE_AD &f, const size_t inputDim=IN_DIM, const size_t outputDim=OUT_DIM)
	update the Jacobian with a new function More...

virtual	~DerivativesCppad ()
	destructor More...

DerivativesCppad *	clone () const
	deep cloning of Jacobian More...

virtual OUT_TYPE_D	forwardZero (const Eigen::VectorXd &x)
	Evaluates the method itself. More...

virtual JAC_TYPE_D	jacobian (const Eigen::VectorXd &x)
	Evaluates the jacobian with respect to the input. More...

virtual void	sparseJacobian (const Eigen::VectorXd &x, Eigen::VectorXd &jac, Eigen::VectorXi &iRow, Eigen::VectorXi &jCol)
	Returns the evaluated jacobian in sparse format. More...

virtual Eigen::VectorXd	sparseJacobianValues (const Eigen::VectorXd &x)
	Returns the non zero values of the jacobian. More...

virtual HES_TYPE_D	hessian (const Eigen::VectorXd &x, const Eigen::VectorXd &lambda)
	Evaluates the hessian (2nd order derivatives with respect to input) of the method. In case of a vector valued function, the method returns the weighted sum of the hessians with weights w. More...

virtual void	sparseHessian (const Eigen::VectorXd &x, const Eigen::VectorXd &lambda, Eigen::VectorXd &hes, Eigen::VectorXi &iRow, Eigen::VectorXi &jCol)
	Returns the weighted sum of hessian of the problem in sparse format. More...

virtual Eigen::VectorXd	sparseHessianValues (const Eigen::VectorXd &x, const Eigen::VectorXd &lambda)
	Returns the non zero elements of the hessian of the problem. More...

Public Member Functions inherited from ct::core::Derivatives< IN_DIM, OUT_DIM, double >
	Derivatives ()

virtual	~Derivatives ()
	default destructor More...

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef ADScalar	AD_SCALAR

Detailed Description

template<int IN_DIM, int OUT_DIM>
class ct::core::DerivativesCppad< IN_DIM, OUT_DIM >

Jacobian using Auto-Diff Codegeneration.

Uses Auto-Diff code generation to compute the Jacobian $J(x_s) = \frac{df}{dx} |_{x=x_s}$ of a regular vector-valued mathematical function $ y = f(x) $ .

x has IN_DIM dimension and y has OUT_DIM dimension. Thus, they can be scalar functions (IN_DIM = 1, OUT_DIM = 1), fixed or variable size (IN_DIM = -1, OUT_DIM = -1) functions.

Note: In fact, this class is called Jacobian but computes also zero order derivatives

Template Parameters

IN_DIM	Input dimensionality of the function (use Eigen::Dynamic (-1) for dynamic size)
OUT_DIM	Output dimensionailty of the function (use Eigen::Dynamic (-1) for dynamic size)

Member Typedef Documentation

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<AD_SCALAR, IN_DIM, 1> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::IN_TYPE_AD

function input vector type

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<AD_SCALAR, OUT_DIM, 1> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::OUT_TYPE_AD

function output vector type

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, IN_DIM, 1> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::IN_TYPE_D

function input vector type double

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, OUT_DIM, 1> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::OUT_TYPE_D

function output vector type

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, OUT_DIM, IN_DIM> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::JAC_TYPE_D

Jacobian type.

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, OUT_DIM, IN_DIM, Eigen::RowMajor> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::JAC_TYPE_ROW_MAJOR

Jocobian type in row-major format.

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, IN_DIM, IN_DIM> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::HES_TYPE_D

template<int IN_DIM, int OUT_DIM>

typedef Eigen::Matrix<double, IN_DIM, IN_DIM, Eigen::RowMajor> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::HES_TYPE_ROW_MAJOR

template<int IN_DIM, int OUT_DIM>

typedef std::function<OUT_TYPE_AD(const IN_TYPE_AD&)> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::FUN_TYPE_AD

template<int IN_DIM, int OUT_DIM>

typedef Derivatives<IN_DIM, OUT_DIM> ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::DerivativesBase

Constructor & Destructor Documentation

template<int IN_DIM, int OUT_DIM>

ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::DerivativesCppad	(	FUN_TYPE_AD &	f,
		int	inputDim = `IN_DIM`,
		int	outputDim = `OUT_DIM`
	)

inline

Constructs the derivatives for autodiff without codegeneration using a FUN_TYPE_AD function.

Warning: If IN_DIM and/our OUT_DIM are set to dynamic (-1), then the actual dimensions of x and y have to be passed here.

Parameters

	f	The function to be autodiffed
[in]	inputDim	inputDim input dimension, must be specified if template parameter IN_DIM is -1 (dynamic)
[in]	outputDim	outputDim output dimension, must be specified if template parameter IN_DIM is -1 (dynamic)

References ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::update().

template<int IN_DIM, int OUT_DIM>

ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::DerivativesCppad ( const DerivativesCppad< IN_DIM, OUT_DIM > & arg )

inline

copy constructor

template<int IN_DIM, int OUT_DIM>

virtual ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::~DerivativesCppad ( )

inlinevirtual

destructor

Member Function Documentation

template<int IN_DIM, int OUT_DIM>

void ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::update	(	FUN_TYPE_AD &	f,
		const size_t	inputDim = `IN_DIM`,
		const size_t	outputDim = `OUT_DIM`
	)

inline

update the Jacobian with a new function

Warning: If IN_DIM and/our OUT_DIM are set to dynamic (-1), then the actual dimensions of x and y have to be passed here.

Parameters

f	new function to compute Jacobian of
inputDim	input dimension, must be specified if template parameter IN_DIM is -1 (dynamic)
outputDim	output dimension, must be specified if template parameter IN_DIM is -1 (dynamic)

Referenced by ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::DerivativesCppad().

template<int IN_DIM, int OUT_DIM>

DerivativesCppad* ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::clone ( ) const

inlinevirtual

deep cloning of Jacobian

Implements ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual OUT_TYPE_D ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::forwardZero ( const Eigen::VectorXd & x )

inlinevirtual

Evaluates the method itself.

Parameters

[in] x The point of evaluation

Returns: The evalution of the method

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual JAC_TYPE_D ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::jacobian ( const Eigen::VectorXd & x )

inlinevirtual

Evaluates the jacobian with respect to the input.

Parameters

[in] x The point of evaluation

Returns: The evaluated jacobian

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual void ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::sparseJacobian	(	const Eigen::VectorXd &	x,
		Eigen::VectorXd &	jac,
		Eigen::VectorXi &	iRow,
		Eigen::VectorXi &	jCol
	)

inlinevirtual

Returns the evaluated jacobian in sparse format.

Parameters

[in]	x	The point of evaluation
[out]	jac	The non zero values of the jacobian
[out]	iRow	The row indices of the non zero values
[out]	jCol	The column indices of the non zero values

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual Eigen::VectorXd ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::sparseJacobianValues ( const Eigen::VectorXd & x )

inlinevirtual

Returns the non zero values of the jacobian.

Parameters

[in] x The point of evaluation

Returns: The non zeros values of the jacobian

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual HES_TYPE_D ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::hessian	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	lambda
	)

inlinevirtual

Evaluates the hessian (2nd order derivatives with respect to input) of the method. In case of a vector valued function, the method returns the weighted sum of the hessians with weights w.

Parameters

[in]	x	The point of evaluation
[in]	lambda	The weights of the sum

Returns: The evaluated hessian

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual void ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::sparseHessian	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	lambda,
		Eigen::VectorXd &	hes,
		Eigen::VectorXi &	iRow,
		Eigen::VectorXi &	jCol
	)

inlinevirtual

Returns the weighted sum of hessian of the problem in sparse format.

Parameters

[in]	x	The point of evaluation
[in]	lambda	The weights of the sum of the hessian
	hes	The non zero values of the hessian
	iRow	The row indices of the non zero values
	jCol	The column indices of the non zero values

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

template<int IN_DIM, int OUT_DIM>

virtual Eigen::VectorXd ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::sparseHessianValues	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	lambda
	)

inlinevirtual

Returns the non zero elements of the hessian of the problem.

Parameters

[in]	x	The point of evaluation
[in]	lambda	The weights of the sum of the hessian

Returns: { description_of_the_return_value }

Reimplemented from ct::core::Derivatives< IN_DIM, OUT_DIM, double >.

References x, and y.

Member Data Documentation

template<int IN_DIM, int OUT_DIM>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef ADScalar ct::core::DerivativesCppad< IN_DIM, OUT_DIM >::AD_SCALAR

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

/home/adrl/code/src/control-toolbox/ct_core/include/ct/core/math/DerivativesCppad.h

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<int IN_DIM, int OUT_DIM> class ct::core::DerivativesCppad< IN_DIM, OUT_DIM >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int IN_DIM, int OUT_DIM>
class ct::core::DerivativesCppad< IN_DIM, OUT_DIM >