BarycentricMesh< T > Class Template Reference

Detailed Description

template<typename T>
class drake::math::BarycentricMesh< T >

Represents a multi-linear function (from vector inputs to vector outputs) by interpolating between points on a mesh using (triangular) barycentric interpolation.

For a technical description of barycentric interpolation, see e.g. Remi Munos and Andrew Moore, "Barycentric Interpolators for Continuous Space and Time Reinforcement Learning", NIPS 1998

Template Parameters

T	The scalar type, which must be double.

#include <drake/math/barycentric.h>

Public Types
typedef std::set< double >	Coordinates
	The mesh is represented by a std::set (to ensure uniqueness and provide logarithmic lookups) of coordinates in each input dimension. More...
typedef std::vector< Coordinates >	MeshGrid

Public Member Functions
	BarycentricMesh (MeshGrid input_grid)
	Constructs the mesh. More...
const MeshGrid &	get_input_grid () const
int	get_input_size () const
int	get_num_mesh_points () const
int	get_num_interpolants () const
void	get_mesh_point (int index, EigenPtr< Eigen::VectorXd > point) const
	Writes the position of a mesh point in the input space referenced by its scalar index to point. More...
VectorX< T >	get_mesh_point (int index) const
	Returns the position of a mesh point in the input space referenced by its scalar index to point. More...
MatrixX< T >	get_all_mesh_points () const
	Returns a matrix with all of the mesh points, one per column. More...
void	EvalBarycentricWeights (const Eigen::Ref< const VectorX< T >> &input, EigenPtr< Eigen::VectorXi > mesh_indices, EigenPtr< VectorX< T >> weights) const
	Writes the mesh indices used for interpolation to mesh_indices, and the interpolating coefficients to weights. More...
void	Eval (const Eigen::Ref< const MatrixX< T >> &mesh_values, const Eigen::Ref< const VectorX< T >> &input, EigenPtr< VectorX< T >> output) const
	Evaluates the function at the input values, by interpolating between the values at mesh_values. More...
VectorX< T >	Eval (const Eigen::Ref< const MatrixX< T >> &mesh_values, const Eigen::Ref< const VectorX< T >> &input) const
	Returns the function evaluated at input. More...
template<typename ValueT = T>
void	EvalWithMixedScalars (const Eigen::Ref< const MatrixX< ValueT >> &mesh_values, const Eigen::Ref< const VectorX< T >> &input, EigenPtr< VectorX< ValueT >> output) const
	Performs Eval, but with the possibility of the values on the mesh having a different scalar type than the values defining the mesh (symbolic::Expression containing decision variables for an optimization problem is an important example) More...
template<typename ValueT = T>
VectorX< ValueT >	EvalWithMixedScalars (const Eigen::Ref< const MatrixX< ValueT >> &mesh_values, const Eigen::Ref< const VectorX< T >> &input) const
	Returns the function evaluated at input. More...
MatrixX< T >	MeshValuesFrom (const std::function< VectorX< T >(const Eigen::Ref< const VectorX< T >> &)> &vector_func) const
	Evaluates vector_func at all input mesh points and extracts the mesh value matrix that should be used to approximate the function with this barycentric interpolation. More...
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	BarycentricMesh (const BarycentricMesh &)=default
BarycentricMesh &	operator= (const BarycentricMesh &)=default
	BarycentricMesh (BarycentricMesh &&)=default
BarycentricMesh &	operator= (BarycentricMesh &&)=default

Member Typedef Documentation

Coordinates

typedef std::set<double> Coordinates

The mesh is represented by a std::set (to ensure uniqueness and provide logarithmic lookups) of coordinates in each input dimension.

Note: The values are type double, not T (We do not plan to take gradients, etc w/ respect to them).

MeshGrid

typedef std::vector<Coordinates> MeshGrid

Constructor & Destructor Documentation

BarycentricMesh() [1/3]

BarycentricMesh ( const BarycentricMesh< T > &  )

default

BarycentricMesh() [2/3]

BarycentricMesh ( BarycentricMesh< T > &&  )

default

BarycentricMesh() [3/3]

BarycentricMesh ( MeshGrid  input_grid )

explicit

Constructs the mesh.

Member Function Documentation

Eval() [1/2]

void Eval	(	const Eigen::Ref< const MatrixX< T >> &	mesh_values,
		const Eigen::Ref< const VectorX< T >> &	input,
		EigenPtr< VectorX< T >>	output
	)		const

Evaluates the function at the input values, by interpolating between the values at mesh_values.

Inputs that are outside the bounding box of the input_grid are interpolated as though they were projected (elementwise) to the closest face of the defined mesh.

Note that the dimension of the output vector is completely defined by the mesh_values argument. This class does not maintain any information related to the size of the output.

Parameters

mesh_values	is a num_outputs by get_num_mesh_points() matrix containing the points to interpolate between. The order of the columns must be consistent with the mesh indices curated by this class, as exposed by get_mesh_point().
input	must be a vector of length get_num_inputs().
output	is the interpolated vector of length num_outputs

Eval() [2/2]

VectorX<T> Eval	(	const Eigen::Ref< const MatrixX< T >> &	mesh_values,
		const Eigen::Ref< const VectorX< T >> &	input
	)		const

Returns the function evaluated at input.

EvalBarycentricWeights()

void EvalBarycentricWeights	(	const Eigen::Ref< const VectorX< T >> &	input,
		EigenPtr< Eigen::VectorXi >	mesh_indices,
		EigenPtr< VectorX< T >>	weights
	)		const

Writes the mesh indices used for interpolation to mesh_indices, and the interpolating coefficients to weights.

Inputs that are outside the bounding box of the input_grid are interpolated as though they were projected (elementwise) to the closest face of the defined mesh.

Parameters

input	must be a vector of length get_num_inputs().
mesh_indices	is a pointer to a vector of length get_num_interpolants().
weights	is a vector of coefficients (which sum to 1) of length get_num_interpolants().

EvalWithMixedScalars() [1/2]

void EvalWithMixedScalars	(	const Eigen::Ref< const MatrixX< ValueT >> &	mesh_values,
		const Eigen::Ref< const VectorX< T >> &	input,
		EigenPtr< VectorX< ValueT >>	output
	)		const

Performs Eval, but with the possibility of the values on the mesh having a different scalar type than the values defining the mesh (symbolic::Expression containing decision variables for an optimization problem is an important example)

Template Parameters

ValueT

defines the scalar type of the mesh_values and the output.

See also

Eval

EvalWithMixedScalars() [2/2]

VectorX<ValueT> EvalWithMixedScalars	(	const Eigen::Ref< const MatrixX< ValueT >> &	mesh_values,
		const Eigen::Ref< const VectorX< T >> &	input
	)		const

Returns the function evaluated at input.

get_all_mesh_points()

MatrixX<T> get_all_mesh_points

(

)

const

Returns a matrix with all of the mesh points, one per column.

get_input_grid()

const MeshGrid& get_input_grid

(

)

const

get_input_size()

int get_input_size

(

)

const

get_mesh_point() [1/2]

void get_mesh_point	(	int	index,
		EigenPtr< Eigen::VectorXd >	point
	)		const

Writes the position of a mesh point in the input space referenced by its scalar index to point.

Parameters

index	must be in [0, get_num_mesh_points).
point	is set to the num_inputs-by-1 location of the mesh point.

get_mesh_point() [2/2]

VectorX<T> get_mesh_point

(

int

index

)

const

Returns the position of a mesh point in the input space referenced by its scalar index to point.

Parameters

index

must be in [0, get_num_mesh_points).

get_num_interpolants()

int get_num_interpolants

(

)

const

get_num_mesh_points()

int get_num_mesh_points

(

)

const

MeshValuesFrom()

MatrixX<T> MeshValuesFrom

(

)

Evaluates vector_func at all input mesh points and extracts the mesh value matrix that should be used to approximate the function with this barycentric interpolation.

MatrixXd mesh_values = bary.MeshValuesFrom(
  [](const auto& x) { return Vector1d(std::sin(x[0])); });

operator=() [1/2]

BarycentricMesh& operator= ( const BarycentricMesh< T > &  )

default

operator=() [2/2]

BarycentricMesh& operator= ( BarycentricMesh< T > &&  )

default

---

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

• drake/math/barycentric.h