This is an extension of the PerSimplexFunction class that uses autodiff encoding for differentiations. More...

#include <PerSimplexAutodiffFunction.hpp>

Inheritance diagram for wmtk::function::PerSimplexAutodiffFunction:

Collaboration diagram for wmtk::function::PerSimplexAutodiffFunction:

Public Types
using	DScalar = DScalar2< double, Eigen::Matrix< double, -1, 1 >, Eigen::Matrix< double, -1, -1 > >

using	Scalar = typename DScalar::Scalar

using	DSVec = Eigen::VectorX< DScalar >

Public Member Functions
	PerSimplexAutodiffFunction (const Mesh &mesh, const PrimitiveType primitive_type, const attribute::MeshAttributeHandle &variable_attribute_handle)

	~PerSimplexAutodiffFunction ()

double	get_value (const simplex::Simplex &domain_simplex) const override
	This function is defined over a simplex (normally a triangle or tetrahedron). More...

Eigen::VectorXd	get_gradient (const simplex::Simplex &domain_simplex, const simplex::Simplex &variable_simplex) const override

Eigen::MatrixXd	get_hessian (const simplex::Simplex &domain_simplex, const simplex::Simplex &variable_simplex) const override

Public Member Functions inherited from wmtk::function::PerSimplexFunction
	PerSimplexFunction (const Mesh &mesh, const PrimitiveType primitive_type, const attribute::MeshAttributeHandle &variable_attribute_handle)

virtual	~PerSimplexFunction ()

const Mesh &	mesh () const

const attribute::MeshAttributeHandle &	attribute_handle () const

int64_t	embedded_dimension () const

Protected Member Functions
std::vector< DSVec >	get_coordinates (const simplex::Simplex &domain_simplex, const std::optional< simplex::Simplex > &variable_simplex_opt={}) const
	This is a helper function that obtains the coordinates of the variables for the function f(x) where f is defined over a domain consists of the input argument domain_tuples. More...

std::vector< DSVec >	get_coordinates (const attribute::Accessor< double > &accessor, const simplex::Simplex &domain_simplex, const std::optional< simplex::Simplex > &variable_simplex_opt={}) const

virtual DScalar	eval (const simplex::Simplex &domain_simplex, const std::vector< DSVec > &coordinates) const =0
	This function defines a function f(x) where f is defined over a simplex domain and the variables for f are the n vertices coordinates of the simplex. More...

Additional Inherited Members
Protected Attributes inherited from wmtk::function::PerSimplexFunction
const PrimitiveType	m_primitive_type

Detailed Description

This is an extension of the PerSimplexFunction class that uses autodiff encoding for differentiations.

Definition at line 18 of file PerSimplexAutodiffFunction.hpp.

Member Typedef Documentation

◆ DScalar

using wmtk::function::PerSimplexAutodiffFunction::DScalar = DScalar2<double, Eigen::Matrix<double, -1, 1>, Eigen::Matrix<double, -1, -1> >

Definition at line 21 of file PerSimplexAutodiffFunction.hpp.

◆ DSVec

using wmtk::function::PerSimplexAutodiffFunction::DSVec = Eigen::VectorX<DScalar>

Definition at line 23 of file PerSimplexAutodiffFunction.hpp.

◆ Scalar

using wmtk::function::PerSimplexAutodiffFunction::Scalar = typename DScalar::Scalar

Definition at line 22 of file PerSimplexAutodiffFunction.hpp.

Constructor & Destructor Documentation

◆ PerSimplexAutodiffFunction()

wmtk::function::PerSimplexAutodiffFunction::PerSimplexAutodiffFunction	(	const Mesh &	mesh,
		const PrimitiveType	primitive_type,
		const attribute::MeshAttributeHandle &	variable_attribute_handle
	)

Definition at line 10 of file PerSimplexAutodiffFunction.cpp.

◆ ~PerSimplexAutodiffFunction()

wmtk::function::PerSimplexAutodiffFunction::~PerSimplexAutodiffFunction ( )

default

Member Function Documentation

◆ eval()

virtual DScalar wmtk::function::PerSimplexAutodiffFunction::eval	(	const simplex::Simplex &	domain_simplex,
		const std::vector< DSVec > &	coordinates
	)		const

protectedpure virtual

This function defines a function f(x) where f is defined over a simplex domain and the variables for f are the n vertices coordinates of the simplex.

The input coordinates are obtained through the get_coordinates function. They are encoded in autodiff type so that the function can be differentiated through autodiff.

Parameters

coordinates

Returns: DScalar

Implemented in wmtk::function::TriangleAMIPS.

Referenced by get_gradient(), get_hessian(), and get_value().

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◆ get_coordinates() [1/2]

std::vector< PerSimplexAutodiffFunction::DSVec > wmtk::function::PerSimplexAutodiffFunction::get_coordinates	(	const attribute::Accessor< double > &	accessor,
		const simplex::Simplex &	domain_simplex,
		const std::optional< simplex::Simplex > &	variable_simplex_opt = `{}`
	)		const

protected

Definition at line 27 of file PerSimplexAutodiffFunction.cpp.

References wmtk::function::utils::get_simplex_attributes(), wmtk::function::PerSimplexFunction::m_primitive_type, wmtk::function::PerSimplexFunction::mesh(), and wmtk::simplex::Simplex::tuple().

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◆ get_coordinates() [2/2]

std::vector< PerSimplexAutodiffFunction::DSVec > wmtk::function::PerSimplexAutodiffFunction::get_coordinates	(	const simplex::Simplex &	domain_simplex,
		const std::optional< simplex::Simplex > &	variable_simplex_opt = `{}`
	)		const

protected

This is a helper function that obtains the coordinates of the variables for the function f(x) where f is defined over a domain consists of the input argument domain_tuples.

The second input argument variable_simplex_opt is an optional simplex that is in the domain that's defined by the domain_tuples. For example, the domain_tuples for a function defined over a triangle is the vector of three vertex tuples of the triangle. And the variable_simplex, when exists, can be one of the three vertices. The function f can then be differentiable wrt the variable_simplex.

Template Parameters

N	The number of the tuples that consist of the domain of the function f(x)

Parameters

domain_tuples	The domain of the function f(x)
variable_simplex_opt	The optional variable_simplex that the function f(x) is differentiating wrt.

Returns: std::array<DSVec, N> The coordinates of the variables for the function f(x) that are in autodiff type

Definition at line 19 of file PerSimplexAutodiffFunction.cpp.

References wmtk::function::PerSimplexFunction::attribute_handle(), wmtk::Mesh::create_const_accessor(), and wmtk::function::PerSimplexFunction::mesh().

Referenced by get_gradient(), get_hessian(), and get_value().

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◆ get_gradient()

Eigen::VectorXd wmtk::function::PerSimplexAutodiffFunction::get_gradient	(	const simplex::Simplex &	domain_simplex,
		const simplex::Simplex &	variable_simplex
	)		const

overridevirtual

Reimplemented from wmtk::function::PerSimplexFunction.

Definition at line 59 of file PerSimplexAutodiffFunction.cpp.

References wmtk::function::PerSimplexFunction::embedded_dimension(), eval(), get_coordinates(), and DScalar2< _Scalar, _Gradient, _Hessian >::getGradient().

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◆ get_hessian()

Eigen::MatrixXd wmtk::function::PerSimplexAutodiffFunction::get_hessian	(	const simplex::Simplex &	domain_simplex,
		const simplex::Simplex &	variable_simplex
	)		const