dim-dimensional tensor-product monomials function. More...

#include <monomials_tp.hpp>

Inheritance diagram for qugar::impl::MonomialsTP< dim, range >:

Collaboration diagram for qugar::impl::MonomialsTP< dim, range >:

Public Types
using	Parent = PolynomialTP<dim, range>
	Parent type.

using	CoefsType = typename Parent::CoefsType
	Coefs type.

template<typename T >
using	Value = typename Parent::template Value<T>
	Value type.

template<typename T >
using	Gradient = typename Parent::template Gradient<T>
	Gradient type.

template<typename T >
using	Hessian = typename Parent::template Hessian<T>
	Hessian type.

template<int N>
using	Interval = ::algoim::Interval<N>
	Algoim's interval alias.

Public Types inherited from qugar::impl::PolynomialTP< dim, 1 >
using	CoefsType
	Coefs type.

Public Types inherited from qugar::impl::DomainFunc< dim, range >
template<int N>
using	Interval = ::algoim::Interval<N>
	Algoim's interval alias.

template<typename T >
using	Value = std::conditional_t<range == 1, T, Vector<T, range>>
	Value type.

template<typename T >
using	Gradient = Vector<Value<T>, dim>
	Gradient type.

template<typename T >
using	Hessian = Vector<Value<T>, num_hessian>
	Hessian (symmetric type).

Public Member Functions
	MonomialsTP (const TensorSizeTP< dim > &order)
	Constructor.

	MonomialsTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

	MonomialsTP (const MonomialsTP< dim, range > &monomials)
	Copy constructor.

std::shared_ptr< MonomialsTP< dim, range > >	create_derivative (const int dir) const
	Creates a derivative of the current MonomialsTP object in the specified direction.

virtual Value< real >	operator() (const Point< dim > &point) const final
	Evaluator operator.

virtual Value< Interval< dim > >	operator() (const Point< dim, Interval< dim > > &point) const final
	Evaluator operator.

virtual Gradient< real >	grad (const Point< dim > &point) const final
	Gradient evaluator operator.

virtual Gradient< Interval< dim > >	grad (const Point< dim, Interval< dim > > &point) const final
	Gradient evaluator operator.

virtual Hessian< real >	hessian (const Point< dim > &point) const final
	Hessian evaluator operator.

template<int dim_aux = dim> requires (dim == dim_aux && dim > 1)
std::shared_ptr< MonomialsTP< dim - 1, range > >	extract_facet (const int local_facet_id) const
	Extracts a facet from the monomials tensor product.

Public Member Functions inherited from qugar::impl::PolynomialTP< dim, 1 >
	PolynomialTP (const TensorSizeTP< dim > &order)
	Constructor.

	PolynomialTP (const TensorSizeTP< dim > &order, const CoefsType &value)
	Constructs a constant value PolynomialTP object with the specified order.

	PolynomialTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

std::size_t	get_num_coefs () const
	Get the number of coeficients.

const std::vector< CoefsType > &	get_coefs () const
	Gets the polynomial coefficients.

const TensorSizeTP< dim > &	get_order () const
	Gets the polynomial order along the parametric directions.

int	get_order (int dir) const
	Gets the polynomial order (degree + 1) along the direction `dir`.

const CoefsType &	get_coef (int index) const
	Retrieves the coefficients at the specified index.

CoefsType &	get_coef (int index)
	Retrieves the coefficients at the specified index.

const CoefsType &	get_coef (const TensorIndexTP< dim > &index) const
	Retrieves the coefficient associated with the given tensor index.

CoefsType &	get_coef (const TensorIndexTP< dim > &index)
	Retrieves the coefficient associated with the given tensor index.

int	get_degree (int dir) const
	Gets the polynomial degree (order - 1) along the direction `dir`.

void	transform_image (const BoundBox< range > &old_domain, const BoundBox< range > &new_domain)
	Transforms (in place) the coefficients of the polynomial from `old_domain` to `new_domain`.

void	coefs_linear_transform (const real scale, const CoefsType &shift)
	Applies a linear transformation to every coefficient.

Public Member Functions inherited from qugar::impl::DomainFunc< dim, range >
	DomainFunc ()=default
	Default constructor.

	DomainFunc (const DomainFunc &)=default
	Default copy constructor.

	DomainFunc (DomainFunc &&)=default
	Default move constructor.

DomainFunc &	operator= (const DomainFunc &)=default
	Default copy assignment operator.

DomainFunc &	operator= (DomainFunc &&)=default
	Default move assignment operator.

virtual	~DomainFunc ()=default
	Default virtual destructor.

Static Public Member Functions
template<typename T >
static Value< T >	horner (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates a monomials using Horner's method.

template<typename T >
static Vector< Value< T >, dim+1 >	horner_der (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates the gradient of the monomials using the Horner's method.

static void	transform_coefs_to_Bezier (const MonomialsTP< dim, range > &monomials, std::vector< CoefsType > &bzr_coefs)
	Transforms the coefficients of monomials to Bezier form.

Private Member Functions
template<typename T >
Value< T >	eval_ (const Point< dim, T > &point) const
	Evaluator operator.

template<typename T >
Gradient< T >	grad_ (const Point< dim, T > &point) const
	Gradient evaluator operator.

template<typename T >
Hessian< T >	hessian_ (const Point< dim, T > &point) const
	Hessian evaluator operator.

Additional Inherited Members
Static Public Attributes inherited from qugar::impl::DomainFunc< dim, range >
static const int	num_hessian = dim * (dim + 1) / 2
	Number of Hessian (symmetric) components.

Protected Attributes inherited from qugar::impl::PolynomialTP< dim, 1 >
TensorSizeTP< dim >	order_
	Order of the polynomial along each parametric direction.

std::vector< CoefsType >	coefs_

Detailed Description

template<int dim, int range = 1>
class qugar::impl::MonomialsTP< dim, range >

dim-dimensional tensor-product monomials function.

Template Parameters

dim	Dimension of the parametric domain.
range	Dimension of the image.

Member Typedef Documentation

◆ CoefsType

template<int dim, int range = 1>

using qugar::impl::MonomialsTP< dim, range >::CoefsType = typename Parent::CoefsType

Coefs type.

◆ Gradient

template<int dim, int range = 1>

template<typename T >

using qugar::impl::MonomialsTP< dim, range >::Gradient = typename Parent::template Gradient<T>

Gradient type.

◆ Hessian

template<int dim, int range = 1>

template<typename T >

using qugar::impl::MonomialsTP< dim, range >::Hessian = typename Parent::template Hessian<T>

Hessian type.

◆ Interval

template<int dim, int range = 1>

template<int N>

using qugar::impl::MonomialsTP< dim, range >::Interval = ::algoim::Interval<N>

Algoim's interval alias.

◆ Parent

template<int dim, int range = 1>

using qugar::impl::MonomialsTP< dim, range >::Parent = PolynomialTP<dim, range>

Parent type.

◆ Value

template<int dim, int range = 1>

template<typename T >

using qugar::impl::MonomialsTP< dim, range >::Value = typename Parent::template Value<T>

Value type.

Constructor & Destructor Documentation

◆ MonomialsTP() [1/3]

template<int dim, int range = 1>

qugar::impl::MonomialsTP< dim, range >::MonomialsTP ( const TensorSizeTP< dim > & order )

explicit

Constructor.

The coefficients vector is allocated by the constructor.

Parameters

order Order of the polynomial along each parametric direction.

◆ MonomialsTP() [2/3]

template<int dim, int range = 1>

qugar::impl::MonomialsTP< dim, range >::MonomialsTP	(	const TensorSizeTP< dim > &	order,
		const std::vector< CoefsType > &	coefs )

Constructor.

Parameters

coefs	Coefficients of the polynomial. The ordering is such that dimension 0 is inner-most, i.e., iterates the fastest, while dimension dim-1 is outer-most and iterates the slowest.
order	Order of the polynomial along each parametric direction.

◆ MonomialsTP() [3/3]

template<int dim, int range = 1>

qugar::impl::MonomialsTP< dim, range >::MonomialsTP ( const MonomialsTP< dim, range > & monomials )

Copy constructor.

Parameters

monomials Monomials to copy.

Member Function Documentation

◆ create_derivative()

template<int dim, int range = 1>

std::shared_ptr< MonomialsTP< dim, range > > qugar::impl::MonomialsTP< dim, range >::create_derivative ( const int dir ) const

nodiscard

Creates a derivative of the current MonomialsTP object in the specified direction.

This function generates a new MonomialsTP object that represents the derivative of the current object in the direction specified by the parameter dir.

Parameters

dir	The direction in which to take the derivative. This should be an integer representing the axis or dimension along which the derivative is computed.

Returns: A std::shared_ptr to a new MonomialsTP object that represents the derivative of the current object in the specified direction.

Note: If the monomials has already order 1 (degree 0) in the specified direction, just a clone of the current object is returned.

◆ eval_()

template<int dim, int range = 1>

template<typename T >

Value< T > qugar::impl::MonomialsTP< dim, range >::eval_ ( const Point< dim, T > & point ) const

nodiscardprivate

Evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

◆ extract_facet()

template<int dim, int range = 1>

template<int dim_aux = dim>
requires (dim == dim_aux && dim > 1)

std::shared_ptr< MonomialsTP< dim - 1, range > > qugar::impl::MonomialsTP< dim, range >::extract_facet ( const int local_facet_id ) const

nodiscard

Extracts a facet from the monomials tensor product.

This function extracts a facet of the monomials tensor product specified by the local facet ID.

Template Parameters

dim	The dimension of the monomials tensor product.
range	The range type of the monomials tensor product.

Parameters

local_facet_id The ID of the local facet to extract.

Returns: A shared pointer to the extracted facet.

◆ grad() [1/2]

template<int dim, int range = 1>

virtual Gradient< real > qugar::impl::MonomialsTP< dim, range >::grad ( const Point< dim > & point ) const

nodiscardfinalvirtual

Gradient evaluator operator.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ grad() [2/2]

template<int dim, int range = 1>

virtual Gradient< Interval< dim > > qugar::impl::MonomialsTP< dim, range >::grad ( const Point< dim, Interval< dim > > & point ) const

nodiscardfinalvirtual

Gradient evaluator operator.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ grad_()

template<int dim, int range = 1>

template<typename T >

Gradient< T > qugar::impl::MonomialsTP< dim, range >::grad_ ( const Point< dim, T > & point ) const

nodiscardprivate

Gradient evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

◆ hessian()

template<int dim, int range = 1>

virtual Hessian< real > qugar::impl::MonomialsTP< dim, range >::hessian ( const Point< dim > & point ) const

nodiscardfinalvirtual

Hessian evaluator operator.

Parameters

point Point at which the function's hessian is evaluated.

Returns: Function hessian at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ hessian_()

template<int dim, int range = 1>

template<typename T >

Hessian< T > qugar::impl::MonomialsTP< dim, range >::hessian_ ( const Point< dim, T > & point ) const

nodiscardprivate

Hessian evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function's hessian is evaluated.

Returns: Function hessian at point.

◆ horner()

template<int dim, int range = 1>

template<typename T >

static Value< T > qugar::impl::MonomialsTP< dim, range >::horner	(	const Point< dim, T > &	point,
		typename std::vector< CoefsType >::const_iterator &	coefs,
		const Vector< int, dim > &	order )

static

Evaluates a monomials using Horner's method.

For the method details check: https://en.wikipedia.org/wiki/Horner%27s_method

The evaluation along the dimensions is performed by recursively calling this function.

Template Parameters

T	Type of the input and output variables.

Parameters

point	Evaluation point.
coefs	Iterator to the coefficients of the polynomial. Their ordering is the same as the coefficients members of the class.
order	Order of the polynomial along the dim dimensions.

Returns: Value of the polynomial at point.

◆ horner_der()

template<int dim, int range = 1>

template<typename T >

static Vector< Value< T >, dim+1 > qugar::impl::MonomialsTP< dim, range >::horner_der	(	const Point< dim, T > &	point,
		typename std::vector< CoefsType >::const_iterator &	coefs,
		const Vector< int, dim > &	order )

static

Evaluates the gradient of the monomials using the Horner's method.

For the method details check: https://en.wikipedia.org/wiki/Horner%27s_method

The evaluation along the dimensions is performed by recursively calling this function.

Template Parameters

T	Type of the input and output variables.

Parameters

point	Evaluation point.
coefs	Iterator to the coefficients of the polynomial. Their ordering is the same as the coefficients members of the class.
order	Order of the polynomial along the dim dimensions.

Returns: The first component of the return vector corresponds to the value of the polynomial itself, while the gradient is stored in the following dim components.

◆ operator()() [1/2]

template<int dim, int range = 1>

virtual Value< real > qugar::impl::MonomialsTP< dim, range >::operator() ( const Point< dim > & point ) const

nodiscardfinalvirtual

Evaluator operator.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ operator()() [2/2]

template<int dim, int range = 1>

virtual Value< Interval< dim > > qugar::impl::MonomialsTP< dim, range >::operator() ( const Point< dim, Interval< dim > > & point ) const

nodiscardfinalvirtual

Evaluator operator.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ transform_coefs_to_Bezier()

template<int dim, int range = 1>

static void qugar::impl::MonomialsTP< dim, range >::transform_coefs_to_Bezier	(	const MonomialsTP< dim, range > &	monomials,
		std::vector< CoefsType > &	bzr_coefs )

static

Transforms the coefficients of monomials to Bezier form.

This function takes the coefficients of monomials and transforms them into the corresponding Bezier coefficients.

Parameters

monomials	Monomials whose coefficients are transformed.
bzr_coefs	A vector containing the Bezier coefficients to be computed.

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

/__w/qugar/qugar/cpp/include/qugar/bezier_tp.hpp
/__w/qugar/qugar/cpp/include/qugar/monomials_tp.hpp

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ CoefsType

◆ Gradient

◆ Hessian

◆ Interval

◆ Parent

◆ Value

Constructor & Destructor Documentation

◆ MonomialsTP() [1/3]

◆ MonomialsTP() [2/3]

◆ MonomialsTP() [3/3]

Member Function Documentation

◆ create_derivative()

◆ eval_()

◆ extract_facet()

◆ grad() [1/2]

◆ grad() [2/2]

◆ grad_()

◆ hessian()

◆ hessian_()

◆ horner()

◆ horner_der()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ transform_coefs_to_Bezier()