Tensor-product uniform B-spline (core functionality) More...

#include </home/runner/work/iganet/iganet/include/bspline.hpp>

Inheritance diagram for iganet::UniformBSplineCore< real_t, GeoDim, Degrees >:

Public Types
template<typename other_t , short_t GeoDim_, short_t... Degrees_>
using	derived_self_type = UniformBSplineCore< other_t, GeoDim_, Degrees_... >
	Deduces the derived self-type when exposed to different class template parameters `real_t` and `GeoDim`, and the `Degrees` parameter pack.

template<template< typename, short_t, short_t... > class BSpline, std::make_signed< short_t >::type degree_elevate = 0>
using	derived_type = BSpline< real_t, GeoDim,(Degrees+degree_elevate)... >
	Deduces the type of the template template parameter `BSpline` when exposed to the class template parameters `real_t` and `GeoDim`, and the `Degrees` parameter pack. The optional template parameter `degree_elevate` can be used to (de-)elevate the degrees by an additive constant.

template<typename other_t >
using	real_derived_self_type = UniformBSplineCore< other_t, GeoDim, Degrees... >
	Deduces the derived self-type when exposed to a different class template parameter `real_t`

template<std::make_signed< short_t >::type degree_elevate = 0>
using	self_type = derived_type< UniformBSplineCore, degree_elevate >
	Deduces the self-type possibly degrees (de-)elevated by the additive constant `degree_elevate`

using	value_type = real_t
	Value type.

Public Member Functions
	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, const utils::TensorArray< geoDim_ > &coeffs, bool clone=false, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.

	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, enum init init=init::greville, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.

	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, utils::TensorArray< geoDim_ > &&coeffs, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.

template<typename other_t >
	UniformBSplineCore (const UniformBSplineCore< other_t, GeoDim, Degrees... > &other, Options< real_t > options=Options< real_t >{})
	Copy constructor.

	UniformBSplineCore (Options< real_t > options=Options< real_t >{})
	Default constructor.

torch::Tensor	as_tensor () const noexcept override
	Returns all coefficients as a single tensor.

int64_t	as_tensor_size () const noexcept override
	Returns the size of the single tensor representation of all coefficients.

const utils::TensorArray< geoDim_ > &	coeffs () const noexcept
	Returns a constant reference to the array of coefficient vectors.

utils::TensorArray< geoDim_ > &	coeffs () noexcept
	Returns a non-constant reference to the array of coefficient vectors.

const torch::Tensor &	coeffs (short_t i) const noexcept
	Returns a constant reference to the coefficient vector in the \(i\)-th dimension.

torch::Tensor &	coeffs (short_t i) noexcept
	Returns a non-constant reference to the coefficient vector in the \(i\)-th dimension.

nlohmann::json	coeffs_to_json () const
	Returns the B-spline object's coefficients as JSON object.

utils::TensorArray< geoDim_ >	coeffs_view () const noexcept
	Returns an array of views to the coefficient vectors.

const auto	coeffs_view (short_t i) const noexcept
	Returns a view to the coefficient vector in the \(i\)-th dimension.

torch::Device	device () const noexcept override
	Returns the `device` property.

int32_t	device_index () const noexcept override
	Returns the `device_index` property.

torch::Dtype	dtype () const noexcept override
	Returns the `dtype` property.

template<deriv deriv = deriv::func, bool memory_optimized = false>
auto	eval (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices) const
	Returns the value of the univariate B-spline object in the points `xi`

template<deriv deriv = deriv::func, bool memory_optimized = false>
auto	eval (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns the value of the univariate B-spline object in the points `xi`

template<typename BSpline >
auto &	from_gismo (BSpline &bspline, bool, bool)

UniformBSplineCore &	from_json (const nlohmann::json &json)
	Updates the B-spline object from JSON object.

UniformBSplineCore &	from_tensor (const torch::Tensor &tensor) noexcept override
	Sets all coefficients from a single tensor.

UniformBSplineCore &	from_xml (const pugi::xml_document &doc, int id=0, std::string label="", int index=-1)
	Updates the B-spline object from XML object.

UniformBSplineCore &	from_xml (const pugi::xml_node &root, int id=0, std::string label="", int index=-1)
	Updates the B-spline object from XML node.

auto	greville (bool interior=false) const
	Returns the Greville abscissae.

void	init_coeffs (enum init init)
	Initializes the B-spline coefficients.

void	init_knots ()
	Initializes the B-spline knots.

bool	is_sparse () const noexcept override
	Returns true if the layout is sparse.

template<typename other_t , short_t GeoDim_, short_t... Degrees_>
bool	isclose (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other, real_t rtol=real_t{1e-5}, real_t atol=real_t{1e-8}) const
	Returns true if both B-spline objects are close up to the given tolerances.

const utils::TensorArray< parDim_ > &	knots () const noexcept
	Returns a constant reference to the array of knot vectors.

utils::TensorArray< parDim_ > &	knots () noexcept
	Returns a non-constant reference to the array of knot vectors.

const torch::Tensor &	knots (short_t i) const noexcept
	Returns a constant reference to the knot vector in the \(i\)-th dimension.

torch::Tensor &	knots (short_t i) noexcept
	Returns a non-constant reference to the knot vector in the \(i\)-th dimension.

nlohmann::json	knots_to_json () const
	Returns the B-spline object's knots as JSON object.

torch::Layout	layout () const noexcept override
	Returns the `layout` property.

void	load (const std::string &filename, const std::string &key="bspline")
	Loads the B-spline from file.

const std::array< int64_t, parDim_ > &	ncoeffs () const noexcept
	Returns a constant reference to the array of coefficient vector dimensions.

int64_t	ncoeffs (short_t i) const noexcept
	Returns the total number of coefficients in the \(i\)-th direction.

int64_t	ncumcoeffs () const noexcept
	Returns the total number of coefficients.

const std::array< int64_t, parDim_ > &	nknots () const noexcept
	Returns a constant reference to the array of knot vector dimensions.

int64_t	nknots (short_t i) const noexcept
	Returns the dimension of the knot vector in the \(i\)-th dimension.

template<typename other_t , short_t GeoDim_, short_t... Degrees_>
bool	operator!= (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other) const
	Returns true if both B-spline objects are different.

template<typename other_t , short_t GeoDim_, short_t... Degrees_>
bool	operator== (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other) const
	Returns true if both B-spline objects are the same.

const Options< real_t > &	options () const noexcept
	Returns a constant reference to the B-spline object's options.

bool	pinned_memory () const noexcept override
	Returns the `pinned_memory` property.

torch::serialize::InputArchive &	read (torch::serialize::InputArchive &archive, const std::string &key="bspline")
	Reads the B-spline from a torch::serialize::InputArchive object.

bool	requires_grad () const noexcept override
	Returns the `requires_grad` property.

void	save (const std::string &filename, const std::string &key="bspline") const
	Saves the B-spline to file.

UniformBSplineCore &	set_requires_grad (bool requires_grad) noexcept override
	Sets the B-spline object's `requires_grad` property.

auto	to_gismo () const
	Converts the B-spline object into a gsBSpline object of the parametric dimension is one and a gsTensorBSpline object otherwise.

template<typename BSpline >
BSpline &	to_gismo (BSpline &bspline, bool, bool) const

nlohmann::json	to_json () const override
	Returns the B-spline object as JSON object.

pugi::xml_document	to_xml (int id=0, std::string label="", int index=-1) const
	Returns the B-spline object as XML object.

pugi::xml_node &	to_xml (pugi::xml_node &root, int id=0, std::string label="", int index=-1) const
	Returns the B-spline object as XML node.

UniformBSplineCore &	transform (const std::function< std::array< real_t, geoDim_ >(const std::array< real_t, parDim_ > &)> transformation)
	Transforms the coefficients based on the given mapping.

template<std::size_t N>
UniformBSplineCore &	transform (const std::function< std::array< real_t, N >(const std::array< real_t, parDim_ > &)> transformation, std::array< short_t, N > dims)
	Transforms the coefficients based on the given mapping.

UniformBSplineCore &	uniform_refine (int numRefine=1, int dim=-1)
	Returns the B-spline object with uniformly refined knot and coefficient vectors.

torch::serialize::OutputArchive &	write (torch::serialize::OutputArchive &archive, const std::string &key="bspline") const
	Writes the B-spline into a torch::serialize::OutputArchive object.







Public Member Functions inherited from iganet::utils::Serializable
virtual void	pretty_print (std::ostream &os=Log(log::info)) const =0
	Returns a string representation of the object.

Public Member Functions inherited from iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>
virtual void	pretty_print (std::ostream &os=Log(log::info)) const noexcept=0
	Returns a string representation.

Static Public Member Functions
static constexpr const short_t &	degree (short_t i) noexcept
	Returns a constant reference to the degree in the \(i\)-th dimension.

static constexpr const std::array< short_t, parDim_ > &	degrees () noexcept
	Returns a constant reference to the array of degrees.

static constexpr short_t	geoDim () noexcept
	Returns the geometric dimension.

static constexpr bool	is_nonuniform () noexcept
	Returns true if the B-spline is non-uniform.

static constexpr bool	is_uniform () noexcept
	Returns true if the B-spline is uniform.

static constexpr short_t	parDim () noexcept
	Returns the parametric dimension.

Protected Member Functions
template<short_t degree, short_t dim, short_t deriv>
auto	eval_basfunc_univariate (const torch::Tensor &xi, const torch::Tensor &knot_indices) const
	Returns the vector of univariate B-spline basis functions (or their derivatives) evaluated in the point `xi`

void	update_coeffs (const utils::TensorArray< parDim_ > &knots, const utils::TensorArray< parDim_ > &knot_indices)
	Updates the B-spline coefficients after knot insertion.

template<short_t degree, short_t dim>
auto	update_coeffs_univariate (const torch::Tensor &knots, const torch::Tensor &knot_indices) const
	Returns the knot insertion matrix.

Protected Attributes
utils::TensorArray< geoDim_ >	coeffs_
	Array storing the coefficients of the control net \(\left(\mathbf{c}_{i_d}\right)_{i_d=1}^{n_d}\), \(\mathbf{c}_{i_d}\in\mathbb{R}^{d_\text{geo}}\).

utils::TensorArray< parDim_ >	knots_
	Array storing the knot vectors \(\left(\left(t_{i_d}\right)_{i_d=1}^{n_d+p_d+1}\right)_{d=1}^{d_\text{par}}\).

std::array< int64_t, parDim_ >	ncoeffs_
	Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\).

std::array< int64_t, parDim_ >	ncoeffs_reverse_
	Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\) in reverse order (needed for coeffs_view)

std::array< int64_t, parDim_ >	nknots_
	Array storing the sizes of the knot vectors \(\left(n_d+p_d+1\right)_{d=1}^{d_\text{par}}\).

Options< real_t >	options_
	Options.

Static Protected Attributes
static constexpr const std::array< short_t, parDim_ >	degrees_ = {Degrees...}
	Array storing the degrees \(\left(p_d\right)_{d=1}^{d_\text{par}}\).

static constexpr const short_t	geoDim_ = GeoDim
	Dimension of the geometric space \(\Omega\subset\mathbb{R}^{d_\text{geo}}\).

static constexpr const short_t	parDim_ = sizeof...(Degrees)
	Dimension of the parametric space \(\hat\Omega=[0,1]^{d_\text{par}}\).

Private Member Functions
template<std::size_t... Is>
torch::Tensor	as_tensor_ (std::index_sequence< Is... >) const noexcept
	Returns all coefficients as a single tensor.

template<int64_t degree, int64_t deriv, int64_t terminal = degree - deriv>
int64_t constexpr	eval_prefactor () const
	Computes the prefactor \(p_d!/(p_d-r_d)! = p_d \cdots (p_d-r_d+1)\).

template<std::size_t... Is>
UniformBSplineCore &	from_tensor_ (std::index_sequence< Is... >, const torch::Tensor &tensor) noexcept
	Sets all coefficients from a single tensor.

Friends
template<typename BSplineCore >
class	BSplineCommon
	Enable access to private members.

Detailed Description

template<typename real_t, short_t GeoDim, short_t... Degrees>
class iganet::UniformBSplineCore< real_t, GeoDim, Degrees >

Tensor-product uniform B-spline (core functionality)

This class implements the core functionality of all B-spline classes and serves as base class for (non-)uniform B-splines.

Mathematically, this class defines a mapping

\[ \mathbf{f}:\hat\Omega \mapsto \Omega \]

from the \(d_\text{par}\)-dimensional parametric space \(\hat\Omega=[0,1]^{d_\text{par}}\) to the \(d_\text{geo}\)-dimensional geometric space \(\Omega\subset\mathbb{R}^{d_\text{geo}}\).

This mapping is defined by tensor-product B-spline basis functions

\[ B_I(\boldsymbol{\xi}) = \bigotimes_{d=1}^{d_\text{par}} B_{i_d,p_d}(\xi_d) \]

and the control points

\[ \mathbf{c}_I = \mathbf{c}_{i_1,i_2,\dots, i_{d_\text{par}}} \in \mathbb{R}^{d_\text{geo}}. \]

Here, \(i_d\) are the local numbers of the univariate B-splines \(\left(B_{i_d,p_d}\right)_{i_d=1}^{n_d}\) in the \(d\)-th parametric dimension, \(p_d\) is the respective degree, and \(n_d\) is the number of univariate B-splines in the \(d\)-th direction. Moreover, \(0\le \xi_{i_d}\le 1\) is the parametric value at which the B-spline is evaluated. The multivariate B-spline function is defined as follows

\[ \mathbf{f}(\boldsymbol{\xi}) = \sum_{I=1}^N B_I(\boldsymbol{\xi}) \mathbf{c}_I \]

Here and below we adopt the vector notation \(\boldsymbol{\xi} = \left(\xi_1,\xi_2,\dots,\xi_{d_\text{par}}\right)^\top\) and combine multiple local indices \(i_1,i_2,\dots,i_{d_\text{par}}\) of univariate B-spline basis functions into the global index \(1\le I \le N\) with \(N=n_1\cdot n_2\cdot\dots\cdot n_{d_\text{par}}\) denoting the total number of multivariate B-splines.

This class implements B-spline functions and their derivatives for 1, 2, 3, and 4 parametric dimensions. The univariate B-splines are uniquely determined by their knot vectors

\[ \left(t_{i_d}\right)_{i_d=1}^{n_d+p_d+1} \]

with \(0\le t_{i_d}\le 1\) and \(t_{i_d}\le t_{i_d+1}\) for all \(i_d\), that is, the knot vectors are given by a non-decreasing sequence of values in the interval \([0,1]\) with the possibility that knot values are repeated.

This class implements the evaluation of B-splines and their derivatives as explained in Chapters 2 and 3 from [2].

Note: C++ uses 0-based indexing so that all of the above formulas need to be shifted by -1. Moreover, all vectors, matrices, and tensors are implemented as torch::Tensor objects and hence adopt Torch's local-to-global mapping. It is therefore imperative to always use Torch's indexing functionality to extract sub-tensors.

Member Typedef Documentation

◆ derived_self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t , short_t GeoDim_, short_t... Degrees_>

using iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::derived_self_type = UniformBSplineCore<other_t, GeoDim_, Degrees_...>

Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack.

◆ derived_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<template< typename, short_t, short_t... > class BSpline, std::make_signed< short_t >::type degree_elevate = 0>

using iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::derived_type = BSpline<real_t, GeoDim, (Degrees + degree_elevate)...>

Deduces the type of the template template parameter BSpline when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant.

◆ real_derived_self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t >

using iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::real_derived_self_type = UniformBSplineCore<other_t, GeoDim, Degrees...>

Deduces the derived self-type when exposed to a different class template parameter real_t

◆ self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<std::make_signed< short_t >::type degree_elevate = 0>

using iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::self_type = derived_type<UniformBSplineCore, degree_elevate>

Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate

◆ value_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

using iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::value_type = real_t

Value type.

Constructor & Destructor Documentation

◆ UniformBSplineCore() [1/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::UniformBSplineCore ( Options< real_t > options = Options<real_t>{} )

inline

Default constructor.

Parameters

[in] options Options configuration

◆ UniformBSplineCore() [2/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::UniformBSplineCore	(	const std::array< int64_t, parDim_ > &	ncoeffs,
		enum init	init = `init::greville`,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	init	Type of initialization
[in]	options	Options configuration

◆ UniformBSplineCore() [3/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::UniformBSplineCore	(	const std::array< int64_t, parDim_ > &	ncoeffs,
		const utils::TensorArray< geoDim_ > &	coeffs,
		bool	clone = `false`,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	coeffs	Vectors of coefficients per parametric dimension
[in]	clone	If true, coefficients will be cloned. Otherwise, coefficients will be aliased
[in]	options	Options configuration

Note: It is not checked whether vectors of coefficients are compatible with the given Options object if clone is false.

◆ UniformBSplineCore() [4/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::UniformBSplineCore	(	const std::array< int64_t, parDim_ > &	ncoeffs,
		utils::TensorArray< geoDim_ > &&	coeffs,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	coeffs	Vectors of coefficients per parametric dimension
[in]	options	Options configuration

Note: It is not checked whether vectors of coefficients are compatible with the given Options object if clone is false.

◆ UniformBSplineCore() [5/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t >

iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::UniformBSplineCore	(	const UniformBSplineCore< other_t, GeoDim, Degrees... > &	other,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Copy constructor.

Parameters

[in]	other	Uniform B-spline object to copy
[in]	options	Options configuration

Member Function Documentation

◆ as_tensor()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Tensor iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::as_tensor ( ) const

inlineoverridevirtualnoexcept

Returns all coefficients as a single tensor.

Returns: Tensor of coefficients

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ as_tensor_()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<std::size_t... Is>

torch::Tensor iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::as_tensor_ ( std::index_sequence< Is... > ) const

inlineprivatenoexcept

Returns all coefficients as a single tensor.

Returns: Tensor of coefficients

◆ as_tensor_size()

template<typename real_t , short_t GeoDim, short_t... Degrees>

int64_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::as_tensor_size ( ) const

inlineoverridevirtualnoexcept

Returns the size of the single tensor representation of all coefficients.

Returns: Size of the tensor

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ coeffs() [1/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const utils::TensorArray< geoDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs ( ) const

inlinenoexcept

Returns a constant reference to the array of coefficient vectors.

Returns: Array of coefficient vectors

◆ coeffs() [2/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray< geoDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs ( )

inlinenoexcept

Returns a non-constant reference to the array of coefficient vectors.

Returns: Array of coefficient vectord

◆ coeffs() [3/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const torch::Tensor & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs ( short_t i ) const

inlinenoexcept

Returns a constant reference to the coefficient vector in the \(i\)-th dimension.

Parameters

[in] i Geometric dimension

Returns: Coefficient vector for the given geometric dimension

◆ coeffs() [4/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Tensor & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs ( short_t i )

inlinenoexcept

Returns a non-constant reference to the coefficient vector in the \(i\)-th dimension.

Parameters

[in] i Geometric dimension

Returns: Coefficient vector for the given geometric dimension

◆ coeffs_to_json()

template<typename real_t , short_t GeoDim, short_t... Degrees>

nlohmann::json iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs_to_json ( ) const

inline

Returns the B-spline object's coefficients as JSON object.

◆ coeffs_view() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray< geoDim_ > iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs_view ( ) const

inlinenoexcept

Returns an array of views to the coefficient vectors.

Returns: Array of views to the coefficient vectors

◆ coeffs_view() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs_view ( short_t i ) const

inlinenoexcept

Returns a view to the coefficient vector in the \(i\)-th dimension.

Parameters

[in] i Geometric dimension

Returns: View of the coefficient vector for the given geometric dimension

◆ degree()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr const short_t & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::degree ( short_t i )

inlinestaticconstexprnoexcept

Returns a constant reference to the degree in the \(i\)-th dimension.

Parameters

[in] i Parametric dimension

Returns: Degree for the given parametric dimension

◆ degrees()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr const std::array< short_t, parDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::degrees ( )

inlinestaticconstexprnoexcept

Returns a constant reference to the array of degrees.

Returns: Array of degrees for all parametric dimensions

◆ device()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Device iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::device ( ) const

inlineoverridevirtualnoexcept

Returns the device property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ device_index()

template<typename real_t , short_t GeoDim, short_t... Degrees>

int32_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::device_index ( ) const

inlineoverridevirtualnoexcept

Returns the device_index property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ dtype()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Dtype iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::dtype ( ) const

inlineoverridevirtualnoexcept

Returns the dtype property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ eval() [1/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval ( const torch::Tensor & xi ) const

inline

Returns the value of the B-spline object in the point xi

This implementation follows the procedure described in Chapters 2 and 3 of [2].

Algorithm: B-spline evaluation

Determine the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} = \left(\xi_1, \dots, \xi_{d_\text{par}}\right)^\top \in \bigotimes_{d=1}^{d_\text{par}} [t_{i_d}, t_{i_d+1}). \]

Evaluate the vectors of univariate B-spline basis functions (or their derivatives) that are non-zero at \(\boldsymbol{\xi}\)

\[ D^{r_d}\mathbf{B}_d = \left( D^{r_d} B_{i_d-p_d,p_d}, \dots, D^{r_d} B_{i_d,p_d} \right)^\top, \]

where \( p_d \) is the degree of the \(d\)-th univariate B-spline and \( r_d \) denotes the requested derivative in the \(d\)-direction.

Multiply the tensor-product of the above row vectors by the column vector of control points

\[ \left( \bigotimes_{d=1}^{d_\text{par}} D^{r_d}\mathbf{B}_d \right) \cdot \mathbf{c}_\mathcal{J}, \]

where \(\mathcal{J}\) is the subset of global indices that belong to the coefficients

\[ \mathbf{c}_{i_1-p_1:i_1,\dots,i_\text{par}-p_\text{par}:i_\text{par}} \]

Template Parameters

deriv Composition of derivative indicators of type deriv

Parameters

[in] xi Point(s) where to evaluate the multivariate B-spline object

Returns: Value(s) of the multivariate B-spline evaluated at the point(s) xi

◆ eval() [2/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval ( const utils::TensorArray< parDim_ > & xi ) const

inline

Returns the value of the B-spline object in the point xi

This implementation follows the procedure described in Chapters 2 and 3 of [2].

Algorithm: B-spline evaluation

Determine the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} = \left(\xi_1, \dots, \xi_{d_\text{par}}\right)^\top \in \bigotimes_{d=1}^{d_\text{par}} [t_{i_d}, t_{i_d+1}). \]

Evaluate the vectors of univariate B-spline basis functions (or their derivatives) that are non-zero at \(\boldsymbol{\xi}\)

\[ D^{r_d}\mathbf{B}_d = \left( D^{r_d} B_{i_d-p_d,p_d}, \dots, D^{r_d} B_{i_d,p_d} \right)^\top, \]

where \( p_d \) is the degree of the \(d\)-th univariate B-spline and \( r_d \) denotes the requested derivative in the \(d\)-direction.

Multiply the tensor-product of the above row vectors by the column vector of control points

\[ \left( \bigotimes_{d=1}^{d_\text{par}} D^{r_d}\mathbf{B}_d \right) \cdot \mathbf{c}_\mathcal{J}, \]

where \(\mathcal{J}\) is the subset of global indices that belong to the coefficients

\[ \mathbf{c}_{i_1-p_1:i_1,\dots,i_\text{par}-p_\text{par}:i_\text{par}} \]

Template Parameters

deriv Composition of derivative indicators of type deriv

Parameters

[in] xi Point(s) where to evaluate the multivariate B-spline object

Returns: Value(s) of the multivariate B-spline evaluated at the point(s) xi

◆ eval() [3/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval	(	const utils::TensorArray< parDim_ > &	xi,
		const utils::TensorArray< parDim_ > &	knot_indices
	)		const

inline

Returns the value of the univariate B-spline object in the points xi

This function implements steps 2-3 of algorithm BSplineEvaluation for univariate B-splines (i.e. \(d_\text{par}=1\))

Template Parameters

deriv Composition of derivative indicators of type deriv

Parameters

[in]	xi	Point(s) where to evaluate the univariate B-spline object
[in]	knot_indices	Knot indices where to evaluate the univariate B-spline object

Returns: Value(s) of the univariate B-spline evaluated at the point(s) xi

◆ eval() [4/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval	(	const utils::TensorArray< parDim_ > &	xi,
		const utils::TensorArray< parDim_ > &	knot_indices,
		const torch::Tensor &	coeff_indices
	)		const

inline

Returns the value of the univariate B-spline object in the points xi

This function implements steps 2-3 of algorithm BSplineEvaluation for univariate B-splines (i.e. \(d_\text{par}=1\))

Template Parameters

deriv Composition of derivative indicators of type deriv

Parameters

[in]	xi	Point(s) where to evaluate the univariate B-spline object
[in]	knot_indices	Knot indices where to evaluate the univariate B-spline object
[in]	coeff_indices	Coefficient indices where to evaluate the univariate B-spline object

Returns: Value(s) of the univariate B-spline evaluated at the point(s) xi

◆ eval_basfunc() [1/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_basfunc ( const torch::Tensor & xi ) const

inline

Returns the vector of multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

Parameters

[in] xi Point(s) where to evaluate the B-spline object

Returns: Multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

◆ eval_basfunc() [2/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_basfunc	(	const torch::Tensor &	xi,
		const torch::Tensor &	knot_indices
	)		const

inline

Returns the vector of multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

Parameters

[in]	xi	Point(s) where to evaluate the B-spline object
[in]	knot_indices	Knot indices where to evaluate the univariate B-spline object

Returns: Multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

◆ eval_basfunc() [3/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_basfunc ( const utils::TensorArray< parDim_ > & xi ) const

inline

Returns the vector of multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

Parameters

[in] xi Point(s) where to evaluate the B-spline object

Returns: Multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

◆ eval_basfunc() [4/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_basfunc	(	const utils::TensorArray< parDim_ > &	xi,
		const utils::TensorArray< parDim_ > &	knot_indices
	)		const

inline

Returns the vector of multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

Parameters

[in]	xi	Point(s) where to evaluate the B-spline object
[in]	knot_indices	Knot indices where to evaluate the univariate B-spline object

Returns: Multivariate B-spline basis functions (or their derivatives) evaluated in the point xi

◆ eval_basfunc_univariate()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<short_t degree, short_t dim, short_t deriv>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_basfunc_univariate	(	const torch::Tensor &	xi,
		const torch::Tensor &	knot_indices
	)		const

inlineprotected

Returns the vector of univariate B-spline basis functions (or their derivatives) evaluated in the point xi

This function implements step 2 of algorithm BSplineEvaluation, that is, it evaluates the vector of univariate B-spline basis functions (or their derivatives) that are non-zero at \(\xi_d \in [t_{i_d}, t_{i_d+1})\)

\[ D^{r_d}\mathbf{B}_d(\xi_d) = \left( D^{r_d} B_{i_d-p_d,p_d}(\xi_d), \dots, D^{r_d} B_{i_d,p_d}(\xi_d) \right)^\top, \]

where \( p_d \) is the degree of the \(d\)-th univariate B-spline and \( r_d \) denotes the requested derivative in the \(d\)-direction.

According to the procedure described in Chapters 2 and 3 of [2] this can be accomplished by the following expression

\[ D^{r_d}\mathbf{B}_d(\xi_d) = \frac{p_d!}{(p_d-r_d)!}\mathbf{R}_1(\xi_d)\cdot \cdots \cdot \mathbf{R}_{p_d-r_d}(\xi_d) D\mathbf{R}_{p_d-r_d+1}\cdot \cdots \cdot D\mathbf{R}_{p_d}(\xi_d), \]

where (cf. Equation (2.20) in [2])

\[ \mathbf{R}_k(\xi_d) = \begin{pmatrix} \frac{t_{i_p+1} - \xi_d}{t_{i_p+1} - t_{i_p+1-k}} & \frac{\xi_d - t_{i_p+1-k}}{t_{i_p+1} - t_{i_p+1-k}} & 0 & \cdots & 0 \\ 0 & \frac{t_{i_p+2} - \xi_d}{t_{i_p+2} - t_{i_p+2-k}} & \frac{\xi_d - t_{i_p+2-k}}{t_{i_p+2} - t_{i_p+1-k}} & \cdots & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ 0 & 0 & \cdots & \frac{t_{i_p+k} - \xi_d}{t_{i_p+k} - t_{i_p}} & \frac{\xi_d - t_{i_p}}{t_{i_p+k} - t_{i_p}} \end{pmatrix} \]

and (cf. Equation (3.30) in [2])

\[ D\mathbf{R}_k(\xi_d) = \begin{pmatrix} \frac{-1}{t_{i_p+1} - t_{i_p+1-k}} & \frac{1}{t_{i_p+1} - t_{i_p+1-k}} & 0 & \cdots & 0 \\ 0 & \frac{-1}{t_{i_p+2} - t_{i_p+2-k}} & \frac{1}{t_{i_p+2} - t_{i_p+1-k}} & \cdots & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ 0 & 0 & \cdots & \frac{-1}{t_{i_p+k} - t_{i_p}} & \frac{1}{t_{i_p+k} - t_{i_p}} \end{pmatrix}. \]

To improve computational efficiency, the prefactor

\[ \frac{p_d!}{(p_d-r_d)!}=p_d \cdots (p_d-r_d+1) \]

is computed as compile-time expression by the eval_prefactor() function.

Moreover, the above expression for \(D^{r_d}\mathbf{B}_d(\xi_d)\) is evaluated as described in Algorithm 2.22 (R-vector version) in [2]) and its generalization to derivatives, respectively.

The algorithm goes as follows:

\(\mathbf{b} = 1\)
For \(k = 1, \dots, p_d-r_d\)
1. \(\mathbf{t}_1 = \left(t_{i_d-k+1},\dots,t_{i_d}\right)\)
2. \(\mathbf{t}_2 = \left(t_{i_d+1},\dots,t_{i_d+k}\right)\)
3. \(\mathbf{w} = \left(\xi_d-\mathbf{t}_1\right)\div\left(\mathbf{t}_2-\mathbf{t}_1\right)\)
4. \(\mathbf{b} = \left[\left(1-\mathbf{w}\right)\odot\mathbf{b}, 0\right] + \left[0, \mathbf{w}\odot\mathbf{b}\right]\)
For \(k = p_d-r_d+1, \dots, p_d\)
1. \(\mathbf{t}_1 = \left(t_{i_d-k+1},\dots,t_{i_d}\right)\)
2. \(\mathbf{t}_2 = \left(t_{i_d+1},\dots,t_{i_d+k}\right)\)
3. \(\mathbf{w} = 1\div\left(\mathbf{t}_2-\mathbf{t}_1\right)\)
4. \(\mathbf{b} = \left[-\mathbf{w}\odot\mathbf{b}, 0\right] + \left[0, \mathbf{w}\odot\mathbf{b}\right]\)

where \(\div\) and \(\odot\) denote the element-wise division and multiplication of vectors, respectively.

◆ eval_from_precomputed() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::BlockTensor< torch::Tensor, 1, geoDim_ > iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_from_precomputed	(	const torch::Tensor &	basfunc,
		const torch::Tensor &	coeff_indices,
		int64_t	numeval,
		torch::IntArrayRef	sizes
	)		const

inlineoverridevirtual

Returns the value of the B-spline object from precomputed basis function.

This function implements steps 2-3 of algorithm BSplineEvaluation for univariate B-splines (i.e. \(d_\text{par}=1\))

Parameters

[in]	basfunc	Value(s) of the multivariate B-spline basis functions evaluated at the point(s) `xi`
[in]	coeff_indices	Indices where to evaluate the coefficients
[in]	numeval	Number of evaluation points
[in]	sizes	Dimension of the result

Returns: Value(s) of the univariate B-spline object

Note: This function does not work of the basis functions are evaluated with memory_optimized flag to true

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ eval_from_precomputed() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::BlockTensor< torch::Tensor, 1, geoDim_ > iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_from_precomputed	(	const utils::TensorArray< parDim_ > &	basfunc,
		const torch::Tensor &	coeff_indices,
		int64_t	numeval,
		torch::IntArrayRef	sizes
	)		const

inlineoverride

Returns the value of the B-spline object from precomputed basis function.

This function implements steps 2-3 of algorithm BSplineEvaluation for univariate B-splines (i.e. \(d_\text{par}=1\))

Parameters

[in]	basfunc	Value(s) of the multivariate B-spline basis functions evaluated at the point(s) `xi`
[in]	coeff_indices	Indices where to evaluate the coefficients
[in]	numeval	Number of evaluation points
[in]	sizes	Dimension of the result

Returns: Value(s) of the univariate B-spline object

Note: This function does not work of the basis functions are evaluated with memory_optimized flag to true

◆ eval_prefactor()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<int64_t degree, int64_t deriv, int64_t terminal = degree - deriv>

int64_t constexpr iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::eval_prefactor ( ) const

inlineconstexprprivate

Computes the prefactor \(p_d!/(p_d-r_d)! = p_d \cdots (p_d-r_d+1)\).

◆ find_coeff_indices() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::find_coeff_indices ( const torch::Tensor & indices ) const

inline

Returns the indices of the coefficients corresponding to the knot indices indices

Parameters

[in] indices Indices of the knot spans

Returns: Indices of the coefficients corresponding to the knot indices

◆ find_coeff_indices() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<bool memory_optimized = false>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::find_coeff_indices ( const utils::TensorArray< parDim_ > & indices ) const

inline

Returns the indices of the coefficients corresponding to the knot indices indices

Parameters

[in] indices Indices of the knot spans

Returns: Indices of the coefficients corresponding to the knot indices

◆ find_knot_indices() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::find_knot_indices ( const torch::Tensor & xi ) const

inlinenoexcept

Returns the indices of knot spans containing xi

This function returns the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} \in [t_{i_1}, t_{i_1+1}) \times [t_{i_2}, t_{i_2+1}) \times \dots \times [t_{i_{d_\text{par}}}, t_{i_{d_\text{par}}+1}). \]

The indices are returned as utils::TensorArray<parDim_> in the same order as provided in xi

Parameters

[in] xi Point(s) where to evaluate the B-spline object

Returns: Indices of the knot spans containing xi

◆ find_knot_indices() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray< parDim_ > iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::find_knot_indices ( const utils::TensorArray< parDim_ > & xi ) const

inlinenoexcept

Returns the indices of knot spans containing xi

This function returns the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} \in [t_{i_1}, t_{i_1+1}) \times [t_{i_2}, t_{i_2+1}) \times \dots \times [t_{i_{d_\text{par}}}, t_{i_{d_\text{par}}+1}). \]

The indices are returned as utils::TensorArray<parDim_> in the same order as provided in xi

Parameters

[in] xi Point(s) where to evaluate the B-spline object

Returns: Indices of the knot spans containing xi

◆ from_gismo()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename BSpline >

auto & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_gismo	(	BSpline &	bspline,
		bool	,
		bool
	)

inline

◆ from_json()

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_json ( const nlohmann::json & json )

inline

Updates the B-spline object from JSON object.

◆ from_tensor()

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_tensor ( const torch::Tensor & tensor )

inlineoverridevirtualnoexcept

Sets all coefficients from a single tensor.

Parameters

[in] tensor Tensor from which to extract the coefficients

Returns: Updated spline object

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ from_tensor_()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<std::size_t... Is>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_tensor_	(	std::index_sequence< Is... >	,
		const torch::Tensor &	tensor
	)

inlineprivatenoexcept

Sets all coefficients from a single tensor.

Returns: Updates spline object

◆ from_xml() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_xml	(	const pugi::xml_document &	doc,
		int	id = `0`,
		std::string	label = `""`,
		int	index = `-1`
	)

inline

Updates the B-spline object from XML object.

◆ from_xml() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::from_xml	(	const pugi::xml_node &	root,
		int	id = `0`,
		std::string	label = `""`,
		int	index = `-1`
	)

inline

Updates the B-spline object from XML node.

◆ geoDim()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr short_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::geoDim ( )

inlinestaticconstexprnoexcept

Returns the geometric dimension.

Returns: Number of geometric dimensions

◆ greville()

template<typename real_t , short_t GeoDim, short_t... Degrees>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::greville ( bool interior = false ) const

inline

Returns the Greville abscissae.

The Greville abscissae are defined as

\[ g_{i_d} = \frac{\xi_{i_d+1} + \xi_{i_d+2} + \dots + \xi_{i_d+p_d+1}}{p_d-1} \]

Parameters

[in] interior If true only interior Greville abscissae are considered

Returns: Array of Greville abscissae

◆ init_coeffs()

template<typename real_t , short_t GeoDim, short_t... Degrees>

void iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::init_coeffs ( enum init init )

inline

Initializes the B-spline coefficients.

◆ init_knots()

template<typename real_t , short_t GeoDim, short_t... Degrees>

void iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::init_knots ( )

inline

Initializes the B-spline knots.

◆ is_nonuniform()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::is_nonuniform ( )

inlinestaticconstexprnoexcept

Returns true if the B-spline is non-uniform.

◆ is_sparse()

template<typename real_t , short_t GeoDim, short_t... Degrees>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::is_sparse ( ) const

inlineoverridevirtualnoexcept

Returns true if the layout is sparse.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ is_uniform()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::is_uniform ( )

inlinestaticconstexprnoexcept

Returns true if the B-spline is uniform.

◆ isclose()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t , short_t GeoDim_, short_t... Degrees_>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::isclose	(	const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &	other,
		real_t	rtol = `real_t{1e-5}`,
		real_t	atol = `real_t{1e-8}`
	)		const

inline

Returns true if both B-spline objects are close up to the given tolerances.

◆ knots() [1/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const utils::TensorArray< parDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots ( ) const

inlinenoexcept

Returns a constant reference to the array of knot vectors.

Returns: Array of knot vectors

◆ knots() [2/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray< parDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots ( )

inlinenoexcept

Returns a non-constant reference to the array of knot vectors.

Returns: Array of knot vectors

◆ knots() [3/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const torch::Tensor & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots ( short_t i ) const

inlinenoexcept

Returns a constant reference to the knot vector in the \(i\)-th dimension.

Parameters

[in] i Parametric dimension

Returns: Knot vector for the given parametric dimension

◆ knots() [4/4]

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Tensor & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots ( short_t i )

inlinenoexcept

Returns a non-constant reference to the knot vector in the \(i\)-th dimension.

Parameters

[in] i Parametric dimension

Returns: Knot vector for the given parametric dimension

◆ knots_to_json()

template<typename real_t , short_t GeoDim, short_t... Degrees>

nlohmann::json iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots_to_json ( ) const

inline

Returns the B-spline object's knots as JSON object.

◆ layout()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Layout iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::layout ( ) const

inlineoverridevirtualnoexcept

Returns the layout property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ load()

template<typename real_t , short_t GeoDim, short_t... Degrees>

void iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::load	(	const std::string &	filename,
		const std::string &	key = `"bspline"`
	)

inline

Loads the B-spline from file.

◆ ncoeffs() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const std::array< int64_t, parDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::ncoeffs ( ) const

inlinenoexcept

Returns a constant reference to the array of coefficient vector dimensions.

Returns: Array of coefficient vector dimensions

◆ ncoeffs() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

int64_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::ncoeffs ( short_t i ) const

inlinenoexcept

Returns the total number of coefficients in the \(i\)-th direction.

Parameters

[in] i Parametric dimension

Returns: Total number of coefficients in given parametric dimension

◆ ncumcoeffs()

template<typename real_t , short_t GeoDim, short_t... Degrees>

int64_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::ncumcoeffs ( ) const

inlinenoexcept

Returns the total number of coefficients.

Returns: Total number of coefficients

◆ nknots() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const std::array< int64_t, parDim_ > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::nknots ( ) const

inlinenoexcept

Returns a constant reference to the array of knot vector dimensions.

Returns: Array of knot vector dimensions

◆ nknots() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

int64_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::nknots ( short_t i ) const

inlinenoexcept

Returns the dimension of the knot vector in the \(i\)-th dimension.

Parameters

[in] i Parametric dimension

Returns: Knot vector dimension for the given parametric dimension

◆ operator!=()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t , short_t GeoDim_, short_t... Degrees_>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::operator!= ( const UniformBSplineCore< other_t, GeoDim_, Degrees_... > & other ) const

inline

Returns true if both B-spline objects are different.

◆ operator==()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t , short_t GeoDim_, short_t... Degrees_>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::operator== ( const UniformBSplineCore< other_t, GeoDim_, Degrees_... > & other ) const

inline

Returns true if both B-spline objects are the same.

◆ options()

template<typename real_t , short_t GeoDim, short_t... Degrees>

const Options< real_t > & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::options ( ) const

inlinenoexcept

Returns a constant reference to the B-spline object's options.

◆ parDim()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr short_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::parDim ( )

inlinestaticconstexprnoexcept

Returns the parametric dimension.

Returns: Number of parametric dimensions

◆ pinned_memory()

template<typename real_t , short_t GeoDim, short_t... Degrees>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::pinned_memory ( ) const

inlineoverridevirtualnoexcept

Returns the pinned_memory property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ read()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::serialize::InputArchive & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::read	(	torch::serialize::InputArchive &	archive,
		const std::string &	key = `"bspline"`
	)

inline

Reads the B-spline from a torch::serialize::InputArchive object.

◆ requires_grad()

template<typename real_t , short_t GeoDim, short_t... Degrees>

bool iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::requires_grad ( ) const

inlineoverridevirtualnoexcept

Returns the requires_grad property.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ save()

template<typename real_t , short_t GeoDim, short_t... Degrees>

void iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::save	(	const std::string &	filename,
		const std::string &	key = `"bspline"`
	)		const

inline

Saves the B-spline to file.

◆ set_requires_grad()

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::set_requires_grad ( bool requires_grad )

inlineoverridevirtualnoexcept

Sets the B-spline object's requires_grad property.

Note: : It is only necessary to set requires_grad to true if gradients with respect to B-spline entities, e.g., the control points should be computed. For computing the gradients with respect to the sampling points the B-spline's requires_grad property can be false.

Implements iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>.

◆ to_gismo() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::to_gismo ( ) const

inline

Converts the B-spline object into a gsBSpline object of the parametric dimension is one and a gsTensorBSpline object otherwise.

◆ to_gismo() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename BSpline >

BSpline & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::to_gismo	(	BSpline &	bspline,
		bool	,
		bool
	)		const

inline

◆ to_json()

template<typename real_t , short_t GeoDim, short_t... Degrees>

nlohmann::json iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::to_json ( ) const

inlineoverridevirtual

Returns the B-spline object as JSON object.

Implements iganet::utils::Serializable.

◆ to_xml() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

pugi::xml_document iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::to_xml	(	int	id = `0`,
		std::string	label = `""`,
		int	index = `-1`
	)		const

inline

Returns the B-spline object as XML object.

◆ to_xml() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

pugi::xml_node & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::to_xml	(	pugi::xml_node &	root,
		int	id = `0`,
		std::string	label = `""`,
		int	index = `-1`
	)		const

inline

Returns the B-spline object as XML node.

◆ transform() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::transform ( const std::function< std::array< real_t, geoDim_ >(const std::array< real_t, parDim_ > &)> transformation )

inline

Transforms the coefficients based on the given mapping.

◆ transform() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<std::size_t N>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::transform	(	const std::function< std::array< real_t, N >(const std::array< real_t, parDim_ > &)>	transformation,
		std::array< short_t, N >	dims
	)

inline

Transforms the coefficients based on the given mapping.

◆ uniform_refine()

template<typename real_t , short_t GeoDim, short_t... Degrees>

UniformBSplineCore & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::uniform_refine	(	int	numRefine = `1`,
		int	dim = `-1`
	)

inline

Returns the B-spline object with uniformly refined knot and coefficient vectors.

If dim = -1, new knot values are inserted uniformly in each knot span in all spatial dimensions. Otherwise, i.e., dim != -1 new knots are only inserted in the specified dimension.

◆ update_coeffs()

template<typename real_t , short_t GeoDim, short_t... Degrees>

void iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::update_coeffs	(	const utils::TensorArray< parDim_ > &	knots,
		const utils::TensorArray< parDim_ > &	knot_indices
	)

inlineprotected

Updates the B-spline coefficients after knot insertion.

◆ update_coeffs_univariate()

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<short_t degree, short_t dim>

auto iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::update_coeffs_univariate	(	const torch::Tensor &	knots,
		const torch::Tensor &	knot_indices
	)		const

inlineprotected

Returns the knot insertion matrix.

This functions implements the Oslo algorithm (Algorithm 4.11 in [2]) to compute the univariate knot insertion matrix from the given knot vector to the new knot vector passed as argument knots.

◆ write()

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::serialize::OutputArchive & iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::write	(	torch::serialize::OutputArchive &	archive,
		const std::string &	key = `"bspline"`
	)		const

inline

Writes the B-spline into a torch::serialize::OutputArchive object.

Friends And Related Symbol Documentation

◆ BSplineCommon

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename BSplineCore >

friend class BSplineCommon

friend

Enable access to private members.

Member Data Documentation

◆ coeffs_

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray<geoDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::coeffs_

protected

Array storing the coefficients of the control net \(\left(\mathbf{c}_{i_d}\right)_{i_d=1}^{n_d}\), \(\mathbf{c}_{i_d}\in\mathbb{R}^{d_\text{geo}}\).

◆ degrees_

template<typename real_t , short_t GeoDim, short_t... Degrees>

constexpr const std::array<short_t, parDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::degrees_ = {Degrees...}

staticconstexprprotected

Array storing the degrees \(\left(p_d\right)_{d=1}^{d_\text{par}}\).

◆ geoDim_

template<typename real_t , short_t GeoDim, short_t... Degrees>

constexpr const short_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::geoDim_ = GeoDim

staticconstexprprotected

Dimension of the geometric space \(\Omega\subset\mathbb{R}^{d_\text{geo}}\).

◆ knots_

template<typename real_t , short_t GeoDim, short_t... Degrees>

utils::TensorArray<parDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::knots_

protected

Array storing the knot vectors \(\left(\left(t_{i_d}\right)_{i_d=1}^{n_d+p_d+1}\right)_{d=1}^{d_\text{par}}\).

◆ ncoeffs_

template<typename real_t , short_t GeoDim, short_t... Degrees>

std::array<int64_t, parDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::ncoeffs_

protected

Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\).

◆ ncoeffs_reverse_

template<typename real_t , short_t GeoDim, short_t... Degrees>

std::array<int64_t, parDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::ncoeffs_reverse_

protected

Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\) in reverse order (needed for coeffs_view)

◆ nknots_

template<typename real_t , short_t GeoDim, short_t... Degrees>

std::array<int64_t, parDim_> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::nknots_

protected

Array storing the sizes of the knot vectors \(\left(n_d+p_d+1\right)_{d=1}^{d_\text{par}}\).

◆ options_

template<typename real_t , short_t GeoDim, short_t... Degrees>

Options<real_t> iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::options_

protected

Options.

◆ parDim_

template<typename real_t , short_t GeoDim, short_t... Degrees>

constexpr const short_t iganet::UniformBSplineCore< real_t, GeoDim, Degrees >::parDim_ = sizeof...(Degrees)

staticconstexprprotected

Dimension of the parametric space \(\hat\Omega=[0,1]^{d_\text{par}}\).

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

include/bspline.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ derived_self_type

◆ derived_type

◆ real_derived_self_type

◆ self_type

◆ value_type

Constructor & Destructor Documentation

◆ UniformBSplineCore() [1/5]

◆ UniformBSplineCore() [2/5]

◆ UniformBSplineCore() [3/5]

◆ UniformBSplineCore() [4/5]

◆ UniformBSplineCore() [5/5]

Member Function Documentation

◆ as_tensor()

◆ as_tensor_()

◆ as_tensor_size()

◆ coeffs() [1/4]

◆ coeffs() [2/4]

◆ coeffs() [3/4]

◆ coeffs() [4/4]

◆ coeffs_to_json()

◆ coeffs_view() [1/2]

◆ coeffs_view() [2/2]

◆ degree()

◆ degrees()

◆ device()

◆ device_index()

◆ dtype()

◆ eval() [1/4]

◆ eval() [2/4]

◆ eval() [3/4]

◆ eval() [4/4]

◆ eval_basfunc() [1/4]

◆ eval_basfunc() [2/4]

◆ eval_basfunc() [3/4]

◆ eval_basfunc() [4/4]

◆ eval_basfunc_univariate()

◆ eval_from_precomputed() [1/2]

◆ eval_from_precomputed() [2/2]

◆ eval_prefactor()

◆ find_coeff_indices() [1/2]

◆ find_coeff_indices() [2/2]

◆ find_knot_indices() [1/2]

◆ find_knot_indices() [2/2]

◆ from_gismo()

◆ from_json()

◆ from_tensor()

◆ from_tensor_()

◆ from_xml() [1/2]

◆ from_xml() [2/2]

◆ geoDim()

◆ greville()

◆ init_coeffs()

◆ init_knots()

◆ is_nonuniform()

◆ is_sparse()

◆ is_uniform()

◆ isclose()

◆ knots() [1/4]

◆ knots() [2/4]

◆ knots() [3/4]

◆ knots() [4/4]

◆ knots_to_json()

◆ layout()

◆ load()

◆ ncoeffs() [1/2]

◆ ncoeffs() [2/2]

◆ ncumcoeffs()

◆ nknots() [1/2]

◆ nknots() [2/2]

◆ operator!=()