iganet::BSplineCommon< BSplineCore > Class Template Reference

B-spline (common high-level functionality) More...

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

Inheritance diagram for iganet::BSplineCommon< BSplineCore >:

Public Types
template<typename real_t , short_t GeoDim, short_t... Degrees>
using	derived_self_type = BSplineCommon< typename BSplineCore::template derived_self_type< real_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 T, std::make_signed< short_t >::type degree_elevate = 0>
using	derived_type = BSplineCommon< typename BSplineCore::template derived_type< T, degree_elevate > >
	Deduces the type of the template template parameter T 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.
using	Ptr = std::shared_ptr< BSplineCommon >
	Shared pointer for BSplineCommon.
template<typename other_t >
using	real_derived_self_type = BSplineCommon< typename BSplineCore::template real_derived_self_type< other_t > >
	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 = BSplineCommon< typename BSplineCore::template self_type< degree_elevate > >
	Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate
using	uPtr = std::unique_ptr< BSplineCommon >
	Unique pointer for BSplineCommon.

Public Member Functions
	BSplineCommon (BSplineCommon &&)=default
	Move constructor.
	BSplineCommon (BSplineCommon &&other, utils::TensorArray< BSplineCore::geoDim_ > &&coeffs)
	Move constructor with external coefficients.
	BSplineCommon (const BSplineCommon &)=default
	Copy constructor.
	BSplineCommon (const BSplineCommon &other, bool clone)
	Copy/clone constructor.
	BSplineCommon (const BSplineCommon &other, const utils::TensorArray< BSplineCore::geoDim_ > &coeffs, bool clone=false)
	Copy constructor with external coefficients.
auto	abs_diff (const BSplineCommon &other, int dim=-1)
	Computes the absolute difference between two compatible B-spline objects.
auto	boundingBox () const
	Computes the bounding box of the B-spline object.
auto	clone () const
	Returns a clone of the B-spline object.
template<bool memory_optimized = false>
auto	curl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.
template<bool memory_optimized = false>
auto	curl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.
auto	diff (const BSplineCommon &other, int dim=-1)
	Computes the difference between two compatible B-spline objects.
template<bool memory_optimized = false>
auto	div (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.
template<bool memory_optimized = false>
auto	div (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.
template<bool memory_optimized = false>
auto	grad (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	grad (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	hess (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	hess (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false, typename Geometry >
auto	icurl (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	icurl (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	idiv (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	idiv (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	igrad (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	igrad (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ihess (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ihess (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ijac (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ijac (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ilapl (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const
	Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false, typename Geometry >
auto	ilapl (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const
	Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.
template<bool memory_optimized = false>
auto	jac (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	jac (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	lapl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const
	Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.
template<bool memory_optimized = false>
auto	lapl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.
BSplineCommon	operator* (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const
	Returns a new B-spline object whose coefficients are scaled by a vector.
BSplineCommon	operator* (typename BSplineCore::value_type s) const
	Returns a new B-spline object whose coefficients are scaled by a scalar.
BSplineCommon &	operator*= (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v)
	Scales the coefficients by a vector.
BSplineCommon &	operator*= (typename BSplineCore::value_type s)
	Scales the coefficients by a scalar.
BSplineCommon	operator+ (const BSplineCommon &other) const
	Returns a new B-spline object whose coefficients are the sum of that of two compatible B-spline objects.
BSplineCommon &	operator+= (const BSplineCommon &other)
	Adds the coefficients of another B-spline object.
BSplineCommon	operator- (const BSplineCommon &other) const
	Returns a new B-spline object whose coefficients are the difference of that of two compatible B-spline objects.
BSplineCommon &	operator-= (const BSplineCommon &other)
	Substracts the coefficients of another B-spline object.
BSplineCommon	operator/ (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const
	Returns a new B-spline object whose coefficients are scaled by a vector.
BSplineCommon	operator/ (typename BSplineCore::value_type s) const
	Returns a new B-spline object whose coefficients are scaled by a scalar.
BSplineCommon &	operator/= (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v)
	Scales the coefficients by a vector.
BSplineCommon &	operator/= (typename BSplineCore::value_type s)
	Scales the coefficients by a scalar.
template<typename Backend = void, typename BSplineCoreColor >
auto	plot (const BSplineCommon< BSplineCoreColor > &color, const nlohmann::json &json={}) const
template<typename Backend = void, typename BSplineCoreColor >
auto	plot (const BSplineCommon< BSplineCoreColor > &color, const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &xi, const nlohmann::json &json={}) const
template<typename Backend = void, typename BSplineCoreColor >
auto	plot (const BSplineCommon< BSplineCoreColor > &color, const utils::TensorArray< BSplineCore::parDim_ > &xi, const nlohmann::json &json={}) const
template<typename Backend = void>
auto	plot (const nlohmann::json &json={}) const
template<typename Backend = void>
auto	plot (const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &xi, const nlohmann::json &json={}) const
template<typename Backend = void>
auto	plot (const utils::TensorArray< BSplineCore::parDim_ > &xi, const nlohmann::json &json={}) const
virtual void	pretty_print (std::ostream &os=Log(log::info)) const noexcept override
	Returns a string representation of the BSplineCommon object.
auto	rotate (std::array< typename BSplineCore::value_type, 3 > angle)
	Rotates the B-spline object by three angles in 3d.
auto	rotate (typename BSplineCore::value_type angle)
	Rotates the B-spline object by an angle in 2d.
auto	scale (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v)
	Scales the B-spline object by a vector.
auto	scale (typename BSplineCore::value_type s, int dim=-1)
	Scales the B-spline object by a scalar.
template<typename real_t >
auto	to () const
	Returns a copy of the B-spline object with real_t type.
template<typename real_t >
auto	to (Options< real_t > options) const
	Returns a copy of the B-spline object with settings from options.
auto	to (torch::Device device) const
	Returns a copy of the B-spline object with settings from device.
auto	translate (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v)
	Translates the B-spline object by a vector.
BSplineCommon &	uniform_refine (int numRefine=1, int dim=-1)
	Returns the B-spline object with uniformly refined knot and coefficient vectors.

Additional Inherited Members
Protected Member Functions inherited from iganet::utils::FullQualifiedName
virtual const std::string &	name () const noexcept
	Returns the full qualified name of the object.
Protected Attributes inherited from iganet::utils::FullQualifiedName
at::optional< std::string >	name_
	String storing the full qualified name of the object.

Detailed Description

template<typename BSplineCore>
class iganet::BSplineCommon< BSplineCore >

B-spline (common high-level functionality)

This class implements some high-level common functionality of all B-spline classes, e.g., plotting which rely on low-level functionality that is implemented differently for uniform and non-uniform B-spline. C++ suggests to use virtual methods for this purpose and implement the common functionality in a base class. However, this is not performant for low-level functionality, e.g., point-wise function evaluation which is called repeatedly. Moreover, virtual methods do not work with templated functions, which is why we implement high-level common functionality here and 'inject' the core functionality by deriving from a particular base class.

Member Typedef Documentation

derived_self_type

template<typename BSplineCore >

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

using iganet::BSplineCommon< BSplineCore >::derived_self_type = BSplineCommon<typename BSplineCore::template derived_self_type< real_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 BSplineCore >

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

using iganet::BSplineCommon< BSplineCore >::derived_type = BSplineCommon< typename BSplineCore::template derived_type<T, degree_elevate> >

Deduces the type of the template template parameter T 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.

Ptr

template<typename BSplineCore >

using iganet::BSplineCommon< BSplineCore >::Ptr = std::shared_ptr<BSplineCommon>

Shared pointer for BSplineCommon.

real_derived_self_type

template<typename BSplineCore >

template<typename other_t >

using iganet::BSplineCommon< BSplineCore >::real_derived_self_type = BSplineCommon< typename BSplineCore::template real_derived_self_type<other_t> >

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

self_type

template<typename BSplineCore >

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

using iganet::BSplineCommon< BSplineCore >::self_type = BSplineCommon<typename BSplineCore::template self_type<degree_elevate> >

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

uPtr

template<typename BSplineCore >

using iganet::BSplineCommon< BSplineCore >::uPtr = std::unique_ptr<BSplineCommon>

Unique pointer for BSplineCommon.

Constructor & Destructor Documentation

BSplineCommon() [1/5]

template<typename BSplineCore >

iganet::BSplineCommon< BSplineCore >::BSplineCommon ( const BSplineCommon< BSplineCore > &  )

default

Copy constructor.

BSplineCommon() [2/5]

template<typename BSplineCore >

iganet::BSplineCommon< BSplineCore >::BSplineCommon ( const BSplineCommon< BSplineCore > &  other, bool  clone  )

inline

Copy/clone constructor.

BSplineCommon() [3/5]

template<typename BSplineCore >

iganet::BSplineCommon< BSplineCore >::BSplineCommon ( const BSplineCommon< BSplineCore > &  other, const utils::TensorArray< BSplineCore::geoDim_ > &  coeffs, bool  clone = false  )

inline

Copy constructor with external coefficients.

BSplineCommon() [4/5]

template<typename BSplineCore >

iganet::BSplineCommon< BSplineCore >::BSplineCommon ( BSplineCommon< BSplineCore > &&  )

default

Move constructor.

BSplineCommon() [5/5]

template<typename BSplineCore >

iganet::BSplineCommon< BSplineCore >::BSplineCommon ( BSplineCommon< BSplineCore > &&  other, utils::TensorArray< BSplineCore::geoDim_ > &&  coeffs  )

inline

Move constructor with external coefficients.

Member Function Documentation

abs_diff()

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::abs_diff ( const BSplineCommon< BSplineCore > &  other, int  dim = -1  )

inline

Computes the absolute difference between two compatible B-spline objects.

If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted

boundingBox()

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::boundingBox ( ) const

inline

Computes the bounding box of the B-spline object.

clone()

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::clone ( ) const

inline

Returns a clone of the B-spline object.

curl() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::curl ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the curl

Returns

Block-tensor with the curl with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}} \times \mathbf{u} = \begin{bmatrix} \mathbf{i}_0 & \cdots & \mathbf{i}_{d_\text{par}} \\ \frac{\partial}{\partial\xi_0} & \cdots & \frac{\partial}{\partial\xi_{d_\text{par}}} \\ u_0 & \cdots & u_{d_\text{par}} \end{bmatrix} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

curl() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::curl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the curl

Returns

Block-tensor with the curl with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}} \times \mathbf{u} = \begin{bmatrix} \mathbf{i}_0 & \cdots & \mathbf{i}_{d_\text{par}} \\ \frac{\partial}{\partial\xi_0} & \cdots & \frac{\partial}{\partial\xi_{d_\text{par}}} \\ u_0 & \cdots & u_{d_\text{par}} \end{bmatrix} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

curl() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::curl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the curl
[in]	knot_indices	Knot indices where to evaluate the curl

Returns

Block-tensor with the curl with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}} \times \mathbf{u} = \begin{bmatrix} \mathbf{i}_0 & \cdots & \mathbf{i}_{d_\text{par}} \\ \frac{\partial}{\partial\xi_0} & \cdots & \frac{\partial}{\partial\xi_{d_\text{par}}} \\ u_0 & \cdots & u_{d_\text{par}} \end{bmatrix} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

curl() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::curl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the curl
[in]	knot_indices	Knot indices where to evaluate the curl
[in]	coeff_indices	Coefficient indices where to evaluate the curl

Returns

Block-tensor with the curl of the B-spline with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

curl = 0, 0, du_y / dx - du_x / dy

Only the third component is returned

curl = du_z / dy - du_y / dz, du_x / dz - du_z / dx, du_y / dx - du_x / dy

diff()

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::diff ( const BSplineCommon< BSplineCore > &  other, int  dim = -1  )

inline

Computes the difference between two compatible B-spline objects.

If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted

div() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::div ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the divergence

Returns

Block-tensor with the divergence with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

div() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::div ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the divergence

Returns

Block-tensor with the divergence with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

div() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::div ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the divergence
[in]	knot_indices	Knot indices where to evaluate the divergence

Returns

Block-tensor with the divergence with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

div() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::div ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the divergence
[in]	knot_indices	Knot indices where to evaluate the divergence
[in]	coeff_indices	Coefficient indices where to evaluate the divergence

Returns

Block-tensor with the divergence of the B-spline with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]

Note

This function can only be applied to B-spline objects with equal parametric and geometric dimensionality.

grad() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::grad ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the gradient

Returns

Block-tensor with the gradient with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]

Note

This function can only be applied to B-spline objects with geometric dimensionality 1, i.e. scalar fields.

grad() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::grad ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the gradient

Returns

Block-tensor with the gradient with respect to the parametric variables xi

\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]

Note

This function can only be applied to B-spline objects with geometric dimensionality 1, i.e. scalar fields.

grad() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::grad ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient

Returns

Block-tensor with the gradient with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]

Note

This function can only be applied to B-spline objects with geometric dimensionality 1, i.e. scalar fields.

grad() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::grad ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient
[in]	coeff_indices	Coefficient indices where to evaluate the gradient

Returns

Block-tensor with the gradient with respect to the parametric variables

\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]

Note

This function can only be applied to B-spline objects with geometric dimensionality 1, i.e. scalar fields.

hess() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::hess ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Hessian

Returns

Block-tensor with the Hessian with respect to the parametric variables xi

\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]

Note

If the B-spline object has geometric dimension larger then one then all Hessian matrices are returned as slices of a rank-3 tensor.

hess() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::hess ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Hessian

Returns

Block-tensor with the Hessian with respect to the parametric variables xi

\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]

Note

If the B-spline object has geometric dimension larger then one then all Hessian matrices are returned as slices of a rank-3 tensor.

hess() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::hess ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the Hessian

Returns

Block-tensor with the Hessian with respect to the parametric variables

\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]

Note

If the B-spline object has geometric dimension larger then one then all Hessian matrices are returned as slices of a rank-3 tensor.

hess() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::hess ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the Hessian
[in]	knot_indices	Knot indices where to evaluate the Hessian
[in]	coeff_indices	Coefficient indices where to evaluate the Hessian

Returns

Block-tensor with the Hessian with respect to the parametric variables

\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]

Note

If the B-spline object has geometric dimension larger then one then all Hessian matrices are returned as slices of a rank-3 tensor.

icurl() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::icurl ( const Geometry &  G, const torch::Tensor &  xi  ) const

inline

Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the curl with respect to the parametric variables

\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

icurl() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::icurl ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the curl with respect to the parametric variables

\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

icurl() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::icurl ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the gradient
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the curl with respect to the physical variables

\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

icurl() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::icurl ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient
[in]	knot_indices_G	Knot indices where to evaluate Jacobian of G

Returns

Block-tensor with the curl with respect to the physical variables

\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

idiv() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::idiv ( const Geometry &  G, const torch::Tensor &  xi  )

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the divergence with respect to the parametric variables

\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]

idiv() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::idiv ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the divergence with respect to the parametric variables

\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]

idiv() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::idiv ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the divergence
[in]	knot_indices	Knot indices where to evaluate the divergence
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the divergence
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the divergence with respect to the physical variables

\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]

idiv() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::idiv ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the divergence
[in]	knot_indices	Knot indices where to evaluate the divergence
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G

Returns

Block-tensor with the divergence with respect to the physical variables

\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]

igrad() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::igrad ( const Geometry &  G, const torch::Tensor &  xi  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the gradient with respect to the parametric variables

\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

igrad() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::igrad ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the gradient with respect to the parametric variables

\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

igrad() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::igrad ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the gradient
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the gradient with respect to the physical variables

\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

igrad() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::igrad ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the gradient
[in]	knot_indices	Knot indices where to evaluate the gradient
[in]	knot_indices_G	Knot indices where to evaluate Jacobian of G

Returns

Block-tensor with the gradient with respect to the physical variables

\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ihess() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ihess ( const Geometry &  G, const torch::Tensor &  xi  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Hessian with respect to the parametric variables

\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ihess() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ihess ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Hessian with respect to the parametric variables

\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ihess() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ihess ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Hessian
[in]	knot_indices	Knot indices where to evaluate the Hessian
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the Hessian
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the Hessian with respect to the physical variables

\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ihess() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ihess ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Hessian
[in]	knot_indices	Knot indices where to evaluate the Hessian
[in]	knot_indices_G	Knot indices where to evaluate Jacobian of G

Returns

Block-tensor with the Hessian with respect to the physical variables

\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ijac() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ijac ( const Geometry &  G, const torch::Tensor &  xi  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ijac() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ijac ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ijac() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ijac ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Jacobian
[in]	knot_indices	Knot indices where to evaluate the Jacobain
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the Jacobian
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the Jacobian with respect to the physical variables

\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ijac() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ijac ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Jacobian
[in]	knot_indices	Knot indices where to evaluate the Jacobian
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G

Returns

Block-tensor with the Jacobian with respect to the physical variables

\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ilapl() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ilapl ( const Geometry &  G, const torch::Tensor &  xi  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Laplacian with respect to the parametric variables

\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ilapl() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ilapl ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

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

Returns

Block-tensor with the Laplacian with respect to the parametric variables

\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ilapl() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ilapl ( const Geometry &  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G, const torch::Tensor &  coeff_indices_G  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Laplacian
[in]	knot_indices	Knot indices where to evaluate the Laplacian
[in]	knot_indices_G	Knot indices where to evaluate the Jacobian of G
[in]	coeff_indices	Coefficient indices where to evaluate the Laplacian
[in]	coeff_indices_G	Coefficient indices where to evaluate the Jacobian of G

Returns

Block-tensor with the Laplacian with respect to the physical variables

\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

ilapl() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false, typename Geometry >

auto iganet::BSplineCommon< BSplineCore >::ilapl ( const Geometry  G, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const utils::TensorArray< Geometry::parDim()> &  knot_indices_G  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.

Template Parameters

Geometry

Type of the geometry B-spline object

Parameters

[in]	G	B-spline geometry object
[in]	xi	Point(s) where to evaluate the Laplacian
[in]	knot_indices	Knot indices where to evaluate the Laplacian
[in]	knot_indices_G	Knot indices where to evaluate Jacobian of G

Returns

Block-tensor with the Laplacian with respect to the physical variables

\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]

jac() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::jac ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Jacobian

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]

jac() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::jac ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Jacobian

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]

jac() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::jac ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the Jacobian
[in]	knot_indices	Knot indices where to evaluate the Jacobian

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]

jac() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::jac ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the Jacobian
[in]	knot_indices	Knot indices where to evaluate the Jacobian
[in]	coeff_indices	Coefficient indices where to evaluate the Jacobian

Returns

Block-tensor with the Jacobian with respect to the parametric variables

\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]

Note

Since the B-spline evaluation function computes the specified derivatives for all variables simultaneously we compute the transpose of the Jacobian and return its tranposed, hence, the Jacobian.

lapl() [1/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::lapl ( const torch::Tensor &  xi ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Laplacian

Returns

Block-tensor with the Laplacian with respect to the parametric variables xi

\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]

Note

If the B-spline object has geometric dimension larger then one then all Laplacians are returned as a vector.

lapl() [2/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::lapl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]

xi

Point(s) where to evaluate the Laplacian

Returns

Block-tensor with the Laplacian with respect to the parametric variables xi

\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]

Note

If the B-spline object has geometric dimension larger then one then all Laplacians are returned as a vector.

lapl() [3/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::lapl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the Laplacian
[in]	knot_indices	Knot indices where to evaluate the Laplacian

Returns

Block-tensor with the Laplacian with respect to the parametric variables

\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]

Note

If the B-spline object has geometric dimension larger then one then all Laplacian matrices are returned as a vector.

lapl() [4/4]

template<typename BSplineCore >

template<bool memory_optimized = false>

auto iganet::BSplineCommon< BSplineCore >::lapl ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const utils::TensorArray< BSplineCore::parDim_ > &  knot_indices, const torch::Tensor &  coeff_indices  ) const

inline

Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.

Parameters

[in]	xi	Point(s) where to evaluate the Laplacian
[in]	knot_indices	Knot indices where to evaluate the Laplacian
[in]	coeff_indices	Coefficient indices where to evaluate the Laplacian

Returns

Block-tensor with the Laplacian with respect to the parametric variables

\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]

Note

If the B-spline object has geometric dimension larger then one then all Laplacians are returned as a vector.

make_shared() [1/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, const utils::TensorArray< BSplineCore::geoDim_ > &  coeffs, bool  clone = false, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as shared pointer.

make_shared() [2/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, enum init  init = init::greville, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as shared pointer.

make_shared() [3/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, utils::TensorArray< BSplineCore::geoDim_ > &&  coeffs, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as shared pointer.

make_shared() [4/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( const std::array< std::vector< typename BSplineCore::value_type >, BSplineCore::parDim_ > &  kv, const utils::TensorArray< BSplineCore::geoDim_ > &  coeffs, bool  clone = false, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as shared pointer.

make_shared() [5/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( const std::array< std::vector< typename BSplineCore::value_type >, BSplineCore::parDim_ > &  kv, enum init  init = init::greville, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as shared pointer.

make_shared() [6/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_shared ( Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{} )

inlinestatic

Creates a new B-spline object as shared pointer.

make_unique() [1/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, const utils::TensorArray< BSplineCore::geoDim_ > &  coeffs, bool  clone = false, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as unique pointer.

make_unique() [2/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, enum init  init = init::greville, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as unique pointer.

make_unique() [3/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( const std::array< int64_t, BSplineCore::parDim_ > &  ncoeffs, utils::TensorArray< BSplineCore::geoDim_ > &&  coeffs, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as unique pointer.

make_unique() [4/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( const std::array< std::vector< typename BSplineCore::value_type >, BSplineCore::parDim_ > &  kv, const utils::TensorArray< BSplineCore::geoDim_ > &  coeffs, bool  clone = false, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as unique pointer.

make_unique() [5/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( const std::array< std::vector< typename BSplineCore::value_type >, BSplineCore::parDim_ > &  kv, enum init  init = init::greville, Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{}  )

inlinestatic

Creates a new B-spline object as unique pointer.

make_unique() [6/6]

template<typename BSplineCore >

static Ptr iganet::BSplineCommon< BSplineCore >::make_unique ( Options< typename BSplineCore::value_type >  options = Options<typename BSplineCore::value_type>{} )

inlinestatic

Creates a new B-spline object as unique pointer.

operator*() [1/2]

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator* ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v ) const

inline

Returns a new B-spline object whose coefficients are scaled by a vector.

operator*() [2/2]

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator* ( typename BSplineCore::value_type  s ) const

inline

Returns a new B-spline object whose coefficients are scaled by a scalar.

operator*=() [1/2]

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator*= ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v )

inline

Scales the coefficients by a vector.

operator*=() [2/2]

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator*= ( typename BSplineCore::value_type  s )

inline

Scales the coefficients by a scalar.

operator+()

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator+ ( const BSplineCommon< BSplineCore > &  other ) const

inline

Returns a new B-spline object whose coefficients are the sum of that of two compatible B-spline objects.

Note

This method does not check if the knot vectors of the two B-spline objects are compatible. It simply adds the two coefficients arrays and throws an error if their sizes do not match. Any compatibility checks must be performed outside.

operator+=()

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator+= ( const BSplineCommon< BSplineCore > &  other )

inline

Adds the coefficients of another B-spline object.

Note

This method does not check if the knot vectors of the two B-spline objects are compatible. It simply adds the two coefficients arrays and throws an error if their sizes do not match. Any compatibility checks must be performed outside.

operator-()

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator- ( const BSplineCommon< BSplineCore > &  other ) const

inline

Returns a new B-spline object whose coefficients are the difference of that of two compatible B-spline objects.

Note

This method does not check if the knot vectors of the two B-spline objects are compatible. It simply subtracts the coefficients arrays of two B-spline objects from each other and throws an error if their sizes do not match. Any compatibility checks must be performed outside.

operator-=()

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator-= ( const BSplineCommon< BSplineCore > &  other )

inline

Substracts the coefficients of another B-spline object.

Note

This method does not check if the knot vectors of the two B-spline objects are compatible. It simply substracts the two coefficients arrays and throws an error if their sizes do not match. Any compatibility checks must be performed outside.

operator/() [1/2]

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator/ ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v ) const

inline

Returns a new B-spline object whose coefficients are scaled by a vector.

operator/() [2/2]

template<typename BSplineCore >

BSplineCommon iganet::BSplineCommon< BSplineCore >::operator/ ( typename BSplineCore::value_type  s ) const

inline

Returns a new B-spline object whose coefficients are scaled by a scalar.

operator/=() [1/2]

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator/= ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v )

inline

Scales the coefficients by a vector.

operator/=() [2/2]

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::operator/= ( typename BSplineCore::value_type  s )

inline

Scales the coefficients by a scalar.

plot() [1/6]

template<typename BSplineCore >

template<typename Backend = void, typename BSplineCoreColor >

auto iganet::BSplineCommon< BSplineCore >::plot ( const BSplineCommon< BSplineCoreColor > &  color, const nlohmann::json &  json = {}  ) const

inline

Plots the B-spline object colored by another B-spline object

Parameters

[in]	color	B-spline object representing the color
[in]	json	JSON configuration

Returns

Plot of the B-spline object

plot() [2/6]

template<typename BSplineCore >

template<typename Backend = void, typename BSplineCoreColor >

auto iganet::BSplineCommon< BSplineCore >::plot ( const BSplineCommon< BSplineCoreColor > &  color, const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &  xi, const nlohmann::json &  json = {}  ) const

inline

Plots the B-spline object colored by another B-spline object together with a set of sampling points

Parameters

[in]	color	B-spline object representing the color
[in]	xi	Vector of sampling points
[in]	json	JSON configuration

Returns

Plot of the B-spline object

plot() [3/6]

template<typename BSplineCore >

template<typename Backend = void, typename BSplineCoreColor >

auto iganet::BSplineCommon< BSplineCore >::plot ( const BSplineCommon< BSplineCoreColor > &  color, const utils::TensorArray< BSplineCore::parDim_ > &  xi, const nlohmann::json &  json = {}  ) const

inline

Plots the B-spline object colored by another B-spline object together with a set of sampling points

Parameters

[in]	color	B-spline object representing the color
[in]	xi	Sampling points
[in]	json	JSON configuration

Returns

Plot of the B-spline object

plot() [4/6]

template<typename BSplineCore >

template<typename Backend = void>

auto iganet::BSplineCommon< BSplineCore >::plot ( const nlohmann::json &  json = {} ) const

inline

Plots the B-spline object

Parameters

[in]

json

JSON configuration

Returns

Plot of the B-spline object

plot() [5/6]

template<typename BSplineCore >

template<typename Backend = void>

auto iganet::BSplineCommon< BSplineCore >::plot ( const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &  xi, const nlohmann::json &  json = {}  ) const

inline

Plots the B-spline object together with a set of sampling points

Parameters

[in]	xi	Vector of sampling points
[in]	json	JSON configuration

Returns

Plot of the B-spline object

plot() [6/6]

template<typename BSplineCore >

template<typename Backend = void>

auto iganet::BSplineCommon< BSplineCore >::plot ( const utils::TensorArray< BSplineCore::parDim_ > &  xi, const nlohmann::json &  json = {}  ) const

inline

Plots the B-spline object together with a set of sampling points

Parameters

[in]	xi	Sampling points
[in]	json	JSON configuration

Returns

Plot of the B-spline object

pretty_print()

template<typename BSplineCore >

virtual void iganet::BSplineCommon< BSplineCore >::pretty_print ( std::ostream &  os = Log(log::info) ) const

inlineoverridevirtualnoexcept

Returns a string representation of the BSplineCommon object.

Implements iganet::utils::FullQualifiedName.

rotate() [1/2]

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::rotate ( std::array< typename BSplineCore::value_type, 3 >  angle )

inline

Rotates the B-spline object by three angles in 3d.

rotate() [2/2]

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::rotate ( typename BSplineCore::value_type  angle )

inline

Rotates the B-spline object by an angle in 2d.

scale() [1/2]

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::scale ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v )

inline

Scales the B-spline object by a vector.

scale() [2/2]

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::scale ( typename BSplineCore::value_type  s, int  dim = -1  )

inline

Scales the B-spline object by a scalar.

to() [1/3]

template<typename BSplineCore >

template<typename real_t >

auto iganet::BSplineCommon< BSplineCore >::to ( ) const

inline

Returns a copy of the B-spline object with real_t type.

to() [2/3]

template<typename BSplineCore >

template<typename real_t >

auto iganet::BSplineCommon< BSplineCore >::to ( Options< real_t >  options ) const

inline

Returns a copy of the B-spline object with settings from options.

to() [3/3]

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::to ( torch::Device  device ) const

inline

Returns a copy of the B-spline object with settings from device.

translate()

template<typename BSplineCore >

auto iganet::BSplineCommon< BSplineCore >::translate ( std::array< typename BSplineCore::value_type, BSplineCore::geoDim()>  v )

inline

Translates the B-spline object by a vector.

uniform_refine()

template<typename BSplineCore >

BSplineCommon & iganet::BSplineCommon< BSplineCore >::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.

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

• include/bspline.hpp