Base class for second order tensor. More...

Detailed Description

Base class for second order tensor.

The storage space is (3, 3).

#include <R2.h>

Inheritance diagram for R2:

[legend]

Public Member Functions
	R2 (const SR2 &S)
	Form a full R2 from a symmetric tensor.

	R2 (const WR2 &W)
	Form a full R2 from a skew-symmetric tensor.

R2	rotate (const Rot &r) const
	Rotate using a Rodrigues vector.

R2	rotate (const R2 &R) const
	Rotate using a rotation matrix.

R3	drotate (const Rot &r) const
	Derivative of the rotated tensor w.r.t. the Rodrigues vector.

R4	drotate (const R2 &R) const
	Derivative of the rotated tensor w.r.t. the rotation matrix.

Vec	row (Size i) const
	Row.

Vec	col (Size i) const
	Coluomn.

R2	transpose () const
	transpose

Public Member Functions inherited from PrimitiveTensor< R2, 3, 3 >
	PrimitiveTensor ()=default
	Special member functions.

	PrimitiveTensor (const ATensor &tensor, Size intmd_dim)
	Construct from an ATensor and infer dynamic shape.

	PrimitiveTensor (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor and extract dynamic shape given dynamic dimension.

	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &dynamic_shape, Size intmd_dim)
	Construct from an ATensor given dynamic shape.

	PrimitiveTensor (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	operator neml2::Tensor () const
	Implicit conversion to a Tensor (discards information on the fixed base shape)

Scalar	operator() (Args... i) const
	Single-element accessor.

Public Member Functions inherited from TensorBase< R2 >
	TensorBase ()=default
	Default constructor.

	TensorBase (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor with given dynamic dimension.

	TensorBase (const ATensor &tensor, TraceableTensorShape dynamic_shape, Size intmd_dim)
	Construct from an ATensor with given dynamic shape.

	TensorBase (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	TensorBase (double)=delete

	TensorBase (float)=delete

	TensorBase (int)=delete

R2	variable_data () const
	Variable data without function graph.

R2	contiguous () const

R2	clone () const
	Clone (take ownership)

R2	detach () const
	Discard function graph.

R2	to (const TensorOptions &options) const
	Change tensor options.

R2	operator- () const
	Negation.

Size	batch_dim () const

Size	base_dim () const

Size	dynamic_dim () const

Size	static_dim () const

Size	intmd_dim () const

TraceableTensorShape	batch_sizes () const

TensorShapeRef	base_sizes () const

const TraceableTensorShape &	dynamic_sizes () const

TensorShapeRef	static_sizes () const

TensorShapeRef	intmd_sizes () const

TraceableSize	batch_size (Size i) const

Size	base_size (Size i) const

const TraceableSize &	dynamic_size (Size i) const

Size	static_size (Size i) const

Size	intmd_size (Size i) const

R2	dynamic_index (indexing::TensorIndicesRef indices) const

R2	intmd_index (indexing::TensorIndicesRef indices) const

neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const

R2	dynamic_slice (Size d, const indexing::Slice &index) const

R2	intmd_slice (Size d, const indexing::Slice &index) const

neml2::Tensor	base_slice (Size d, const indexing::Slice &index) const

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	base_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	base_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

R2	dynamic_expand (const TraceableTensorShape &shape) const

R2	intmd_expand (TensorShapeRef shape) const

neml2::Tensor	base_expand (TensorShapeRef shape) const

R2	batch_expand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_expand (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

R2	dynamic_expand (const TraceableSize &size, Size d) const

R2	intmd_expand (Size size, Size d) const

neml2::Tensor	base_expand (Size size, Size d) const

R2	dynamic_expand_as (const neml2::Tensor &other) const

R2	intmd_expand_as (const neml2::Tensor &other) const

neml2::Tensor	base_expand_as (const neml2::Tensor &other) const

R2	batch_expand_as (const neml2::Tensor &other) const

neml2::Tensor	static_expand_as (const neml2::Tensor &other) const

R2	dynamic_reshape (const TraceableTensorShape &shape) const

R2	intmd_reshape (TensorShapeRef shape) const

neml2::Tensor	base_reshape (TensorShapeRef shape) const

R2	batch_reshape (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_reshape (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

R2	dynamic_squeeze (Size d) const

R2	intmd_squeeze (Size d) const

neml2::Tensor	base_squeeze (Size d) const

R2	dynamic_unsqueeze (Size d, Size n=1) const

R2	intmd_unsqueeze (Size d, Size n=1) const

neml2::Tensor	base_unsqueeze (Size d, Size n=1) const

R2	dynamic_transpose (Size d1, Size d2) const

R2	intmd_transpose (Size d1, Size d2) const

neml2::Tensor	base_transpose (Size d1, Size d2) const

R2	dynamic_movedim (Size old_dim, Size new_dim) const

R2	intmd_movedim (Size old_dim, Size new_dim) const

neml2::Tensor	base_movedim (Size old_dim, Size new_dim) const

R2	dynamic_flatten () const

R2	intmd_flatten () const

neml2::Tensor	base_flatten () const

R2	batch_flatten () const
	Flatten batch dimensions.

neml2::Tensor	static_flatten () const
	Flatten static dimensions.

Static Public Member Functions
static R2	fill (const CScalar &a, const TensorOptions &options=default_tensor_options())
	Fill the diagonals with a11 = a22 = a33 = a.

static R2	fill (const Scalar &a)

static R2	fill (const CScalar &a11, const CScalar &a22, const CScalar &a33, const TensorOptions &options=default_tensor_options())
	Fill the diagonals with a11, a22, a33.

static R2	fill (const Scalar &a11, const Scalar &a22, const Scalar &a33)

static R2	fill (const CScalar &a11, const CScalar &a22, const CScalar &a33, const CScalar &a23, const CScalar &a13, const CScalar &a12, const TensorOptions &options=default_tensor_options())
	Fill symmetric entries.

static R2	fill (const Scalar &a11, const Scalar &a22, const Scalar &a33, const Scalar &a23, const Scalar &a13, const Scalar &a12)

static R2	skew (const Vec &v)
	Skew matrix from Vec.

static R2	identity (const TensorOptions &options=default_tensor_options())
	Identity.

Static Public Member Functions inherited from PrimitiveTensor< R2, 3, 3 >
static R2	create (const TensorDataContainer &data, Size intmd_dim=0, const TensorOptions &options=default_tensor_options())
	Arbitrary tensor from a nested container with inferred batch dimension.

static R2	einsum (c10::string_view equation, TensorList tensors)
	Einstein summation along base dimensions.

static R2	empty (const TensorOptions &options=default_tensor_options())

static R2	empty (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static R2	zeros (const TensorOptions &options=default_tensor_options())

static R2	zeros (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static R2	ones (const TensorOptions &options=default_tensor_options())

static R2	ones (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static R2	full (const CScalar &init, const TensorOptions &options=default_tensor_options())

static R2	full (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const CScalar &init, const TensorOptions &options=default_tensor_options())

static R2	rand (const TensorOptions &options=default_tensor_options())

static R2	rand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const TensorOptions &options=default_tensor_options())

static R2	fill (Args &&... args)

Static Public Member Functions inherited from TensorBase< R2 >
static R2	empty_like (const R2 &other)

static R2	zeros_like (const R2 &other)
	Zero tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static R2	ones_like (const R2 &other)
	Unit tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static R2	full_like (const R2 &other, const CScalar &init)

static R2	rand_like (const R2 &other)

Additional Inherited Members
Public Types inherited from PrimitiveTensor< R2, 3, 3 >
using	base_sizes_sequence
	Base shape sequence.

Static Public Attributes inherited from PrimitiveTensor< R2, 3, 3 >
static const TensorShape	const_base_sizes
	The base shape.

static constexpr Size	const_base_dim
	The base dim.

static constexpr Size	const_base_numel
	The base numel.

Protected Member Functions inherited from PrimitiveTensor< R2, 3, 3 >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Protected Member Functions inherited from TensorBase< R2 >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Constructor & Destructor Documentation

◆ R2() [1/2]

R2 ( const SR2 & S )

Form a full R2 from a symmetric tensor.

Parameters

S	Mandel-convention symmetric tensor

◆ R2() [2/2]

R2 ( const WR2 & W )

Form a full R2 from a skew-symmetric tensor.

Parameters

W	skew-vector convention skew-symmetric tensor

Member Function Documentation

◆ col()

Vec col ( Size i ) const

Coluomn.

◆ drotate() [1/2]

R4 drotate ( const R2 & R ) const

Derivative of the rotated tensor w.r.t. the rotation matrix.

◆ drotate() [2/2]

R3 drotate ( const Rot & r ) const

Derivative of the rotated tensor w.r.t. the Rodrigues vector.

◆ fill() [1/6]

R2 fill	(	const CScalar &	a,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill the diagonals with a11 = a22 = a33 = a.

◆ fill() [2/6]

R2 fill	(	const CScalar &	a11,
		const CScalar &	a22,
		const CScalar &	a33,
		const CScalar &	a23,
		const CScalar &	a13,
		const CScalar &	a12,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill symmetric entries.

◆ fill() [3/6]

R2 fill	(	const CScalar &	a11,
		const CScalar &	a22,
		const CScalar &	a33,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill the diagonals with a11, a22, a33.

◆ fill() [4/6]

R2 fill ( const Scalar & a )

staticnodiscard

◆ fill() [5/6]

R2 fill	(	const Scalar &	a11,
		const Scalar &	a22,
		const Scalar &	a33 )

staticnodiscard

◆ fill() [6/6]

R2 fill	(	const Scalar &	a11,
		const Scalar &	a22,
		const Scalar &	a33,
		const Scalar &	a23,
		const Scalar &	a13,
		const Scalar &	a12 )

staticnodiscard

◆ identity()

R2 identity ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

Identity.

◆ rotate() [1/2]

R2 rotate ( const R2 & R ) const

Rotate using a rotation matrix.

◆ rotate() [2/2]

R2 rotate ( const Rot & r ) const

Rotate using a Rodrigues vector.

◆ row()

Vec row ( Size i ) const

Row.

◆ skew()

R2 skew ( const Vec & v )

staticnodiscard

Skew matrix from Vec.

◆ transpose()

R2 transpose ( ) const

transpose

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ R2() [1/2]

◆ R2() [2/2]

Member Function Documentation

◆ col()

◆ drotate() [1/2]

◆ drotate() [2/2]

◆ fill() [1/6]

◆ fill() [2/6]

◆ fill() [3/6]

◆ fill() [4/6]

◆ fill() [5/6]

◆ fill() [6/6]

◆ identity()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ row()

◆ skew()

◆ transpose()