Base class for second order tensor. More...

Detailed Description

template<class Derived>
class neml2::R2Base< Derived >

Base class for second order tensor.

The storage space is (3, 3).

#include <R2Base.h>

Inheritance diagram for R2Base< Derived >:

[legend]

Public Member Functions
	operator SR2 () const
	Conversion operator to symmetric second order tensor.

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

Derived	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.

Scalar	operator() (Size i, Size j) const
	Accessor.

Vec	row (Size i) const
	Row.

Vec	col (Size i) const
	Coluomn.

Scalar	det () const
	Determinant.

Scalar	inner (const R2 &other) const
	Double contraction ij,ij.

R4	outer (const R2 &other) const
	Outer product ij,kl.

Derived	inverse () const
	Inversion.

Derived	transpose () const
	transpose

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

	PrimitiveTensor (const ATensor &tensor, Size batch_dim)
	Construct from another ATensor given batch dimension.

	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor given batch shape.

	PrimitiveTensor (const Tensor &tensor)
	Copy constructor.

	PrimitiveTensor (const ATensor &tensor)
	Construct from another ATensor and infer batch dimension.

	operator Tensor () const
	Implicit conversion to a Tensor and loses information on the fixed base shape.

Public Member Functions inherited from TensorBase< Derived >
	TensorBase ()=default
	Special member functions.

	TensorBase (const ATensor &tensor, Size batch_dim)
	Construct from another ATensor with given batch dimension.

	TensorBase (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor with given batch shape.

	TensorBase (const neml2::Tensor &tensor)
	Copy constructor.

	TensorBase (double)=delete

	TensorBase (float)=delete

	TensorBase (int)=delete

Derived	variable_data () const

Derived	clone () const

Derived	detach () const
	Discard function graph.

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

Derived	operator- () const
	Negation.

bool	batched () const
	Whether the tensor is batched.

Size	batch_dim () const
	Return the number of batch dimensions.

Size	base_dim () const
	Return the number of base dimensions.

const TraceableTensorShape &	batch_sizes () const
	Return the batch size.

TraceableSize	batch_size (Size index) const
	Return the size of a batch axis.

TensorShapeRef	base_sizes () const
	Return the base size.

Size	base_size (Size index) const
	Return the size of a base axis.

Size	base_storage () const
	Return the flattened storage needed just for the base indices.

Derived	batch_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the batch dimensions.

neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the base dimensions.

Derived	batch_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a batch dimension.

neml2::Tensor	base_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a base dimension.

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

void	batch_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)

Derived	batch_expand (const TraceableTensorShape &batch_shape) const

Derived	batch_expand (const TraceableSize &batch_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given batch dimension.

neml2::Tensor	base_expand (TensorShapeRef base_shape) const
	Return a new view of the tensor with values broadcast along the base dimensions.

neml2::Tensor	base_expand (Size base_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given base dimension.

Derived	batch_expand_as (const neml2::Tensor &other) const
	Expand the batch to have the same shape as another tensor.

neml2::Tensor	base_expand_as (const neml2::Tensor &other) const
	Expand the base to have the same shape as another tensor.

Derived	batch_expand_copy (const TraceableTensorShape &batch_shape) const
	Return a new tensor with values broadcast along the batch dimensions.

neml2::Tensor	base_expand_copy (TensorShapeRef base_shape) const
	Return a new tensor with values broadcast along the base dimensions.

Derived	batch_reshape (const TraceableTensorShape &batch_shape) const
	Reshape batch dimensions.

neml2::Tensor	base_reshape (TensorShapeRef base_shape) const
	Reshape base dimensions.

Derived	batch_unsqueeze (Size d) const
	Unsqueeze a batch dimension.

neml2::Tensor	base_unsqueeze (Size d) const
	Unsqueeze a base dimension.

Derived	batch_transpose (Size d1, Size d2) const
	Transpose two batch dimensions.

neml2::Tensor	base_transpose (Size d1, Size d2) const
	Transpose two base dimensions.

neml2::Tensor	base_flatten () const
	Flatten base dimensions.

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

static Derived	fill (const Scalar &a)

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

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

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

static Derived	fill (const CScalar &a11, const CScalar &a12, const CScalar &a13, const CScalar &a21, const CScalar &a22, const CScalar &a23, const CScalar &a31, const CScalar &a32, const CScalar &a33, const TensorOptions &options=default_tensor_options())
	Fill all entries.

static Derived	fill (const Scalar &a11, const Scalar &a12, const Scalar &a13, const Scalar &a21, const Scalar &a22, const Scalar &a23, const Scalar &a31, const Scalar &a32, const Scalar &a33)

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

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

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

static Derived	empty (const TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

static Derived	empty (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.

static Derived	zeros (const TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.

static Derived	zeros (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.

static Derived	ones (const TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.

static Derived	ones (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.

static Derived	full (const CScalar &init, const TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.

static Derived	full (const TraceableTensorShape &batch_shape, const CScalar &init, const TensorOptions &options=default_tensor_options())
	Full tensor given batch shape.

static Tensor	identity_map (const TensorOptions &)
	Derived tensor classes should define identity_map where appropriate.

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

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

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

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

static Derived	linspace (const Derived &start, const Derived &end, Size nstep, Size dim=0)
	Create a new tensor by adding a new batch dimension with linear spacing between `start` and `end`.

static Derived	logspace (const Derived &start, const Derived &end, Size nstep, Size dim=0, const CScalar &base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
Static Public Attributes inherited from PrimitiveTensor< Derived, 3, 3 >
static const TensorShape	const_base_sizes
	The base shape.

static constexpr Size	const_base_dim
	The base dim.

static const Size	const_base_storage
	The base storage.

Protected Attributes inherited from TensorBase< Derived >
TraceableTensorShape	_batch_sizes
	Traceable batch sizes.

Member Function Documentation

◆ col()

template<class Derived >

Vec col ( Size i ) const

Coluomn.

◆ det()

template<class Derived >

Scalar det ( ) const

Determinant.

◆ drotate() [1/2]

template<class Derived >

R4 drotate ( const R2 & R ) const

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

◆ drotate() [2/2]

template<class Derived >

R3 drotate ( const Rot & r ) const

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

◆ fill() [1/8]

template<class Derived >

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

staticnodiscard

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

◆ fill() [2/8]

template<class Derived >

Derived fill	(	const CScalar &	a11,
		const CScalar &	a12,
		const CScalar &	a13,
		const CScalar &	a21,
		const CScalar &	a22,
		const CScalar &	a23,
		const CScalar &	a31,
		const CScalar &	a32,
		const CScalar &	a33,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill all entries.

◆ fill() [3/8]

template<class Derived >

Derived 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() [4/8]

template<class Derived >

Derived 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() [5/8]

template<class Derived >

Derived fill ( const Scalar & a )

staticnodiscard

◆ fill() [6/8]

template<class Derived >

Derived fill	(	const Scalar &	a11,
		const Scalar &	a12,
		const Scalar &	a13,
		const Scalar &	a21,
		const Scalar &	a22,
		const Scalar &	a23,
		const Scalar &	a31,
		const Scalar &	a32,
		const Scalar &	a33 )

staticnodiscard

◆ fill() [7/8]

template<class Derived >

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

staticnodiscard

◆ fill() [8/8]

template<class Derived >

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

staticnodiscard

◆ identity()

template<class Derived >

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

staticnodiscard

Identity.

◆ inner()

template<class Derived >

Scalar inner ( const R2 & other ) const

Double contraction ij,ij.

◆ inverse()

template<class Derived >

Derived inverse ( ) const

Inversion.

◆ operator SR2()

template<class Derived >

operator SR2 ( ) const

explicit

Conversion operator to symmetric second order tensor.

◆ operator()()

template<class Derived >

Scalar operator()	(	Size	i,
		Size	j ) const

Accessor.

◆ outer()

template<class Derived >

R4 outer ( const R2 & other ) const

Outer product ij,kl.

◆ rotate() [1/2]

template<class Derived >

Derived rotate ( const R2 & R ) const

Rotate using a rotation matrix.

◆ rotate() [2/2]

template<class Derived >

Derived rotate ( const Rot & r ) const

Rotate using a Rodrigues vector.

◆ row()

template<class Derived >

Vec row ( Size i ) const

Row.

◆ skew()

template<class Derived >

Derived skew ( const Vec & v )

staticnodiscard

Skew matrix from Vec.

◆ transpose()

template<class Derived >

Derived transpose ( ) const

transpose

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ col()

◆ det()

◆ drotate() [1/2]

◆ drotate() [2/2]

◆ fill() [1/8]

◆ fill() [2/8]

◆ fill() [3/8]

◆ fill() [4/8]

◆ fill() [5/8]

◆ fill() [6/8]

◆ fill() [7/8]

◆ fill() [8/8]

◆ identity()

◆ inner()

◆ inverse()

◆ operator SR2()

◆ operator()()

◆ outer()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ row()

◆ skew()

◆ transpose()