The symmetric second order tensor. More...

Detailed Description

The symmetric second order tensor.

Mandel notation is used, and so the storage space is (6).

#include <SR2.h>

Inheritance diagram for SR2:

[legend]

Public Member Functions
	SR2 (const R2 &T)
	Symmetrize an R2 then fill.

SR2	rotate (const Rot &r) const
	Rotate.

SR2	rotate (const R2 &R) const

SFR3	drotate (const Rot &r) const
	Derivative of the rotated tensor w.r.t. the Rodrigues vector.

SFFR4	drotate (const R2 &R) const

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

Scalar	tr () const
	Trace.

SR2	vol () const
	Volumetric part of the tensor.

SR2	dev () const
	Deviatoric part of the tensor.

Scalar	det () const
	Determinant.

Scalar	inner (const SR2 &other) const
	Double contraction ij,ij.

Scalar	norm_sq () const
	Norm squared.

Scalar	norm (Real eps=0) const
	Norm.

SSR4	outer (const SR2 &other) const
	Outer product ij,kl -> ijkl.

SR2	inverse () const
	Inversion.

SR2	transpose () const
	Transpose, no-op.

Public Member Functions inherited from PrimitiveTensor< SR2, 6 >
	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< SR2 >
	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 (Real)=delete

SR2	variable_data () const

SR2	clone () const

SR2	detach () const
	Discard function graph.

SR2	to (const TensorOptions &options) const
	Change tensor options.

SR2	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.

SR2	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.

SR2	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, Real v)

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

void	base_index_put_ (indexing::TensorIndicesRef indices, Real v)

SR2	batch_expand (const TraceableTensorShape &batch_shape) const

SR2	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.

SR2	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.

SR2	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.

SR2	batch_reshape (const TraceableTensorShape &batch_shape) const
	Reshape batch dimensions.

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

SR2	batch_unsqueeze (Size d) const
	Unsqueeze a batch dimension.

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

SR2	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 SR2	fill (const Real &a, const TensorOptions &options=default_tensor_options())
	Fill the diagonals with a11 = a22 = a33 = a.

static SR2	fill (const Scalar &a)

static SR2	fill (const Real &a11, const Real &a22, const Real &a33, const TensorOptions &options=default_tensor_options())
	Fill the diagonals with a11, a22, a33.

static SR2	fill (const Scalar &a11, const Scalar &a22, const Scalar &a33)

static SR2	fill (const Real &a11, const Real &a22, const Real &a33, const Real &a23, const Real &a13, const Real &a12, const TensorOptions &options=default_tensor_options())
	Fill all entries.

static SR2	fill (const Scalar &a11, const Scalar &a22, const Scalar &a33, const Scalar &a23, const Scalar &a13, const Scalar &a12)

static SR2	identity (const TensorOptions &options=default_tensor_options())
	Identity.

static SSR4	identity_map (const TensorOptions &options=default_tensor_options())
	The derivative of a SR2 with respect to itself.

Static Public Member Functions inherited from PrimitiveTensor< SR2, 6 >
static SR2	create (const TensorDataContainer &data, const TensorOptions &options=default_tensor_options())
	Arbitrary tensor from a nested container with inferred batch dimension.

static SR2	empty (const TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

static SR2	empty (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.

static SR2	zeros (const TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.

static SR2	zeros (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.

static SR2	ones (const TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.

static SR2	ones (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.

static SR2	full (Real init, const TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.

static SR2	full (const TraceableTensorShape &batch_shape, Real 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< SR2 >
static SR2	empty_like (const SR2 &other)

static SR2	zeros_like (const SR2 &other)
	Zero tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static SR2	ones_like (const SR2 &other)
	Unit tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static SR2	full_like (const SR2 &other, Real init)

static SR2	linspace (const SR2 &start, const SR2 &end, Size nstep, Size dim=0)
	Create a new tensor by adding a new batch dimension with linear spacing between `start` and `end`.

static SR2	logspace (const SR2 &start, const SR2 &end, Size nstep, Size dim=0, Real base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
Static Public Attributes inherited from PrimitiveTensor< SR2, 6 >
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.

Constructor & Destructor Documentation

◆ SR2()

SR2 ( const R2 & T )

Symmetrize an R2 then fill.

Member Function Documentation

◆ det()

Scalar det ( ) const

Determinant.

◆ dev()

SR2 dev ( ) const

Deviatoric part of the tensor.

◆ drotate() [1/2]

SFFR4 drotate ( const R2 & R ) const

◆ drotate() [2/2]

SFR3 drotate ( const Rot & r ) const

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

◆ fill() [1/6]

SR2 fill	(	const Real &	a,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

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

◆ fill() [2/6]

SR2 fill	(	const Real &	a11,
		const Real &	a22,
		const Real &	a33,
		const Real &	a23,
		const Real &	a13,
		const Real &	a12,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill all entries.

◆ fill() [3/6]

SR2 fill	(	const Real &	a11,
		const Real &	a22,
		const Real &	a33,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

Fill the diagonals with a11, a22, a33.

◆ fill() [4/6]

SR2 fill ( const Scalar & a )

staticnodiscard

◆ fill() [5/6]

SR2 fill	(	const Scalar &	a11,
		const Scalar &	a22,
		const Scalar &	a33 )

staticnodiscard

◆ fill() [6/6]

SR2 fill	(	const Scalar &	a11,
		const Scalar &	a22,
		const Scalar &	a33,
		const Scalar &	a23,
		const Scalar &	a13,
		const Scalar &	a12 )

staticnodiscard

◆ identity()

SR2 identity ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

Identity.

◆ identity_map()

SSR4 identity_map ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

The derivative of a SR2 with respect to itself.

◆ inner()

Scalar inner ( const SR2 & other ) const

Double contraction ij,ij.

◆ inverse()

SR2 inverse ( ) const

Inversion.

◆ norm()

Scalar norm ( Real eps = 0 ) const

Norm.

◆ norm_sq()

Scalar norm_sq ( ) const

Norm squared.

◆ operator()()

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

Accessor.

◆ outer()

SSR4 outer ( const SR2 & other ) const

Outer product ij,kl -> ijkl.

◆ rotate() [1/2]

SR2 rotate ( const R2 & R ) const

◆ rotate() [2/2]

SR2 rotate ( const Rot & r ) const

Rotate.

◆ tr()

Scalar tr ( ) const

Trace.

◆ transpose()

SR2 transpose ( ) const

Transpose, no-op.

◆ vol()

SR2 vol ( ) const

Volumetric part of the tensor.

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ SR2()

Member Function Documentation

◆ det()

◆ dev()

◆ 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()

◆ identity_map()

◆ inner()

◆ inverse()

◆ norm()

◆ norm_sq()

◆ operator()()

◆ outer()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ tr()

◆ transpose()

◆ vol()