The (logical) symmetric second order tensor. More...

Detailed Description

The (logical) symmetric second order tensor.

Mandel notation is used, and so the logical 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() (TorchSize i, TorchSize 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 FixedDimTensor< SR2, 6 >
	FixedDimTensor ()=default
	Default constructor.

	FixedDimTensor (const torch::Tensor &tensor, TorchSize batch_dim)
	Construct from another torch::Tensor given batch dimension.

	FixedDimTensor (const torch::Tensor &tensor)
	Construct from another torch::Tensor and infer batch dimension.

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

Public Member Functions inherited from BatchTensorBase< Derived >
	BatchTensorBase ()=default
	Default constructor.

	BatchTensorBase (const torch::Tensor &tensor, TorchSize batch_dim)
	Construct from another torch::Tensor.

	BatchTensorBase (const Derived &tensor)
	Copy constructor.

	BatchTensorBase (Real)=delete

bool	batched () const
	Whether the tensor is batched.

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

TorchSize &	batch_dim ()
	Return a writable reference to the batch dimension.

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

TorchShapeRef	batch_sizes () const
	Return the batch size.

TorchSize	batch_size (TorchSize index) const
	Return the length of some batch axis.

TorchShapeRef	base_sizes () const
	Return the base size.

TorchSize	base_size (TorchSize index) const
	Return the length of some base axis.

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

Derived	batch_index (TorchSlice indices) const
	Get a batch.

BatchTensor	base_index (const TorchSlice &indices) const
	Return an index sliced on the base dimensions.

void	batch_index_put (TorchSlice indices, const torch::Tensor &other)
	Set a index sliced on the batch dimensions to a value.

void	base_index_put (const TorchSlice &indices, const torch::Tensor &other)
	Set a index sliced on the base dimensions to a value.

Derived	batch_expand (TorchShapeRef batch_size) const
	Return a new view of the tensor with values broadcast along the batch dimensions.

BatchTensor	base_expand (TorchShapeRef base_size) const
	Return a new view of the tensor with values broadcast along the base dimensions.

template<class Derived2 >
Derived	batch_expand_as (const Derived2 &other) const
	Expand the batch to have the same shape as another tensor.

template<class Derived2 >
Derived2	base_expand_as (const Derived2 &other) const
	Expand the base to have the same shape as another tensor.

Derived	batch_expand_copy (TorchShapeRef batch_size) const
	Return a new tensor with values broadcast along the batch dimensions.

BatchTensor	base_expand_copy (TorchShapeRef base_size) const
	Return a new tensor with values broadcast along the base dimensions.

Derived	batch_reshape (TorchShapeRef batch_shape) const
	Reshape batch dimensions.

BatchTensor	base_reshape (TorchShapeRef base_shape) const
	Reshape base dimensions.

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

Derived	list_unsqueeze () const
	Unsqueeze on the special list batch dimension.

BatchTensor	base_unsqueeze (TorchSize d) const
	Unsqueeze a base dimension.

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

BatchTensor	base_transpose (TorchSize d1, TorchSize d2) const
	Transpose two base dimensions.

BatchTensor	base_movedim (TorchSize d1, TorchSize d2) const
	Move two base dimensions.

Derived	clone (torch::MemoryFormat memory_format=torch::MemoryFormat::Contiguous) const
	Clone (take ownership)

Derived	detach () const
	Discard function graph.

Derived	to (const torch::TensorOptions &options) const
	Send to options.

Derived	operator- () const
	Negation.

Derived	batch_sum (TorchSize d) const
	Sum on a batch index.

Derived	list_sum () const
	Sum on the list index (TODO: replace with class)

Static Public Member Functions
static SR2	fill (const Real &a, const torch::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 torch::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 torch::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 torch::TensorOptions &options=default_tensor_options())
	Identity.

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

Static Public Member Functions inherited from FixedDimTensor< SR2, 6 >
static SR2	empty (const torch::TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

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

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

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

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

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

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

static SR2	full (TorchShapeRef batch_shape, Real init, const torch::TensorOptions &options=default_tensor_options())
	Full tensor given batch shape.

static BatchTensor	identity_map (const torch::TensorOptions &)
	Derived tensor classes should define identity_map where appropriate.

Static Public Member Functions inherited from BatchTensorBase< Derived >
static Derived	empty_like (const Derived &other)
	Empty tensor like another, i.e. same batch and base shapes, same tensor options, etc.

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, Real init)

static Derived	linspace (const Derived &start, const Derived &end, TorchSize nstep, TorchSize dim=0, TorchSize batch_dim=-1)
	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, TorchSize nstep, TorchSize dim=0, TorchSize batch_dim=-1, Real base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
Static Public Attributes inherited from FixedDimTensor< SR2, 6 >
static const TorchShape	const_base_sizes
	The base shape.

static constexpr TorchSize	const_base_dim
	The base dim.

static const TorchSize	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 torch::TensorOptions &	options = default_tensor_options() )

static

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 torch::TensorOptions &	options = default_tensor_options() )

static

Fill all entries.

◆ fill() [3/6]

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

static

Fill the diagonals with a11, a22, a33.

◆ fill() [4/6]

SR2 fill ( const Scalar & a )

static

◆ fill() [5/6]

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

static

◆ fill() [6/6]

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

static

◆ identity()

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

static

Identity.

◆ identity_map()

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

static

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()	(	TorchSize	i,
		TorchSize	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()