R2 Class Reference

Second order tensor without symmetry. More...

Detailed Description

Second order tensor without symmetry.

The storage space is (3,3).

#include <R2.h>

Inheritance diagram for R2:

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 (const Rot &r)
	Form rotation matrix from vector.
Public Member Functions inherited from R2Base< R2 >
	operator SR2 () const
	Conversion operator to symmetric second order 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.
Scalar	operator() (Size i, Size j) const
	Accessor.
R2	inverse () const
	Inversion.
R2	transpose () const
	transpose
Public Member Functions inherited from PrimitiveTensor< Derived, S >
	PrimitiveTensor ()=default
	Default constructor.
	PrimitiveTensor (const torch::Tensor &tensor, Size batch_dim)
	Construct from another torch::Tensor given batch dimension.
	PrimitiveTensor (const torch::Tensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another torch::Tensor given batch shape.
template<class Derived2 >
	PrimitiveTensor (const TensorBase< Derived2 > &tensor)
	Copy constructor.
	PrimitiveTensor (const torch::Tensor &tensor)
	Construct from another torch::Tensor 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
	Default constructor.
	TensorBase (const torch::Tensor &tensor, Size batch_dim)
	Construct from another torch::Tensor with given batch dimension.
	TensorBase (const torch::Tensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another torch::Tensor with given batch shape.
template<class Derived2 >
	TensorBase (const TensorBase< Derived2 > &tensor)
	Copy constructor.
	TensorBase (Real)=delete
Derived	variable_data () const
Derived	clone (torch::MemoryFormat memory_format=torch::MemoryFormat::Contiguous) const
Derived	detach () const
	Discard function graph.
Derived	to (const torch::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.
void	batch_index_put_ (indexing::TensorIndicesRef indices, const torch::Tensor &other)
void	batch_index_put_ (indexing::TensorIndicesRef indices, Real v)
void	base_index_put_ (indexing::TensorIndicesRef indices, const torch::Tensor &other)
void	base_index_put_ (indexing::TensorIndicesRef indices, Real 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.
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 (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 R4	identity_map (const torch::TensorOptions &options=default_tensor_options())
	The derivative of a R2 with respect to itself.
Static Public Member Functions inherited from R2Base< R2 >
static R2	fill (const Real &a, const torch::TensorOptions &options=default_tensor_options())
	Fill the diagonals with a11 = a22 = a33 = a.
static R2	fill (const Scalar &a)
static R2	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 R2	fill (const Scalar &a11, const Scalar &a22, const Scalar &a33)
static R2	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 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	fill (const Real &a11, const Real &a12, const Real &a13, const Real &a21, const Real &a22, const Real &a23, const Real &a31, const Real &a32, const Real &a33, const torch::TensorOptions &options=default_tensor_options())
	Fill all entries.
static R2	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 R2	skew (const Vec &v)
	Skew matrix from Vec.
static R2	identity (const torch::TensorOptions &options=default_tensor_options())
	Identity.
Static Public Member Functions inherited from PrimitiveTensor< Derived, S >
static Derived	empty (const torch::TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.
static Derived	empty (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.
static Derived	zeros (const torch::TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.
static Derived	zeros (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.
static Derived	ones (const torch::TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.
static Derived	ones (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.
static Derived	full (Real init, const torch::TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.
static Derived	full (const TraceableTensorShape &batch_shape, Real init, const torch::TensorOptions &options=default_tensor_options())
	Full tensor given batch shape.
static Tensor	identity_map (const torch::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)
	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, 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, Real base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
Static Public Attributes inherited from PrimitiveTensor< Derived, S >
static const TensorShape	const_base_sizes = {S...}
	The base shape.
static constexpr Size	const_base_dim = sizeof...(S)
	The base dim.
static const Size	const_base_storage = utils::storage_size({S...})
	The base storage.

Constructor & Destructor Documentation

R2() [1/3]

R2

(

const SR2 &

S

)

Form a full R2 from a symmetric tensor.

Parameters

S	Mandel-convention symmetric tensor

R2() [2/3]

R2

(

const WR2 &

W

)

Form a full R2 from a skew-symmetric tensor.

Parameters

W	skew-vector convention skew-symmetric tensor

R2() [3/3]

R2 ( const Rot & r )

explicit

Form rotation matrix from vector.

Parameters

r	rotation vector

Member Function Documentation

identity_map()

R4 identity_map ( const torch::TensorOptions & options = default_tensor_options() )

static

The derivative of a R2 with respect to itself.