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:

[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 (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.

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.

R2	inverse () const
	Inversion.

R2	transpose () const
	transpose

Public Member Functions inherited from PrimitiveTensor< R2, 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< R2 >
	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

R2	variable_data () const

R2	clone () const

R2	detach () const
	Discard function graph.

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

R2	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.

R2	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.

R2	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)

R2	batch_expand (const TraceableTensorShape &batch_shape) const

R2	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.

R2	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.

R2	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.

R2	batch_reshape (const TraceableTensorShape &batch_shape) const
	Reshape batch dimensions.

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

R2	batch_unsqueeze (Size d) const
	Unsqueeze a batch dimension.

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

R2	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 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 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	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 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 TensorOptions &options=default_tensor_options())
	Identity.

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

static R2	empty (const TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

static R2	empty (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.

static R2	zeros (const TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.

static R2	zeros (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.

static R2	ones (const TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.

static R2	ones (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.

static R2	full (const CScalar &init, const TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.

static R2	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< 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	linspace (const R2 &start, const R2 &end, Size nstep, Size dim=0)
	Create a new tensor by adding a new batch dimension with linear spacing between `start` and `end`.

static R2	logspace (const R2 &start, const R2 &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< R2, 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< R2 >
TraceableTensorShape	_batch_sizes
	Traceable batch sizes.

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 TensorOptions & options = default_tensor_options() )

staticnodiscard

The derivative of a R2 with respect to itself.

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ R2() [1/3]

◆ R2() [2/3]

◆ R2() [3/3]

Member Function Documentation

◆ identity_map()