The symmetric fourth order tensor, with symmetry in the first two dimensionss as well as in the last two dimensions. More...

Detailed Description

The symmetric fourth order tensor, with symmetry in the first two dimensionss as well as in the last two dimensions.

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

#include <SSR4.h>

Inheritance diagram for SSR4:

[legend]

Public Member Functions
	SSR4 (const R4 &T)
	Initialize with the symmetrized fourth order tensor.

SSR4	rotate (const Rot &r) const
	Rotate.

SSFR5	drotate (const Rot &r) const
	Derivative of the rotated tensor w.r.t. the Rodrigues vector.

SSSSR8	drotate_self (const Rot &r) const
	Derivative of the rotated tensor w.r.t. itself.

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

SSR4	inverse () const
	Inversion.

SSSSR8	dinverse () const
	Derivative of inverse with respect to self.

SSR4	transpose_minor () const
	Transpose minor axes, no-op.

SSR4	transpose_major () const
	Transpose major axes.

Public Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
	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.

	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 SSR4	identity (const torch::TensorOptions &options=default_tensor_options())
	Create the identity tensor \(\delta_{ij}\delta_{kl}\).

static SSR4	identity_sym (const torch::TensorOptions &options=default_tensor_options())
	Create the symmetric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2\).

static SSR4	identity_vol (const torch::TensorOptions &options=default_tensor_options())
	Create the volumetric identity tensor \(\delta_{ij}\delta_{kl}/3\).

static SSR4	identity_dev (const torch::TensorOptions &options=default_tensor_options())
	Create the deviatoric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2 - \delta_{ij}\delta_{kl}/3\).

static SSR4	identity_C1 (const torch::TensorOptions &options=default_tensor_options())
	Building block for C1 constant.

static SSR4	identity_C2 (const torch::TensorOptions &options=default_tensor_options())
	Building block for C2 constant.

static SSR4	identity_C3 (const torch::TensorOptions &options=default_tensor_options())
	Building block for C3 constant.

static SSR4	isotropic_E_nu (const Scalar &E, const Scalar &nu)
	Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

static SSR4	isotropic_E_nu (const Real &E, const Real &nu, const torch::TensorOptions &options=default_tensor_options())
	Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

static SSR4	fill_C1_C2_C3 (const Scalar &C1, const Scalar &C2, const Scalar &C3)
	Create the fourth order elasticity tensor given the three non-zero coefficients.

static SSR4	fill_C1_C2_C3 (const Real &C1, const Real &C2, const Real &C3, const torch::TensorOptions &options=default_tensor_options())
	Create the fourth order elasticity tensor given the three non-zero coefficients.

static SSSSR8	identity_map (const torch::TensorOptions &options=default_tensor_options())
	The derivative of a SSR4 with respect to itself.

Static Public Member Functions inherited from PrimitiveTensor< SSR4, 6, 6 >
static SSR4	empty (const torch::TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

static SSR4	empty (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.

static SSR4	zeros (const torch::TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.

static SSR4	zeros (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.

static SSR4	ones (const torch::TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.

static SSR4	ones (const TraceableTensorShape &batch_shape, const torch::TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.

static SSR4	full (Real init, const torch::TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.

static SSR4	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< SSR4, 6, 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

◆ SSR4()

SSR4 ( const R4 & T )

Initialize with the symmetrized fourth order tensor.

Member Function Documentation

◆ dinverse()

SSSSR8 dinverse ( ) const

Derivative of inverse with respect to self.

◆ drotate()

SSFR5 drotate ( const Rot & r ) const

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

◆ drotate_self()

SSSSR8 drotate_self ( const Rot & r ) const

Derivative of the rotated tensor w.r.t. itself.

◆ fill_C1_C2_C3() [1/2]

SSR4 fill_C1_C2_C3	(	const Real &	C1,
		const Real &	C2,
		const Real &	C3,
		const torch::TensorOptions &	options = default_tensor_options() )

static

Create the fourth order elasticity tensor given the three non-zero coefficients.

◆ fill_C1_C2_C3() [2/2]

SSR4 fill_C1_C2_C3	(	const Scalar &	C1,
		const Scalar &	C2,
		const Scalar &	C3 )

static

Create the fourth order elasticity tensor given the three non-zero coefficients.

◆ identity()

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

static

Create the identity tensor \(\delta_{ij}\delta_{kl}\).

◆ identity_C1()

SSR4 identity_C1 ( const torch::TensorOptions & options = default_tensor_options() )

static

Building block for C1 constant.

◆ identity_C2()

SSR4 identity_C2 ( const torch::TensorOptions & options = default_tensor_options() )

static

Building block for C2 constant.

◆ identity_C3()

SSR4 identity_C3 ( const torch::TensorOptions & options = default_tensor_options() )

static

Building block for C3 constant.

◆ identity_dev()

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

static

Create the deviatoric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2 - \delta_{ij}\delta_{kl}/3\).

◆ identity_map()

SSSSR8 identity_map ( const torch::TensorOptions & options = default_tensor_options() )

static

The derivative of a SSR4 with respect to itself.

◆ identity_sym()

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

static

Create the symmetric identity tensor \(\delta_{ik}\delta_{jl}/2 + \delta_{il}\delta_{jk}/2\).

◆ identity_vol()

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

static

Create the volumetric identity tensor \(\delta_{ij}\delta_{kl}/3\).

◆ inverse()

SSR4 inverse ( ) const

Inversion.

◆ isotropic_E_nu() [1/2]

SSR4 isotropic_E_nu	(	const Real &	E,
		const Real &	nu,
		const torch::TensorOptions &	options = default_tensor_options() )

static

Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

◆ isotropic_E_nu() [2/2]

SSR4 isotropic_E_nu	(	const Scalar &	E,
		const Scalar &	nu )

static

Create the fourth order elasticity tensor given the Young's modulus and the Poisson's ratio.

◆ operator()()

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

Accessor.

◆ rotate()

SSR4 rotate ( const Rot & r ) const

Rotate.

◆ transpose_major()

SSR4 transpose_major ( ) const

Transpose major axes.

◆ transpose_minor()

SSR4 transpose_minor ( ) const

Transpose minor axes, no-op.

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ SSR4()

Member Function Documentation

◆ dinverse()

◆ drotate()

◆ drotate_self()

◆ fill_C1_C2_C3() [1/2]

◆ fill_C1_C2_C3() [2/2]

◆ identity()

◆ identity_C1()

◆ identity_C2()

◆ identity_C3()

◆ identity_dev()

◆ identity_map()

◆ identity_sym()

◆ identity_vol()

◆ inverse()

◆ isotropic_E_nu() [1/2]

◆ isotropic_E_nu() [2/2]

◆ operator()()

◆ rotate()

◆ transpose_major()

◆ transpose_minor()