mrpro.data.Rotation

class mrpro.data.Rotation(quaternions: torch.Tensor | NestedSequence[float], normalize: bool = True, copy: bool = True)[source]

Bases: Module

A container for Rotations.

A pytorch implementation of scipy.spatial.transform.Rotation. For more information see the scipy documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.transform.Rotation.html

Differences compared to scipy.spatial.transform.Rotation:

torch.nn.Module based, the quaternions are a Parameter
.apply is replaced by call/forward.
not all features are implemented. Notably, mrp, davenport, and reduce are missing.
arbitrary number of batching dimensions

__init__(quaternions: torch.Tensor | NestedSequence[float], normalize: bool = True, copy: bool = True)[source]

Initialize a new Rotation.

Instead of calling this method, also consider the different from_* class methods to construct a Rotation.

Parameters:

quaternions – Rotatation quaternions. If these requires_grad, the resulting Rotation will require gradients
normalize – If the quaternions should be normalized. Only disable if you are sure the quaternions are already normalized
copy – Always ensure that a copy of the quaternions is created. If both normalize and copy are False, the quaternions Parameter of this instance will be a view if the quaternions passed in.

Methods

`__init__`(quaternions[, normalize, copy])	Initialize a new Rotation.
`add_module`(name, module)	Add a child module to the current module.
`align_vectors`()	Estimate a rotation to optimally align two sets of vectors.
`apply`(fn)	Apply `fn` recursively to every submodule (as returned by `.children()`) as well as self.
`approx_equal`(other[, atol, degrees])	Determine if another rotation is approximately equal to this one.
`as_davenport`(axes, order[, degrees])	Not implemented.
`as_euler`(seq[, degrees])	Represent as Euler angles.
`as_matrix`()	Represent as rotation matrix.
`as_mrp`()	Not implemented.
`as_quat`([canonical])	Represent as quaternions.
`as_rotvec`([degrees])	Represent as rotation vectors.
`bfloat16`()	Casts all floating point parameters and buffers to `bfloat16` datatype.
`buffers`([recurse])	Return an iterator over module buffers.
`children`()	Return an iterator over immediate children modules.
`compile`(args, *kwargs)	Compile this Module's forward using `torch.compile()`.
`concatenate`(rotations)	Concatenate a sequence of Rotation objects into a single object.
`cpu`()	Move all model parameters and buffers to the CPU.
`cuda`([device])	Move all model parameters and buffers to the GPU.
`double`()	Casts all floating point parameters and buffers to `double` datatype.
`eval`()	Set the module in evaluation mode.
`extra_repr`()	Set the extra representation of the module.
`float`()	Casts all floating point parameters and buffers to `float` datatype.
`forward`(vectors[, inverse])	Apply this rotation to a set of vectors.
`from_davenport`(axes, order, angles[, degrees])	Not implemented.
`from_euler`(seq, angles[, degrees])	Initialize from Euler angles.
`from_matrix`(matrix)	Initialize from rotation matrix.
`from_mrp`(mrp)	Not implemented.
`from_quat`(quaternions)	Initialize from quaternions.
`from_rotvec`(rotvec[, degrees])	Initialize from rotation vector.
`get_buffer`(target)	Return the buffer given by `target` if it exists, otherwise throw an error.
`get_extra_state`()	Return any extra state to include in the module's state_dict.
`get_parameter`(target)	Return the parameter given by `target` if it exists, otherwise throw an error.
`get_submodule`(target)	Return the submodule given by `target` if it exists, otherwise throw an error.
`half`()	Casts all floating point parameters and buffers to `half` datatype.
`identity`([shape])	Get identity rotation(s).
`inv`()	Invert this rotation.
`ipu`([device])	Move all model parameters and buffers to the IPU.
`load_state_dict`(state_dict[, strict, assign])	Copy parameters and buffers from `state_dict` into this module and its descendants.
`magnitude`()	Get the magnitude(s) of the rotation(s).
`mean`([weights, dim, keepdim])	Get the mean of the rotations.
`modules`()	Return an iterator over all modules in the network.
`named_buffers`([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
`named_children`()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
`named_modules`([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
`named_parameters`([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
`parameters`([recurse])	Return an iterator over module parameters.
`random`([num, random_state])	Generate uniformly distributed rotations.
`register_backward_hook`(hook)	Register a backward hook on the module.
`register_buffer`(name, tensor[, persistent])	Add a buffer to the module.
`register_forward_hook`(hook, *[, prepend, ...])	Register a forward hook on the module.
`register_forward_pre_hook`(hook, *[, ...])	Register a forward pre-hook on the module.
`register_full_backward_hook`(hook[, prepend])	Register a backward hook on the module.
`register_full_backward_pre_hook`(hook[, prepend])	Register a backward pre-hook on the module.
`register_load_state_dict_post_hook`(hook)	Register a post hook to be run after module's `load_state_dict` is called.
`register_module`(name, module)	Alias for `add_module()`.
`register_parameter`(name, param)	Add a parameter to the module.
`register_state_dict_pre_hook`(hook)	Register a pre-hook for the `state_dict()` method.
`requires_grad_`([requires_grad])	Change if autograd should record operations on parameters in this module.
`set_extra_state`(state)	Set extra state contained in the loaded state_dict.
`share_memory`()	See `torch.Tensor.share_memory_()`.
`state_dict`(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
`to`(args, *kwargs)	Move and/or cast the parameters and buffers.
`to_empty`(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
`train`([mode])	Set the module in training mode.
`type`(dst_type)	Casts all parameters and buffers to `dst_type`.
`xpu`([device])	Move all model parameters and buffers to the XPU.
`zero_grad`([set_to_none])	Reset gradients of all model parameters.

Attributes

`T_destination`
`call_super_init`
`dump_patches`
`quaternion_w`	Get w component of the quaternion.
`quaternion_x`	Get x component of the quaternion.
`quaternion_y`	Get y component of the quaternion.
`quaternion_z`	Get z component of the quaternion.
`shape`	Return the batch shape of the Rotation.
`single`	Returns true if this a single rotation.
`training`

add_module(name: str, module: Module | None) → None

Add a child module to the current module.

The module can be accessed as an attribute using the given name.

Parameters:

name (str) – name of the child module. The child module can be accessed from this module using the given name
module (Module) – child module to be added to the module.

Estimate a rotation to optimally align two sets of vectors.

For more information, see scipy.spatial.transform.Rotation.align_vectors. This will move to cpu, invoke scipy, convert to tensor, move back to device of a.

apply(fn: Callable[[Module], None]) → T

Apply fn recursively to every submodule (as returned by .children()) as well as self.

Typical use includes initializing the parameters of a model (see also nn-init-doc).

Parameters:: fn (Module -> None) – function to be applied to each submodule
Returns:: self
Return type:: Module

Example:

>>> @torch.no_grad()
>>> def init_weights(m):
>>>     print(m)
>>>     if type(m) == nn.Linear:
>>>         m.weight.fill_(1.0)
>>>         print(m.weight)
>>> net = nn.Sequential(nn.Linear(2, 2), nn.Linear(2, 2))
>>> net.apply(init_weights)
Linear(in_features=2, out_features=2, bias=True)
Parameter containing:
tensor([[1., 1.],
        [1., 1.]], requires_grad=True)
Linear(in_features=2, out_features=2, bias=True)
Parameter containing:
tensor([[1., 1.],
        [1., 1.]], requires_grad=True)
Sequential(
  (0): Linear(in_features=2, out_features=2, bias=True)
  (1): Linear(in_features=2, out_features=2, bias=True)
)

approx_equal(other: Rotation, atol: float = 1e-06, degrees: bool = False) → Tensor[source]

Determine if another rotation is approximately equal to this one.

Equality is measured by calculating the smallest angle between the rotations, and checking to see if it is smaller than atol.

Parameters:

other – Object containing the rotations to measure against this one.
atol – The absolute angular tolerance, below which the rotations are considered equal.
degrees – If True and atol is given, then atol is measured in degrees. If False (default), then atol is measured in radians.

Returns:

Whether the rotations are approximately equal, bool if object contains a single rotation and Tensor if object contains multiple rotations.

Return type:

approx_equal

as_davenport(axes: Tensor, order: str, degrees: bool = False) → Tensor[source]: Not implemented.

as_euler(seq: str, degrees: bool = False) → Tensor[source]

Represent as Euler angles.

Any orientation can be expressed as a composition of 3 elementary rotations. Once the axis sequence has been chosen, Euler angles define the angle of rotation around each respective axis [EULb].

The algorithm from [BER2022] has been used to calculate Euler angles for the rotation about a given sequence of axes.

Euler angles suffer from the problem of gimbal lock [GIM], where the representation loses a degree of freedom and it is not possible to determine the first and third angles uniquely. In this case, a warning is raised, and the third angle is set to zero. Note however that the returned angles still represent the correct rotation.

Parameters:

seq – 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations [EULb]. Adjacent axes cannot be the same. Extrinsic and intrinsic rotations cannot be mixed in one function call.
degrees – Returned angles are in degrees if this flag is True, else they are in radians

Returns:

shape (3,) or (…, 3), depending on shape of inputs used to initialize object. The returned angles are in the range:

First angle belongs to [-180, 180] degrees (both inclusive)
Third angle belongs to [-180, 180] degrees (both inclusive)
Second angle belongs to:

[-90, 90] degrees if all axes are different (like xyz)

[0, 180] degrees if first and third axes are the same (like zxz)

Return type:

angles

References

[EULb] (1,2)

Euler Angles https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations

[BER2022]

Bernardes E, Viollet S (2022) Quaternion to Euler angles conversion: A direct, general and computationally efficient method. PLoS ONE 17(11) https://doi.org/10.1371/journal.pone.0276302

[GIM]

Gimbal lock https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics

as_matrix() → Tensor[source]

Represent as rotation matrix.

3D rotations can be represented using rotation matrices, which are 3 x 3 real orthogonal matrices with determinant equal to +1 [ROTb].

Returns:: shape (…, 3, 3), depends on shape of inputs used for initialization.
Return type:: matrix

References

[ROTb]

Rotation matrix https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions

as_mrp() → Tensor[source]: Not implemented.

as_quat(canonical: bool = False) → Tensor[source]

Represent as quaternions.

Active rotations in 3 dimensions can be represented using unit norm quaternions [QUAb]. The mapping from quaternions to rotations is two-to-one, i.e. quaternions q and -q, where -q simply reverses the sign of each component, represent the same spatial rotation. The returned value is in scalar-last (x, y, z, w) format.

Parameters:: canonical – Whether to map the redundant double cover of rotation space to a unique “canonical” single cover. If True, then the quaternion is chosen from {q, -q} such that the w term is positive. If the w term is 0, then the quaternion is chosen such that the first nonzero term of the x, y, and z terms is positive.
Returns:: shape (…, 4,), depends on shape of inputs used for initialization.
Return type:: quaternions

References

[QUAb]

Quaternions https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

as_rotvec(degrees: bool = False) → Tensor[source]

Represent as rotation vectors.

A rotation vector is a 3 dimensional vector which is co-directional to the axis of rotation and whose norm gives the angle of rotation [ROTc].

Parameters:: degrees – Returned magnitudes are in degrees if this flag is True, else they are in radians
Returns:: Shape (…, 3), depends on shape of inputs used for initialization.
Return type:: rotvec

References

[ROTc]

Rotation vector https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation#Rotation_vector

bfloat16() → T

Casts all floating point parameters and buffers to bfloat16 datatype.

Note

This method modifies the module in-place.

Returns:: self
Return type:: Module

buffers(recurse: bool = True) → Iterator[Tensor]

Return an iterator over module buffers.

Parameters:: recurse (bool) – if True, then yields buffers of this module and all submodules. Otherwise, yields only buffers that are direct members of this module.
Yields:: torch.Tensor – module buffer

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> for buf in model.buffers():
>>>     print(type(buf), buf.size())
<class 'torch.Tensor'> (20L,)
<class 'torch.Tensor'> (20L, 1L, 5L, 5L)

children() → Iterator[Module]

Return an iterator over immediate children modules.

Yields:: Module – a child module

compile(*args, **kwargs)

Compile this Module’s forward using torch.compile().

This Module’s __call__ method is compiled and all arguments are passed as-is to torch.compile().

See torch.compile() for details on the arguments for this function.

classmethod concatenate(rotations: Sequence[Rotation]) → Self[source]

Concatenate a sequence of Rotation objects into a single object.

Parameters:: rotations – The rotations to concatenate.
Returns:: The concatenated rotations.
Return type:: concatenated

cpu() → T

Move all model parameters and buffers to the CPU.

Note

This method modifies the module in-place.

Returns:: self
Return type:: Module

cuda(device: int | device | None = None) → T

Move all model parameters and buffers to the GPU.

This also makes associated parameters and buffers different objects. So it should be called before constructing optimizer if the module will live on GPU while being optimized.

Note

This method modifies the module in-place.

Parameters:: device (int, optional) – if specified, all parameters will be copied to that device
Returns:: self
Return type:: Module

double() → T

Casts all floating point parameters and buffers to double datatype.

Note

This method modifies the module in-place.

Returns:: self
Return type:: Module

eval() → T

Set the module in evaluation mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

This is equivalent with self.train(False).

See locally-disable-grad-doc for a comparison between .eval() and several similar mechanisms that may be confused with it.

Returns:: self
Return type:: Module

extra_repr() → str

Set the extra representation of the module.

To print customized extra information, you should re-implement this method in your own modules. Both single-line and multi-line strings are acceptable.

float() → T

Casts all floating point parameters and buffers to float datatype.

Note

This method modifies the module in-place.

Returns:: self
Return type:: Module

forward(vectors: NestedSequence[float] | torch.Tensor | SpatialDimension[torch.Tensor] | SpatialDimension[float], inverse: bool = False) → torch.Tensor | SpatialDimension[torch.Tensor][source]

Apply this rotation to a set of vectors.

If the original frame rotates to the final frame by this rotation, then its application to a vector can be seen in two ways:

As a projection of vector components expressed in the final frame to the original frame.
As the physical rotation of a vector being glued to the original frame as it rotates. In this case the vector components are expressed in the original frame before and after the rotation.

In terms of rotation matrices, this application is the same as self.as_matrix() @ vectors.

Parameters:

vectors – Shape(…, 3). Each vectors[i] represents a vector in 3D space. A single vector can either be specified with shape (3, ) or (1, 3). The number of rotations and number of vectors given must follow standard pytorch broadcasting rules.
inverse – If True then the inverse of the rotation(s) is applied to the input vectors.

Returns:

Result of applying rotation on input vectors. Shape depends on the following cases:

If object contains a single rotation (as opposed to a stack with a single rotation) and a single vector is specified with shape (3,), then rotated_vectors has shape (3,).

In all other cases, rotated_vectors has shape (..., 3), where ... is determined by broadcasting.

Return type:

rotated_vectors

classmethod from_davenport(axes: Tensor, order: str, angles: Tensor, degrees: bool = False)[source]: Not implemented.

classmethod from_euler(seq: str, angles: torch.Tensor | NestedSequence[float] | float, degrees: bool = False) → Self[source]

Initialize from Euler angles.

Rotations in 3-D can be represented by a sequence of 3 rotations around a sequence of axes. In theory, any three axes spanning the 3-D Euclidean space are enough. In practice, the axes of rotation are chosen to be the basis vectors.

The three rotations can either be in a global frame of reference (extrinsic) or in a body centred frame of reference (intrinsic), which is attached to, and moves with, the object under rotation [EULa].

Parameters:

seq – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
angles – (…, [1 or 2 or 3]), matching the number of axes in seq. Euler angles specified in radians (degrees is False) or degrees (degrees is True).
degrees – If True, then the given angles are assumed to be in degrees. Otherwise they are assumed to be in radians

Returns:

Object containing the rotation represented by the sequence of rotations around given axes with given angles.

Return type:

rotation

References

[EULa]

Euler angles https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations

classmethod from_matrix(matrix: torch.Tensor | NestedSequence[float]) → Self[source]

Initialize from rotation matrix.

Rotations in 3 dimensions can be represented with 3 x 3 proper orthogonal matrices [ROTa]. If the input is not proper orthogonal, an approximation is created using the method described in [MAR2008].

Parameters:: matrix – A single matrix or a stack of matrices, shape (…, 3, 3)
Returns:: Object containing the rotations represented by the rotation matrices.
Return type:: rotation

References

[ROTa]

Rotation matrix https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions

[MAR2008]

Landis Markley F (2008) Unit Quaternion from Rotation Matrix, Journal of guidance, control, and dynamics 31(2),440-442.

classmethod from_mrp(mrp: Tensor) → Self[source]: Not implemented.

classmethod from_quat(quaternions: torch.Tensor | NestedSequence[float]) → Self[source]

Initialize from quaternions.

3D rotations can be represented using unit-norm quaternions [QUAa].

Parameters:: quaternions – shape (…, 4) Each row is a (possibly non-unit norm) quaternion representing an active rotation, in scalar-last (x, y, z, w) format. Each quaternion will be normalized to unit norm.
Returns:: Object containing the rotations represented by input quaternions.
Return type:: rotation

References

[QUAa]

Quaternions and spatial rotation https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

classmethod from_rotvec(rotvec: torch.Tensor | NestedSequence[float], degrees: bool = False) → Self[source]

Initialize from rotation vector.

A rotation vector is a 3 dimensional vector which is co-directional to the axis of rotation and whose norm gives the angle of rotation.

Parameters:

rotvec – shape (…, 3), the rotation vectors.
degrees – If True, then the given angles are assumed to be in degrees, otherwise radians.

get_buffer(target: str) → Tensor

Return the buffer given by target if it exists, otherwise throw an error.

See the docstring for get_submodule for a more detailed explanation of this method’s functionality as well as how to correctly specify target.

Parameters:: target – The fully-qualified string name of the buffer to look for. (See get_submodule for how to specify a fully-qualified string.)
Returns:: The buffer referenced by target
Return type:: torch.Tensor
Raises:: AttributeError – If the target string references an invalid path or resolves to something that is not a buffer

get_extra_state() → Any

Return any extra state to include in the module’s state_dict.

Implement this and a corresponding set_extra_state() for your module if you need to store extra state. This function is called when building the module’s state_dict().

Note that extra state should be picklable to ensure working serialization of the state_dict. We only provide provide backwards compatibility guarantees for serializing Tensors; other objects may break backwards compatibility if their serialized pickled form changes.

Returns:: Any extra state to store in the module’s state_dict
Return type:: object

get_parameter(target: str) → Parameter

Return the parameter given by target if it exists, otherwise throw an error.

See the docstring for get_submodule for a more detailed explanation of this method’s functionality as well as how to correctly specify target.

Parameters:: target – The fully-qualified string name of the Parameter to look for. (See get_submodule for how to specify a fully-qualified string.)
Returns:: The Parameter referenced by target
Return type:: torch.nn.Parameter
Raises:: AttributeError – If the target string references an invalid path or resolves to something that is not an nn.Parameter

get_submodule(target: str) → Module

Return the submodule given by target if it exists, otherwise throw an error.

For example, let’s say you have an nn.Module A that looks like this:

A(
    (net_b): Module(
        (net_c): Module(
            (conv): Conv2d(16, 33, kernel_size=(3, 3), stride=(2, 2))
        )
        (linear): Linear(in_features=100, out_features=200, bias=True)
    )
)

(The diagram shows an nn.Module A. A has a nested submodule net_b, which itself has two submodules net_c and linear. net_c then has a submodule conv.)

To check whether or not we have the linear submodule, we would call get_submodule("net_b.linear"). To check whether we have the conv submodule, we would call get_submodule("net_b.net_c.conv").

The runtime of get_submodule is bounded by the degree of module nesting in target. A query against named_modules achieves the same result, but it is O(N) in the number of transitive modules. So, for a simple check to see if some submodule exists, get_submodule should always be used.

Parameters:: target – The fully-qualified string name of the submodule to look for. (See above example for how to specify a fully-qualified string.)
Returns:: The submodule referenced by target
Return type:: torch.nn.Module
Raises:: AttributeError – If the target string references an invalid path or resolves to something that is not an nn.Module

half() → T

Casts all floating point parameters and buffers to half datatype.

Note

This method modifies the module in-place.

Returns:: self
Return type:: Module

classmethod identity(shape: int | None | tuple[int, ...] = None) → Self[source]

Get identity rotation(s).

Composition with the identity rotation has no effect.

Parameters:: shape – Number of identity rotations to generate. If None (default), then a single rotation is generated.
Returns:: identity – The identity rotation.
Return type:: Rotation object

inv() → Self[source]

Invert this rotation.

Composition of a rotation with its inverse results in an identity transformation.

Returns:: Object containing inverse of the rotations in the current instance.
Return type:: inverse

ipu(device: int | device | None = None) → T

Move all model parameters and buffers to the IPU.

This also makes associated parameters and buffers different objects. So it should be called before constructing optimizer if the module will live on IPU while being optimized.

Note

This method modifies the module in-place.

Parameters:: device (int, optional) – if specified, all parameters will be copied to that device
Returns:: self
Return type:: Module

load_state_dict(state_dict: Mapping[str, Any], strict: bool = True, assign: bool = False)

Copy parameters and buffers from state_dict into this module and its descendants.

If strict is True, then the keys of state_dict must exactly match the keys returned by this module’s state_dict() function.

Warning

If assign is True the optimizer must be created after the call to load_state_dict unless get_swap_module_params_on_conversion() is True.

Parameters:

state_dict (dict) – a dict containing parameters and persistent buffers.
strict (bool, optional) – whether to strictly enforce that the keys in state_dict match the keys returned by this module’s state_dict() function. Default: True
assign (bool, optional) – When False, the properties of the tensors in the current module are preserved while when True, the properties of the Tensors in the state dict are preserved. The only exception is the requires_grad field of Default: ``False`

Returns:

missing_keys is a list of str containing any keys that are expected
by this module but missing from the provided state_dict.
unexpected_keys is a list of str containing the keys that are not
expected by this module but present in the provided state_dict.

Return type:

NamedTuple with missing_keys and unexpected_keys fields

Note

If a parameter or buffer is registered as None and its corresponding key exists in state_dict, load_state_dict() will raise a RuntimeError.

magnitude() → Tensor[source]

Get the magnitude(s) of the rotation(s).

Returns:: Angles in radians. The magnitude will always be in the range [0, pi].
Return type:: magnitude

mean(weights: torch.Tensor | NestedSequence[float] | None = None, dim: None | int | Sequence[int] = None, keepdim: bool = False) → Self[source]

Get the mean of the rotations.

The mean used is the chordal L2 mean (also called the projected or induced arithmetic mean) [HAR2013]. If A is a set of rotation matrices, then the mean M is the rotation matrix that minimizes the following loss function: \(L(M) = \sum_{i = 1}^{n} w_i \lVert \mathbf{A}_i - \mathbf{M} \rVert^2\),

where \(w_i\)’s are the weights corresponding to each matrix.

Optionally, if A is a set of Rotation matrices with multiple batch dimensions, the dimensions to reduce over can be specified.

Parameters:

weights – Weights describing the relative importance of the rotations. If None (default), then all values in weights are assumed to be equal.
dim – Batch Dimensions to reduce over. None will always return a single Rotation.
keepdim – Keep reduction dimensions as length-1 dimensions.

Returns:

mean – Object containing the mean of the rotations in the current instance.

Return type:

Rotation instance

References

[HAR2013]

Hartley R, Li H (2013) Rotation Averaging. International Journal of Computer Vision (103) https://link.springer.com/article/10.1007/s11263-012-0601-0

modules() → Iterator[Module]

Return an iterator over all modules in the network.

Yields:: Module – a module in the network

Note

Duplicate modules are returned only once. In the following example, l will be returned only once.

Example:

>>> l = nn.Linear(2, 2)
>>> net = nn.Sequential(l, l)
>>> for idx, m in enumerate(net.modules()):
...     print(idx, '->', m)

0 -> Sequential(
  (0): Linear(in_features=2, out_features=2, bias=True)
  (1): Linear(in_features=2, out_features=2, bias=True)
)
1 -> Linear(in_features=2, out_features=2, bias=True)

named_buffers(prefix: str = '', recurse: bool = True, remove_duplicate: bool = True) → Iterator[Tuple[str, Tensor]]

Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.

Parameters:

prefix (str) – prefix to prepend to all buffer names.
recurse (bool, optional) – if True, then yields buffers of this module and all submodules. Otherwise, yields only buffers that are direct members of this module. Defaults to True.
remove_duplicate (bool, optional) – whether to remove the duplicated buffers in the result. Defaults to True.

Yields:

(str, torch.Tensor) – Tuple containing the name and buffer

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> for name, buf in self.named_buffers():
>>>     if name in ['running_var']:
>>>         print(buf.size())

named_children() → Iterator[Tuple[str, Module]]

Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.

Yields:: (str, Module) – Tuple containing a name and child module

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> for name, module in model.named_children():
>>>     if name in ['conv4', 'conv5']:
>>>         print(module)

named_modules(memo: Set[Module] | None = None, prefix: str = '', remove_duplicate: bool = True)

Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.

Parameters:

memo – a memo to store the set of modules already added to the result
prefix – a prefix that will be added to the name of the module
remove_duplicate – whether to remove the duplicated module instances in the result or not

Yields:

(str, Module) – Tuple of name and module

Note

Duplicate modules are returned only once. In the following example, l will be returned only once.

Example:

>>> l = nn.Linear(2, 2)
>>> net = nn.Sequential(l, l)
>>> for idx, m in enumerate(net.named_modules()):
...     print(idx, '->', m)

0 -> ('', Sequential(
  (0): Linear(in_features=2, out_features=2, bias=True)
  (1): Linear(in_features=2, out_features=2, bias=True)
))
1 -> ('0', Linear(in_features=2, out_features=2, bias=True))

named_parameters(prefix: str = '', recurse: bool = True, remove_duplicate: bool = True) → Iterator[Tuple[str, Parameter]]

Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.

Parameters:

prefix (str) – prefix to prepend to all parameter names.
recurse (bool) – if True, then yields parameters of this module and all submodules. Otherwise, yields only parameters that are direct members of this module.
remove_duplicate (bool, optional) – whether to remove the duplicated parameters in the result. Defaults to True.

Yields:

(str, Parameter) – Tuple containing the name and parameter

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> for name, param in self.named_parameters():
>>>     if name in ['bias']:
>>>         print(param.size())

parameters(recurse: bool = True) → Iterator[Parameter]

Return an iterator over module parameters.

This is typically passed to an optimizer.

Parameters:: recurse (bool) – if True, then yields parameters of this module and all submodules. Otherwise, yields only parameters that are direct members of this module.
Yields:: Parameter – module parameter

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> for param in model.parameters():
>>>     print(type(param), param.size())
<class 'torch.Tensor'> (20L,)
<class 'torch.Tensor'> (20L, 1L, 5L, 5L)

property quaternion_w: Tensor: Get w component of the quaternion.

property quaternion_x: Tensor: Get x component of the quaternion.

property quaternion_y: Tensor: Get y component of the quaternion.

property quaternion_z: Tensor: Get z component of the quaternion.

Generate uniformly distributed rotations.

Parameters:

num – Number of random rotations to generate. If None (default), then a single rotation is generated.
random_state – If random_state is None, the numpy.random.RandomState singleton is used. If random_state is an int, a new RandomState instance is used, seeded with random_state. If random_state is already a Generator or RandomState instance then that instance is used.

Returns:

Contains a single rotation if num is None. Otherwise contains a stack of num rotations.

Return type:

random_rotation

register_backward_hook(hook: Callable[[Module, Tuple[Tensor, ...] | Tensor, Tuple[Tensor, ...] | Tensor], None | Tuple[Tensor, ...] | Tensor]) → RemovableHandle

Register a backward hook on the module.

This function is deprecated in favor of register_full_backward_hook() and the behavior of this function will change in future versions.

Returns:: a handle that can be used to remove the added hook by calling handle.remove()
Return type:: torch.utils.hooks.RemovableHandle

register_buffer(name: str, tensor: Tensor | None, persistent: bool = True) → None

Add a buffer to the module.

This is typically used to register a buffer that should not to be considered a model parameter. For example, BatchNorm’s running_mean is not a parameter, but is part of the module’s state. Buffers, by default, are persistent and will be saved alongside parameters. This behavior can be changed by setting persistent to False. The only difference between a persistent buffer and a non-persistent buffer is that the latter will not be a part of this module’s state_dict.

Buffers can be accessed as attributes using given names.

Parameters:

name (str) – name of the buffer. The buffer can be accessed from this module using the given name
tensor (Tensor or None) – buffer to be registered. If None, then operations that run on buffers, such as cuda, are ignored. If None, the buffer is not included in the module’s state_dict.
persistent (bool) – whether the buffer is part of this module’s state_dict.

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> self.register_buffer('running_mean', torch.zeros(num_features))

register_forward_hook(hook: Callable[[T, Tuple[Any, ...], Any], Any | None] | Callable[[T, Tuple[Any, ...], Dict[str, Any], Any], Any | None], *, prepend: bool = False, with_kwargs: bool = False, always_call: bool = False) → RemovableHandle

Register a forward hook on the module.

The hook will be called every time after forward() has computed an output.

If with_kwargs is False or not specified, the input contains only the positional arguments given to the module. Keyword arguments won’t be passed to the hooks and only to the forward. The hook can modify the output. It can modify the input inplace but it will not have effect on forward since this is called after forward() is called. The hook should have the following signature:

hook(module, args, output) -> None or modified output

If with_kwargs is True, the forward hook will be passed the kwargs given to the forward function and be expected to return the output possibly modified. The hook should have the following signature:

hook(module, args, kwargs, output) -> None or modified output

Parameters:

hook (Callable) – The user defined hook to be registered.
prepend (bool) – If True, the provided hook will be fired before all existing forward hooks on this torch.nn.modules.Module. Otherwise, the provided hook will be fired after all existing forward hooks on this torch.nn.modules.Module. Note that global forward hooks registered with register_module_forward_hook() will fire before all hooks registered by this method. Default: False
with_kwargs (bool) – If True, the hook will be passed the kwargs given to the forward function. Default: False
always_call (bool) – If True the hook will be run regardless of whether an exception is raised while calling the Module. Default: False

Returns:

a handle that can be used to remove the added hook by calling handle.remove()

Return type:

torch.utils.hooks.RemovableHandle

register_forward_pre_hook(hook: Callable[[T, Tuple[Any, ...]], Any | None] | Callable[[T, Tuple[Any, ...], Dict[str, Any]], Tuple[Any, Dict[str, Any]] | None], *, prepend: bool = False, with_kwargs: bool = False) → RemovableHandle

Register a forward pre-hook on the module.

The hook will be called every time before forward() is invoked.

If with_kwargs is false or not specified, the input contains only the positional arguments given to the module. Keyword arguments won’t be passed to the hooks and only to the forward. The hook can modify the input. User can either return a tuple or a single modified value in the hook. We will wrap the value into a tuple if a single value is returned (unless that value is already a tuple). The hook should have the following signature:

hook(module, args) -> None or modified input

If with_kwargs is true, the forward pre-hook will be passed the kwargs given to the forward function. And if the hook modifies the input, both the args and kwargs should be returned. The hook should have the following signature:

hook(module, args, kwargs) -> None or a tuple of modified input and kwargs

Parameters:

hook (Callable) – The user defined hook to be registered.
prepend (bool) – If true, the provided hook will be fired before all existing forward_pre hooks on this torch.nn.modules.Module. Otherwise, the provided hook will be fired after all existing forward_pre hooks on this torch.nn.modules.Module. Note that global forward_pre hooks registered with register_module_forward_pre_hook() will fire before all hooks registered by this method. Default: False
with_kwargs (bool) – If true, the hook will be passed the kwargs given to the forward function. Default: False

Returns:

a handle that can be used to remove the added hook by calling handle.remove()

Return type:

torch.utils.hooks.RemovableHandle

register_full_backward_hook(hook: Callable[[Module, Tuple[Tensor, ...] | Tensor, Tuple[Tensor, ...] | Tensor], None | Tuple[Tensor, ...] | Tensor], prepend: bool = False) → RemovableHandle

Register a backward hook on the module.

The hook will be called every time the gradients with respect to a module are computed, i.e. the hook will execute if and only if the gradients with respect to module outputs are computed. The hook should have the following signature:

hook(module, grad_input, grad_output) -> tuple(Tensor) or None

The grad_input and grad_output are tuples that contain the gradients with respect to the inputs and outputs respectively. The hook should not modify its arguments, but it can optionally return a new gradient with respect to the input that will be used in place of grad_input in subsequent computations. grad_input will only correspond to the inputs given as positional arguments and all kwarg arguments are ignored. Entries in grad_input and grad_output will be None for all non-Tensor arguments.

For technical reasons, when this hook is applied to a Module, its forward function will receive a view of each Tensor passed to the Module. Similarly the caller will receive a view of each Tensor returned by the Module’s forward function.

Warning

Modifying inputs or outputs inplace is not allowed when using backward hooks and will raise an error.

Parameters:

hook (Callable) – The user-defined hook to be registered.
prepend (bool) – If true, the provided hook will be fired before all existing backward hooks on this torch.nn.modules.Module. Otherwise, the provided hook will be fired after all existing backward hooks on this torch.nn.modules.Module. Note that global backward hooks registered with register_module_full_backward_hook() will fire before all hooks registered by this method.

Returns:

a handle that can be used to remove the added hook by calling handle.remove()

Return type:

torch.utils.hooks.RemovableHandle

register_full_backward_pre_hook(hook: Callable[[Module, Tuple[Tensor, ...] | Tensor], None | Tuple[Tensor, ...] | Tensor], prepend: bool = False) → RemovableHandle

Register a backward pre-hook on the module.

The hook will be called every time the gradients for the module are computed. The hook should have the following signature:

hook(module, grad_output) -> tuple[Tensor] or None

The grad_output is a tuple. The hook should not modify its arguments, but it can optionally return a new gradient with respect to the output that will be used in place of grad_output in subsequent computations. Entries in grad_output will be None for all non-Tensor arguments.

For technical reasons, when this hook is applied to a Module, its forward function will receive a view of each Tensor passed to the Module. Similarly the caller will receive a view of each Tensor returned by the Module’s forward function.

Warning

Modifying inputs inplace is not allowed when using backward hooks and will raise an error.

Parameters:

hook (Callable) – The user-defined hook to be registered.
prepend (bool) – If true, the provided hook will be fired before all existing backward_pre hooks on this torch.nn.modules.Module. Otherwise, the provided hook will be fired after all existing backward_pre hooks on this torch.nn.modules.Module. Note that global backward_pre hooks registered with register_module_full_backward_pre_hook() will fire before all hooks registered by this method.

Returns:

a handle that can be used to remove the added hook by calling handle.remove()

Return type:

torch.utils.hooks.RemovableHandle

register_load_state_dict_post_hook(hook)

Register a post hook to be run after module’s load_state_dict is called.

It should have the following signature::: hook(module, incompatible_keys) -> None

The module argument is the current module that this hook is registered on, and the incompatible_keys argument is a NamedTuple consisting of attributes missing_keys and unexpected_keys. missing_keys is a list of str containing the missing keys and unexpected_keys is a list of str containing the unexpected keys.

The given incompatible_keys can be modified inplace if needed.

Note that the checks performed when calling load_state_dict() with strict=True are affected by modifications the hook makes to missing_keys or unexpected_keys, as expected. Additions to either set of keys will result in an error being thrown when strict=True, and clearing out both missing and unexpected keys will avoid an error.

Returns:: a handle that can be used to remove the added hook by calling handle.remove()
Return type:: torch.utils.hooks.RemovableHandle

register_module(name: str, module: Module | None) → None: Alias for add_module().

register_parameter(name: str, param: Parameter | None) → None

Add a parameter to the module.

The parameter can be accessed as an attribute using given name.

Parameters:

name (str) – name of the parameter. The parameter can be accessed from this module using the given name
param (Parameter or None) – parameter to be added to the module. If None, then operations that run on parameters, such as cuda, are ignored. If None, the parameter is not included in the module’s state_dict.

register_state_dict_pre_hook(hook)

Register a pre-hook for the state_dict() method.

These hooks will be called with arguments: self, prefix, and keep_vars before calling state_dict on self. The registered hooks can be used to perform pre-processing before the state_dict call is made.

requires_grad_(requires_grad: bool = True) → T

Change if autograd should record operations on parameters in this module.

This method sets the parameters’ requires_grad attributes in-place.

This method is helpful for freezing part of the module for finetuning or training parts of a model individually (e.g., GAN training).

See locally-disable-grad-doc for a comparison between .requires_grad_() and several similar mechanisms that may be confused with it.

Parameters:: requires_grad (bool) – whether autograd should record operations on parameters in this module. Default: True.
Returns:: self
Return type:: Module

set_extra_state(state: Any) → None

Set extra state contained in the loaded state_dict.

This function is called from load_state_dict() to handle any extra state found within the state_dict. Implement this function and a corresponding get_extra_state() for your module if you need to store extra state within its state_dict.

Parameters:: state (dict) – Extra state from the state_dict

property shape: Size: Return the batch shape of the Rotation.

share_memory() → T: See torch.Tensor.share_memory_().

property single: bool: Returns true if this a single rotation.

state_dict(*args, destination=None, prefix='', keep_vars=False)

Return a dictionary containing references to the whole state of the module.

Both parameters and persistent buffers (e.g. running averages) are included. Keys are corresponding parameter and buffer names. Parameters and buffers set to None are not included.

Note

The returned object is a shallow copy. It contains references to the module’s parameters and buffers.

Warning

Currently state_dict() also accepts positional arguments for destination, prefix and keep_vars in order. However, this is being deprecated and keyword arguments will be enforced in future releases.

Warning

Please avoid the use of argument destination as it is not designed for end-users.

Parameters:

destination (dict, optional) – If provided, the state of module will be updated into the dict and the same object is returned. Otherwise, an OrderedDict will be created and returned. Default: None.
prefix (str, optional) – a prefix added to parameter and buffer names to compose the keys in state_dict. Default: ''.
keep_vars (bool, optional) – by default the Tensor s returned in the state dict are detached from autograd. If it’s set to True, detaching will not be performed. Default: False.

Returns:

a dictionary containing a whole state of the module

Return type:

dict

Example:

>>> # xdoctest: +SKIP("undefined vars")
>>> module.state_dict().keys()
['bias', 'weight']

to(*args, **kwargs)

Move and/or cast the parameters and buffers.

This can be called as

to(device=None, dtype=None, non_blocking=False)

to(dtype, non_blocking=False)

to(tensor, non_blocking=False)

to(memory_format=torch.channels_last)

Its signature is similar to torch.Tensor.to(), but only accepts floating point or complex dtypes. In addition, this method will only cast the floating point or complex parameters and buffers to dtype (if given). The integral parameters and buffers will be moved device, if that is given, but with dtypes unchanged. When non_blocking is set, it tries to convert/move asynchronously with respect to the host if possible, e.g., moving CPU Tensors with pinned memory to CUDA devices.

See below for examples.

Note

This method modifies the module in-place.

Parameters:

device (torch.device) – the desired device of the parameters and buffers in this module
dtype (torch.dtype) – the desired floating point or complex dtype of the parameters and buffers in this module
tensor (torch.Tensor) – Tensor whose dtype and device are the desired dtype and device for all parameters and buffers in this module
memory_format (torch.memory_format) – the desired memory format for 4D parameters and buffers in this module (keyword only argument)

Returns:

self

Return type:

Module

Examples:

>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> linear = nn.Linear(2, 2)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
        [-0.5113, -0.2325]])
>>> linear.to(torch.double)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
        [-0.5113, -0.2325]], dtype=torch.float64)
>>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_CUDA1)
>>> gpu1 = torch.device("cuda:1")
>>> linear.to(gpu1, dtype=torch.half, non_blocking=True)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
        [-0.5112, -0.2324]], dtype=torch.float16, device='cuda:1')
>>> cpu = torch.device("cpu")
>>> linear.to(cpu)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
        [-0.5112, -0.2324]], dtype=torch.float16)

>>> linear = nn.Linear(2, 2, bias=None).to(torch.cdouble)
>>> linear.weight
Parameter containing:
tensor([[ 0.3741+0.j,  0.2382+0.j],
        [ 0.5593+0.j, -0.4443+0.j]], dtype=torch.complex128)
>>> linear(torch.ones(3, 2, dtype=torch.cdouble))
tensor([[0.6122+0.j, 0.1150+0.j],
        [0.6122+0.j, 0.1150+0.j],
        [0.6122+0.j, 0.1150+0.j]], dtype=torch.complex128)

to_empty(*, device: int | str | device | None, recurse: bool = True) → T

Move the parameters and buffers to the specified device without copying storage.

Parameters:

device (torch.device) – The desired device of the parameters and buffers in this module.
recurse (bool) – Whether parameters and buffers of submodules should be recursively moved to the specified device.

Returns:

self

Return type:

Module

train(mode: bool = True) → T

Set the module in training mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

Parameters:: mode (bool) – whether to set training mode (True) or evaluation mode (False). Default: True.
Returns:: self
Return type:: Module

type(dst_type: dtype | str) → T

Casts all parameters and buffers to dst_type.

Note

This method modifies the module in-place.

Parameters:: dst_type (type or string) – the desired type
Returns:: self
Return type:: Module

xpu(device: int | device | None = None) → T

Move all model parameters and buffers to the XPU.

This also makes associated parameters and buffers different objects. So it should be called before constructing optimizer if the module will live on XPU while being optimized.

Note

This method modifies the module in-place.

Parameters:: device (int, optional) – if specified, all parameters will be copied to that device
Returns:: self
Return type:: Module

zero_grad(set_to_none: bool = True) → None

Reset gradients of all model parameters.

See similar function under torch.optim.Optimizer for more context.

Parameters:: set_to_none (bool) – instead of setting to zero, set the grads to None. See torch.optim.Optimizer.zero_grad() for details.