import collections
import math, numbers
import torch, warnings
from torch import nn, linalg
from .operation import broadcast_inputs
from .basics import cumops_, cummul_, cumprod_
from .basics import vec2skew, cumops, cummul, cumprod
from torch.utils._pytree import tree_map, tree_flatten
from .operation import SO3_Log, SE3_Log, RxSO3_Log, Sim3_Log
from .operation import so3_Exp, se3_Exp, rxso3_Exp, sim3_Exp
from .operation import SO3_Act, SE3_Act, RxSO3_Act, Sim3_Act
from .operation import SO3_Mul, SE3_Mul, RxSO3_Mul, Sim3_Mul
from .operation import SO3_Inv, SE3_Inv, RxSO3_Inv, Sim3_Inv
from .operation import SO3_Act4, SE3_Act4, RxSO3_Act4, Sim3_Act4
from .operation import SO3_AdjXa, SE3_AdjXa, RxSO3_AdjXa, Sim3_AdjXa
from .operation import SO3_AdjTXa, SE3_AdjTXa, RxSO3_AdjTXa, Sim3_AdjTXa
from .operation import so3_Jl_inv, se3_Jl_inv, rxso3_Jl_inv, sim3_Jl_inv
from torch.nn.modules.utils import _single, _pair, _triple, _quadruple, _ntuple
HANDLED_FUNCTIONS = ['__getitem__', '__setitem__', 'cpu', 'cuda', 'float', 'double',
'to', 'detach', 'view', 'view_as', 'squeeze', 'unsqueeze', 'cat',
'stack', 'split', 'hsplit', 'dsplit', 'vsplit', 'tensor_split',
'chunk', 'concat', 'column_stack', 'dstack', 'vstack', 'hstack',
'index_select', 'masked_select', 'movedim', 'moveaxis', 'narrow',
'permute', 'reshape', 'row_stack', 'scatter', 'scatter_add', 'clone',
'swapaxes', 'swapdims', 'take', 'take_along_dim', 'tile', 'copy',
'transpose', 'unbind', 'gather', 'repeat', 'expand', 'expand_as',
'index_select', 'masked_select', 'index_copy', 'index_copy_',
'select', 'select_scatter', 'index_put','index_put_', 'copy_']
class LieType:
'''LieTensor Type Base Class'''
def __init__(self, dimension, embedding, manifold):
self._dimension = torch.Size([dimension]) # Data dimension
self._embedding = torch.Size([embedding]) # Embedding dimension
self._manifold = torch.Size([manifold]) # Manifold dimension
@property
def dimension(self):
return self._dimension
@property
def embedding(self):
return self._embedding
@property
def manifold(self):
return self._manifold
@property
def on_manifold(self):
return self.dimension == self.manifold
def add_(self, input, other):
if self.on_manifold:
other1 = torch.Tensor.as_subclass(input, torch.Tensor)
other2 = torch.Tensor.as_subclass(other, torch.Tensor)
return input.copy_(other1 + other2[..., :self.manifold[0]])
raise NotImplementedError("Instance has no add_ attribute.")
def Log(self, X):
if self.on_manifold:
raise AttributeError("Lie Algebra has no Log attribute")
raise NotImplementedError("Instance has no Log attribute.")
def Exp(self, x):
if not self.on_manifold:
raise AttributeError("Lie Group has no Exp attribute")
raise NotImplementedError("Instance has no Exp attribute.")
def Inv(self, x):
if self.on_manifold:
return - x
raise NotImplementedError("Instance has no Inv attribute.")
def Act(self, X, p):
""" action on a points tensor(*, 3[4]) (homogeneous)"""
if not self.on_manifold:
raise AttributeError("Lie Group has no Act attribute")
raise NotImplementedError("Instance has no Act attribute.")
def Mul(self, X, Y):
if not self.on_manifold:
raise AttributeError("Lie Group has no Mul attribute")
raise NotImplementedError("Instance has no Mul attribute.")
def Retr(self, X, a):
if self.on_manifold:
raise AttributeError("Has no Retr attribute")
return a.Exp() * X
def Adj(self, X, a):
''' X * Exp(a) = Exp(Adj) * X '''
if not self.on_manifold:
raise AttributeError("Lie Group has no Adj attribute")
raise NotImplementedError("Instance has no Adj attribute.")
def AdjT(self, X, a):
''' Exp(a) * X = X * Exp(AdjT) '''
if not self.on_manifold:
raise AttributeError("Lie Group has no AdjT attribute")
raise NotImplementedError("Instance has no AdjT attribute.")
def Jinvp(self, X, p):
if not self.on_manifold:
raise AttributeError("Lie Group has no Jinvp attribute")
raise NotImplementedError("Instance has no Jinvp attribute.")
def matrix(self, input):
""" To 4x4 matrix """
X = input.Exp() if self.on_manifold else input
I = torch.eye(4, dtype=X.dtype, device=X.device)
I = I.view([1] * (X.dim() - 1) + [4, 4])
return X.unsqueeze(-2).Act(I).transpose(-1,-2)
def rotation(self, input):
raise NotImplementedError("Rotation is not implemented for the instance.")
def translation(self, input):
warnings.warn("Instance has no translation. Zero vector(s) is returned.")
return torch.zeros(input.lshape + (3,), dtype=input.dtype, device=input.device,
requires_grad=input.requires_grad)
def scale(self, input):
warnings.warn("Instance has no scale. Scalar one(s) is returned.")
return torch.ones(input.lshape + (1,), dtype=input.dtype, device=input.device,
requires_grad=input.requires_grad)
@classmethod
def to_tuple(cls, input):
out = tuple()
for i in input:
if not isinstance(i, collections.abc.Iterable):
out += (i,)
else:
out += tuple(i)
return out
@classmethod
def identity(cls, *args, **kwargs):
raise NotImplementedError("Instance has no identity.")
@classmethod
def identity_like(cls, *args, **kwargs):
return cls.identity(*args, **kwargs)
def randn_like(self, *args, sigma=1.0, **kwargs):
return self.randn(*args, sigma=sigma, **kwargs)
def randn(self, *args, **kwargs):
raise NotImplementedError("randn not implemented yet")
@classmethod
def cumops(self, X, dim, ops):
return cumops(X, dim, ops)
@classmethod
def cummul(self, X, dim):
return cummul(X, dim)
@classmethod
def cumprod(self, X, dim, left = True):
return cumprod(X, dim, left)
@classmethod
def cumops_(self, X, dim, ops):
return cumops_(X, dim, ops)
@classmethod
def cummul_(self, X, dim):
return cummul_(X, dim)
@classmethod
def cumprod_(self, X, dim):
return cumprod_(X, dim)
class SO3Type(LieType):
def __init__(self):
super().__init__(4, 4, 3)
def Log(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
x = SO3_Log.apply(X)
return LieTensor(x, ltype=so3_type)
def Act(self, X, p):
assert not self.on_manifold and isinstance(p, torch.Tensor)
assert p.shape[-1]==3 or p.shape[-1]==4, "Invalid Tensor Dimension"
X = X.tensor() if hasattr(X, 'ltype') else X
input, out_shape = broadcast_inputs(X, p)
if p.shape[-1]==3:
out = SO3_Act.apply(*input)
else:
out = SO3_Act4.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
return out.view(out_shape + (dim,))
def Mul(self, X, Y):
# Transform on transform
X = X.tensor() if hasattr(X, 'ltype') else X
if not self.on_manifold and isinstance(Y, LieTensor) and not Y.ltype.on_manifold:
Y = Y.tensor() if hasattr(Y, 'ltype') else Y
input, out_shape = broadcast_inputs(X, Y)
out = SO3_Mul.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=SO3_type)
# Transform on points
if not self.on_manifold and isinstance(Y, torch.Tensor):
return self.Act(X, Y)
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=SO3_type)
raise NotImplementedError('Invalid __mul__ operation')
def Inv(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
out = SO3_Inv.apply(X)
return LieTensor(out, ltype=SO3_type)
def Adj(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = SO3_AdjXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=so3_type)
def AdjT(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = SO3_AdjTXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=so3_type)
def Jinvp(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
(X, a), out_shape = broadcast_inputs(X, a)
out = (so3_Jl_inv(SO3_Log.apply(X)) @ a.unsqueeze(-1)).squeeze(-1)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=so3_type)
@classmethod
def identity(cls, *size, **kwargs):
data = torch.tensor([0., 0., 0., 1.], **kwargs)
return LieTensor(data.repeat(size+(1,)), ltype=SO3_type)
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
data = so3_type.Exp(so3_type.randn(*size, sigma=sigma, **kwargs)).detach()
return LieTensor(data, ltype=SO3_type).requires_grad_(requires_grad)
@classmethod
def add_(cls, input, other):
return input.copy_(LieTensor(other[..., :3], ltype=so3_type).Exp() * input)
def matrix(self, input):
""" To 3x3 matrix """
I = torch.eye(3, dtype=input.dtype, device=input.device)
I = I.view([1] * (input.dim() - 1) + [3, 3])
return input.unsqueeze(-2).Act(I).transpose(-1,-2)
def rotation(self, input):
return input
def identity_(self, X):
X.fill_(0)
X.index_fill_(dim=-1, index=torch.tensor([-1], device=X.device), value=1)
return X
def Jr(self, X):
"""
Right jacobian of SO(3)
"""
return X.Log().Jr()
class so3Type(LieType):
def __init__(self):
super().__init__(3, 4, 3)
def Exp(self, x):
x = x.tensor() if hasattr(x, 'ltype') else x
X = so3_Exp.apply(x)
return LieTensor(X, ltype=SO3_type)
def Mul(self, X, Y):
X = X.tensor() if hasattr(X, 'ltype') else X
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=so3_type)
raise NotImplementedError('Invalid __mul__ operation')
@classmethod
def identity(cls, *size, **kwargs):
return SO3_type.Log(SO3_type.identity(*size, **kwargs))
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
assert isinstance(sigma, numbers.Number), 'Only accepts sigma as a single number'
size = self.to_tuple(size)
data = torch.randn(*(size + torch.Size([3])), **kwargs)
dist = data.norm(dim=-1, keepdim=True)
theta = sigma * torch.randn(*(size + torch.Size([1])), **kwargs)
return LieTensor(data / dist * theta, ltype=so3_type).requires_grad_(requires_grad)
def matrix(self, input):
""" To 3x3 matrix """
X = input.Exp()
I = torch.eye(3, dtype=X.dtype, device=X.device)
I = I.view([1] * (X.dim() - 1) + [3, 3])
return X.unsqueeze(-2).Act(I).transpose(-1,-2)
def rotation(self, input):
return input.Exp().rotation()
def Jr(self, x):
"""
Right jacobian of so(3)
"""
K = vec2skew(x)
theta = torch.linalg.norm(x, dim=-1, keepdim=True).unsqueeze(-1)
I = torch.eye(3, device=x.device, dtype=x.dtype).expand(x.lshape+(3, 3))
Jr = I - (1-theta.cos())/theta**2 * K + (theta - theta.sin())/theta**3 * K@K
return torch.where(theta>torch.finfo(theta.dtype).eps, Jr, I)
class SE3Type(LieType):
def __init__(self):
super().__init__(7, 7, 6)
def Log(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
x = SE3_Log.apply(X)
return LieTensor(x, ltype=se3_type)
def Act(self, X, p):
assert not self.on_manifold and isinstance(p, torch.Tensor)
assert p.shape[-1]==3 or p.shape[-1]==4, "Invalid Tensor Dimension"
X = X.tensor() if hasattr(X, 'ltype') else X
input, out_shape = broadcast_inputs(X, p)
if p.shape[-1]==3:
out = SE3_Act.apply(*input)
else:
out = SE3_Act4.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
return out.view(out_shape + (dim,))
def Mul(self, X, Y):
# Transform on transform
X = X.tensor() if hasattr(X, 'ltype') else X
if not self.on_manifold and isinstance(Y, LieTensor) and not Y.ltype.on_manifold:
Y = Y.tensor() if hasattr(Y, 'ltype') else Y
input, out_shape = broadcast_inputs(X, Y)
out = SE3_Mul.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=SE3_type)
# Transform on points
if not self.on_manifold and isinstance(Y, torch.Tensor):
return self.Act(X, Y)
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=SE3_type)
raise NotImplementedError('Invalid __mul__ operation')
def Inv(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
out = SE3_Inv.apply(X)
return LieTensor(out, ltype=SE3_type)
def rotation(self, input):
return LieTensor(input.tensor()[..., 3:7], ltype=SO3_type)
def translation(self, input):
return input.tensor()[..., 0:3]
def Adj(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = SE3_AdjXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=se3_type)
def AdjT(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = SE3_AdjTXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=se3_type)
def Jinvp(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
(X, a), out_shape = broadcast_inputs(X, a)
out = (se3_Jl_inv(SE3_Log.apply(X)) @ a.unsqueeze(-1)).squeeze(-1)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=se3_type)
@classmethod
def identity(cls, *size, **kwargs):
data = torch.tensor([0., 0., 0., 0., 0., 0., 1.], **kwargs)
return LieTensor(data.repeat(size+(1,)), ltype=SE3_type)
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
data = se3_type.Exp(se3_type.randn(*size, sigma=sigma, **kwargs)).detach()
return LieTensor(data, ltype=SE3_type).requires_grad_(requires_grad)
@classmethod
def add_(cls, input, other):
return input.copy_(LieTensor(other[..., :6], ltype=se3_type).Exp() * input)
class se3Type(LieType):
def __init__(self):
super().__init__(6, 7, 6)
def Exp(self, x):
x = x.tensor() if hasattr(x, 'ltype') else x
X = se3_Exp.apply(x)
return LieTensor(X, ltype=SE3_type)
def Mul(self, X, Y):
X = X.tensor() if hasattr(X, 'ltype') else X
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=se3_type)
raise NotImplementedError('Invalid __mul__ operation')
def rotation(self, input):
return input.Exp().rotation()
def translation(self, input):
return input.Exp().translation()
@classmethod
def identity(cls, *size, **kwargs):
return SE3_type.Log(SE3_type.identity(*size, **kwargs))
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
# convert different types of inputs to SE3 sigma
if not isinstance(sigma, collections.abc.Iterable):
sigma = _quadruple(sigma)
elif len(sigma)==2:
rotation_sigma = _single(sigma[-1])
translation_sigma = _triple(sigma[0])
sigma = translation_sigma + rotation_sigma
else:
assert len(sigma)==4, 'Only accepts a tuple of sigma in size 1, 2, or 4.'
size = self.to_tuple(size)
rotation = so3_type.randn(*size, sigma=sigma[-1], **kwargs).detach().tensor()
sigma = torch.tensor([sigma[0], sigma[1], sigma[2]], **kwargs)
translation = sigma * torch.randn(*(size + torch.Size([3])), **kwargs)
data = torch.cat([translation, rotation], dim=-1)
return LieTensor(data, ltype=se3_type).requires_grad_(requires_grad)
class Sim3Type(LieType):
def __init__(self):
super().__init__(8, 8, 7)
def Log(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
x = Sim3_Log.apply(X)
return LieTensor(x, ltype=sim3_type)
def Act(self, X, p):
assert not self.on_manifold and isinstance(p, torch.Tensor)
assert p.shape[-1]==3 or p.shape[-1]==4, "Invalid Tensor Dimension"
X = X.tensor() if hasattr(X, 'ltype') else X
input, out_shape = broadcast_inputs(X, p)
if p.shape[-1]==3:
out = Sim3_Act.apply(*input)
else:
out = Sim3_Act4.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
return out.view(out_shape + (dim,))
def Mul(self, X, Y):
# Transform on transform
X = X.tensor() if hasattr(X, 'ltype') else X
if not self.on_manifold and isinstance(Y, LieTensor) and not Y.ltype.on_manifold:
Y = Y.tensor() if hasattr(Y, 'ltype') else Y
input, out_shape = broadcast_inputs(X, Y)
out = Sim3_Mul.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=Sim3_type)
# Transform on points
if not self.on_manifold and isinstance(Y, torch.Tensor):
return self.Act(X, Y)
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=Sim3_type)
raise NotImplementedError('Invalid __mul__ operation')
def Inv(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
out = Sim3_Inv.apply(X)
return LieTensor(out, ltype=Sim3_type)
def Adj(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = Sim3_AdjXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=sim3_type)
def AdjT(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = Sim3_AdjTXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=sim3_type)
def Jinvp(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
(X, a), out_shape = broadcast_inputs(X, a)
out = (sim3_Jl_inv(Sim3_Log.apply(X)) @ a.unsqueeze(-1)).squeeze(-1)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=sim3_type)
def rotation(self, input):
return LieTensor(input.tensor()[..., 3:7], ltype=SO3_type)
def translation(self, input):
return input.tensor()[..., 0:3]
def scale(self, input):
return input.tensor()[..., 7:8]
@classmethod
def identity(cls, *size, **kwargs):
data = torch.tensor([0., 0., 0., 0., 0., 0., 1., 1.], **kwargs)
return LieTensor(data.repeat(size+(1,)), ltype=Sim3_type)
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
data = sim3_type.Exp(sim3_type.randn(*size, sigma=sigma, **kwargs)).detach()
return LieTensor(data, ltype=Sim3_type).requires_grad_(requires_grad)
@classmethod
def add_(cls, input, other):
return input.copy_(LieTensor(other[..., :7], ltype=sim3_type).Exp() * input)
class sim3Type(LieType):
def __init__(self):
super().__init__(7, 8, 7)
def Exp(self, x):
x = x.tensor() if hasattr(x, 'ltype') else x
X = sim3_Exp.apply(x)
return LieTensor(X, ltype=Sim3_type)
def Mul(self, X, Y):
X = X.tensor() if hasattr(X, 'ltype') else X
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=sim3_type)
raise NotImplementedError('Invalid __mul__ operation')
def rotation(self, input):
return input.Exp().rotation()
def translation(self, input):
return input.Exp().translation()
def scale(self, input):
return input.Exp().scale()
@classmethod
def identity(cls, *size, **kwargs):
return Sim3_type.Log(Sim3_type.identity(*size, **kwargs))
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
if not isinstance(sigma, collections.abc.Iterable):
sigma = _ntuple(5, "_penta")(sigma)
elif len(sigma)==3:
rotation_sigma = _single(sigma[-2])
scale_sigma = _single(sigma[-1])
translation_sigma = _triple(sigma[0])
sigma = translation_sigma+rotation_sigma+scale_sigma
else:
assert len(sigma)==5, 'Only accepts a tuple of sigma in size 1, 3, or 5.'
size = self.to_tuple(size)
rotation = so3_type.randn(*size, sigma=sigma[-2], **kwargs).detach().tensor()
scale = sigma[-1] * torch.randn(*(size + torch.Size([1])), **kwargs)
sigma = torch.tensor([sigma[0], sigma[1], sigma[2]], **kwargs)
translation = sigma * torch.randn(*(size + torch.Size([3])), **kwargs)
data = torch.cat([translation, rotation, scale], dim=-1)
return LieTensor(data, ltype=sim3_type).requires_grad_(requires_grad)
class RxSO3Type(LieType):
def __init__(self):
super().__init__(5, 5, 4)
def Log(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
x = RxSO3_Log.apply(X)
return LieTensor(x, ltype=rxso3_type)
def Act(self, X, p):
assert not self.on_manifold and isinstance(p, torch.Tensor)
assert p.shape[-1]==3 or p.shape[-1]==4, "Invalid Tensor Dimension"
X = X.tensor() if hasattr(X, 'ltype') else X
input, out_shape = broadcast_inputs(X, p)
if p.shape[-1]==3:
out = RxSO3_Act.apply(*input)
else:
out = RxSO3_Act4.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
return out.view(out_shape + (dim,))
def Mul(self, X, Y):
# Transform on transform
X = X.tensor() if hasattr(X, 'ltype') else X
if not self.on_manifold and isinstance(Y, LieTensor) and not Y.ltype.on_manifold:
Y = Y.tensor() if hasattr(Y, 'ltype') else Y
input, out_shape = broadcast_inputs(X, Y)
out = RxSO3_Mul.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=RxSO3_type)
# Transform on points
if not self.on_manifold and isinstance(Y, torch.Tensor):
return self.Act(X, Y)
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=RxSO3_type)
raise NotImplementedError('Invalid __mul__ operation')
def Inv(self, X):
X = X.tensor() if hasattr(X, 'ltype') else X
out = RxSO3_Inv.apply(X)
return LieTensor(out, ltype=RxSO3_type)
def Adj(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = RxSO3_AdjXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=rxso3_type)
def AdjT(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
input, out_shape = broadcast_inputs(X, a)
out = RxSO3_AdjTXa.apply(*input)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=rxso3_type)
def Jinvp(self, X, a):
X = X.tensor() if hasattr(X, 'ltype') else X
a = a.tensor() if hasattr(a, 'ltype') else a
(X, a), out_shape = broadcast_inputs(X, a)
out = (rxso3_Jl_inv(RxSO3_Log.apply(X)) @ a.unsqueeze(-1)).squeeze(-1)
dim = -1 if out.nelement() != 0 else X.shape[-1]
out = out.view(out_shape + (dim,))
return LieTensor(out, ltype=rxso3_type)
def rotation(self, input):
return LieTensor(input.tensor()[..., 0:4], ltype=SO3_type)
def scale(self, input):
return input.tensor()[..., 4:5]
@classmethod
def identity(cls, *size, **kwargs):
data = torch.tensor([0., 0., 0., 1., 1.], **kwargs)
return LieTensor(data.repeat(size+(1,)), ltype=RxSO3_type)
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
data = rxso3_type.Exp(rxso3_type.randn(*size, sigma=sigma, **kwargs)).detach()
return LieTensor(data, ltype=RxSO3_type).requires_grad_(requires_grad)
@classmethod
def add_(cls, input, other):
return input.copy_(LieTensor(other[..., :4], ltype=rxso3_type).Exp() * input)
class rxso3Type(LieType):
def __init__(self):
super().__init__(4, 5, 4)
def Exp(self, x):
x = x.tensor() if hasattr(x, 'ltype') else x
X = rxso3_Exp.apply(x)
return LieTensor(X, ltype=RxSO3_type)
def Mul(self, X, Y):
X = X.tensor() if hasattr(X, 'ltype') else X
# (scalar or tensor) * manifold
if self.on_manifold:
return LieTensor(torch.mul(X, Y), ltype=rxso3_type)
raise NotImplementedError('Invalid __mul__ operation')
def rotation(self, input):
return input.Exp().rotation()
def scale(self, input):
return input.Exp().scale()
@classmethod
def identity(cls, *size, **kwargs):
return RxSO3_type.Log(RxSO3_type.identity(*size, **kwargs))
def randn(self, *size, sigma=1.0, requires_grad=False, **kwargs):
if not isinstance(sigma, collections.abc.Iterable):
sigma = _pair(sigma)
else:
assert len(sigma)==2, 'Only accepts a tuple of sigma in size 1 or 2.'
size = self.to_tuple(size)
rotation = so3_type.randn(*size, sigma=sigma[0], **kwargs).tensor()
scale = sigma[1] * torch.randn(*(size + torch.Size([1])), **kwargs)
data = torch.cat([rotation, scale], dim=-1)
return LieTensor(data, ltype=rxso3_type).requires_grad_(requires_grad)
SO3_type, so3_type = SO3Type(), so3Type()
SE3_type, se3_type = SE3Type(), se3Type()
Sim3_type, sim3_type = Sim3Type(), sim3Type()
RxSO3_type, rxso3_type = RxSO3Type(), rxso3Type()
[docs]class LieTensor(torch.Tensor):
r""" A sub-class of :obj:`torch.Tensor` to represent Lie Algebra and Lie Group.
Args:
data (:obj:`Tensor`, or :obj:`list`, or ':obj:`int`...'): A
:obj:`Tensor` object, or constructing a :obj:`Tensor`
object from :obj:`list`, which defines tensor data, or from
':obj:`int`...', which defines tensor shape.
The shape of :obj:`Tensor` object should be compatible
with Lie Type :obj:`ltype`, otherwise error will be raised.
ltype (:obj:`ltype`): Lie Type, either **Lie Group** or **Lie Algebra** is listed below:
Returns:
LieTensor corresponding to Lie Type :obj:`ltype`.
.. list-table:: List of :obj:`ltype` for **Lie Group**
:widths: 25 25 30 30
:header-rows: 1
* - Representation
- :obj:`ltype`
- :obj:`shape`
- Alias Class
* - Rotation
- :obj:`SO3_type`
- :obj:`(*, 4)`
- :meth:`SO3`
* - Translation + Rotation
- :obj:`SE3_type`
- :obj:`(*, 7)`
- :meth:`SE3`
* - Translation + Rotation + Scale
- :obj:`Sim3_type`
- :obj:`(*, 8)`
- :meth:`Sim3`
* - Rotation + Scale
- :obj:`RxSO3_type`
- :obj:`(*, 5)`
- :meth:`RxSO3`
.. list-table:: List of :obj:`ltype` for **Lie Algebra**
:widths: 25 25 30 30
:header-rows: 1
* - Representation
- :obj:`ltype`
- :obj:`shape`
- Alias Class
* - Rotation
- :obj:`so3_type`
- :obj:`(*, 3)`
- :meth:`so3`
* - Translation + Rotation
- :obj:`se3_type`
- :obj:`(*, 6)`
- :meth:`se3`
* - Translation + Rotation + Scale
- :obj:`sim3_type`
- :obj:`(*, 7)`
- :meth:`sim3`
* - Rotation + Scale
- :obj:`rxso3_type`
- :obj:`(*, 4)`
- :meth:`rxso3`
Note:
Two attributes :obj:`shape` and :obj:`lshape` are available for LieTensor.
The only differece is the :obj:`lshape` hides the last dimension of :obj:`shape`,
since :obj:`lshape` takes the data in the last dimension as a single :obj:`ltype` item.
See LieTensor method :meth:`lview` for more details.
Examples:
>>> import torch
>>> import pypose as pp
>>> data = torch.randn(3, 3, requires_grad=True, device='cuda:0')
>>> pp.LieTensor(data, ltype=pp.so3_type)
so3Type LieTensor:
tensor([[ 0.9520, 0.4517, 0.5834],
[-0.8106, 0.8197, 0.7077],
[-0.5743, 0.8182, -1.2104]], device='cuda:0', grad_fn=<AliasBackward0>)
Alias class for specific LieTensor is recommended:
>>> pp.so3(data)
so3Type LieTensor:
tensor([[ 0.9520, 0.4517, 0.5834],
[-0.8106, 0.8197, 0.7077],
[-0.5743, 0.8182, -1.2104]], device='cuda:0', grad_fn=<AliasBackward0>)
See more alias classes at `Table 1 for Lie Group <#id1>`_ and `Table 2 for Lie Algebra <#id2>`_.
Other constructors:
- From list.
>>> pp.so3([0, 0, 0])
so3Type LieTensor:
tensor([0., 0., 0.])
- From ints.
>>> pp.so3(2, 3)
so3Type LieTensor:
tensor([[0., 0., 0.],
[0., 0., 0.]])
Note:
Alias class for LieTensor is recommended.
For example, the following usage is equivalent:
- :obj:`pp.LieTensor(tensor, ltype=pp.so3_type)`
- :obj:`pp.so3(tensor)` (This is preferred).
Note:
All attributes from Tensor are available for LieTensor, e.g., :obj:`dtype`,
:obj:`device`, and :obj:`requires_grad`. See more details at
`tensor attributes <https://pytorch.org/docs/stable/tensor_attributes.html>`_.
Example:
>>> data = torch.randn(1, 3, dtype=torch.float64, device="cuda", requires_grad=True)
>>> pp.so3(data) # All Tensor attributes are available for LieTensor
so3Type LieTensor:
tensor([[-1.5948, 0.3113, -0.9807]], device='cuda:0', dtype=torch.float64,
grad_fn=<AliasBackward0>)
Note:
In most of the cases, Lie Group is expected to be used, therefore we only provide
`converting functions <https://pypose.org/docs/main/convert/>`_ between Lie Groups
and other data structures, e.g., transformation matrix, Euler angle, etc. The users
can convert data between Lie Group and Lie algebra with :obj:`Exp` and :obj:`Log`.
"""
def __init__(self, *data, ltype:LieType):
assert self.shape[-1:] == ltype.dimension, 'The last dimension of a LieTensor has to be ' \
'corresponding to their LieType. More details go to {}. If this error happens in an ' \
'optimization process, where LieType is not a necessary structure, we suggest to ' \
'call .tensor() to convert a LieTensor to Tensor before passing it to an optimizer. ' \
'If this still happens, create an issue on GitHub please.'.format(
'https://pypose.org/docs/main/generated/pypose.LieTensor')
self.ltype = ltype
@staticmethod
def __new__(cls, *data, ltype):
tensor = data[0] if isinstance(data[0], torch.Tensor) else torch.Tensor(*data)
return torch.Tensor.as_subclass(tensor, LieTensor)
def __repr__(self):
if hasattr(self, 'ltype'):
return self.ltype.__class__.__name__ + \
' %s:\n'%(self.__class__.__name__) + super().__repr__()
else:
return super().__repr__()
[docs] def new_empty(self, shape):
return torch.Tensor.as_subclass(torch.empty(shape), LieTensor)
@classmethod
def __torch_function__(cls, func, types, args=(), kwargs={}):
ltypes = (torch.Tensor if t is LieTensor or Parameter else t for t in types)
data = torch.Tensor.__torch_function__(func, ltypes, args, kwargs)
if data is not None and func.__name__ in HANDLED_FUNCTIONS:
args, spec = tree_flatten(args)
ltype = [arg.ltype for arg in args if isinstance(arg, LieTensor)][0]
def warp(t):
if isinstance(t, torch.Tensor) and not isinstance(t, cls):
lt = torch.Tensor.as_subclass(t, LieTensor)
lt.ltype = ltype
if lt.shape[-1:] != lt.ltype.dimension:
link = 'https://pypose.org/docs/main/generated/pypose.LieTensor'
warnings.warn('Tensor Shape Invalid by calling {}, ' \
'go to {}'.format(func, link))
return lt
return t
return tree_map(warp, data)
return data
@property
def lshape(self) -> torch.Size:
r'''
LieTensor Shape (shape of torch.Tensor by ignoring the last dimension)
Returns:
torch.Size
Note:
- The only difference from :obj:`shape` is the last dimension is hidden,
since :obj:`lshape` takes the last dimension as a single :obj:`ltype` item.
- The last dimension can also be accessed via :obj:`LieTensor.ltype.dimension`.
Examples:
>>> x = pp.randn_SE3(2)
>>> x.lshape
torch.Size([2])
>>> x.shape
torch.Size([2, 7])
>>> x.ltype.dimension
torch.Size([7])
'''
return self.shape[:-1]
[docs] def lview(self, *shape):
r'''
Returns a new LieTensor with the same data as the self tensor but of a different
:obj:`lshape`.
Args:
shape (torch.Size or int...): the desired size
Returns:
A new lieGroup tensor sharing with the same data as the self tensor but of a
different shape.
Note:
The only difference from :meth:`view` is the last dimension is hidden.
See `Tensor.view <https://tinyurl.com/mrds8nmd>`_
for its usage.
Examples:
>>> x = pp.randn_so3(2,2)
>>> x.shape
torch.Size([2, 2, 3])
>>> x.lview(-1).lshape
torch.Size([4])
'''
return self.view(*shape+self.ltype.dimension)
[docs] def Exp(self):
r'''
See :meth:`pypose.Exp`
'''
return self.ltype.Exp(self)
[docs] def Log(self):
r'''
See :meth:`pypose.Log`
'''
return self.ltype.Log(self)
[docs] def Inv(self):
r'''
See :meth:`pypose.Inv`
'''
return self.ltype.Inv(self)
[docs] def Act(self, p):
r'''
See :meth:`pypose.Act`
'''
return self.ltype.Act(self, p)
[docs] def add(self, other, alpha=1):
r'''
See :meth:`pypose.add`
'''
return self.clone().add_(other = alpha * other)
[docs] def add_(self, other, alpha=1):
r'''
See :meth:`pypose.add_`
'''
return self.ltype.add_(self, other = alpha * other)
def __add__(self, other):
return self.add(other=other)
def __mul__(self, other):
r'''
See :meth:`pypose.mul`
'''
return self.ltype.Mul(self, other)
def __matmul__(self, other):
r'''
See :meth:`pypose.matmul`
'''
if isinstance(other, LieTensor):
return self.ltype.Mul(self, other)
else: # Same with: self.ltype.matrix(self) @ other
return self.Act(other)
[docs] def Retr(self, a):
r'''
See :meth:`pypose.Retr`
'''
return self.ltype.Retr(self, a)
[docs] def Adj(self, a):
r'''
See :meth:`pypose.Adj`
'''
return self.ltype.Adj(self, a)
[docs] def AdjT(self, a):
r'''
See :meth:`pypose.AdjT`
'''
return self.ltype.AdjT(self, a)
[docs] def Jinvp(self, p):
r'''
See :meth:`pypose.Jinvp`
'''
return self.ltype.Jinvp(self, p)
[docs] def Jr(self):
r'''
See :meth:`pypose.Jr`
'''
return self.ltype.Jr(self)
[docs] def tensor(self) -> torch.Tensor:
r'''
See :meth:`pypose.tensor`
'''
return torch.Tensor.as_subclass(self, torch.Tensor)
[docs] def matrix(self) -> torch.Tensor:
r'''
See :meth:`pypose.matrix`
'''
return self.ltype.matrix(self)
[docs] def translation(self) -> torch.Tensor:
r'''
See :meth:`pypose.translation`
'''
return self.ltype.translation(self)
[docs] def rotation(self):
r'''
See :meth:`pypose.rotation`
'''
return self.ltype.rotation(self)
[docs] def scale(self) -> torch.Tensor:
r'''
See :meth:`pypose.scale`
'''
return self.ltype.scale(self)
[docs] def euler(self, eps=2e-4) -> torch.Tensor:
r'''
See :meth:`pypose.euler`
'''
data = self.rotation().tensor()
x, y = data[..., 0], data[..., 1]
z, w = data[..., 2], data[..., 3]
xx, yy, zz, ww = x*x, y*y, z*z, w*w
t0 = 2 * (w * x + y * z)
t1 = (ww + zz) - (xx + yy)
t2 = 2 * (w * y - z * x) / (xx + yy + zz + ww)
t3 = 2 * (w * z + x * y)
t4 = (ww + xx) - (yy + zz)
roll = torch.atan2(t0, t1)
pitch = torch.asin(t2.clamp(-1, 1))
# sigularity when pitch angle ~ +/-pi/2
flag = -1. + eps < t2 < 1. - eps
yaw1 = torch.atan2(t3, t4)
yaw2 = -2 * torch.sign(t2) * torch.atan2(x, w)
yaw = torch.where(flag, yaw1, yaw2)
return torch.stack([roll, pitch, yaw], dim=-1)
[docs] def identity_(self):
r'''
Inplace set the LieTensor to identity.
Return:
LieTensor: the :obj:`self` LieTensor
Note:
The translation part, if there is, is set to zeros, while the
rotation part is set to identity quaternion.
Example:
>>> x = pp.randn_SO3(2)
>>> x
SO3Type LieTensor:
tensor([[-0.0724, 0.1970, 0.0022, 0.9777],
[ 0.3492, 0.4998, -0.5310, 0.5885]])
>>> x.identity_()
SO3Type LieTensor:
tensor([[0., 0., 0., 1.],
[0., 0., 0., 1.]])
'''
return self.ltype.identity_(self)
[docs] def cumops(self, dim, ops):
r"""
See :func:`pypose.cumops`
"""
return self.ltype.cumops(self, dim, ops)
[docs] def cummul(self, dim):
r"""
See :func:`pypose.cummul`
"""
return self.ltype.cummul(self, dim)
[docs] def cumprod(self, dim, left = True):
r"""
See :func:`pypose.cumprod`
"""
return self.ltype.cumprod(self, dim, left)
[docs] def cumops_(self, dim, ops):
r"""
Inplace version of :func:`pypose.cumops`
"""
return self.ltype.cumops_(self, dim, ops)
[docs] def cummul_(self, dim):
r"""
Inplace version of :func:`pypose.cummul`
"""
return self.ltype.cummul_(self, dim)
[docs] def cumprod_(self, dim):
r"""
Inplace version of :func:`pypose.cumprod`
"""
return self.ltype.cumprod_(self, dim)
[docs]class Parameter(LieTensor, nn.Parameter):
r'''
A kind of LieTensor that is to be considered a module parameter.
Parameters are of :meth:`LieTensor` and :meth:`torch.nn.Parameter`,
that have a very special property when used with Modules: when
they are assigned as Module attributes they are automatically
added to the list of its parameters, and will appear, e.g., in
:meth:`parameters()` iterator.
Args:
data (LieTensor): parameter LieTensor.
requires_grad (bool, optional): if the parameter requires
gradient. Default: ``True``
Examples:
>>> import torch, pypose as pp
>>> x = pp.Parameter(pp.randn_SO3(2))
>>> x.Log().sum().backward()
>>> x.grad
tensor([[0.8590, 1.4069, 0.6261, 0.0000],
[1.2869, 1.0748, 0.5385, 0.0000]])
'''
def __init__(self, data, **kwargs):
self.ltype = data.ltype
def __new__(cls, data=None, requires_grad=True):
if data is None:
data = torch.tensor([])
return LieTensor._make_subclass(cls, data, requires_grad)
def __deepcopy__(self, memo):
if id(self) in memo:
return memo[id(self)]
else:
result = type(self)(self.clone(memory_format=torch.preserve_format))
memo[id(self)] = result
return result
