o oi`&@sddlmZddlmZmZddlmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZddlmZmZmZmZmZddlmZGdddeZd S) ) annotations)Optionaloverload) DeviceDtypeModule ParameterTensorcomplexrandstacktensor zeros_like) KORNIA_CHECKKORNIA_CHECK_IS_TENSOR)check_so2_matrixcheck_so2_matrix_shapecheck_so2_t_shapecheck_so2_theta_shapecheck_so2_z_shape)Vector2cseZdZdZd5fdd Zd6d d Zd7d dZed8ddZed9ddZd:ddZe d;ddZ e ddd Zd;d!d"Zed?d$d%Ze &d@dAd-d.ZdBd/d0Ze &d@dAd1d2Zd;d3d4ZZS)CSo2a(Base class to represent the So2 group. The SO(2) is the group of all rotations about the origin of two-dimensional Euclidean space :math:`R^2` under the operation of composition. See more: https://en.wikipedia.org/wiki/Orthogonal_group#Special_orthogonal_group We internally represent the rotation by a complex number. Example: >>> real = torch.tensor([1.0]) >>> imag = torch.tensor([2.0]) >>> So2(torch.complex(real, imag)) Parameter containing: tensor([1.+2.j], requires_grad=True) zr returnNonecs(tt|t|t||_dS)aConstruct the base class. Internally represented by complex number `z`. Args: z: Complex number with the shape of :math:`(B, 1)` or :math:`(B)`. Example: >>> real = torch.tensor(1.0) >>> imag = torch.tensor(2.0) >>> So2(torch.complex(real, imag)).z Parameter containing: tensor(1.+2.j, requires_grad=True) N)super__init__rrr_z)selfr __class__P/home/ubuntu/.local/lib/python3.10/site-packages/kornia/geometry/liegroup/so2.pyr6s z So2.__init__strcCs|jSN)rrr!r!r"__repr__Lsz So2.__repr__idx int | slicecCst|j|Sr$)rr)rr'r!r!r" __getitem__OszSo2.__getitem__rightcCdSr$r!rr*r!r!r"__mul__Rz So2.__mul__cCr+r$r!r,r!r!r"r-Ur. So2 | TensorcCs|j}t|trt||jSt|ttfrMt|trt||jd}|jd}|j}|j}t ||||||||fd}t|trI|St|St dt |)zPerform a left-multiplication either rotation concatenation or point-transform. Args: right: the other So2 transformation. Return: The resulting So2 transformation. ).r).zNot So2 or Tensor type. Got: ) r isinstancerrr rdatarealimagr TypeErrortype)rr*rxyr4r5outr!r!r"r-Xs    & cCs|jS)z5Return the underlying data with shape :math:`(B, 1)`.)rr%r!r!r"ruszSo2.zthetacCst|tt||S)aiConvert elements of lie algebra to elements of lie group. Args: theta: angle in radians of shape :math:`(B, 1)` or :math:`(B)`. Example: >>> v = torch.tensor([3.1415/2]) >>> s = So2.exp(v) >>> s Parameter containing: tensor([4.6329e-05+1.j], requires_grad=True) )rrr cossin)r;r!r!r"expzszSo2.expcCs|jj|jjS)aConvert elements of lie group to elements of lie algebra. Example: >>> real = torch.tensor([1.0]) >>> imag = torch.tensor([3.0]) >>> So2(torch.complex(real, imag)).log() tensor([1.2490], grad_fn=) )rr5atan2r4r%r!r!r"logs zSo2.logcCs:t|t|}t||fd}t||fd}t||fdS)a]Convert elements from vector space to lie algebra. Returns matrix of shape :math:`(B, 2, 2)`. Args: theta: angle in radians of shape :math:`(B)`. Example: >>> theta = torch.tensor(3.1415/2) >>> So2.hat(theta) tensor([[0.0000, 1.5707], [1.5707, 0.0000]]) r1)rrr )r;rrow0row1r!r!r"hats zSo2.hatomegacCst||dS)a@Convert elements from lie algebra to vector space. Returns vector of shape :math:`(B,)`. Args: omega: 2x2-matrix representing lie algebra. Example: >>> v = torch.ones(3) >>> omega = So2.hat(v) >>> So2.vee(omega) tensor([1., 1., 1.]) ).rr0)r)rDr!r!r"veeszSo2.veecCs<t|jj|jj fd}t|jj|jjfd}t||fdS)aConvert the complex number to a rotation matrix of shape :math:`(B, 2, 2)`. Example: >>> s = So2.identity() >>> m = s.matrix() >>> m tensor([[1., -0.], [0., 1.]], grad_fn=) r1)r rr4r5)rrArBr!r!r"matrixs z So2.matrixrGcCs*t|t|t|d|d}||S)aICreate So2 from a rotation matrix. Args: matrix: the rotation matrix to convert of shape :math:`(B, 2, 2)`. Example: >>> m = torch.eye(2) >>> s = So2.from_matrix(m) >>> s.z Parameter containing: tensor(1.+0.j, requires_grad=True) ).rr).r0r)rrr )clsrGrr!r!r" from_matrixszSo2.from_matrixN batch_size Optional[int]deviceOptional[Device]dtypeOptional[Dtype]cCsVtd||d}td||d}|dur$t|dkdd||}||}|t||S)aCreate a So2 group representing an identity rotation. Args: batch_size: the batch size of the underlying data. device: device to place the result on. dtype: dtype of the result. Example: >>> s = So2.identity(batch_size=2) >>> s Parameter containing: tensor([1.+0.j, 1.+0.j], requires_grad=True) g?rLrNgNr0batch_size must be positivemsg)r rrepeatr rHrJrLrN real_data imag_datar!r!r"identitys  z So2.identitycCstd|jS)zReturn the inverse transformation. Example: >>> s = So2.identity() >>> s.inverse().z Parameter containing: tensor(1.+0.j, requires_grad=True) r0)rrr%r!r!r"inverses z So2.inversecCsd|durt|dkddt|f||d}t|f||d}ntd||d}td||d}|t||S)aECreate a So2 group representing a random rotation. Args: batch_size: the batch size of the underlying data. device: device to place the result on. dtype: dtype of the result. Example: >>> s = So2.random() >>> s = So2.random(batch_size=3) Nr0rQrRrPr!)rr r rUr!r!r"random sz So2.randomcCs:t|jjdkr t|jnd}|||jj|jjjS)zReturn the adjoint matrix of shape :math:`(B, 2, 2)`. Example: >>> s = So2.identity() >>> s.adjoint() tensor([[1., -0.], [0., 1.]], grad_fn=) rN)lenrshaperXrLr4rNrG)rrJr!r!r"adjoint#s z So2.adjoint)rr rr)rr#)r'r(rr)r*rrr)r*r rr )r*r/rr/)rr )r;r rr)r;r rr )rDr rr )rGr rr)NNN)rJrKrLrMrNrOrr)rr)__name__ __module__ __qualname____doc__rr&r)rr-propertyr staticmethodr>r@rCrErG classmethodrIrXrYrZr] __classcell__r!r!rr"r$s<              rN) __future__rtypingrr kornia.corerrrrr r r r r rkornia.core.checkrrkornia.geometry.liegroup._utilsrrrrrkornia.geometry.vectorrrr!r!r!r"s 0