3j]SSKJr SSKJrJrJrJr SSKrSSKJr SSK J r SSK J r J r JrJrJrJrJr SSKJr "SS \R*5rSS S S \\R.S S 4S jjrg))pi)AnyOptionalTupleUnionN)nn)KORNIA_CHECK_TYPE)axis_angle_to_quaternioneuler_from_quaternionnormalize_quaternionquaternion_from_eulerquaternion_to_axis_anglequaternion_to_rotation_matrixrotation_matrix_to_quaternion)batched_dot_productc T^\rSrSr%Sr\\R\R4\ S'S\\R\R4SS4U4Sjjr S\ S \ SS4S jr S \\R\4SS4S jrS\4S jrS\\\4SS4SjrSJSjrS\S\R\4SS4SjrS\S\R\4SS4SjrS\S\R\4SS4SjrS\\R\4SS4SjrS\\RS\4SS4SjrS\\RS\4SS4SjrS\\R\4SS4SjrS\\R\4SS4SjrS\\R\4SS4SjrS\\R\4SS4SjrS\SS4Sjr \!S\R4Sj5r"\!S\#\R\R\R\R44S j5r$\!S\R4S!j5r%\!S\R4S"j5r&\!S\R4S#j5r'\!S\R4S$j5r(\!S\R4S%j5r)\!S\R4S&j5r*\!S\R4S'j5r+\!S\R4S(j5r,\!S\#\S)44S*j5r-\!S\R4S+j5r.S\R4S,jr/\0S-\RSS4S.j5r1\0S/\RS0\RS1\RSS4S2j5r2S\#\R\R\R44S3jr3\0S4\RSS4S5j5r4S\R4S6jr5\0SKS7\6\S8\S\\Rn4S9\\RpS4SS4S:jj5r9\0S;\S<\S=\S>\SS4 S?j5r:\0SKS7\6\S8\S\\Rn4S9\\RpS4SS4S@jj5r;SASS\SS4SBjrSJSEjr?SJSFjr@SJSGjrAS\R4SHjrBSIrCU=rD$)M Quaternion)agBase class to represent a Quaternion. A quaternion is a four dimensional vector representation of a rotation transformation in 3d. See more: https://en.wikipedia.org/wiki/Quaternion The general definition of a quaternion is given by: .. math:: Q = a + b \cdot \mathbf{i} + c \cdot \mathbf{j} + d \cdot \mathbf{k} Thus, we represent a rotation quaternion as a contiguous torch.Tensor structure to perform rigid bodies transformations: .. math:: Q = \begin{bmatrix} q_w & q_x & q_y & q_z \end{bmatrix} Example: >>> q = Quaternion.identity(batch_size=4) >>> q.data tensor([[1., 0., 0., 0.], [1., 0., 0., 0.], [1., 0., 0., 0.], [1., 0., 0., 0.]]) >>> q.real tensor([1., 1., 1., 1.]) >>> q.vec tensor([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]) _datadatareturnNc>[TU]5 [U[R[ R 45(d[S[U535eXl g)aConstruct a quaternion from torch.Tensor or parameter data. Args: data: torch.Tensor or parameter containing the quaternion data with the shape of :math:`(B, 4)`. Example: >>> # Create with torch.tensor(no gradients tracked by default) >>> data = torch.tensor([1., 0., 0., 0.]) >>> q1 = Quaternion(data) >>> # Create with parameter (gradients tracked) >>> param_data = torch.nn.Parameter(torch.tensor([1., 0., 0., 0.])) >>> q2 = Quaternion(param_data) z+Expected torch.Tensor or nn.Parameter, got N) super__init__ isinstancetorchTensorr Parameter TypeErrortyper)selfr __class__s T/home/wildlama/miniconda3/lib/python3.13/site-packages/kornia/geometry/quaternion.pyrQuaternion.__init__OsF $r|| <==I$t*VW W argskwargscL[URR"U0UD65$)zMove and/or cast the quaternion data. Args: *args: Arguments to pass to torch.Tensor.to() **kwargs: Keyword arguments to pass to torch.Tensor.to() Returns: A new Quaternion with converted data. )rrto)r!r&r's r#r) Quaternion.tods!$**--8899r%valuec[U[[45(a>[R"XR R UR RS9nOW[U[R5(a8URUR R UR RS9n[R"URRUR5nURRU5URU5-nUR!5S:XaUR#U5nO [R$"XR5n[R&"U5R)S5R"/URQSP76n[R*"UR)S5U/SS9n[-U5$![a5n[SURRSUR35UeSnAff=f) a)Convert a scalar, torch.Tensor, or numeric value to a scalar quaternion. A scalar quaternion has the form [real, 0, 0, 0] where real is the input value. Args: value: The scalar, torch.Tensor, or numeric value to convert. Returns: A Quaternion object representing the scalar quaternion. devicedtypezCannot broadcast shapes z and Nrdim)rintfloatrtensorrr.r/rr)broadcast_shapesrealshape RuntimeError ValueErrorexpandr3 expand_as broadcast_to zeros_like unsqueezecatr)r!r+ target_shapee broadcastedexpanded_valuezerosscalar_quat_datas r#_to_scalar_quaternion Quaternion._to_scalar_quaternionps ec5\ * *LLyy/?/?tyyWE u|| , ,HHDII$4$4DIIOOHLE d 11$))//5;;OLii&&|4u||L7QQ  99;! "__[9N#//7H7HIN  0::2>EE_~G[G[_]^_!99n&>&>r&BE%JPRS*++' d7 7Hekk][\bc c ds25G H 0HH cUR$Nrr!s r#__repr__Quaternion.__repr__s))r%idxc2[URU5$rKrr)r!rPs r# __getitem__Quaternion.__getitem__s$))C.))r%c.[UR*5$)zInverts the sign of the quaternion data. Example: >>> q = Quaternion.identity() >>> -q.data tensor([-1., -0., -0., -0.]) rRrMs r#__neg__Quaternion.__neg__s499*%%r%rightc[U[5(a"[URUR-5$URU5n[URUR-5$)aAdd a given quaternion, scalar, or torch.Tensor. Args: right: the quaternion, scalar, or torch.Tensor to add. Example: >>> q1 = Quaternion.identity() >>> q2 = Quaternion(torch.tensor([2., 0., 1., 1.])) >>> q3 = q1 + q2 >>> q3.data tensor([3., 0., 1., 1.]) )rrrrH)r!rX right_quats r#__add__Quaternion.__add__sQ eZ ( (dii%**45 533E:Jdii*//9: :r%c0[U[5(a"[URUR- 5$URU5nURUR- n[U[R 5(a URn[U5$)a%Subtract a given quaternion, scalar, or torch.Tensor. Args: right: the quaternion, scalar, or torch.Tensor to subtract. Example: >>> q1 = Quaternion(torch.tensor([2., 0., 1., 1.])) >>> q2 = Quaternion.identity() >>> q3 = q1 - q2 >>> q3.data tensor([1., 0., 1., 1.]) )rrrrHrr)r!rXrZ result_datas r#__sub__Quaternion.__sub__sr eZ ( (dii%**45 533E:J))joo5K+r||44).. k* *r%c~[U[5(aURUR-[URUR5- nURSUR-URSUR--[ R RURURSS9-n[[ R"USU4S55$URU5nURUR-[URUR5- nURSUR-URSUR--[ R RURURSS9-n[[ R"USU4S55$)N.Nr0r2) rrr8rvecrlinalgcrossrArH)r!rXnew_realnew_vecrZs r#__mul__Quaternion.__mul__sl eZ ( (yy5::-0CDHHeii0XXH )$uyy0**Y'$((23,,$$TXXuyyb$AB  eii))>DII-0CIMMSWS[S[0\\ NN9 % 0ii "Y]]2 3ll  b A B  %))Xi%8'$BBGHHr%c[U[5(aXR5-$[U[[45(a>[ R "XRRURRS9nO8URURRURRS9nUR5S:XaGURURS5RS5RUR5nO*URS5RUR5nURU- n[U[R5(a URn[U5$)Nr-r.rr0)rrinvr4r5rr6rr.r/r)r3r=r@rr)r!rX right_tensordivisorr^s r#__div__Quaternion.__div__s eZ ( ())+% %%#u..$||E)):J:JRVR[R[RaRab $xxtyy/?/?tyyxW !Q&&0061BCMMbQ[[\`\e\ef'004>>tyyI))g-K+r||44).. k* *r%c$URU5$rK)rt)r!rXs r# __truediv__Quaternion.__truediv__ s||E""r%c,URU5nX -$)zDRight addition (left + self) where left is a scalar or torch.Tensor.rHr!rjrls r#__radd__Quaternion.__radd__..t4 r%c,URU5nX - $)zGRight subtraction (left - self) where left is a scalar or torch.Tensor.rzr{s r#__rsub__Quaternion.__rsub__r~r%c,URU5nX - $zDRight division (left / self) where left is a scalar or torch.Tensor.rzr{s r# __rtruediv__Quaternion.__rtruediv__r~r%c$URU5$r)r)r!rjs r#__rdiv__Quaternion.__rdiv__s  &&r%tcNURSnURRSSS9n[R"US:gURU- URS-5nX-R 5nX-R 5U-n[[R"XV4S55$)zReturn the power of a quaternion raised to exponent t. Args: t: raised exponent. Example: >>> q = Quaternion(torch.tensor([1., .5, 0., 0.])) >>> q_pow = q**2 rbr0T)r3keepdimr) polar_anglercnormrwherecossinrrA)r!rthetavec_normnwxyzs r#__pow__Quaternion.__pow__#s  +88==R=6 KKA txx(':DHHqL I YOO yoo!#%))QHb122r%cUR$)z5Return the underlying data with shape :math:`(B, 4)`.rrMs r#rQuaternion.data5szzr%c^URURURUR4$)z>Return a tuple with the underlying coefficients in WXYZ order.)rxyzrMs r#coeffsQuaternion.coeffs:s#vvtvvtvvtvv--r%cUR$)zkReturn the real part with shape :math:`(B,)`. Alias for :func: `~kornia.geometry.quaternion.Quaternion.w` )rrMs r#r8Quaternion.real?s vv r%c(URSSS24$)zDReturn the vector with the imaginary part with shape :math:`(B, 3)`..NrLrMs r#rcQuaternion.vecHsyyab!!r%cUR$)zuReturn the underlying data with shape :math:`(B, 4)`. Alias for :func:`~kornia.geometry.quaternion.Quaternion.data` rLrMs r#q Quaternion.qMs yyr%cUR$)ztReturn a scalar with the real with shape :math:`(B,)`. Alias for :func: `~kornia.geometry.quaternion.Quaternion.w` )r8rMs r#scalarQuaternion.scalarUsyyr%c URS$)z/Return the :math:`q_w` with shape :math:`(B,)`.rprLrMs r#r Quaternion.w^yy  r%c URS$)z/Return the :math:`q_x` with shape :math:`(B,)`.).rrLrMs r#r Quaternion.xcrr%c URS$)z/Return the :math:`q_y` with shape :math:`(B,)`.).rLrMs r#r Quaternion.yhrr%c URS$)z/Return the :math:`q_z` with shape :math:`(B,)`.).r1rLrMs r#r Quaternion.zmrr%.c@[URR5$)zBReturn the shape of the underlying data with shape :math:`(B, 4)`.)tuplerr9rMs r#r9Quaternion.shapersTYY__%%r%cXURUR5- R5$)zReturn the polar angle with shape :math:`(B,1)`. Example: >>> q = Quaternion.identity() >>> q.polar_angle tensor(0.) )rracosrMs r#rQuaternion.polar_anglews" diik)//11r%c,[UR5$)zConvert the quaternion to a rotation matrix of shape :math:`(B, 3, 3)`. Example: >>> q = Quaternion.identity() >>> m = q.matrix() >>> m tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) )rrrMs r#matrixQuaternion.matrixs-TYY77r%rc$U"[U55$)zCreate a quaternion from a rotation matrix. Args: matrix: the rotation matrix to convert of shape :math:`(B, 3, 3)`. Example: >>> m = torch.eye(3)[None] >>> q = Quaternion.from_matrix(m) >>> q.data tensor([[1., 0., 0., 0.]]) )r)clsrs r# from_matrixQuaternion.from_matrixs0899r%rollpitchyawc^[XUS9upEpg[R"XEXg4S5nU"U5$)aVCreate a quaternion from Euler angles. Args: roll: the roll euler angle. pitch: the pitch euler angle. yaw: the yaw euler angle. Example: >>> roll, pitch, yaw = torch.tensor(0), torch.tensor(1), torch.tensor(0) >>> q = Quaternion.from_euler(roll, pitch, yaw) >>> q.data tensor([0.8776, 0.0000, 0.4794, 0.0000]) )rrrr0)r rstack) rrrrrrrrrs r# from_eulerQuaternion.from_eulers1 +sK a KKq b )1v r%cn[URURURUR5$)aConvert the quaternion to a triple of Euler angles (roll, pitch, yaw). Example: >>> q = Quaternion(torch.tensor([2., 0., 1., 1.])) >>> roll, pitch, yaw = q.to_euler() >>> roll tensor(2.0344) >>> pitch tensor(1.5708) >>> yaw tensor(2.2143) )r rrrrrMs r#to_eulerQuaternion.to_eulers%%TVVTVVTVVTVVDDr% axis_anglec$U"[U55$)a"Create a quaternion from axis-angle representation. Args: axis_angle: rotation vector of shape :math:`(B, 3)`. Example: >>> axis_angle = torch.tensor([[1., 0., 0.]]) >>> q = Quaternion.from_axis_angle(axis_angle) >>> q.data tensor([[0.8776, 0.4794, 0.0000, 0.0000]]) )r )rrs r#from_axis_angleQuaternion.from_axis_angles+J788r%c,[UR5$)zConvert the quaternion to an axis-angle representation. Example: >>> q = Quaternion.identity() >>> axis_angle = q.to_axis_angle() >>> axis_angle tensor([0., 0., 0.]) )rrrMs r# to_axis_angleQuaternion.to_axis_angles( 22r% batch_sizer.r/cj[R"/SQX#S9nUbURUS5nU"U5$)aCreate a quaternion representing an identity rotation. Args: batch_size: the batch size of the underlying data. device: device to place the result on. dtype: dtype of the result. Example: >>> q = Quaternion.identity() >>> q.data tensor([1., 0., 0., 0.]) )?rrr-r)rr6repeat)rrr.r/rs r#identityQuaternion.identitys5(||0M  !;;z1-D4yr%rrrrc>U"[R"XX4/55$)a}Create a quaternion from the data coefficients. Args: w: a float representing the :math:`q_w` component. x: a float representing the :math:`q_x` component. y: a float representing the :math:`q_y` component. z: a float representing the :math:`q_z` component. Example: >>> q = Quaternion.from_coeffs(1., 0., 0., 0.) >>> q.data tensor([1., 0., 0., 0.]) )rr6)rrrrrs r# from_coeffsQuaternion.from_coeffss 5<<q -..r%cUbU4OSn[R"S/UQ7X#S9upVnSU- R5S[-U-R 5-nSU- R5S[-U-R 5-n UR5S[-U-R 5-n UR5S[-U-R 5-n U"[R "XX4S55$)a{Create a random unit quaternion of shape :math:`(B, 4)`. Uniformly distributed across the rotation space as per: http://planning.cs.uiuc.edu/node198.html Args: batch_size: the batch size of the underlying data. device: device to place the result on. dtype: dtype of the result. Example: >>> q = Quaternion.random() >>> q = Quaternion.random(batch_size=2) r1r-rrr0)rrandsqrtrrrr) rrr.r/ rand_shaper1r2r3q1q2q3q4s r#randomQuaternion.randoms*'1&>> q0 = Quaternion.identity() >>> q1 = Quaternion(torch.tensor([1., .5, 0., 0.])) >>> q2 = q0.slerp(q1, .3) )r r normalizerq)r!rrq0s r#slerpQuaternion.slerp,s= "j) ^^  \\^VVX]q(((r%rc<URRSSU5$)zCompute the norm (magnitude) of the quaternion. Args: keepdim: whether to retain the last dimension. Returns: The norm of the quaternion(s) as a torch.Tensor. Example: >>> q = Quaternion.identity() >>> q.norm() tensor(1.) rr0)rr)r!rs r#rQuaternion.norm@s yy~~aW--r%c>[[UR55$)zReturn a normalized (unit) quaternion. Returns: The normalized quaternion. Example: >>> q = Quaternion(torch.tensor([2., 1., 0., 0.])) >>> q_norm = q.normalize() )rr rrMs r#rQuaternion.normalizeRs.tyy9::r%cv[[R"URSUR*4S55$)zCompute the conjugate of the quaternion. Returns: The conjugate quaternion, with the vector part negated. Example: >>> q = Quaternion(torch.tensor([1., 2., 3., 4.])) >>> q_conj = q.conj() rbr0)rrrAr8rcrMs r#conjQuaternion.conj_s.%))TYYy%9DHH9$ErJKKr%cDUR5UR5- $)zCompute the inverse of the quaternion. Returns: The inverse quaternion. Example: >>> q = Quaternion.identity() >>> q_inv = q.inv() )r squared_normrMs r#rqQuaternion.invlsyy{T..000r%cb[URUR5URS--$)zCompute the squared norm (magnitude) of the quaternion. Returns: The squared norm of the quaternion(s) as a torch.Tensor. Example: >>> q = Quaternion.identity() >>> q.squared_norm() tensor(1.) r)rrcr8rMs r#rQuaternion.squared_normys&#488TXX6AEEr%r)rr)NNN)F)E__name__ __module__ __qualname____firstlineno____doc__rrrrr__annotations__rrr)r5rHstrrNr4slicerSrVr[r_rhrmrtrwr|rrrrpropertyrrrr8rcrrrrrrr9rr classmethodrrrrrrr.r/rrrrboolrrrrqr__static_attributes__ __classcell__)r"s@r#rr)s!F r||+ ,,U5<<#=>4* : :s :| :&,5u1D+E&,,&,P#*uS%Z0*\* &;U<u#DE;,;(+U<u#DE+,+0MU<u#DEM,M, IU5<<#67 IL I+U5<<u#DE+,+.#u||\5'H!I#l# U5<<#67 L  U5<<#67 L  u||U':!;  'U5<<#67'L'33<3$ell.ellELL%,, TU..ell"U\\""5<< !5<<!!!5<<!!!5<<!!!5<<!!&uS#X&& 2U\\ 2 2 8 8 : :, : :ell5<<ellWc&E% ellELL HIE  9 9, 9 9 3u|| 3%)15*. SMdC-.U[[$&'   0/E/e//%/L//&%)15*. 6SM6dC-.6U[[$&' 6  66:) ))<)(.D.U\\.$ ; L 1 Fell F Fr%rQrrc0URn[U[5 URSnUcURU-U- nOUR UR URS9nUR5U:wa[SUR5SU35eXR5- nUR[R"U5-U-nURnUR[R[R4;aUR5n[R R#U5upg[R$"U5nUR U5nUSS2U4n XR'5- n [U R)S55$)a?Compute (weighted) average of multiple quaternions. Args: Q (Quaternion): quaternion object containing data of shape (M, 4). w (torch.Tensor, optional): Weights of shape (M,). If None, uniform weights are used. Returns: Quaternion: averaged quaternion (shape (4,)), wrapped back in the Quaternion class. rN)r/zweights length z" must match number of quaternions )rr rr9Tr)r.r/numelr;sumrdiagfloat16bfloat16r5rdeighargmaxrr@) r rrMA orig_dtype eigenvalues eigenvectorsmax_idxq_avgs r#average_quaternionsrs= 66Da$ 1 Ay VVd]a  DDDJJD / 779>qwwyk9[\][^_` ` K FFUZZ] "T )Jww5==%..11 GGI % 1 1! 4Kll;'G??:.L G $E JJL E eooa( ))r%rK)mathrtypingrrrrrrkornia.core.checkr kornia.geometry.conversionsr r r r rrrkornia.geometry.linalgrModulerrrrr%r#r"se,.. /7\ F\ F~#*<#*HU\\,B#*l#*r%