Ei7hSSKrSSKJr SSKJr SrSrSrSr S r S r S r S r "S S5rg)N) solve_banded)Rotationc[R"[U5SS45nUSS2S4*USS2SS4'USS2S4USS2SS4'USS2S4USS2SS4'USS2S4*USS2SS4'USS2S4*USS2SS4'USS2S4USS2SS4'U$)zCreate skew-symmetric matrices corresponding to vectors. Parameters ---------- x : ndarray, shape (n, 3) Set of vectors. Returns ------- ndarray, shape (n, 3, 3) Nrr)npzeroslen)xresults e/home/mande/repo/quber/.venv/lib/python3.13/site-packages/scipy/spatial/transform/_rotation_spline.py_create_skew_matrixrsXXs1vq!n %FAwhF1a7O1gF1a7O1gF1a7OAwhF1a7OAwhF1a7O1gF1a7O Mc0[R"SX5$)z5Compute the product of stack of matrices and vectors.z ijk,ik->ij)r einsum)Abs r _matrix_vector_product_of_stacksrs 99\1 ((rc [RRUSS9n[R"U5nUS:nXnSSU-[R"SU-5- - US-- X#'U)nXnSSUS---X#'[ U5n[R "[U5SS45n[R"S5US S &US S ===SU-- sss&US S ===US S 2S S 4[R"XU5-- sss&U$) aCompute matrices to transform angular rates to rot. vector derivatives. The matrices depend on the current attitude represented as a rotation vector. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. Returns ------- ndarray, shape (n, 3, 3) raxis-C6??rUUUUUU?gllV?rN) r linalgnorm empty_liketanremptyr identitymatmul)rotvecsrkmasknmskewr s r"_angular_rate_to_rotvec_dot_matrixr(!s 99>>'> *D dA $;D B38bffS2X..."a%7AG 5D BURU]"AG w 'D XXs7|Q* +F AF1I 1ItI 1I1dD=!BIId$999I Mrc [RRUSS9n[R"U5n[R"U5nUS:nXnS[R"U5- US-- X$'U[R "U5- US-- X4'U)nXnSUS-S- - X$'SUS-S - - X4'[ U5n[R"[U5SS45n[R"S5US S &US S ===US S 2S S 4U--sss&US S ===US S 2S S 4[R"Xf5-- sss&U$) aCompute matrices to transform rot. vector derivatives to angular rates. The matrices depend on the current attitude represented as a rotation vector. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. Returns ------- ndarray, shape (n, 3, 3) rrrrrrUUUUUU?xN) r rrrcossinrr r r!r")r#rk1k2r%r&r'r s r"_rotvec_dot_to_angular_rate_matrixr1Ds2 99>>'> *D t B t B $;D BBFF2J"')BHRVVBZ27*BH 5D BR1Wr\!BHrQw}$BH w 'D XXs7|Q* +F AF1I 1IAtTM"T))I 1IAtTM"RYYt%:::I Mrc[RRUSS9n[R"X-SS9n[R"X5n[R"X5n[R"X5n[R "U5n[R "U5n[R "U5n US:n X*n U *[R "U 5-S[R"U 5S- -- U S-- Xz'SU -S[R "U 5--U [R"U 5-- U S-- X'U [R "U 5- U S-- X'U )n X*n S U S-S - - Xz'S U S-S - -X'S U S-S- - X'USS2S4nUSS2S4nUSS2S4nU SS2S4n X7U-X---X--$)aCompute the non-linear term in angular acceleration. The angular acceleration contains a quadratic term with respect to the derivative of the rotation vector. This function computes that. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. rotvecs_dot : ndarray, shape (n, 3) Set of rotation vector derivatives. Returns ------- ndarray, shape (n, 3) rrrrrrgi<1r+r,N)r rrsumcrossrr.r-) r# rotvecs_dotrdpcpccpdccpr/r0k3r%r&s r$_angular_acceleration_nonlinear_termr?ks" 99>>'> *D %A .B ' 'B ((7 C 88K $D t B t B t B $;D BbffRj 1r Q#7727BBHR!bffRj.(2r ?:bAgEBHRVVBZ27*BH 5D BbAgm#BHrQw&BHR1Ws]"BH AtGB AtGB AtGB AtGB b28# $ry 00rc,[[U5U5$)a Compute angular rates given rotation vectors and its derivatives. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. rotvecs_dot : ndarray, shape (n, 3) Set of rotation vector derivatives. Returns ------- ndarray, shape (n, 3) )rr1)r#r9s r_compute_angular_raterAs ,*73[ BBrc0[X5[X5-$)afCompute angular acceleration given rotation vector and its derivatives. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. rotvecs_dot : ndarray, shape (n, 3) Set of rotation vector derivatives. rotvecs_dot_dot : ndarray, shape (n, 3) Set of rotation vector second derivatives. Returns ------- ndarray, shape (n, 3) )rAr?)r#r9rotvecs_dot_dots r_compute_angular_accelerationrDs "' ; 0 F GHrc$[R"S5n[R"[U55n[R"U[S9nUSS2S4USS&USSUSS2SS4--- n[R"U[S9nX6SS&USUSS2SS4-- n[R"U[S9nUSS2S4USS&USUSS2SS4-- n[R"U[S9nX8SS&USSUSS2SS4--- n[R"S[U5-5=p[R "UR 5UR 5U 45n [R "UR 5UR 5U 45n [R "UR 5UR 5[R"US545n SnSn[R"X-S-S[U5-45nU UX-U - U 4'U$)a Create a 3-diagonal block matrix as banded. The matrix has the following structure: DB... ADB.. .ADB. ..ADB ...AD The blocks A, B and D are 3-by-3 matrices. The D matrices has the form d * I. Parameters ---------- A : ndarray, shape (n, 3, 3) Stack of A blocks. B : ndarray, shape (n, 3, 3) Stack of B blocks. d : ndarray, shape (n + 1,) Values for diagonal blocks. Returns ------- ndarray, shape (11, 3 * (n + 1)) Matrix in the banded form as used by `scipy.linalg.solve_banded`. rdtypeNrr5) r aranger rinthstackravelrepeatr )rBdind ind_blocksA_iA_jB_iB_jdiag_idiag_jijvaluesulr s r_create_block_3_diagonal_matrixr\s8 ))A,C3q6"J -- %C D\CF1Jq$}-- ..C -- %C F1z!T4-( ((C -- %C D\CF1z!T4-( ((C -- %C F1Jq$}-- ..CiiCF ++F 399; V45A 399; V45A YY 1779bii1o> ?F A A XXquqy!c!f*- .F!F1519a< Mrc6\rSrSrSrSrSrSrSrS Sjr Sr g ) RotationSplineaW Interpolate rotations with continuous angular rate and acceleration. The rotation vectors between each consecutive orientation are cubic functions of time and it is guaranteed that angular rate and acceleration are continuous. Such interpolation are analogous to cubic spline interpolation. Refer to [1]_ for math and implementation details. Parameters ---------- times : array_like, shape (N,) Times of the known rotations. At least 2 times must be specified. rotations : `Rotation` instance Rotations to perform the interpolation between. Must contain N rotations. Methods ------- __call__ References ---------- .. [1] `Smooth Attitude Interpolation `_ Examples -------- >>> from scipy.spatial.transform import Rotation, RotationSpline >>> import numpy as np Define the sequence of times and rotations from the Euler angles: >>> times = [0, 10, 20, 40] >>> angles = [[-10, 20, 30], [0, 15, 40], [-30, 45, 30], [20, 45, 90]] >>> rotations = Rotation.from_euler('XYZ', angles, degrees=True) Create the interpolator object: >>> spline = RotationSpline(times, rotations) Interpolate the Euler angles, angular rate and acceleration: >>> angular_rate = np.rad2deg(spline(times, 1)) >>> angular_acceleration = np.rad2deg(spline(times, 2)) >>> times_plot = np.linspace(times[0], times[-1], 100) >>> angles_plot = spline(times_plot).as_euler('XYZ', degrees=True) >>> angular_rate_plot = np.rad2deg(spline(times_plot, 1)) >>> angular_acceleration_plot = np.rad2deg(spline(times_plot, 2)) On this plot you see that Euler angles are continuous and smooth: >>> import matplotlib.pyplot as plt >>> plt.plot(times_plot, angles_plot) >>> plt.plot(times, angles, 'x') >>> plt.title("Euler angles") >>> plt.show() The angular rate is also smooth: >>> plt.plot(times_plot, angular_rate_plot) >>> plt.plot(times, angular_rate, 'x') >>> plt.title("Angular rate") >>> plt.show() The angular acceleration is continuous, but not smooth. Also note that the angular acceleration is not a piecewise-linear function, because it is different from the second derivative of the rotation vector (which is a piecewise-linear function as in the cubic spline). >>> plt.plot(times_plot, angular_acceleration_plot) >>> plt.plot(times, angular_acceleration, 'x') >>> plt.title("Angular acceleration") >>> plt.show() g& .>c USR5n[U5n[U5n[SUSS-USS2SS4- SUSS-USS2SS4- SSUSS- SUSS- --5nSUSSUSS2S4S--USSUSS2S4S----nUS==SUS- USR U5--ss'US==SUS- USR US5--ss'[ UR 5Hn [XR5n [USSU SS5n X- n [SX|R55n U RS 5n [R"XSS- 5nXSS&[R"XRS[R"U 5--:5(dM O [XR5n [R "XBSS45nX*4$) Nrrrr3r4)r5r5)rbr)copyr(r1r\dotrangeMAX_ITERrr?rrKreshaper absallTOLvstack)selfdt angular_ratesr#angular_rate_firstrA_invMb0 iterationr9 delta_betarangular_rates_newdeltas r_solve_for_angular_rates'RotationSpline._solve_for_angular_ratesKs*1-224 .w 727; + a Ob2tT!12 2 !BK"QrT4-. . RWq2ab6z) * , '#2,CRCI"!44!"+12t8  2234 1RUU1X\\*<=== 2!bf*quyyr):;;;t}}-I:1LK= k#2.0JA ,VQ B  1 9 9' B FF,Sb/AABE!2#2 vvehh!bff5F.G*GHHII.7qH  #5Sb7I"JK ))rcSSKJn UR(a [S5eUR 5R S:a [S5e[ U5S:Xa [S5e[R"U[S9nUR S:wa [S 5e[ U5[ U5:wa$[S [ U5S [ U5S 35e[R"U5n[R"US:*5(a [S 5eUSSR5USS-R5nXTSS2S4- n[ U5S:XaUnOURXFU5upgUSS2S4n[R"S[ U5S- S45nSU-XF--XG--US-- US'SU-SU-U-- XG-- US-- US'XhS'SUS'XlX lU"X5Ulg)Nr)PPolyz,`rotations` must be a sequence of rotations.rz?Rotations with more than 1 leading dimension are not supported.rz.`rotations` must contain at least 2 rotations.rFz`times` must be 1-dimensional.zLExpected number of rotations to be equal to number of timestamps given, got z rotations and z timestamps.z9Values in `times` must be in a strictly increasing order.rbr3rr4)scipy.interpolater{single ValueErroras_quatndimr r asarrayfloatdiffanyinv as_rotvecrxr times rotations interpolator) rmrrr{rnr#ror9coeffs r__init__RotationSpline.__init__ls +   KL L     # #a 'Q  y>Q MN N 5. ::?=> > u:Y '$$' N#34$$'J<|=> > WWU^ 66"'??12 2Sb>%%')AB-7BBDQW+- y>Q 'K)-)F)F7*, &M4[!SZ!^Q/0L2#55&'*,'2aK!b&="88&'*,'2a aa "!%/rcUS;a [S5e[R"U[S9nURS:a [S5eURS:Hn[R "U5nUR U5nUS:Xax[R"URUSS9nUS-nSXUS:'[UR5S- nUS- XUUS- :'URU[R"U5-nO]US:XaUR US5n[XH5nO9US :Xa1UR US5nUR US 5n [XHU 5nOeU(aUSnU$) a~Compute interpolated values. Parameters ---------- times : float or array_like Times of interest. order : {0, 1, 2}, optional Order of differentiation: * 0 (default) : return Rotation * 1 : return the angular rate in rad/sec * 2 : return the angular acceleration in rad/sec/sec Returns ------- Interpolated Rotation, angular rate or acceleration. )rrrz`order` must be 0, 1 or 2.rFrz&`times` must be at most 1-dimensional.rright)sider)r~r rrr atleast_1dr searchsortedrr rr from_rotvecrArD) rmrorder singe_timer#index n_segmentsr r9rCs r__call__RotationSpline.__call__sW$  !9: : 5. ::>EF FZZ1_  e$##E* A:OODJJGDE QJE E!) TZZ1,J,6NE*q.( )^^E*X-A-A'-JJF aZ++E15K*7@F aZ++E15K"//q9O273BDF 5 AYF r)rrrN)r) __name__ __module__ __qualname____firstlineno____doc__rgrkrxrr__static_attributes__rrr^r^s&JXH C*B10f2rr^)numpyr scipy.linalgr _rotationrrrr(r1r?rArDr\r^rrrrsH%,) F$N,1^B$H(8vVVr