sg7hddlZddlmZddlmZdZdZdZdZ d Z d Z d Z d Z Gd dZy)N) solve_banded)Rotationctjt|ddf}|dddf |ddddf<|dddf|ddddf<|dddf|ddddf<|dddf |ddddf<|dddf |ddddf<|dddf|ddddf<|S)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 [/var/www/html/venv/lib/python3.12/site-packages/scipy/spatial/transform/_rotation_spline.py_create_skew_matrixrsXXs1vq!n %FAwhF1a7O1gF1a7O1gF1a7OAwhF1a7OAwhF1a7O1gF1a7O Mc0tjd||S)z5Compute the product of stack of matrices and vectors.z ijk,ik->ij)r einsum)Abs r _matrix_vector_product_of_stacksrs 99\1a ((rc  tjj|d}tj|}|dkD}||}dd|ztjd|zz z |dzz ||<|}||}dd|dzzz||<t |}tj t|ddf}tjd|d d |d d xxxd|zz ccc|d d xxx|d d d d ftj||zz ccc|S) a=Compute 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 dB38bffS2X..."a%7AdG 5D dBURU]"AdG w 'D XXs7|Q* +F AF1I 1ItI 1I1dD=!BIIdD$999I Mrc tjj|d}tj|}tj|}|dkD}||}dtj|z |dzz ||<|tj |z |dzz ||<|}||}d|dzdz z ||<d|dzd z z ||<t |}tjt|ddf}tjd|d d |d d xxx|d d d d f|zzccc|d d xxx|d d d d ftj||zz ccc|S) a=Compute 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_matrixr1Ds@ 99>>'> *D t B t B $;D dBBFF2J"')BtHRVVBZ27*BtH 5D dBR1Wr\!BtHrQw}$BtH w 'D XXs7|Q* +F AF1I 1IAtTM"T))I 1IAtTM"RYYtT%:::I Mrctjj|d}tj||zd}tj||}tj||}tj||}tj |}tj |}tj |} |dkD} || } | tj | zdtj| dz zz | dzz || <d| zdtj | zz| tj| zz | dzz || <| tj | z | dzz | | <| } || } d | dzd z z || <d | dzd z z|| <d | dzdz z | | <|dddf}|dddf}|dddf}| dddf} |||z||zzz| |zzS)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 ((7B C 88K $D t B t B t B $;D dBbffRj 1r Q#7727BBtHR!bffRj.(2r ?:bAgEBtHRVVBZ27*BtH 5D dBbAgm#BtHrQw&BtHR1Ws]"BtH AtGB AtGB AtGB AtGB b28# $rDy 00rc,tt||S)a1Compute angular rates given rotation vectors and its derivatives. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. rotvecs_dot : ndarray, shape (n, 3) Set of rotation vector derivatives. Returns ------- ndarray, shape (n, 3) )rr1)r#r9s r_compute_angular_raterAs ,*73[ BBrc4t||t||zS)aCompute angular acceleration given rotation vector and its derivatives. Parameters ---------- rotvecs : ndarray, shape (n, 3) Set of rotation vectors. rotvecs_dot : ndarray, shape (n, 3) Set of rotation vector derivatives. rotvecs_dot_dot : ndarray, shape (n, 3) Set of rotation vector second derivatives. Returns ------- ndarray, shape (n, 3) )rAr?)r#r9rotvecs_dot_dots r_compute_angular_accelerationrDs$ "'? ; 0+ F GHrc.tjd}tjt|}tj|t}|dddf|dd|dd|ddddfzzz }tj|t}||dd|d|ddddfzz }tj|t}|dddf|dd|d|ddddfzz }tj|t}||dd|dd|ddddfzzz }tjdt|zx} } tj |j |j | f} tj |j |j | f} tj |j |j tj|df} d}d}tj||zdzdt|zf}| ||| z| z | f<|S)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$}-- ..C -- %C CF1z!T4-( ((C -- %C D\CF1z!T4-( ((C -- %C CF1Jq$}-- ..CiiCF ++FV 399; V45A 399; V45A YY 1779bii1o> ?F A A XXq1uqy!c!f*- .F!F1q519a< Mrc,eZdZdZdZdZdZdZddZy) RotationSplinea7 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 |dj}t|}t|}td|ddz|ddddfz d|ddz|ddddfz dd|ddz d|ddz zz}d|dd|dddfdzz|dd|dddfdzzzz}|dxxd|dz |dj |zzcc<|dxxd|dz |dj |dzzcc<t |j D]} t||} t|dd| dd} || z } td|| j} | jd } tj| |ddz }| |ddtj||jdtj| zzksnt||} tj ||ddf}|| fS) Nrrrr3r4)r5r5)rar)copyr(r1r\dotrangeMAX_ITERrr?rrKreshaper absallTOLvstack)selfdt angular_ratesr#angular_rate_firstrA_invMb0 iterationr9 delta_betarangular_rates_newdeltas r_solve_for_angular_ratesz'RotationSpline._solve_for_angular_ratesKs1*1-224 .w 727; + a Ob2tT!12 2 !BK"QrT4-. . RWq2ab6z) * , '#2,CRCI"!44!"+12t8  2234 1RUU1X\\*<=== 2!bf*quyyr):;;;t}}- I:1mLK= k#2.0JZA ,VQ B  1 9 9' B FF,}Sb/AABE!2M#2 vvedhh!bff5F.G*GHHI 7q-H  #5}Sb7I"JK k))rcddlm}|jr tdt |dk(r tdt j |t}|jdk7r tdt |t |k7r-tdjt |t |t j|}t j|dkr td |dd j|ddzj}||dddfz }t |d k(r|}n|j|||\}}|dddf}t jd t |dz d f}d|z||zz||zz|d zz |d<d |zd |z|zz ||zz |d zz |d<||d <d|d <||_||_||||_y)Nr)PPolyz,`rotations` must be a sequence of rotations.rz.`rotations` must contain at least 2 rotations.rFz`times` must be 1-dimensional.zkExpected number of rotations to be equal to number of timestamps given, got {} rotations and {} timestamps.z9Values in `times` must be in a strictly increasing order.rarr3rr4)scipy.interpolaterysingle ValueErrorr r asarrayfloatndimformatdiffanyinv as_rotvecrwr times rotations interpolator) rlrrryrmr#rnr9coeffs r__init__zRotationSpline.__init__ls+   KL L y>Q MN N 5. ::?=> > u:Y '2%fS^SZ@B B WWU^ 66"'?12 2Sb>%%')AB-7BBD"QW+- y>Q 'K)-)F)FM7*, &M;4[!SZ!^Q/0L2 #55;&'*,'2aK!b&="88;&'*,'2a aa "!%/rc|dvr tdtj|t}|jdkDr td|jdk(}tj |}|j |}|dk(r{tj|j|d}|dz}d||dk<t|jdz }|dz |||dz kD<|j|tj|z}n]|dk(r|j |d}t||}n9|d k(r2|j |d}|j |d } t||| }nJ|r|d}|S) aCompute 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 r}r~r atleast_1dr searchsortedrr rr from_rotvecrArD) rlrorder singe_timer#index n_segmentsr r9rCs r__call__zRotationSpline.__call__s_$  !9: : 5. ::>EF FZZ1_  e$##E* A:OODJJGDE QJE E%!) TZZ1,J,6NE%*q.( )^^E*X-A-A'-JJF aZ++E15K*7K@F aZ++E15K"//q9O27K3BDF 5 AYF rN)r) __name__ __module__ __qualname____doc__rfrjrwrrrrr^r^s&JXH C*B,0\2rr^)numpyr scipy.linalgr _rotationrrrr(r1r?rArDr\r^rrrrsH%,) F$N,1^B$H(8vQQr