python - 使用numpy区分两个 "symmetrical"数组

Question

我有两个以弧度为单位的角度值数组。这两个阵列关于已知的恒定角是对称的。数组如图所示:

示例值如下:

   one = [ 2.98153965 -1.33298928  2.94993567 -1.39909924  2.99214403  3.00138863
  3.04390642 -1.59098448 -1.65660299 -1.73146174 -1.8166248  -2.85595599
 -2.02035274 -2.64530394 -2.26451127 -2.3982946  -2.52735954 -2.17570346
 -2.77544658 -2.88566686 -1.84913768 -3.07261908 -1.66738719 -1.6029932
 -1.54596053 -1.50177363 -1.46133745 -1.42288915 -1.38241718  2.79925996
 -1.30775884 -1.27309395  2.72153718 -1.20592812 -1.18113435 -1.15029987]

two = [-1.30507254  2.9385436  -1.36415496  2.95897805 -1.43845065 -1.48295087
 -1.53346541  3.09685482 -3.11358085 -3.0466034  -2.95794156 -1.9128659
 -2.75067133 -2.13826992 -2.51567194 -2.39565127 -2.28148844 -2.65519436
 -2.05312249 -1.95523663 -2.98473857 -1.75415233  3.13322155  3.06539723
  3.00595703  2.95378704  2.90786779  2.86730208  2.831318   -1.34113191
  2.77057495  2.74479777 -1.23620286  2.70046364  2.68129889  2.66380717]

可以看出，这些值是“跟随”两条对称的arctan线，我的问题是我如何区分这两者，并得到这样的东西:

我已经尝试了几种方法，但无法想出一种适用于所有情况的通用方法，通常会有一个被误解的部分分配给错误的数组。

欢迎任何想法!谢谢!

Answer 1

这是一个最小化连续点之间的距离以及斜率变化(由参数 lam 加权)的解决方案。仅距离在交叉点处失效。

import numpy as np

one = list(map(float, """ 2.98153965 -1.33298928  2.94993567 -1.39909924  2.99214403  3.00138863
  3.04390642 -1.59098448 -1.65660299 -1.73146174 -1.8166248  -2.85595599
 -2.02035274 -2.64530394 -2.26451127 -2.3982946  -2.52735954 -2.17570346
 -2.77544658 -2.88566686 -1.84913768 -3.07261908 -1.66738719 -1.6029932
 -1.54596053 -1.50177363 -1.46133745 -1.42288915 -1.38241718  2.79925996
 -1.30775884 -1.27309395  2.72153718 -1.20592812 -1.18113435 -1.15029987""".split()))

two = list(map(float, """-1.30507254  2.9385436  -1.36415496  2.95897805 -1.43845065 -1.48295087
 -1.53346541  3.09685482 -3.11358085 -3.0466034  -2.95794156 -1.9128659
 -2.75067133 -2.13826992 -2.51567194 -2.39565127 -2.28148844 -2.65519436
 -2.05312249 -1.95523663 -2.98473857 -1.75415233  3.13322155  3.06539723
  3.00595703  2.95378704  2.90786779  2.86730208  2.831318   -1.34113191
  2.77057495  2.74479777 -1.23620286  2.70046364  2.68129889  2.66380717""".split()))

data = np.array([one, two])

dd = (data[[[0, 1], [1, 0]], 1:] - data[:, None, :-1] + np.pi)%(2*np.pi) - np.pi
dde2 = np.einsum('ijk,ijk->jk', dd, dd)

xovr1 = np.argmin(dde2, axis=0)
pick1 = np.r_[0, np.cumsum(xovr1) & 1]

d2d = dd[:, :, None, 1:] - dd[[[1, 0], [0, 1]], :, :-1]
d2de2 = np.r_['2', np.zeros((2, 2, 1)), np.einsum('ijkl,ijkl->jkl', d2d, d2d)]

lam = 0.5
e2 = (dde2[:, None, :] + lam * d2de2).reshape(4, -1)

xovr2 = np.argmin(e2, axis=0)>>1
pick2 = np.r_[0, np.cumsum(xovr2) & 1]

print('by position only')
print(data[pick1, np.arange(data.shape[1])])
print(data[1-pick1, np.arange(data.shape[1])])

print('by position and slope')
print(data[pick2, np.arange(data.shape[1])])
print(data[1-pick2, np.arange(data.shape[1])])


# by position only
# [ 2.98153965  2.9385436   2.94993567  2.95897805  2.99214403  3.00138863
#   3.04390642  3.09685482 -3.11358085 -3.0466034  -2.95794156 -2.85595599
#  -2.75067133 -2.64530394 -2.51567194 -2.3982946  -2.52735954 -2.65519436
#  -2.77544658 -2.88566686 -2.98473857 -3.07261908  3.13322155  3.06539723
#   3.00595703  2.95378704  2.90786779  2.86730208  2.831318    2.79925996
#   2.77057495  2.74479777  2.72153718  2.70046364  2.68129889  2.66380717]
# [-1.30507254 -1.33298928 -1.36415496 -1.39909924 -1.43845065 -1.48295087
#  -1.53346541 -1.59098448 -1.65660299 -1.73146174 -1.8166248  -1.9128659
#  -2.02035274 -2.13826992 -2.26451127 -2.39565127 -2.28148844 -2.17570346
#  -2.05312249 -1.95523663 -1.84913768 -1.75415233 -1.66738719 -1.6029932
#  -1.54596053 -1.50177363 -1.46133745 -1.42288915 -1.38241718 -1.34113191
#  -1.30775884 -1.27309395 -1.23620286 -1.20592812 -1.18113435 -1.15029987]
# by position and slope
# [ 2.98153965  2.9385436   2.94993567  2.95897805  2.99214403  3.00138863
#   3.04390642  3.09685482 -3.11358085 -3.0466034  -2.95794156 -2.85595599
#  -2.75067133 -2.64530394 -2.51567194 -2.39565127 -2.28148844 -2.17570346
#  -2.05312249 -1.95523663 -1.84913768 -1.75415233 -1.66738719 -1.6029932
#  -1.54596053 -1.50177363 -1.46133745 -1.42288915 -1.38241718 -1.34113191
#  -1.30775884 -1.27309395 -1.23620286 -1.20592812 -1.18113435 -1.15029987]
# [-1.30507254 -1.33298928 -1.36415496 -1.39909924 -1.43845065 -1.48295087
#  -1.53346541 -1.59098448 -1.65660299 -1.73146174 -1.8166248  -1.9128659
#  -2.02035274 -2.13826992 -2.26451127 -2.3982946  -2.52735954 -2.65519436
#  -2.77544658 -2.88566686 -2.98473857 -3.07261908  3.13322155  3.06539723
#   3.00595703  2.95378704  2.90786779  2.86730208  2.831318    2.79925996
#   2.77057495  2.74479777  2.72153718  2.70046364  2.68129889  2.66380717]