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docs(base): fix the angle_std formula and the angle_mean and angle_wrap parameter docs - #253
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…ap parameter docs - angle_std: the formula had sin in both components of the mean vector, it is cos and sin; say what R is, that the result is the same as scipy.stats.circstd, and what happens as R tends to zero - angle_mean: the parameter was documented as v but is theta, and the range had a stray bracket; the result is in [-pi, pi]; say that a cancelling set of angles has no defined mean - angle_wrap: the parameter was documented as v but is theta Documentation only.
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What is wrong
Documentation only, in
spatialmath/base/vectors.py:angle_stdsinin both components of the mean vector; the code (and the correct formula) iscosandsinRisangle_meanv, it istheta; the range is written[-\pi, \pi)]with a stray bracket and the result can be exactly\pitheta, range[-\pi, \pi]angle_wrapv, it isthetathetaAdded
angle_stdis the same quantity asscipy.stats.circstdwith its default arguments. I checked this on 300 random samples, the largest difference is 2e-16.angle_meanhas no defined value when the unit vectors cancel (for example0andpi; it returnspi/2because of rounding error)No code changes.
Found while checking, not changed here
angle_stdcan returnnanfor a set of identical angles. The mean resultant lengthRcan come out as1 + 2e-16, so-2 * log(R)is slightly negative and the square root fails with "invalid value encountered in sqrt". For examplenp.full(100, -2.9). I counted 33 failures in 378 combinations of angle and sample size. I will send that as a separate PR.