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A circular von Mises distribution.
This implementation uses polar coordinates. The ``loc`` and ``value`` args
can be any real number (to facilitate unconstrained optimization), but are
interpreted as angles modulo 2 pi.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = VonMises(torch.tensor([1.0]), torch.tensor([1.0]))
>>> m.sample() # von Mises distributed with loc=1 and concentration=1
tensor([1.9777])
:param torch.Tensor loc: an angle in radians.
:param torch.Tensor concentration: concentration parameter
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VonMises._loc s xx{{5<<((r c < V ^8 d QhRS[ /# rZ r )rE rF s "r rG rH s 3 3 3r c T V P P \ P 4 # r )r4 r\ r r] r^ s &r _concentrationVonMises._concentration s !!$$U\\22r c < V ^8 d QhRS[ /# rZ r )rE rF s "r rG rH s J JV Jr c Z V P p^^^V^, , , P 4 , pV^V, P 4 ,
^V, , p^V^, , ^V, , p^V, V, p\ P ! VR8 WT4 # ) gh㈵>)rc sqrtr r )rM kappataurho _proposal_r_proposal_r_taylors & r rl VonMises._proposal_r s ##1q5!8|#))++a#g^^%%!e)436za#g. Y .{{54<);IIr c B V P V4 p\ P ! W P P V P
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P 4 # )a
The sampling algorithm for the von Mises distribution is based on the
following paper: D.J. Best and N.I. Fisher, "Efficient simulation of the
von Mises distribution." Applied Statistics (1979): 152-157.
Sampling is always done in double precision internally to avoid a hang
in _rejection_sample() for small values of the concentration, which
starts to happen for single precision around 1e-4 (see issue #88443).
r# ) _extended_shaper emptyr_ r$ r3 r% r? rc rl r\ )rM sample_shaper( r s && r sampleVonMises.sample sl $$\2 KKYY__TXX__ M IIt**D,<,+. ." O MM - -.> ?M((//+.C . . 5 5k BM:c
N N Os A/BBc < V ^8 d QhRS[ /# rZ r )rE rF s "r rG rH s f r c V P # )z(
The provided mean is the circular one.
r3 r^ s &r mean
VonMises.mean s
xxr c < V ^8 d QhRS[ /# rZ r )rE rF s "r rG rH s f r c V P # r r r^ s &r mode
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The provided variance is the circular one.
rS )r! r4 expr^ s &r varianceVonMises.variance s>
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