a
    h                     @   s   d dl Z d dlmZ d dlZd dlZd dlmZ d dlmZ d dlm	Z	 d dl
mZmZ dgZdd	 Zg d
Zg dZg dZg dZeegZeegZdddZejjdd ZG dd de	ZdS )    N)Optional)Tensor)constraints)Distribution)broadcast_alllazy_propertyVonMisesc                 C   s*   t |}| }|r&| | |  }q|S N)listpop)yZcoefresult r   K/var/www/auris/lib/python3.9/site-packages/torch/distributions/von_mises.py
_eval_poly   s
    r   )g      ?g$@g03@g,?N?g2t?gIx?gtHZr?)	 e3E?g-5?gՒ+Hub?gJNYgTPÂ?g'gZ?gUL+ߐg;^p?)      ?gY?g(z?g*O?gZ9?g.h?gӰ٩=5?)	r   g.kg?VmgtZOZ?g<Q g'8`?gP⥝gqJ:N?g;PJ4qc                 C   s   |dks|dksJ | d }|| }t |t| }|dkrF|  | }| }d|  }| d|    t |t|   }t| dk ||}|S )zX
    Returns ``log(I_order(x))`` for ``x > 0``,
    where `order` is either 0 or 1.
    r      g      @r   )r   _COEF_SMALLabslog_COEF_LARGEtorchwhere)xorderr   smallZlarger   r   r   r   _log_modified_bessel_fnE   s    "r   c                 C   s   t j|jt j| jd}| st jd|j | j| jd}| \}}}t 	t
j| }	d||	  ||	  }
|||
  }|d|  | dk||  d | dkB }| rt ||d  |
  |}||B }q|t
j |  dt
j  t
j S )Ndtypedevice)   r      r   r   )r   zerosshapeboolr    allZrandr   Zunbindcosmathpir   anyr   signacos)locconcentrationZ
proposal_rr   doneuu1u2u3zfcacceptr   r   r   _rejection_sample\   s    ,
r8   c                       s   e Zd ZdZejejdZejZdZ	de
e
ee dd fddZdd	 Zee
d
ddZee
d
ddZee
d
ddZe e fddZd fdd	Zee
d
ddZee
d
ddZee
d
ddZ  ZS )r   aX  
    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
    )r-   r.   FN)r-   r.   validate_argsreturnc                    s6   t ||\| _| _| jj}t }t ||| d S r	   )r   r-   r.   r$   r   Sizesuper__init__)selfr-   r.   r9   batch_shapeZevent_shape	__class__r   r   r=      s    zVonMises.__init__c                 C   sL   | j r| | | jt|| j  }|tdtj  t	| jdd }|S )Nr"   r   r   )
_validate_argsZ_validate_sampler.   r   r'   r-   r(   r   r)   r   )r>   valuelog_probr   r   r   rE      s    
zVonMises.log_prob)r:   c                 C   s   | j tjS r	   )r-   tor   doubler>   r   r   r   _loc   s    zVonMises._locc                 C   s   | j tjS r	   )r.   rF   r   rG   rH   r   r   r   _concentration   s    zVonMises._concentrationc                 C   sh   | j }ddd|d     }|d|   d|  }d|d  d|  }d| | }t|dk ||S )Nr      r"   gh㈵>)rJ   sqrtr   r   )r>   kappataurho_proposal_rZ_proposal_r_taylorr   r   r   rP      s    zVonMises._proposal_rc                 C   s@   |  |}tj|| jj| jjd}t| j| j| j	|
| jjS )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   )Z_extended_shaper   emptyrI   r   r-   r    r8   rJ   rP   rF   )r>   Zsample_shaper$   r   r   r   r   sample   s    
zVonMises.samplec                    s\   zt  |W S  tyV   | jd}| j|}| j|}t| |||d Y S 0 d S )NrC   )r9   )r<   expandNotImplementedError__dict__getr-   r.   type)r>   r?   Z	_instancer9   r-   r.   r@   r   r   rS      s    zVonMises.expandc                 C   s   | j S )z8
        The provided mean is the circular one.
        r-   rH   r   r   r   mean   s    zVonMises.meanc                 C   s   | j S r	   rX   rH   r   r   r   mode   s    zVonMises.modec                 C   s$   dt | jddt | jdd   S )z<
        The provided variance is the circular one.
        r   rB   r   )r   r.   exprH   r   r   r   variance   s    zVonMises.variance)N)N)__name__
__module____qualname____doc__r   realZpositiveZarg_constraintsZsupportZhas_rsampler   r   r%   r=   rE   r   rI   rJ   rP   r   Zno_gradr;   rR   rS   propertyrY   rZ   r\   __classcell__r   r   r@   r   r   l   s6    		)r   )r(   typingr   r   Z	torch.jitr   Ztorch.distributionsr   Z torch.distributions.distributionr   Ztorch.distributions.utilsr   r   __all__r   Z_I0_COEF_SMALLZ_I0_COEF_LARGEZ_I1_COEF_SMALLZ_I1_COEF_LARGEr   r   r   ZjitZscript_if_tracingr8   r   r   r   r   r   <module>   s&   		

