o
    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| | |  }|s
|S N)listpop)yZcoefresult r   c/home/www/facesmatcher.com/frenv_anti/lib/python3.10/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r#|  | }| }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   ZsmallZlarger   r   r   r   _log_modified_bessel_fnE   s   "r   c                 C   s   t j|jt j| jd}| slt jd|j | j| jd}| \}}}t 	t
j| }	d||	  ||	  }
|||
  }|d|  | dk||  d | dkB }| rht ||d  |
  |}||B }| r|t
j |  dt
j  t
j S )Ndtypedevice)   r      r   r   )r   Z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   ,
r6   c                	       s   e Zd ZdZejejdZejZdZ		dde
de
dee ddf fd	d
Zdd Zede
fddZede
fddZede
fddZe e fddZd fdd	Zede
fddZede
fddZede
f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,   FNr+   r,   validate_argsreturnc                    s6   t ||\| _| _| jj}t }t ||| d S r	   )r   r+   r,   r"   r   Sizesuper__init__)selfr+   r,   r7   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   rC      s   
zVonMises.log_probc                 C      | j tjS r	   )r+   tor   doubler<   r   r   r   _loc      zVonMises._locc                 C   rD   r	   )r,   rE   r   rF   rG   r   r   r   _concentration   rI   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   emptyrH   r   r+   r   r6   rJ   rP   rE   )r<   Zsample_shaper"   r   r   r   r   sample   s   

zVonMises.samplec                    sX   zt  |W S  ty+   | jd}| j|}| j|}t| |||d Y S w )NrA   )r7   )r:   expandNotImplementedError__dict__getr+   r,   type)r<   r=   Z	_instancer7   r+   r,   r>   r   r   rS      s   zVonMises.expandc                 C      | j S )z8
        The provided mean is the circular one.
        r+   rG   r   r   r   mean   s   zVonMises.meanc                 C   rX   r	   rY   rG   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   r@   r   )r   r,   exprG   r   r   r   variance   s   zVonMises.variancer	   )__name__
__module____qualname____doc__r   realZpositiveZarg_constraintsZsupportZhas_rsampler   r   r#   r;   rC   r   rH   rJ   rP   r   Zno_gradr9   rR   rS   propertyrZ   r[   r]   __classcell__r   r   r>   r   r   l   s>    		)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_tracingr6   r   r   r   r   r   <module>   s(   		

