a
    h{                     @   st  U d dl Z d dlZd dlmZ d dlmZ d dlZd dlmZmZ ddl	m
Z
 ddlmZ ddlmZ dd	lmZ dd
lmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlm Z  ddl!m"Z" ddl#m$Z$ ddl%m&Z& ddl'm(Z( ddl)m*Z*m+Z+m,Z, ddl-m.Z.m/Z/ ddl0m1Z1 ddl2m3Z3 ddl4m5Z5 ddl6m7Z7 ddl8m9Z9 ddl:m;Z; ddl<m=Z=m>Z? i Z@eAeBeCeCf ef eDd< i ZEeAeBeCeCf ef eDd < d!d"gZFd#d! ZGeG d$d% d%ZHd&d' ZId(d) ZJd*d+ ZKd,d- ZLeeed.d/d"ZMeGe
e
d0d1 ZNeGeed2d3 ZOeGeed4d5 ZPeGeed6d7 ZQeGeed8d9 ZReGeed:d; ZSeGeed<d= ZTeGeed>d? ZUeGeed@dA ZVeGe"e"dBdC ZWeGe e dDdE ZXeGe$e$dFdG ZYeGe(e(dHdI ZZeGe,e,dJdK Z[eGe/e,dLdM Z\eGe,e/dNdO Z]eGe/e/dPdQ Z^eGe1e1dRdS Z_eGe3e3dTdU Z`eGe5e5dVdW ZaeGe7e7dXdY ZbeGe9e9dZd[ ZceGe;e;d\d] ZdeGe
e7d^d_ ZeeGeed`da ZfeGee5dbdc ZgeGeeddde ZheGeedfdg ZieGee1dhdi ZjeGee;djdk ZkeGee5dldm ZleGeedndo ZmeGee1dpdq ZneGee;drds ZoeGeeeGeeeGee5eGee;dtdu ZpeGeedvdw ZqeGee"dxdy ZreGee1dzd{ ZseGeeeGeeeGee5eGee;d|d} ZteGeed~d ZueGee"dd ZveGee1dd ZweGe"eeGe"eeGe"eeGe"eeGe"e5eGe"e;dd ZxeGe"e1dd ZyeGe(eeGe(eeGe(eeGe(eeGe(e5eGe(e;dd ZzeGe(e1dd Z{eGe1eeGe1eeGe1eeGe1eeGe1e5eGe1e;dd Z|eGe1e"dd Z}eGe1e(dd Z~eGe5eeGe5eeGe5e;dd ZeGe5edd ZeGe5edd ZeGe5e1dd ZeGe7e
eGe7edd ZeGe;edd ZeGe;edd ZeGe;edd ZeGe;edd ZeGe;e"dd ZeGe;e1dd ZeGe;e5dd ZeGe&e&dd ZeGeedd Zdd ZdS )    N)total_ordering)Callable)infTensor   )	Bernoulli)Beta)Binomial)Categorical)Cauchy)ContinuousBernoulli)	Dirichlet)Distribution)ExponentialFamily)Exponential)Gamma)	Geometric)Gumbel)
HalfNormal)Independent)Laplace)_batch_lowrank_logdet_batch_lowrank_mahalanobisLowRankMultivariateNormal)_batch_mahalanobisMultivariateNormal)Normal)OneHotCategorical)Pareto)Poisson)TransformedDistribution)Uniform)_sum_rightmosteuler_constant_KL_REGISTRY_KL_MEMOIZEregister_klkl_divergencec                    sV   t  ts"t tr"td  t tsDttrDtd  fdd}|S )a[  
    Decorator to register a pairwise function with :meth:`kl_divergence`.
    Usage::

        @register_kl(Normal, Normal)
        def kl_normal_normal(p, q):
            # insert implementation here

    Lookup returns the most specific (type,type) match ordered by subclass. If
    the match is ambiguous, a `RuntimeWarning` is raised. For example to
    resolve the ambiguous situation::

        @register_kl(BaseP, DerivedQ)
        def kl_version1(p, q): ...
        @register_kl(DerivedP, BaseQ)
        def kl_version2(p, q): ...

    you should register a third most-specific implementation, e.g.::

        register_kl(DerivedP, DerivedQ)(kl_version1)  # Break the tie.

    Args:
        type_p (type): A subclass of :class:`~torch.distributions.Distribution`.
        type_q (type): A subclass of :class:`~torch.distributions.Distribution`.
    z6Expected type_p to be a Distribution subclass but got z6Expected type_q to be a Distribution subclass but got c                    s   | t  f< t  | S N)r$   r%   clear)funtype_ptype_q D/var/www/auris/lib/python3.9/site-packages/torch/distributions/kl.py	decoratorV   s    zregister_kl.<locals>.decorator)
isinstancetype
issubclassr   	TypeError)r,   r-   r0   r.   r+   r/   r&   3   s    c                   @   s*   e Zd ZdgZdd Zdd Zdd ZdS )	_Matchtypesc                 G   s
   || _ d S r(   r6   )selfr6   r.   r.   r/   __init__b   s    z_Match.__init__c                 C   s   | j |j kS r(   r7   )r8   otherr.   r.   r/   __eq__e   s    z_Match.__eq__c                 C   s8   t | j|jD ]$\}}t||s& dS ||ur q4qdS )NFT)zipr6   r3   )r8   r:   xyr.   r.   r/   __le__h   s    
z_Match.__le__N)__name__
__module____qualname__	__slots__r9   r;   r?   r.   r.   r.   r/   r5   ^   s   r5   c           	         s    fddt D }|stS tdd |D j\}}tdd |D j\}}t ||f }t ||f }||urtd j dj d|j d|j d		t |S )
zP
    Find the most specific approximate match, assuming single inheritance.
    c                    s,   g | ]$\}}t  |rt |r||fqS r.   )r3   ).0Zsuper_pZsuper_qr+   r.   r/   
<listcomp>u   s   z _dispatch_kl.<locals>.<listcomp>c                 s   s   | ]}t | V  qd S r(   )r5   rD   mr.   r.   r/   	<genexpr>       z_dispatch_kl.<locals>.<genexpr>c                 s   s   | ]}t t| V  qd S r(   )r5   reversedrF   r.   r.   r/   rH      rI   zAmbiguous kl_divergence(z, z). Please register_kl())r$   NotImplementedminr6   warningswarnr@   RuntimeWarning)	r,   r-   matchesZleft_pZleft_qZright_qZright_pZleft_funZ	right_funr.   r+   r/   _dispatch_klq   s&    rR   c                 C   s   t | tS )zI
    Helper function for obtaining infinite KL Divergence throughout
    )torchZ	full_liker   Ztensorr.   r.   r/   _infinite_like   s    rU   c                 C   s   t j| | S )z2
    Utility function for calculating x log x
    )rS   ZspecialZxlogyrT   r.   r.   r/   _x_log_x   s    rV   c                 C   sD   |  d}|  d}| d|| dd}|| jdd S )zp
    Utility function for calculating the trace of XX^{T} with X having arbitrary trailing batch dimensions
       N)sizeZreshapepowsumshape)ZbmatnrG   Z
flat_tracer.   r.   r/   _batch_trace_XXT   s    

r_   )pqreturnc                 C   s   zt t| t|f }W n8 tyP   tt| t|}|t t| t|f< Y n0 |tu rvtd| jj d|jj || |S )a"  
    Compute Kullback-Leibler divergence :math:`KL(p \| q)` between two distributions.

    .. math::

        KL(p \| q) = \int p(x) \log\frac {p(x)} {q(x)} \,dx

    Args:
        p (Distribution): A :class:`~torch.distributions.Distribution` object.
        q (Distribution): A :class:`~torch.distributions.Distribution` object.

    Returns:
        Tensor: A batch of KL divergences of shape `batch_shape`.

    Raises:
        NotImplementedError: If the distribution types have not been registered via
            :meth:`register_kl`.
    z(No KL(p || q) is implemented for p type z and q type )r%   r2   KeyErrorrR   rL   NotImplementedError	__class__r@   )r`   ra   r*   r.   r.   r/   r'      s    c                 C   s   | j tjj|j tjj| j   }t||j dk< d|| j dk< d| j  tjj|jtjj| j  }t||j dk< d|| j dk< || S Nr   r   )probsrS   nnZ
functionalZsoftpluslogitsr   r`   ra   t1t2r.   r.   r/   _kl_bernoulli_bernoulli   s    rm   c           	      C   s   | j | j }|j |j }|j  |j  |  }| j  | j  |  }| j |j  t| j  }| j|j t| j }|| t| }|| | | | S r(   )concentration1concentration0lgammarS   digamma)	r`   ra   Zsum_params_pZsum_params_qrk   rl   t3t4t5r.   r.   r/   _kl_beta_beta   s    ru   c                 C   sh   | j |j k  rtd| j | j| j|j  | j   |j    }| j |j k}t|| ||< |S )NzKKL between Binomials where q.total_count > p.total_count is not implemented)Ztotal_countanyrd   rg   ri   log1prU   )r`   ra   klZinf_idxsr.   r.   r/   _kl_binomial_binomial   s    (ry   c                 C   sD   | j | j|j  }t||j dk|< d|| j dk|< |dS )Nr   rW   )rg   ri   r   Z	expand_asr\   )r`   ra   tr.   r.   r/   _kl_categorical_categorical   s    r{   c                 C   sL   | j | j|j  }|  t| j  }|  t|j  }|| | S r(   )meanri   _cont_bern_log_normrS   rw   rg   r`   ra   rk   rl   rr   r.   r.   r/   -_kl_continuous_bernoulli_continuous_bernoulli   s    r   c                 C   s|   | j d}|j d}| |  }| j  |j   d}| j |j  }| j  | d }|| || d S )NrW   )concentrationr\   rp   rq   	unsqueeze)r`   ra   Zsum_p_concentrationZsum_q_concentrationrk   rl   rr   rs   r.   r.   r/   _kl_dirichlet_dirichlet  s    r   c                 C   s"   |j | j  }|  }|| d S Nr   ratelog)r`   ra   Z
rate_ratiork   r.   r.   r/   _kl_exponential_exponential  s    
r   c                 C   s   t | t |kstddd | jD }|j}| j| }tjj| |dd}|j| | }t|||D ]*\}}}	|| |	 }
|t	|
t
|j8 }qh|S )NzThe cross KL-divergence between different exponential families cannot                             be computed using Bregman divergencesc                 S   s   g | ]}|   qS r.   )detachZrequires_grad_)rD   npr.   r.   r/   rE      rI   z+_kl_expfamily_expfamily.<locals>.<listcomp>T)Zcreate_graph)r2   rd   Z_natural_paramsZ_log_normalizerrS   ZautogradZgradr\   r<   r"   lenevent_shape)r`   ra   Z	p_nparamsZ	q_nparamsZ	lg_normalZ	gradientsresultZpnpZqnpgZtermr.   r.   r/   _kl_expfamily_expfamily  s    
r   c                 C   sn   |j | j|j   }t|j t| j  }| j |j  t| j  }|j| j | j | j  }|| | | S r(   )r   r   r   rS   rp   rq   r`   ra   rk   rl   rr   rs   r.   r.   r/   _kl_gamma_gamma+  s
    r   c                 C   sl   | j |j  }|j|j  }| j|j  }|  | | }|t }t|d|   | }|| | dt  S r   )scalelocr   _euler_gammarS   exprp   )r`   ra   Zct1Zct2Zct3rk   rl   rr   r.   r.   r/   _kl_gumbel_gumbel4  s    r   c                 C   s$   |    t|j | j  |j S r(   )entropyrS   rw   rg   ri   r`   ra   r.   r.   r/   _kl_geometric_geometric?  s    r   c                 C   s   t | j|jS r(   )_kl_normal_normal	base_distr   r.   r.   r/   _kl_halfnormal_halfnormalD  s    r   c                 C   sV   | j |j  }| j|j  }|  }||j  }|t| | j   }|| | d S r   )r   r   absr   rS   r   )r`   ra   scale_ratioZloc_abs_diffrk   rl   rr   r.   r.   r/   _kl_laplace_laplaceI  s    

r   c                 C   s   | j |j krtdt|j|j|jt| j| j| j }t|j|j|j| j |j}|jj|j	d }t
jj|j|dd}| j|j d}t| j|j 	d }t|| j 	d }t|| j}	|| | |	 }
d||
 | | j d   S )NzKL-divergence between two Low Rank Multivariate Normals with                          different event shapes cannot be computedrX   FupperrW         ?r   )r   
ValueErrorr   _unbroadcasted_cov_factor_unbroadcasted_cov_diag_capacitance_trilr   r   mTr   rS   linalgsolve_triangularr\   r_   rsqrtsqrtmatmul)r`   ra   term1term3	qWt_qDinvAterm21term22Zterm23Zterm24term2r.   r.   r/   7_kl_lowrankmultivariatenormal_lowrankmultivariatenormalT  s6    
	r   c           	      C   s   | j |j krtdt|j|j|jd| jjddd 	d  }t
|j|j|j| j |j}|jj|jd }tjj|j|dd}t| j|j d }t|| j}|| }d|| | | j d	   S )
NKL-divergence between two (Low Rank) Multivariate Normals with                          different event shapes cannot be computedrY   rX   rW   Zdim1Zdim2Fr   r   r   )r   r   r   r   r   r   _unbroadcasted_scale_trildiagonalr   r\   r   r   r   r   rS   r   r   r_   r   r   )	r`   ra   r   r   r   r   r   r   r   r.   r.   r/   0_kl_multivariatenormal_lowrankmultivariatenormalv  s.    
	r   c                 C   s$  | j |j krtdd|jjddd d t| j| j| j	 }t
|j|j| j }tj|jjd d | jjd d }| j d }|j|||f }| j||| jdf }t| j |||f }ttjj||dd}	ttjj||dd}
|	|
 }d	|| | | j d   S )
Nr   rY   rX   rW   r   r   Fr   r   )r   r   r   r   r   r\   r   r   r   r   r   r   rS   _C_infer_sizer]   expandZ
cov_factorrZ   Z
diag_embedr   r_   r   r   )r`   ra   r   r   combined_batch_shaper^   q_scale_trilZp_cov_factorZ
p_cov_diagr   r   r   r.   r.   r/   0_kl_lowrankmultivariatenormal_multivariatenormal  s>    

r   c           	      C   s   | j |j krtd|jjddd d| jjddd d }tj|jj	d d | jj	d d }| j d }|j
|||f }| j
|||f }ttjj||dd}t|j|j| j }|d|| |   S )	NzvKL-divergence between two Multivariate Normals with                          different event shapes cannot be computedrX   rW   r   r   Fr   r   )r   r   r   r   r   r\   rS   r   r   r]   r   r_   r   r   r   r   )	r`   ra   Z
half_term1r   r^   r   Zp_scale_trilr   r   r.   r.   r/   )_kl_multivariatenormal_multivariatenormal  s(    
r   c                 C   sB   | j |j  d}| j|j |j  d}d|| d |   S NrY   r   r   r   r[   r   r   )r`   ra   Z	var_ratiork   r.   r.   r/   r     s    r   c                 C   s   t | j|jS r(   )r{   Z_categoricalr   r.   r.   r/   '_kl_onehotcategorical_onehotcategorical  s    r   c                 C   sX   | j |j  }|j| j }|j|  }|  }|| | d }t|| jj|jjk < |S r   )r   alphar   r   supportlower_bound)r`   ra   r   Zalpha_ratiork   rl   r   r.   r.   r/   _kl_pareto_pareto  s    
r   c                 C   s&   | j | j  |j    | j |j   S r(   r   r   r.   r.   r/   _kl_poisson_poisson  s    r   c                 C   s.   | j |j krt| j|jkr tt| j|jS r(   )Z
transformsrd   r   r'   r   r   r.   r.   r/   _kl_transformed_transformed  s
    r   c                 C   s<   |j |j | j | j   }t||j| jk|j | j k B < |S r(   )highlowr   r   r`   ra   r   r.   r.   r/   _kl_uniform_uniform  s    r   c                 C   s    |    | j|j  |j  S r(   )r   rg   r   r   r   r.   r.   r/   _kl_bernoulli_poisson   s    r   c                 C   s,   |    | j|j  t|j  |  S r(   )r   r|   ri   rS   rw   rg   r}   r   r.   r.   r/   _kl_beta_continuous_bernoulli  s    
r   c                 C   s
   t | jS r(   )rU   rn   r   r.   r.   r/   _kl_beta_infinity  s    r   c                 C   s,   |    |j  |j| j| j| j    S r(   )r   r   r   rn   ro   r   r.   r.   r/   _kl_beta_exponential  s    r   c                 C   sp   |    }|j |j|j   }|jd | j | j| j    }|j| j | j| j  }|| | | S r   )r   r   rp   r   r   rn   rq   ro   r   r.   r.   r/   _kl_beta_gamma  s    
r   c           	      C   s   | j | j | j  }|jd}|   }d|d tj   }|d|  | j | j d  |d d }|j| }|jdd }|| || | |  S r   )	rn   ro   r   r[   r   mathpir   r   )	r`   ra   ZE_beta
var_normalrk   rl   rr   rs   rt   r.   r.   r/   _kl_beta_normal+  s    

r   c                 C   s>   |    |j|j   }t||j| jjk|j| jjk B < |S r(   )r   r   r   r   r   r   r   upper_boundr   r.   r.   r/   _kl_beta_uniform:  s     r   c                 C   s
   t | jS r(   )rU   rg   r   r.   r.   r/   !_kl_continuous_bernoulli_infinityD  s    r   c                 C   s"   |    t|j |j| j  S r(   )r   rS   r   r   r|   r   r.   r.   r/   $_kl_continuous_bernoulli_exponentialI  s    r   c                 C   sz   |    }dtdtj t|j|j   t|j }| jt| j	 d|j | j	  dt|j  }|| | S )Nr   g       @)
r   r   r   r   rS   Zsquarer   r   Zvariancer|   r~   r.   r.   r/   _kl_continuous_bernoulli_normalR  s    
( r   c              	   C   sV   |    |j|j   }ttt|j| jj	t
|j| jjt|t |S r(   )r   r   r   r   rS   wheremaxger   r   ler   	ones_liker   r   r.   r.   r/    _kl_continuous_bernoulli_uniform^  s    r   c                 C   s
   t | jS r(   rU   r   r   r.   r.   r/   _kl_exponential_infinityk  s    r   c                 C   sB   |j | j  }|j t| }|| |j  |jt  dt  S r   )r   r   rS   r   rp   r   )r`   ra   Zratiork   r.   r.   r/   _kl_exponential_gammas  s    r   c                 C   sR   | j |j }|j|j }| d }t|| |d  }| }|| | | S r   )r   r   r   r   rS   r   
reciprocal)r`   ra   scale_rate_prodloc_scale_ratiork   rl   rr   r.   r.   r/   _kl_exponential_gumbel  s    r   c                 C   sp   |j d}| jd}dt|| d tj  }| }|j| j }|jdd }|d || | |  S r   )	r   r[   r   rS   r   r   r   r   r   )r`   ra   r   Zrate_sqrrk   rl   rr   rs   r.   r.   r/   _kl_exponential_normal  s    r   c                 C   s
   t | jS r(   )rU   r   r   r.   r.   r/   _kl_gamma_infinity  s    r   c                 C   s&   |    |j  |j| j | j  S r(   )r   r   r   r   r   r.   r.   r/   _kl_gamma_exponential  s    r   c                 C   s~   | j |j }|j|j }| jd | j  | j  | j }| | j|  }t|d|	  
| j  | }|| | S r   )r   r   r   r   rq   rp   r   rS   r   r   r[   )r`   ra   Zbeta_scale_prodr   rk   rl   rr   r.   r.   r/   _kl_gamma_gumbel  s     r   c                 C   s   |j d}| jd}dt|| d tj  | j | j  }d| jd| j  | }|j	| j | j }d|j	d }|| jd | j
   || | |  S r   )r   r[   r   rS   r   r   r   r   rp   r   rq   )r`   ra   r   Zbeta_sqrrk   rl   rr   rs   r.   r.   r/   _kl_gamma_normal  s"    r   c                 C   s
   t | jS r(   rU   r   r   r.   r.   r/   _kl_gumbel_infinity  s    r   c                 C   sx   | j |j  }|tdtj   }tj| d dd }| j| j t  |j |j  dd }| | | td  S )NrY   r      r   )r   r   r   r   r   r[   r   r   )r`   ra   Zparam_ratiork   rl   rr   r.   r.   r/   _kl_gumbel_normal  s
    &r   c                 C   s
   t | jS r(   r   r   r.   r.   r/   _kl_laplace_infinity  s    r   c                 C   s~   |j d}| j d| }dtd| tj  }d| jd }| j|j }d|jd }| | || | |  d S r   )r   r[   rS   r   r   r   r   )r`   ra   r   Zscale_sqr_var_ratiork   rl   rr   rs   r.   r.   r/   _kl_laplace_normal  s    r   c                 C   s
   t | jS r(   r   r   r.   r.   r/   _kl_normal_infinity  s    r   c                 C   s|   | j |j }| j|j d}|j |j }| d }|| }t| d|  | }| | | ddtdtj    S r   )r   r   r[   r   rS   r   r   r   )r`   ra   Zmean_scale_ratioZvar_scale_sqr_ratior   rk   rl   rr   r.   r.   r/   _kl_normal_gumbel  s    r   c                 C   s   | j |j  }| j|j }|| j }t|}tdtj | j td|d  }|t	td|  }| || |j  ddtdtj    S )NrY   g      r   r   )
r   r   rS   r   r   r   r   r   r[   erf)r`   ra   Zloc_diffr   Zloc_diff_scale_ratiork   rl   rr   r.   r.   r/   _kl_normal_laplace  s    

(r   c                 C   s
   t | jS r(   )rU   r   r   r.   r.   r/   _kl_pareto_infinity  s    r   c                 C   sZ   | j |j }| j|  }| j }| j| | jd  }|| | d }t|| jdk< |S r   )r   r   r   r   r   r   )r`   ra   r   rk   rl   rr   r   r.   r.   r/   _kl_pareto_exponential!  s    
r   c                 C   s   | j  | j  }| j | }|j |j|j   }d|j | }|j| j | j  | jd  }|| | | d }t|| jdk< |S r   )r   r   r   r   r   rp   r   r   r`   ra   common_termrk   rl   rr   rs   r   r.   r.   r/   _kl_pareto_gamma,  s    r   c           	      C   s   d|j d }| j | jd  }tdtj |j  | j | j   }| j }| j|d | jd  }| j| |j d}|| || |  d }t	|| jdk< |S )NrY   r   )
r   r[   r   r   r   r   r   r   r   r   )	r`   ra   r   r   rk   rl   rr   rs   r   r.   r.   r/   _kl_pareto_normal;  s    &
r   c                 C   s
   t | jS r(   r   r   r.   r.   r/   _kl_poisson_infinityH  s    r   c                 C   s   | j | j }t|}|jd t| j t| j |  | }|jd td| j  td| j  |  | }|j |j  |j|j   }|| | | }t|| j |j	j
k| j|j	jk B < |S r   )r   r   rS   r   rn   rV   ro   rp   r   r   r   r   r   r.   r.   r/   _kl_uniform_betaN  s.    
 r   c              	   C   sh   |    | j|j  t|j  |  }ttt	| j
|jjt| j|jjt|t |S r(   )r   r|   ri   rS   rw   rg   r}   r   r   r   r   r   r   r   r   r   r   r   r   r.   r.   r/    _kl_uniform_continuous_bernoullif  s     
r   c                 C   sB   |j | j| j  d | j| j |j    }t|| j|jjk < |S )NrY   )r   r   r   r   r   r   r   r   r.   r.   r/   _kl_uniform_exponetialx  s    ,r   c                 C   s   | j | j }| }|j |j|j   }d|j t| j t| j |  | }|j| j | j  d }| | | | }t|| j|jj	k < |S )Nr   rY   )
r   r   r   r   rp   r   rV   r   r   r   r   r.   r.   r/   _kl_uniform_gamma  s    r  c                 C   sn   |j | j| j  }| j|j |j  }| j|j |j  }| d||   }|t| t|   }|| S )Nr   )r   r   r   r   r   rS   r   )r`   ra   r   Zhigh_loc_diffZlow_loc_diffrk   rl   r.   r.   r/   _kl_uniform_gumbel  s    r  c                 C   st   | j | j }ttjd |j |  }|dd }| j | j d|j  d d}|d||  |jd  S )NrY      r   )	r   r   r   r   r   r   r   r[   r   )r`   ra   r   rk   rl   rr   r.   r.   r/   _kl_uniform_normal  s
     r  c                 C   sl   | j | j }|j|j|j |  }t| j t| j | | }||jd  | }t|| j|jj	k < |S r   )
r   r   r   r   r[   r   rV   r   r   r   )r`   ra   Zsupport_uniformrk   rl   r   r.   r.   r/   _kl_uniform_pareto  s    r  c                 C   s*   | j |j krtt| j|j}t|| j S r(   )Zreinterpreted_batch_ndimsrd   r'   r   r"   r   r.   r.   r/   _kl_independent_independent  s    r  c                 C   sD   | j |j  d| j|j d  }d| j  |j   }|| S )NrY      r   rj   r.   r.   r/   _kl_cauchy_cauchy  s    (r  c                  C   s^   dg} t tdd dD ]$\}}| d|j d|j d qd| }tjrZt j|7  _d	S )
zHAppends a list of implemented KL functions to the doc for kl_divergence.zLKL divergence is currently implemented for the following distribution pairs:c                 S   s   | d j | d j fS rf   )r@   )Zp_qr.   r.   r/   <lambda>  rI   z_add_kl_info.<locals>.<lambda>)keyz* :class:`~torch.distributions.z#` and :class:`~torch.distributions.`z
	N)sortedr$   appendr@   joinr'   __doc__)rowsr`   ra   Zkl_infor.   r.   r/   _add_kl_info  s    
r  )r   rN   	functoolsr   typingr   rS   r   r   Z	bernoullir   betar   Zbinomialr	   Zcategoricalr
   Zcauchyr   Zcontinuous_bernoullir   Z	dirichletr   distributionr   Z
exp_familyr   Zexponentialr   gammar   Z	geometricr   Zgumbelr   Zhalf_normalr   Zindependentr   Zlaplacer   Zlowrank_multivariate_normalr   r   r   Zmultivariate_normalr   r   normalr   Zone_hot_categoricalr   Zparetor   Zpoissonr   Ztransformed_distributionr    uniformr!   utilsr"   r#   r   r$   dicttupler2   __annotations__r%   __all__r&   r5   rR   rU   rV   r_   r'   rm   ru   ry   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r.   r.   r.   r/   <module>   s  
+
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