o
    Eb[N                     @   s"  d dl Zd dlZd dlm  mZ d dlZdZ	e
ede	Ze
ede	 Zedej Zedej ZdZedZejd Zejd Zejd Zg d	Zd
d Zdd Zd%ddZd%ddZdd Zd%ddZd%ddZd%ddZ dd Z!dd Z"d%dd Z#d!d" Z$d%d#d$Z%dS )&    N         i<         )gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?c                 C   s6   d|  }t | d |  td  |t t||    S )N      ?r   )nplog_LOG_2PIZpolyval_STIRLING_COEFFS)nZrn r   6/usr/lib/python3/dist-packages/scipy/stats/_ksstats.py_log_nfactorial_div_n_pow_n\   s   .r   c                 C   s   t | ddS )z%clips a probability to range 0<=p<=1.        r   )r	   Zclip)pr   r   r   
_clip_probf   s   r   Tc                 C   s   t || |}t|S )z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r	   wherer   )cdfprobZsfprobcdfr   r   r   r   _select_and_clip_probk   s   r   c                 C   s^  |dkr
t dd|S | | }|dkrt dd|S tt|}|| }d| d }t||g}td|d }d||  }	t|}
d}|D ]}||
|d < || }|	|d   |9  < qGtd| d d| d||   }d| | |	d< td|D ]}|
d|| d  ||d d|f< q||	|dddf< tj	|	dd	|dddf< t
t|d }| }d}d}|dkr|d rt||}||7 }t||}|d9 }t||d |d f tkr|t }|t7 }|d }|dks||d |d f }td| d D ]}|| |  }t|tk r|t9 }|t8 }q|dkr't||}t |d| |S )
zComputes the Kolmogorov CDF:  Pr(D_n <= d) using the MTW approach to
    the Durbin matrix algorithm.

    Durbin (1968); Marsaglia, Tsang, Wang (2003). [1], [3].
    r   r         ?r   r   r   N)Zaxis)r   intr	   ceilzerosarangeemptymaxrangeZflipZeyeshapematmulabs_EP128_E128_EM128ldexp)r   dr   ZndkhmHZintmvwZfacjttiZHpwrnnexpntZHexpntr   r   r   r   _kolmogn_DMTWq   s`   
"&
r4   c           	      C   s   | dkr| | d || d }}nLt | d d\}}|dkrN||d kr8|| | d || | d }}n'|d | | d || d | d }}n|d | d || | d }}t|d dt||fS )z0Compute the endpoints of the interval for row i.r   r   r   )divmodr   min)	r1   r   llceilfroundfj1j2Zip1div2Zip1mod2r   r   r   _pomeranz_compute_j1j2   s   $,"r<   c                  C   s  | | }t t|}d||  }t|d| }|dkrdnd}|dkr&dnd}d|d  }	t|	}
t|	}t|	}d|
d< d|d< d|d< d}||  d| |  dd|  |  }}}td|	D ]&}|
|d  | | |
|< ||d  | | ||< ||d  | | ||< qdt|	g}t|	g}d|d< d\}}td| |||\}}tdd|  d D ]}|}||}}||}}|d t|| |||\}}|dks|d|  d kr|
}n|d r|n|}|| d }|dkr:t	||| || |  |d| }|| }|| d }||||  |d|< dt
|  k r*tk r4n n|t9 }|t8 }|| | }q|| |  }td| d D ]}t|tkrZ|t9 }|t7 }||9 }qH|dkrkt||}t|d| |}|S )	z[Computes Pr(D_n <= d) using the Pomeranz recursion algorithm.

    Pomeranz (1974) [2]
    r   r   r   r   r   )r   r   r   N)r   r	   Zfloorr6   r   r    r   r<   fillZconvolver   r&   r$   r%   r#   r'   r   ) r   xr   tr7   fgr8   r9   ZnpwrsZgpowerZ	twogpowerZonem2gpowerr3   Zg_over_nZtwo_g_over_nZone_minus_two_g_over_nr+   ZV0ZV1ZV0sZV1sr:   r;   r1   Zk1ZpwrsZln2convZ
conv_startZconv_lenZansr   r   r   _kolmogn_Pomeranz   sl   


(



("
rC   c           %   	   C   s.  |dkrt dd|dS |dkrt dd|dS t| | }|d |d |d |d f\}}}}t d | }|tk rAt dd|dS t|}	| }
td }d| d|  }d| d	|  t d }td
d|   d }td	d|   d }td| d|   d }td| d|   d }d| d|d   }td}t	t
d| tj }t|ddD ]G}d| d
 }|d |d |d }}}t|	d| }td|
||  |||  ||  |||  ||  ||  g}||9 }||7 }q||	9 }|t9 }|t|d| d|d  d|d  g }tt d | }	t|dd}|d }t| }tj| }|	| } t||  }!|!tt d|  9 }!|d  |!7  < t|| ||  | |  }"|"tt d|  9 }"|d  |"7  < t| d tt|d }#||# }|s|d9 }|d  d
7  < t|}$|$S )aP  Computes the Pelz-Good approximation to Prob(Dn <= x) with 0<=x<=1.

    Start with Li-Chien, Korolyuk approximation:
        Prob(Dn <= x) ~ K0(z) + K1(z)/sqrt(n) + K2(z)/n + K3(z)/n**1.5
    where z = x*sqrt(n).
    Transform each K_(z) using Jacobi theta functions into a form suitable
    for small z.
    Pelz-Good (1976). [6]
    r   r   r   r   r   r   r         r         @   i      `   iZ   r   r   H      iP  
   i          @)r   r	   sqrt_PI_SQUARED_MIN_LOGexp_PI_FOUR_PI_SIXr   r   r   pir    ZpowerZarray_SQRT2PIr   _SQRT3sumlen)%r   r>   r   zZzsquaredZzthreeZzfourZzsixZqlogqZk1aZk1bZk2aZk2bZk2cZk3dZk3cZk3bZk3aZK0to3Zmaxkr)   r+   ZmsquaredZmfourZmsixZqpowerZcoeffsksZksquaredZsqrt3zZkspiZqpwersZk2extraZk3extraZpowers_of_nZKsumr   r   r   _kolmogn_PelzGood"  sl   
$



*
ra   c                 C   sP  t | r| S t| | ks| dkrt jS |dkrtdd|dS |dkr*tdd|dS | | }|dkrr|dkr=tdd|dS | dkrWt t d| d d|   d| d  }nt t| | t 	d| d   }t|d| |dS || d krdd| |   }td| ||dS |dkrdt
j| | }td| ||dS || }| dkr|d	krt| |d
d}t|d| |dS |dkrt| |d
d}t|d| |dS dt
j| | }td| ||dS |s|dkrdS |dkrdt
j| | }t|S |dkrd}n| dkr| |d  dkrt| |d
d}nt| |d
d}t|d| |dS )zComputes the CDF(or SF) for the two-sided Kolmogorov-Smirnov statistic.

    x must be of type float, n of type integer.

    Simard & L'Ecuyer (2011) [7].
    r   r   r   rD   r      r   r   g0q&?Tr   g      w@g@g      2@i g      ?gffffff?)r	   isnanr   nanr   prodr   rV   r   r
   scipyspecialZsmirnovr4   rC   r   ra   )r   r>   r   r?   ZprobZ	nxsquaredr   r   r   r   _kolmognu  sX   
,$
rh   c                    sH  t  r S t  ks dkrt jS |dks|dkrdS  | }|dkr`|dkr,dS  dkrDt t d d   d| d  }nt t  d t d| d   }|d  d  S | d krrdd|  d     S |dkrdt	j
j|  S |d }t||d   }t|d| } fd	d
}t	jj|||ddS )zvComputes the PDF for the two-sided Kolmogorov-Smirnov statistic.

    x must be of type float, n of type integer.
    r   r   r   r   rb   r   r   g      @c                    s
   t  | S N)kolmogn)_xr   r   r   _kk  s   
z_kolmogn_p.<locals>._kkrF   )ZdxZorder)r	   rc   r   rd   re   r   rV   r   r
   rf   ZstatsZksoneZpdfr6   ZmiscZ
derivative)r   r>   r?   Zprddeltarm   r   rl   r   
_kolmogn_p  s.   
((ro   c                    s   t  r S t  ks dkrt jS dkrd  S |dkr"dS t t tj d    }|d  krB|d   d S t 	t |d    }|dd   krY|S t
t   }t|dd   } fdd}tjj|d  |dd	S )
zeComputes the PPF/ISF of kolmogn.

    n of type integer, n>= 1
    p is the CDF, q the SF, p+q=1
    r   r   r   r   rR   c                    s   t  |  S ri   )rh   )r>   r   r   r   r   <lambda>  s    z_kolmogni.<locals>.<lambda>g+=)Zxtol)r	   rc   r   rd   rV   r
   rf   rg   ZloggammaZexpm1scuZ	_kolmogcirS   r6   optimizeZbrentq)r   r   r_   rn   r>   Zx1Z_fr   rp   r   	_kolmogni  s$   
$rt   c           	      C   s   t j| ||dgdt jt jt jgd}|D ](\}}}}t |r$||d< qt||kr1td| tt|||d|d< q|jd }|S )a  Computes the CDF for the two-sided Kolmogorov-Smirnov distribution.

    The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x),
    for a sample of size n drawn from a distribution with CDF F(t), where
    D_n &= sup_t |F_n(t) - F(t)|, and
    F_n(t) is the Empirical Cumulative Distribution Function of the sample.

    Parameters
    ----------
    n : integer, array_like
        the number of samples
    x : float, array_like
        The K-S statistic, float between 0 and 1
    cdf : bool, optional
        whether to compute the CDF(default=true) or the SF.

    Returns
    -------
    cdf : ndarray
        CDF (or SF it cdf is False) at the specified locations.

    The return value has shape the result of numpy broadcasting n and x.
    N)Z	op_dtypes.n is not integral: rD   r   )	r	   nditerZfloat64Zbool_rc   r   
ValueErrorrh   operands)	r   r>   r   it_nrk   _cdfr^   resultr   r   r   rj     s   

rj   c                 C   sn   t | |dg}|D ]%\}}}t |r||d< q
t||kr&td| tt|||d< q
|jd }|S )a  Computes the PDF for the two-sided Kolmogorov-Smirnov distribution.

    Parameters
    ----------
    n : integer, array_like
        the number of samples
    x : float, array_like
        The K-S statistic, float between 0 and 1

    Returns
    -------
    pdf : ndarray
        The PDF at the specified locations

    The return value has shape the result of numpy broadcasting n and x.
    N.ru   r   )r	   rv   rc   r   rw   ro   rx   )r   r>   ry   rz   rk   r^   r|   r   r   r   kolmognp  s   

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S )a  Computes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution.

    Parameters
    ----------
    n : integer, array_like
        the number of samples
    q : float, array_like
        Probabilities, float between 0 and 1
    cdf : bool, optional
        whether to compute the PPF(default=true) or the ISF.

    Returns
    -------
    ppf : ndarray
        PPF (or ISF if cdf is False) at the specified locations

    The return value has shape the result of numpy broadcasting n and x.
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