
    sg                     p   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 d dlmZmZ d dlmZ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$Z$m%Z% d dlm&Z& d dl'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z- d dl.m/Z/ d dl0m1Z1 d dl2m3Z3m4Z4 d dl5m6Z6 d dl7m8Z8m9Z9 d dl:m;Z; d Z<d Z=d Z>d Z?y)    )Sum)Add)Mul)Integeroopi)Pow)EqNe)DummySymbolsymbols)	factorial)exp)sqrt)	Piecewise)
DiracDelta)gamma)Integral)simplify)IndexedIndexedBase)ExprCondPair)PoissonBetaExponentialPMultinomialMultivariateBeta)Normal)PoissonDistribution)CompoundPSpaceCompoundDistribution)MarginalDistribution)pspacedensity)ignore_warningsc            
          t        d      } t        dd      }t        |dd      }t        | |      }t        t	        |      t
              sJ t        |t        ||j                              t        |      k(  sJ t        ddd	      }t        d
|d      } t        |      d      j                         t        d      dt        t              z  z  k(  sJ t         t        |t        |d	            |             t        d      t        | d	z
  dz   dz        z  dt        t              z  z  k(  sJ t         t        |      |             t        d      t        | dz   dz        z  dt        t              z  z  k(  sJ y )NxlTpositive      N1r      N2
         )r   r   r   
isinstancer%   r"   r&   r
   symbolr!   r    doitr   r   r   r   )r)   r*   rateXr/   r1   s         M/var/www/html/venv/lib/python3.12/site-packages/sympy/stats/tests/test_mix.pytest_densityr;      sQ   sAsT"A1a=D4AfQi0001bt{{+,0CA0FFFF	a	B	b!	B72;q> DHbbk$::::*GB2q	*1-.Qa!eaZKM""Ad2hJ/0 0 0KGBKN#tBxQTE"H'=r$r({'KKKK    c                     t        dd      \  } }}t        dd||      }t        d| |d         }t        ||d   f      }t	        t        d      t        t        t	        t        d      t        t        dd      t        t        t        d            t        d                  t        t        d	d      t        t        t        d            t        d
                  t        t        t        t        t        d            t        d                  t        d            t        t        t        t        t        d            t        d
                  t        d                  t        t        t        t        t        d            t        d            t        t        t        d            t        d
                  t        d                  t        t        d      d            t        t        t        dd            t        d            t        t        t        dd      t        t        t        d            t        d                        t        t        t        t        t        d            t        d                  t        d            t        t        t        t        d            t        d            t        t        dd      t        d                  t        t        t        t        d            t        d
            t        t        t        t        d            t        d            t        d                        } ||      |k(  sJ y )Nza1 p1 p2Tr+   Cr-   Br   p1p2r0   a1)r   r   r   r$   r   r   r   r   r   r	   r   r   r   r
   r   r   )rC   r@   rA   r>   r?   MGRmgrcs          r:   test_MarginalDistributionrF   )   sg   d3JBBCB#Ab!A$'A
q1Q4'
*Cvc{Il3wqztd#W[-EAJ& fTD1Ks$gaj13	'+fSk2GAJ?@'"+N	'+fSk2GAJ?@'"+N4P s7;vc{+WQZ8Ks$gaj134;AJ@'A T"$ &)vdT/J)KBK&F4$7Ks$gaj13 4gk&+.
;<gbkJF3K('!*5td#WR[13F3K('!*5F3K('!*5wr{CEFD  q6T>>r<   c                  `   t        dd      } t        d|       }t        t        |      t              sJ t        t        |      j                  t
              sJ |j                  j                  j                  d      j                         t        d      t        t        d            z  k(  sJ y )NYr0   ZrB   )	r   r5   r%   r"   distributionr#   pdfr7   r   )rH   rI   s     r:   test_compound_distributionrM   @   s    QAQAfQi000fQi,,.BCCC88  $$Q',,.#b'#c"g,2FFFFr<   c                  ~   t        dd      t        dd      }} t        d      }t        t	        t        d      t        t        |       t        |dz
        z  |dt        f      z  t        |      z  |dt        f      |t         df      }t        t	        t        d      t        t        |       t        |dz
        z  |dt        f      z  t        |      z  |dt        f      |dt        f      }t        t        | |z   d            dk(  sJ t        t        | |z   d            dk(  sJ t        t              5  t        || z   dk  d	      j                  t              j                  |      sJ t        || z   dkD  d	      j                  t              j                  |      sJ 	 d d d        y # 1 sw Y   y xY w)
NrH   r0   EkrB   r-   r   F)evaluate)r   r   r   r   r   r   r   r   r   r   r
   r   r'   UserWarningrewritedummy_eq)rH   rO   rP   expr1expr2s        r:   test_mix_expressionrW   G   s   3?KQ/qAc
ASR#qb'*QU2C*CaBZ " l2J "#bS!.ESR#qb'*QU2C*CaBZ " l2J "#Q-ERAq\?aRAq\?a		% NQU+33H=FFuMMMQU+33H=FFuMMMN N Ns   :A/F33F<N)@sympy.concrete.summationsr   sympy.core.addr   sympy.core.mulr   sympy.core.numbersr   r   r   sympy.core.powerr	   sympy.core.relationalr
   r   sympy.core.symbolr   r   r   (sympy.functions.combinatorial.factorialsr   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   'sympy.functions.special.delta_functionsr   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   sympy.simplify.simplifyr   sympy.tensor.indexedr   r   r   sympy.statsr   r   r   r   r   r   sympy.stats.crv_typesr    sympy.stats.drv_typesr!   sympy.stats.compound_rvr"   r#   sympy.stats.joint_rvr$   sympy.stats.rvr%   r&   sympy.testing.pytestr'   r;   rF   rM   rW    r<   r:   <module>rp      sq    )   0 0   * 6 6 > 6 9 : > 9 . , 7 =7 7 ( 5 H 5 * 0L.GNr<   