ó
9­\c           @   s  d  d l  m Z m Z m Z m Z m Z 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 m Z d  d l m Z d  d l m Z e d	 ƒ \ Z Z Z Z Z d
 „  Z d „  Z d „  Z d „  Z  d „  Z! d „  Z" d „  Z# e d „  ƒ Z$ d S(   iÿÿÿÿ(   t   symbolst   pit   oot   St   expt   sqrtt   besselkt   Indexed(   t   density(   t   marginal_distribution(   t   JointRV(   t   Normal(   t   raisest   XFAIL(   t	   integrate(   t   Matrixs	   x y z a bc             s  t  d d d g d d g d d g g ƒ ‰  t ˆ  ƒ d d ƒ d d t k sS t ‚ t t ‡  f d †  ƒ t t d „  ƒ t  d d d d g d d d g d d d g d d d g g ƒ }  t  d	 t d d g ƒ t d d g d d g g ƒ ƒ } t ˆ  ƒ t t ƒ t | ƒ t t ƒ k st ‚ t	 |  d d ƒ d d ƒ d d t k sMt ‚ t
 t ˆ  ƒ t t ƒ t t t f t t t f ƒ j ƒ  d k s”t ‚ t  d
 d d g t d g d t g g ƒ } t | ƒ d d ƒ t d t d d t ƒ d t t t t ƒ k st ‚ t t d „  ƒ d  S(   Nt   Ai   i   i    c              s   ˆ  d S(   Ni   (    (    (   t   m(    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   <lambda>   t    c           S   s(   t  d d d g d d g d d g g ƒ S(   Nt   Mi   i   i    (   R   (    (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyR      R   t   Bi   t   Ct   Niþÿÿÿc           S   s(   t  d d d g d d g d d g g ƒ S(   NR   i   i   iÿÿÿÿ(   R   (    (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyR      R   (   R   R   R   t   AssertionErrorR   t
   ValueErrorR   t   xt   yR	   R   R   t   evalfR   R   (   t   nt   pR   (    (   R   s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_Normal   s    *)
?60/G*Mc             s+  d d l  m ‰  ˆ  d d d g d d g d d g g d ƒ }  t |  ƒ d d ƒ d d t k sf t ‚ t t |  ƒ t t ƒ t t t f t t t f ƒ j	 ƒ  d k s­ t ‚ t
 t ‡  f d †  ƒ ˆ  d	 d d g t d g d t g g d ƒ } t | ƒ d d ƒ d d t t t t ƒ k s't ‚ d  S(
   Niÿÿÿÿ(   t   MultivariateTt   Ti    i   i   i   c              s+   ˆ  d d d g d d g d d g g d ƒ S(   NR!   i   i   iÿÿÿÿ(    (    (   R    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyR   !   R   t   t2(   t   sympy.stats.joint_rv_typesR    R   R   R   R   R   R   R   R   R   R   R   (   t   t1R"   (    (   R    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_MultivariateTDist   s    -)"%-c             s   d d l  m ‰  t t ‡  f d †  ƒ ˆ  d d d g d d g d d g g ƒ }  t |  ƒ d d ƒ t d ƒ t d t d ƒ ƒ t k sŽ t	 ‚ ˆ  d	 d d g t
 d g d t g g ƒ } t | ƒ d d ƒ t d t ƒ t d t d d
 t d t
 t ƒ ƒ t t t
 t ƒ k st	 ‚ d  S(   Niÿÿÿÿ(   t   Laplacec              s(   ˆ  d d d g d d g d d g g ƒ S(   NR!   i   i   (    (    (   R&   (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyR   '   R   t   Li   i    i   i   t   L1i   (   t   sympy.stats.crv_typesR&   R   R   R   R   R   R   R   R   R   R   (   R'   R(   (    (   R&   s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_multivariate_laplace%   s    *>*c             s  d d l  m ‰  d d l m }  ˆ  d d d d d ƒ } t | ƒ d d ƒ d	 t d
 ƒ t t ƒ k sm t ‚ t	 t
 ‡  f d †  ƒ t | d ƒ d ƒ d t d ƒ |  t d ƒ d ƒ d t t ƒ |  t d ƒ d ƒ k sä t ‚ t | t ƒ d ƒ t t d ƒ d ƒ d k st ‚ d  S(   Niÿÿÿÿ(   t   NormalGamma(   t   gammat   Gi   i   i   i   i    iüÿÿÿc              s   ˆ  d d d d d ƒ S(   NR-   i   i   i   iÿÿÿÿ(    (    (   R+   (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyR   3   R   i    i
   i   i   i€   (   R#   R+   t   sympyR,   R   R   R   R   R   R   R   R	   R   R   (   R,   t   ng(    (   R+   s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_NormalGamma.   s    5Oc          C   sä   d d l  m }  d d l m } |  d d d g d d g d d g g d ƒ } t | | d ƒ t ƒ t d ƒ t d d d | t d d d ƒ t d	 ƒ d k s¬ t ‚ t	 t | d ƒ t ƒ t t
 t
 f ƒ d k sà t ‚ d  S(
   Niÿÿÿÿ(   R    (   t
   polar_liftR!   i    i   i   i   i   (   R#   R    R.   R1   R	   R   R   R   R   R   R   (   R    R1   R!   (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt%   test_JointPSpace_margial_distribution8   s    -+4c          C   s  d d l  m }  d „  d	 Dƒ \ } } t | d d | | d d t d ƒ d ƒ d t } t d | ƒ } t | ƒ d d ƒ t d ƒ d t k sŸ t ‚ t | j	 j
 |  ƒ sº t ‚ t | d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t t ƒ k st ‚ d  S(
   Niÿÿÿÿ(   t   JointDistributionHandmadec         s   s   |  ] } t  d  | ƒ Vq d S(   R   N(   R   (   t   .0t   i(    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pys	   <genexpr>B   s    i   i   R   iþÿÿÿi    (   i   i   (   t   sympy.stats.joint_rvR3   R   R   R   R
   R   R   t
   isinstancet   pspacet   distributionR	   R   (   R3   t   x1t   x2t   pdft   X(    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_JointRV@   s    ;/c          C   sp   d d l  m }  d d l m } t d t t g d d g d d g g ƒ } |  | | d ƒ ƒ t k sl t ‚ d  S(   Niÿÿÿÿ(   t   simplify(   t   ER   i   i    (   R.   R?   t   sympy.statsR@   R   R   R   R   (   R?   R@   R   (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_expectationI   s    *c          C   s\   d d l  m }  t d t t g d d g d d g g ƒ } |  | ƒ t t f k sX t ‚ d  S(   Niÿÿÿÿ(   R@   R   i   i    (   RA   R@   R   R   R   R   (   R@   R   (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   test_joint_vector_expectationO   s    *N(%   R.   R    R   R   R   R   R   R   R   RA   R   R6   R	   R#   R
   R)   R   t   sympy.utilities.pytestR   R   t   sympy.integrals.integralsR   t   sympy.matricesR   R   R   t   zt   at   bR   R%   R*   R0   R2   R>   RB   RC   (    (    (    s>   lib/python2.7/site-packages/sympy/stats/tests/test_joint_rv.pyt   <module>   s    :		
			
				