
&]\c           @` s<  d  d l  m Z m Z m Z d  d l Z d  d l m Z m Z d  d l 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 j Z d  d l m Z d  d l j j Z d	 e f d
     YZ d e f d     YZ d e f d     YZ d e f d     YZ d e f d     YZ  d e f d     YZ! d e f d     YZ" d e f d     YZ# d e f d     YZ$ d d d  Z% d   Z& d   Z' d    Z( d!   Z) d"   Z* d#   Z+ d$   Z, d%   Z- d&   Z. d'   Z/ d(   Z0 d)   Z1 d*   Z2 d+   Z3 d,   Z4 d-   Z5 d.   Z6 d/   Z7 d S(0   i    (   t   divisiont   print_functiont   absolute_importN(   t   arrayt   sqrt(   t   assert_array_almost_equalt   assert_equalt   assert_almost_equalt   assert_allclose(   t   raises(   t   xrange(   t	   integrate(   t   gammat	   TestChebyc           B` s,   e  Z d    Z d   Z d   Z d   Z RS(   c         C` s6  t  j d  } t  j d  } t j d d  } z@ t  j d  } t  j d  } t  j d  } t  j d  } Wd  t j |   Xt | j d g d	  t | j d d g d	  t | j d d d
 g d	  t | j d d d d g d	  t | j d d d d d g d	  t | j d d d d d d g d	  d  S(   Ni    i   t   allt   ignorei   i   i   i   i   iiii(   t   ortht   chebyct   npt   seterrR   t   c(   t   selft   C0t   C1t   olderrt   C2t   C3t   C4t   C5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_chebyc   s    "c         C` s  t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t | j d g d  t | j d d g d  t | j d d d g d  t | j d d d	 d g d  t | j d d d
 d d g d  t | j d d d d d d g d  d  S(   Ni    i   i   i   i   i   i   iiii(   R   t   chebysR   R   (   R   t   S0t   S1t   S2t   S3t   S4t   S5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_chebys$   s    "c         C` s  t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t | j d g d  t | j d d g d  t | j d d d g d  t | j d d d	 d g d  t | j d
 d d d d g d  t | j d d d d d d g d  d  S(   Ni    i   i   i   i   i   i   iii   ii   i(   R   t   chebytR   R   (   R   t   T0t   T1t   T2t   T3t   T4t   T5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_chebyt2   s    "c         C` s  t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t | j d g d  t | j d d g d  t | j d d d g d  t | j d	 d d
 d g d  t | j d d d d d g d  t | j d d d d d d g d  d  S(   Ni    i   i   i   i   i   i   ii   ii   ii    ii   (   R   t   chebyuR   R   (   R   t   U0t   U1t   U2t   U3t   U4t   U5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_chebyu@   s    "(   t   __name__t
   __module__R   R%   R-   R5   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR      s   			t   TestGegenbauerc           B` s   e  Z d    Z RS(   c         C` s  d t  j j   d } t  j | d k  r5 d } n  t j d |  } t j d |  } t j d |  } t j d |  } t j d |  } t j d |  } t | j t d g  d	  t | j t d | d g  d	  t | j t d | | d d | g  d	  t | j t d t j | d  d d
 | | d d g  d d  t | j t d t j | d  d d t j | d  d d | | d g  d d  t | j t d t j | d  d d t j | d  d d t j | d  d g  d d  d  S(   Ni   g      ?i    gɿi   i   i   i   i   ig      @i   ig      @ii   g      .@(	   R   t   randomt   anyR   t
   gegenbauerR   R   R   t   poch(   R   t   at   Ca0t   Ca1t   Ca2t   Ca3t   Ca4t   Ca5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_gegenbauerQ   s$    	#/15#5(   R6   R7   RD   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR8   O   s   t   TestHermitec           B` s   e  Z d    Z d   Z RS(   c         C` s  t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t  j d  } t | j d g d  t | j d d g d  t | j d d d g d  t | j d	 d d
 d g d  t | j d d d d d g d  t | j d d d d d d g d  d  S(   Ni    i   i   i   i   i   i   ii   ii   ii   i    i`ix   (   R   t   hermiteR   R   (   R   t   H0t   H1t   H2t   H3t   H4t   H5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_hermiteh   s    "c         C` s  t  j d t d  d g  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  |  } t j d  |  t d  }	 t j d  |  d }
 t j d  |  d t d  } t j d  |  d	 } t j d  |  d	 t d  } t | j | j d
  t | j |	 j d
  t | j |
 j d
  t | j | j d
  t | j | j d
  t | j | j d
  d  S(   Ng      ?i   i    i   i   i   i   g       @g      @i   (   R   t   poly1dR   R   t   hermitenormRF   R   R   (   R   t   psubRG   RH   RI   RJ   RK   RL   t   he0t   he1t   he2t   he3t   he4t   he5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_hermitenormv   s&    ##(   R6   R7   RM   RW   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyRE   g   s   	t   _test_sh_legendrec           B` s   e  Z d    Z RS(   c         C` su  t  j d d g  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  |  } t j d  |  }	 t j d  |  }
 t j d  |  } t j d  |  } t j d  |  } t | j | j d  t | j |	 j d  t | j |
 j d  t | j | j d  t | j | j d	  t | j | j d	  d  S(
   Ni   ii    i   i   i   i   i   i   (   R   RN   R   t   sh_legendret   legendreR   R   (   R   RP   t   Ps0t   Ps1t   Ps2t   Ps3t   Ps4t   Ps5t   pse0t   pse1t   pse2t   pse3t   pse4t   pse5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_sh_legendre   s&    (   R6   R7   Rg   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyRX      s   t   _test_sh_chebytc           B` s   e  Z d    Z RS(   c         C` su  t  j d d g  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  |  } t j d  |  }	 t j d  |  }
 t j d  |  } t j d  |  } t j d  |  } t | j | j d  t | j |	 j d  t | j |
 j d  t | j | j d  t | j | j d	  t | j | j d	  d  S(
   Ni   ii    i   i   i   i   i   i   (   R   RN   R   t	   sh_chebytR&   R   R   (   R   RP   t   Ts0t   Ts1t   Ts2t   Ts3t   Ts4t   Ts5t   tse0t   tse1t   tse2t   tse3t   tse4t   tse5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_sh_chebyt   s&    (   R6   R7   Rv   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyRh      s   t   _test_sh_chebyuc           B` s   e  Z d    Z RS(   c         C` su  t  j d d g  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  } t j d  |  } t j d  |  }	 t j d  |  }
 t j d  |  } t j d  |  } t j d  |  } t | j | j d  t | j |	 j d  t | j |
 j d  t | j | j d  t | j | j d	  t | j | j d
  d  S(   Ni   ii    i   i   i   i   i   i   i   (   R   RN   R   t	   sh_chebyuR.   R   R   (   R   RP   t   Us0t   Us1t   Us2t   Us3t   Us4t   Us5t   use0t   use1t   use2t   use3t   use4t   use5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_sh_chebyu   s&    (   R6   R7   R   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyRw      s   t   _test_sh_jacobic           B` s   e  Z d    Z RS(   c         C` sr  d   } t  j d d g  } d t  j j   } | d d t  j j   } t j d | |  } t j d | |  } t j d | |  } t j d | |  } t j d | |  }	 t j d | |  }
 t j d | | | d  |  | d |  } t j d | | | d  |  | d |  } t j d | | | d  |  | d |  } t j d | | | d  |  | d |  } t j d | | | d  |  | d |  } t j d | | | d  |  | d |  } t | j | j d	  t | j | j d	  t | j | j d	  t | j | j d	  t |	 j | j d	  t |
 j | j d	  d  S(
   Nc         S` s.   t  |  d  t  |  |  t  d |  |  S(   Ni   i   (   R   (   t   nt   p(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   <lambda>   s    i   ii   i   i    i   i   i   (   R   RN   R9   R   t	   sh_jacobit   jacobiR   R   (   R   t   convRP   t   qR   t   G0t   G1t   G2t   G3t   G4t   G5t   ge0t   ge1t   ge2t   ge3t   ge4t   ge5(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_sh_jacobi   s,    	000000(   R6   R7   R   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR      s   t   TestCallc           B` s   e  Z d    Z RS(   c         C` s   g  } xM t  d  D]? } | j g  d t d |  j   D] } | j   ^ q9  q Wt j d d  } zL xE | D]= } t |  } t | d  t j	 | j
  d  d | qr WWd  t j |   Xd  S(   Ni   sW  
                orth.jacobi(%(n)d,0.3,0.9)
                orth.sh_jacobi(%(n)d,0.3,0.9)
                orth.genlaguerre(%(n)d,0.3)
                orth.laguerre(%(n)d)
                orth.hermite(%(n)d)
                orth.hermitenorm(%(n)d)
                orth.gegenbauer(%(n)d,0.3)
                orth.chebyt(%(n)d)
                orth.chebyu(%(n)d)
                orth.chebyc(%(n)d)
                orth.chebys(%(n)d)
                orth.sh_chebyt(%(n)d)
                orth.sh_chebyu(%(n)d)
                orth.legendre(%(n)d)
                orth.sh_legendre(%(n)d)
                R   R   R   g)\(?t   err_msg(   R
   t   extendt   dictt   splitt   stripR   R   t   evalR   RN   t   coef(   R   t   polyR   t   xR   t   pstrR   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt	   test_call   s    	4$(   R6   R7   R   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR      s   t   TestGenlaguerrec           B` s   e  Z d    Z RS(   c         C` s   t  t j d d d t d  d  t  t j d d d t d  d  t  t j d d d t t j d d g   t  t j d d d t t j d d g   d  S(	   Ni   t   monici    g       @g       ii   i(   R   R   t   genlaguerret   Falset   TrueR   RN   (   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_regression  s    %%.(   R6   R7   R   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s   gV瞯<g+=c         ` sR  |  | t   \ } }	 }
 t j |  } | | d  d   t j f |  } t j | |	 | j  } d t j | j    } | d  d   t j f | | } t | t j	 |  | |  t |	 j
   |
 | |  d     t j    f d   | |  } t j   |  |	  } d | d k  r)d n | d d } t | d | d | d  S(   Ni   c         S` s   |  d d |  d |  d S(   Ni   i   (    (   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   /  s    c         ` s     |    |   S(   N(    (   R   (   t   ft   weight_func(    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   0  s    gư>i
   i    t   rtol(   R   R   t   aranget   newaxist   dott   TR   t   diagonalR   t   eyet   sumR   t   quadt   vdot(   t	   root_funct	   eval_funcR   R=   t   bt   NR   t   atolR   t   wt   muR   t   vt   vvt   vdt   resIt   resG(    (   R   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   verify_gauss_quad  s    "!	!$c       	   C` s  d   }  d   } d   } t  } | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	  | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d t j d d d  \ } } t j d  \ } } t | | d d  t | | d d  t j d d d  \ } } t j d d   \ } }	 t | | d d  t | |	 d d  t j d d d! t  \ }
 } t j d d d! t  \ } } } t |
 | d d  t | | d d  t j	 | d d!  d" d  \ } } t | | d# | t
 t t j d$ d d  t
 t t j d% d d  t
 t t j d! d& d  t
 t t j d! d d&  t
 t t j d! d& d&  d  S('   Nc         ` s      f d   S(   Nc         ` s   t  j |     |  S(   N(   t   sct   roots_jacobi(   R   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   6  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   6  s    c         ` s      f d   S(   Nc         ` s   t  j |     |  S(   N(   R   t   eval_jacobi(   R   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   7  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   7  s    c         ` s      f d   S(   Nc         ` s   d |    d |   S(   Ni   (    (   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   8  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   8  s    g      g      g      g      ?i   i   R   g-q=id   gdy=g      ?g7QE=i   gvIh%L=g?i   gvIh%<=g7QU=g=
ףp=2@gL;@ǧG@gɿg      @g9Q@i   g        g+=g      @g      @i   iR   i    gffffff
@i(   R   R   R   t   roots_legendreR   t   roots_gegenbauerR   R   R   R   t   assert_raisest
   ValueError(   t   rft   eft   wft   vgqt   xjt   wjt   xlt   wlt   xct   wcR   R   t   yR   t   mt   muIt   muI_err(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_jacobi5  sb    			4--4:::::4::44-::-4:-!$c       	   C` s  d   }  d   } d   } t  } | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d  | |  d d  | d d  | d d  d d d	  | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d d
 d | |  d d  | d d  | d d  d d d	 d
 d | |  d d  | d d  | d d  d d d d
 d t j d d d t  \ } } t j d d d t  \ } } } t | | d d  t | | d d  t j | d d  d d  \ }	 }
 t | |	 d  |
 t t	 t j d d d  t t	 t j d! d d  t t	 t j d d d  t t	 t j d d d"  t t	 t j d d# d"  d  S($   Nc         ` s      f d   S(   Nc         ` s   t  j |     |  S(   N(   R   t   roots_sh_jacobi(   R   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   w  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   w  s    c         ` s      f d   S(   Nc         ` s   t  j |     |  S(   N(   R   t   eval_sh_jacobi(   R   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   x  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   x  s    c         ` s      f d   S(   Nc         ` s   d |     |   d S(   Ng      ?(    (   R   (   R=   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   y  s    (    (   R=   R   (    (   R=   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR   y  s    g      g      ?g        g      ?i   i   R   g-q=id   gdy=g      ?gvIh%<=i   g7QE=i   g?gL;@g=
ףp=2@ǧG@g?g|=g9Q@g      @g(#=gvIh%L=i   g+=i    R   gffffff
@ii(
   R   R   R   R   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_sh_jacobiv  sP    			4--4::4::4::44-:::::-!$c    
   	   C` s  t  j }  t j } t j d  j } t |  | | t j t j d  t |  | | t j t j d d d t |  | | t j t j d d d t  j d t	  \ } } t  j d t
  \ } } } t | | d d  t | | d d  t j | t j t j  \ } }	 t | | d |	 t  j d	 t	  \ } } t  j d	 t
  \ } } } t | | d d  t | | d d  t t |  | d d  t t t  j d
  t t t  j d  d  S(   Ni   i   R   gvIh%<=id   g-q=g+=R   i   i    gffffff
@(   R   t   roots_hermiteR   t   eval_hermiteRF   R   R   R   t   infR   R   R   R   R   R   R   R   (
   t   rootft   evalft   weightfR   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_hermite  s&    		 &&"c          ` s   d     d d   f d  }  |  d d d |  d d d |  d	 d d |  d
 d d |  d d d |  d d d |  d d d |  d d d |  d d d |  d d d d  S(   Nc         S` s  t  j |  | j f  } t  j d t  j d | d  | d d  d   f <|  d k rt d  | | d d  d   f | d d  d   f <x t d |   D]l } t d |  | | | d d  d   f t | d |  | | d d  d   f | | d  d   f <q Wn  | S(   Ng      пg      i   i    i   g       @g      ?(   R   t   zerost   sizet   pit   expR   R
   (   R   t   nodest   Ht   k(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   hermite_recursion  s    24mgV瞯<g+=c         ` sz   t  j |   \ } }   |  d |  } t | d d  d   f t j |   | |  t t |  t t j  | |  d  S(   Ni   i(   R   t   _roots_hermite_asyR   R   R   R   R   R   (   R   R   R   R   R   R   (   R   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test  s    ,i   R   g-q=i   i,  i-  i  i  i  i  i  i  (    (   R   (    (   R   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_hermite_asy  s    	
c    
   	   C` sH  t  j }  t j } t j d  j } t |  | | t j t j d  t |  | | t j t j d d d t |  | | t j t j d d d t  j d t	  \ } } t  j d t
  \ } } } t | | d d  t | | d d  t j | t j t j  \ } }	 t | | d |	 t t t  j d	  t t t  j d
  d  S(   Ni   i   R   gvIh%<=id   g-q=g+=R   i    gffffff
@(   R   t   roots_hermitenormR   t   eval_hermitenormRO   R   R   R   R   R   R   R   R   R   R   R   (
   R   R   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_hermitenorm  s    		 &&"c       	   C` s?  d   }  d   } d   } t  } | |  d  | d  | d  d d d  | |  d  | d  | d  d d d d	 d
 | |  d  | d  | d  d d d d	 d | |  d  | d  | d  d d d  | |  d  | d  | d  d d d d	 d | |  d  | d  | d  d d d d	 d
 | |  d  | d  | d  d d d  | |  d  | d  | d  d d d d	 d | |  d  | d  | d  d d d d	 d
 | |  d  | d  | d  d d d  | |  d  | d  | d  d d d d	 d | |  d  | d  | d  d d d d	 d
 | |  d  | d  | d  d d d d	 d | |  d  | d  | d  d d d d	 d
 | |  d  | d  | d  d d d d	 d | |  d  t j | d  d d d  | |  d  t j | d  d d d  | |  d  t j | d  d d d d	 d
 t j d d t  \ } } t j d d t  \ } } } t | | d d  t | | d d  t j	 | d  d d  \ }	 }
 t | |	 d |
 t
 t t j d d  t
 t t j d d  t
 t t j d d  d  S(   Nc         ` s     f d   S(   Nc         ` s   t  j |    |  S(   N(   R   R   (   R   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    c         ` s     f d   S(   Nc         ` s   t  j |    |  S(   N(   R   t   eval_gegenbauer(   R   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    c         ` s     f d   S(   Nc         ` s   d |  d   d S(   Ni   i   g      ?(    (   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    g      пg      g      ?i   i   R   g-q=id   gdy=g?gvIh%<=i   i
   i2   i    i   g+=iR   gffffff
@i   g      (   R   R   t   eval_chebytR   R   R   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_gegenbauer  s>    			+11+11+11+11111((.!c       	   C` s&  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d	 d
  \ } } t	 | | d | t t t j d  t t t j d  d  S(   Ni   g      g      ?i   id   R   g-q=g+=ii   R   i    gffffff
@(   R   R&   R   R   R   t   roots_chebytR   R   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_chebyt$  s    %c          C` sZ   t  j d  \ }  } |  d  |  d } } t | | d  d  d   t |  d d  d  S(   Ni   i
   i   ii    (   R   R   R   (   R   R   t   post   neg(    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_chebyt_symmetry5  s    c          C` s   t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d  t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d d  \ } } t	 | | d	 | t t t j d
  t t t j d  d  S(   Ni   g      g      ?i   id   g+=ii   R   i    gffffff
@(   R   R.   R   R   R   t   roots_chebyut   eval_chebyuR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_chebyu;  s    c       	   C` s&  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d	 d
  \ } } t	 | | d | t t t j d  t t t j d  d  S(   Ni   g       g       @i   id   R   g-q=g+=ii   R   i    gffffff
@(   R   R   R   R   R   t   roots_chebyct   eval_chebycR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_chebycL  s    %c          C` s   t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d  t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d d  \ } } t	 | | d	 | t t t j d
  t t t j d  d  S(   Ni   g       g       @i   id   g+=ii   R   i    gffffff
@(   R   R   R   R   R   t   roots_chebyst   eval_chebysR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_chebys]  s    c       	   C` s&  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d	 d
  \ } } t	 | | d | t t t j d	  t t t j d  d  S(   Ni   g        g      ?i   id   R   gvIh%<=g+=i    i   R   gffffff
@(   R   Ri   R   R   R   t   roots_sh_chebytt   eval_sh_chebytR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_sh_chebytn  s    c       	   C` s&  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d  t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d d  t	 | | d d  t
 j |  d	 d
  \ } } t	 | | d | t t t j d	  t t t j d  d  S(   Ni   g        g      ?i   id   R   gvIh%<=g+=i    i   R   gffffff
@(   R   Rx   R   R   R   t   roots_sh_chebyut   eval_sh_chebyuR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_sh_chebyu  s    c       	   C` s,  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d d d t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d	 d	  t	 | | d	 d	  t
 j |  d
 d  \ } } t	 | | d | t t t j d  t t t j d  d  S(   Ni   g      g      ?i   R   gvIh%<=id   g-q=g+=ii   R   i    gffffff
@(   R   RZ   R   R   R   R   t   eval_legendreR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_legendre  s    c       	   C` s,  t  j d  j }  t t j t  j |  d d d  t t j t  j |  d d d d d t t j t  j |  d d d d d t j d t  \ } } t j d t  \ } } } t	 | | d	 d	  t	 | | d	 d	  t
 j |  d
 d  \ } } t	 | | d | t t t j d
  t t t j d  d  S(   Ni   g        g      ?i   R   gvIh%<=id   g-q=g+=i    i   R   gffffff
@(   R   RY   R   R   R   t   roots_sh_legendret   eval_sh_legendreR   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_sh_legendre  s    c       	   C` s8  t  j d  j }  t t j t  j |  d t j d  t t j t  j |  d t j d d d t t j t  j |  d t j d d d t j d t	  \ } } t j d t
  \ } } } t | | d d  t | | d d  t j |  d	 t j  \ } } t | | d
 | t t t j d	  t t t j d  d  S(   Ni   g        i   R   gvIh%<=id   g-q=g+=i    R   gffffff
@(   R   t   laguerreR   R   R   t   roots_laguerret   eval_laguerreR   R   R   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_laguerre  s    "c          C` s  d   }  d   } d   } t  } | |  d  | d  | d  d t j d  | |  d  | d  | d  d t j d d d	 | |  d  | d  | d  d t j d
 d d | |  d  | d  | d  d t j d  | |  d  | d  | d  d t j d d d	 | |  d  | d  | d  d t j d
 d d	 | |  d  | d  | d  d t j d  | |  d  | d  | d  d t j d d d	 | |  d  | d  | d  d t j d
 d d	 | |  d  | d  | d  d t j d  | |  d  | d  | d  d t j d d d	 | |  d  | d  | d  d t j d
 d d | |  d  | d  | d  d t j d  | |  d  | d  | d  d t j d d d	 | |  d  | d  | d  d t j d
 d d d d t j d d t  \ } } t j d d t  \ } } } t | | d d  t | | d d  t j	 | d  d t j  \ }	 }
 t | |	 d |
 t
 t t j d d  t
 t t j d d  t
 t t j d d  d  S(   Nc         ` s     f d   S(   Nc         ` s   t  j |    |  S(   N(   R   t   roots_genlaguerre(   R   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    c         ` s     f d   S(   Nc         ` s   t  j |    |  S(   N(   R   t   eval_genlaguerre(   R   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    c         ` s     f d   S(   Nc         ` s   |    t  j |   S(   N(   R   R   (   R   (   R=   (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    (    (   R=   (    (   R=   sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyR     s    g      g        i   i   R   gvIh%<=id   g-q=g?i   i
   i2   R   g+=gvIh%L=i   g       @i    gffffff
@i   g(   R   R   R   R   R  R   R   R   R   R   R   R   (   R   R   R   R   R   R   R   R   R   R   R   (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_roots_genlaguerre  s8    			.44.44.44.44.4:$c           C` s   t  j d  d  d  S(   NiA   g?(   R   R&   (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   test_gh_6721  s    (8   t
   __future__R    R   R   t   numpyR   R   R   t   numpy.testingR   R   R   R   t   pytestR	   R   t   scipy._lib.sixR
   t   scipyR   t   scipy.specialt   specialR   R   t   scipy.special.orthogonalt
   orthogonalR   t   objectR   R8   RE   RX   Rh   Rw   R   R   R   R   R   R   R   R   R   R   R   R   R   R  R  R  R
  R  R  R  R  R  (    (    (    sB   lib/python2.7/site-packages/scipy/special/tests/test_orthogonal.pyt   <module>   sJ   "?'!		A	4				-											'