ó
”¼\c           @  s¾  d  d l  m Z m Z d d Ue Z e Z e Z e	 Z
 e Z e Z d  d l m Z m Z m Z m Z m Z m Z m Z e d  \ Z Z Z e d d e \ Z Z Z Z Z  Z! e" d d	 e Z# e" d d
 e Z$ e d d	 e d e d e \ Z% Z& e d d	 e d e d e d e \ Z' Z( e" d d	 e d e d e Z) d   Z* d   Z+ e d d e \ Z, Z e e, d d e e, e e- e, e  e- e,  e- e  Z. e" d d e d e Z/ d d e/ d e e/ d e0 e d d  e- e/ d  Z1 d e# d e- e# d  e e# d d e0 e d  Z2 e e! e e e e e! d e e e e e! d Z3 e d d e \ Z4 Z5 e6 e4 e e4 e5 e5 e4 e e5 e4 e5  e e- e4 d  e- e5 d  e- e4 e5 d  Z7 e d d e \ Z8 Z9 e e9 d e0 e d e8 d d e9 d  e: d e e8 e9 d  Z; e" d d	 e Z< e0 e= e e<  e  d e Z> e" d d e Z? e" d d e Z@ d   ZA d d d  d! d" d# d$ d% d& d' d( d) d* d+ d, d- d. d/ d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 d: d; d< d= d> d? d@ dA dB dC dD dE dF dG dH dI dJ dK dL dM dN dO dP dQ dR dS dT dU dV dW dX dY dZ d[ d\ d] d^ d_ d` da db dc dd de df dg dh di dj dk dl dm dn do dp dq dr ds dt du dv dw dx dy dz d{ d| d} d~ d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d  d” d¢ d£ d¤ d„ d¦ d§ dØ d© dŖ d« d¬ d­ d® dÆ d° d± d² d³ d“ g ZB d  dµ lC mC ZC d  d¶ lD mE ZE d  d lF ZF g  ZG eH d· k rŗx® eI eB  D]  \ ZJ ZK eE   eC   ZL eK d UeC   eL ZL eG eL eK f g 7ZG eF jM jN dø  eF jM jO   eJ eP eB  d¹ d k rĪeF jM jN dŗ d¹ eJ eP eB   qĪqĪWeQ   eG jR d» d¼    x+ eG D]  \ Z ZK eQ d½ e eK f  qWn  d S(¾   i’’’’(   t   print_functiont   divisions   from sympy import *N(   t   at   bt   st   tt   xt   yt   zs   nu beta rhos   a b c d k pt   positivet   kt   realt   negatives   mu1 mu2t   nonzerot   finites   sigma1 sigma2t   lambdac         C  s9   d t  d t | d  t |  | d d | d  S(   Ni   i   (   t   sqrtt   pit   exp(   R   t   mut   sigma(    (    s?   lib/python2.7/site-packages/sympy/benchmarks/bench_meijerint.pyt   normal   s    c         C  s   | t  | |   S(   N(   R   (   R   t   rate(    (    s?   lib/python2.7/site-packages/sympy/benchmarks/bench_meijerint.pyt   exponential   s    s
   alpha betai   t   integeri   s   d1 d2s   nu sigmai    R   t   ut   polarR   c         C  s   t  |  t t t  t t t t  t d t f t t t f d t	 } t  |  t t t  t t t t  t t t f t d t f d t	 } d  S(   Ni    t   meijerg(
   t	   integrateR   R   R   R   R   t   mu1t   sigma1t   oot   True(   t   exprt   res1t   res2(    (    s?   lib/python2.7/site-packages/sympy/benchmarks/bench_meijerint.pyt   E4   s    #%#s    MT(x**nu*Heaviside(x - 1), x, s)s    MT(x**nu*Heaviside(1 - x), x, s)s*   MT((1-x)**(beta - 1)*Heaviside(1-x), x, s)s*   MT((x-1)**(beta - 1)*Heaviside(x-1), x, s)s   MT((1+x)**(-rho), x, s)s   MT(abs(1-x)**(-rho), x, s)sK   MT((1-x)**(beta-1)*Heaviside(1-x) + a*(x-1)**(beta-1)*Heaviside(x-1), x, s)s   MT((x**a-b**a)/(x-b), x, s)s!   MT((x**a-bpos**a)/(x-bpos), x, s)s   MT(exp(-x), x, s)s   MT(exp(-1/x), x, s)s"   MT(log(x)**4*Heaviside(1-x), x, s)s"   MT(log(x)**3*Heaviside(x-1), x, s)s   MT(log(x + 1), x, s)s   MT(log(1/x + 1), x, s)s   MT(log(abs(1 - x)), x, s)s   MT(log(abs(1 - 1/x)), x, s)s   MT(log(x)/(x+1), x, s)s   MT(log(x)**2/(x+1), x, s)s   MT(log(x)/(x+1)**2, x, s)s   MT(erf(sqrt(x)), x, s)s   MT(besselj(a, 2*sqrt(x)), x, s)s*   MT(sin(sqrt(x))*besselj(a, sqrt(x)), x, s)s*   MT(cos(sqrt(x))*besselj(a, sqrt(x)), x, s)s    MT(besselj(a, sqrt(x))**2, x, s)s2   MT(besselj(a, sqrt(x))*besselj(-a, sqrt(x)), x, s)s5   MT(besselj(a - 1, sqrt(x))*besselj(a, sqrt(x)), x, s)s1   MT(besselj(a, sqrt(x))*besselj(b, sqrt(x)), x, s)s:   MT(besselj(a, sqrt(x))**2 + besselj(-a, sqrt(x))**2, x, s)s   MT(bessely(a, 2*sqrt(x)), x, s)s*   MT(sin(sqrt(x))*bessely(a, sqrt(x)), x, s)s*   MT(cos(sqrt(x))*bessely(a, sqrt(x)), x, s)s1   MT(besselj(a, sqrt(x))*bessely(a, sqrt(x)), x, s)s1   MT(besselj(a, sqrt(x))*bessely(b, sqrt(x)), x, s)s    MT(bessely(a, sqrt(x))**2, x, s)s   MT(besselk(a, 2*sqrt(x)), x, s)sE   MT(besselj(a, 2*sqrt(2*sqrt(x)))*besselk(a, 2*sqrt(2*sqrt(x))), x, s)s1   MT(besseli(a, sqrt(x))*besselk(a, sqrt(x)), x, s)s1   MT(besseli(b, sqrt(x))*besselk(a, sqrt(x)), x, s)s#   MT(exp(-x/2)*besselk(a, x/2), x, s)s>   LT((t-apos)**bpos*exp(-cpos*(t-apos))*Heaviside(t-apos), t, s)s   LT(t**apos, t, s)s   LT(Heaviside(t), t, s)s   LT(Heaviside(t - apos), t, s)s   LT(1 - exp(-apos*t), t, s)sB   LT((exp(2*t)-1)*exp(-bpos - t)*Heaviside(t)/2, t, s, noconds=True)s   LT(exp(t), t, s)s   LT(exp(2*t), t, s)s   LT(exp(apos*t), t, s)s   LT(log(t/apos), t, s)s   LT(erf(t), t, s)s   LT(sin(apos*t), t, s)s   LT(cos(apos*t), t, s)s"   LT(exp(-apos*t)*sin(bpos*t), t, s)s"   LT(exp(-apos*t)*cos(bpos*t), t, s)s%   LT(besselj(0, t), t, s, noconds=True)s%   LT(besselj(1, t), t, s, noconds=True)s&   FT(Heaviside(1 - abs(2*apos*x)), x, k)s2   FT(Heaviside(1-abs(apos*x))*(1-abs(apos*x)), x, k)s#   FT(exp(-apos*x)*Heaviside(x), x, k)s0   IFT(1/(apos + 2*pi*I*x), x, posk, noconds=False)s1   IFT(1/(apos + 2*pi*I*x), x, -posk, noconds=False)s!   IFT(1/(apos + 2*pi*I*x), x, negk)s%   FT(x*exp(-apos*x)*Heaviside(x), x, k)s/   FT(exp(-apos*x)*sin(bpos*x)*Heaviside(x), x, k)s   FT(exp(-apos*x**2), x, k)s-   IFT(sqrt(pi/apos)*exp(-(pi*k)**2/apos), k, x)s   FT(exp(-apos*abs(x)), x, k)s=   integrate(normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)s?   integrate(x*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)sB   integrate(x**2*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)sB   integrate(x**3*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)sk   integrate(normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)sm   integrate(x*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)sm   integrate(y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)so   integrate(x*y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)ss   integrate((x+y+1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)s|   integrate((x+y-1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),                   (x, -oo, oo), (y, -oo, oo), meijerg=True)sv   integrate(x**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),                (x, -oo, oo), (y, -oo, oo), meijerg=True)sp   integrate(y**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)s9   integrate(exponential(x, rate), (x, 0, oo), meijerg=True)s;   integrate(x*exponential(x, rate), (x, 0, oo), meijerg=True)s>   integrate(x**2*exponential(x, rate), (x, 0, oo), meijerg=True)s   E(1)s   E(x*y)s	   E(x*y**2)s   E((x+y+1)**2)s   E(x+y+1)s   E((x+y-1)**2)s-   integrate(betadist, (x, 0, oo), meijerg=True)s/   integrate(x*betadist, (x, 0, oo), meijerg=True)s2   integrate(x**2*betadist, (x, 0, oo), meijerg=True)s(   integrate(chi, (x, 0, oo), meijerg=True)s*   integrate(x*chi, (x, 0, oo), meijerg=True)s-   integrate(x**2*chi, (x, 0, oo), meijerg=True)s/   integrate(chisquared, (x, 0, oo), meijerg=True)s1   integrate(x*chisquared, (x, 0, oo), meijerg=True)s4   integrate(x**2*chisquared, (x, 0, oo), meijerg=True)sD   integrate(((x-k)/sqrt(2*k))**3*chisquared, (x, 0, oo), meijerg=True)s*   integrate(dagum, (x, 0, oo), meijerg=True)s,   integrate(x*dagum, (x, 0, oo), meijerg=True)s/   integrate(x**2*dagum, (x, 0, oo), meijerg=True)s&   integrate(f, (x, 0, oo), meijerg=True)s(   integrate(x*f, (x, 0, oo), meijerg=True)s+   integrate(x**2*f, (x, 0, oo), meijerg=True)s)   integrate(rice, (x, 0, oo), meijerg=True)s.   integrate(laplace, (x, -oo, oo), meijerg=True)s0   integrate(x*laplace, (x, -oo, oo), meijerg=True)s3   integrate(x**2*laplace, (x, -oo, oo), meijerg=True)s=   integrate(log(x) * x**(k-1) * exp(-x) / gamma(k), (x, 0, oo))sE   integrate(sin(z*x)*(x**2-1)**(-(y+S(1)/2)), (x, 1, oo), meijerg=True)sI   integrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)sK   integrate(besselj(0,x)*besselj(1,x)*besselk(0,x), (x, 0, oo), meijerg=True)s>   integrate(besselj(a,x)*besselj(b,x)/x, (x,0,oo), meijerg=True)s   hyperexpand(meijerg((-s - a/2 + 1, -s + a/2 + 1), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), (a/2, -a/2), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), 1))sŌ  gammasimp(S('2**(2*s)*(-pi*gamma(-a + 1)*gamma(a + 1)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 3/2)*gamma(a + s + 1)/(a*(a + s)) - gamma(-a - 1/2)*gamma(-a + 1)*gamma(a + 1)*gamma(a + 3/2)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a + s + 1)*gamma(a - s + 1)/(a*(-a + s)))*gamma(-2*s + 1)*gamma(s + 1)/(pi*s*gamma(-a - 1/2)*gamma(a + 3/2)*gamma(-s + 1)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 1)*gamma(a - s + 3/2))'))s   mellin_transform(E1(x), x, s)s3   inverse_mellin_transform(gamma(s)/s, s, x, (0, oo))s$   mellin_transform(expint(a, x), x, s)s   mellin_transform(Si(x), x, s)s^   inverse_mellin_transform(-2**s*sqrt(pi)*gamma((s + 1)/2)/(2*s*gamma(-s/2 + 1)), s, x, (-1, 0))s#   mellin_transform(Ci(sqrt(x)), x, s)sW   inverse_mellin_transform(-4**s*sqrt(pi)*gamma(s)/(2*s*gamma(-s + S(1)/2)),s, u, (0, 1))s   laplace_transform(Ci(x), x, s)s%   laplace_transform(expint(a, x), x, s)s%   laplace_transform(expint(1, x), x, s)s%   laplace_transform(expint(2, x), x, s)s3   inverse_laplace_transform(-log(1 + s**2)/2/s, s, u)s-   inverse_laplace_transform(log(s + 1)/s, s, x)s6   inverse_laplace_transform((s - log(s + 1))/s**2, s, x)s   laplace_transform(Chi(x), x, s)s   laplace_transform(Shi(x), x, s)s>   integrate(exp(-z*x)/x, (x, 1, oo), meijerg=True, conds="none")sA   integrate(exp(-z*x)/x**2, (x, 1, oo), meijerg=True, conds="none")s@   integrate(exp(-z*x)/x**3, (x, 1, oo), meijerg=True,conds="none")s1   integrate(-cos(x)/x, (x, tpos, oo), meijerg=True)s1   integrate(-sin(x)/x, (x, tpos, oo), meijerg=True)s,   integrate(sin(x)/x, (x, 0, z), meijerg=True)s-   integrate(sinh(x)/x, (x, 0, z), meijerg=True)s%   integrate(exp(-x)/x, x, meijerg=True)s(   integrate(exp(-x)/x**2, x, meijerg=True)s$   integrate(cos(u)/u, u, meijerg=True)s%   integrate(cosh(u)/u, u, meijerg=True)s(   integrate(expint(1, x), x, meijerg=True)s(   integrate(expint(2, x), x, meijerg=True)s!   integrate(Si(x), x, meijerg=True)s!   integrate(Ci(u), u, meijerg=True)s"   integrate(Shi(x), x, meijerg=True)s"   integrate(Chi(u), u, meijerg=True)s2   integrate(Si(x)*exp(-x), (x, 0, oo), meijerg=True)s8   integrate(expint(1, x)*sin(x), (x, 0, oo), meijerg=True)(   t   time(   t   clear_cachet   __main__t   .i
   s   %st   keyc         C  s	   |  d S(   Ni    (    (   R   (    (    s?   lib/python2.7/site-packages/sympy/benchmarks/bench_meijerint.pyt   <lambda>ū   t    s   %.2fs %s(S   t
   __future__R    R   t   laplace_transformt   LTt   fourier_transformt   FTt   mellin_transformt   MTt   inverse_fourier_transformt   IFTt   inverse_laplace_transformt   ILTt   inverse_mellin_transformt   IMTt	   sympy.abcR   R   R   R   R   R   R   t   symbolst   nut   betat   rhoR    t   apost   bpost   cpost   dpost   poskt   pt   SymbolR
   t   negkR   t   mu2R   t   sigma2R   R   R   t   alphat   gammat   betadistt   kintR   t   chit
   chisquaredt   dagumt   d1t   d2R   t   ft   nupost   sigmapost   besselit   riceR   t   abst   laplaceR   t   tposR$   t   benchR%   t   sympy.core.cacheR&   t   syst   timingst   __name__t	   enumeratet   nt   stringt   _tt   stdoutt   writet   flusht   lent   printt   sort(    (    (    s?   lib/python2.7/site-packages/sympy/benchmarks/bench_meijerint.pyt   <module>   s  4$$		A?<:b4#			)