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364 lines
10 KiB
Python
364 lines
10 KiB
Python
"""Random variable generators.
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distributions on the real line:
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------------------------------
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normal (Gaussian)
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lognormal
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negative exponential
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gamma
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beta
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distributions on the circle (angles 0 to 2pi)
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---------------------------------------------
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circular uniform
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von Mises
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Translated from anonymously contributed C/C++ source.
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Multi-threading note: the random number generator used here is not
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thread-safe; it is possible that two calls return the same random
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value. See whrandom.py for more info.
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"""
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import whrandom
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from whrandom import random, uniform, randint, choice, randrange # For export!
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from math import log, exp, pi, e, sqrt, acos, cos, sin
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# Interfaces to replace remaining needs for importing whrandom
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# XXX TO DO: make the distribution functions below into methods.
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def makeseed(a=None):
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"""Turn a hashable value into three seed values for whrandom.seed().
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None or no argument returns (0, 0, 0), to seed from current time.
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"""
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if a is None:
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return (0, 0, 0)
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a = hash(a)
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a, x = divmod(a, 256)
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a, y = divmod(a, 256)
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a, z = divmod(a, 256)
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x = (x + a) % 256 or 1
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y = (y + a) % 256 or 1
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z = (z + a) % 256 or 1
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return (x, y, z)
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def seed(a=None):
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"""Seed the default generator from any hashable value.
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None or no argument seeds from current time.
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"""
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x, y, z = makeseed(a)
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whrandom.seed(x, y, z)
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class generator(whrandom.whrandom):
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"""Random generator class."""
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def __init__(self, a=None):
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"""Constructor. Seed from current time or hashable value."""
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self.seed(a)
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def seed(self, a=None):
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"""Seed the generator from current time or hashable value."""
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x, y, z = makeseed(a)
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whrandom.whrandom.seed(self, x, y, z)
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def new_generator(a=None):
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"""Return a new random generator instance."""
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return generator(a)
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# Housekeeping function to verify that magic constants have been
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# computed correctly
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def verify(name, expected):
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computed = eval(name)
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if abs(computed - expected) > 1e-7:
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raise ValueError, \
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'computed value for %s deviates too much (computed %g, expected %g)' % \
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(name, computed, expected)
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# -------------------- normal distribution --------------------
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NV_MAGICCONST = 4*exp(-0.5)/sqrt(2.0)
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verify('NV_MAGICCONST', 1.71552776992141)
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def normalvariate(mu, sigma):
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# mu = mean, sigma = standard deviation
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# Uses Kinderman and Monahan method. Reference: Kinderman,
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# A.J. and Monahan, J.F., "Computer generation of random
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# variables using the ratio of uniform deviates", ACM Trans
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# Math Software, 3, (1977), pp257-260.
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while 1:
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u1 = random()
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u2 = random()
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z = NV_MAGICCONST*(u1-0.5)/u2
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zz = z*z/4.0
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if zz <= -log(u2):
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break
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return mu+z*sigma
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# -------------------- lognormal distribution --------------------
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def lognormvariate(mu, sigma):
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return exp(normalvariate(mu, sigma))
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# -------------------- circular uniform --------------------
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def cunifvariate(mean, arc):
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# mean: mean angle (in radians between 0 and pi)
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# arc: range of distribution (in radians between 0 and pi)
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return (mean + arc * (random() - 0.5)) % pi
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# -------------------- exponential distribution --------------------
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def expovariate(lambd):
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# lambd: rate lambd = 1/mean
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# ('lambda' is a Python reserved word)
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u = random()
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while u <= 1e-7:
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u = random()
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return -log(u)/lambd
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# -------------------- von Mises distribution --------------------
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TWOPI = 2.0*pi
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verify('TWOPI', 6.28318530718)
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def vonmisesvariate(mu, kappa):
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# mu: mean angle (in radians between 0 and 2*pi)
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# kappa: concentration parameter kappa (>= 0)
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# if kappa = 0 generate uniform random angle
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# Based upon an algorithm published in: Fisher, N.I.,
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# "Statistical Analysis of Circular Data", Cambridge
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# University Press, 1993.
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# Thanks to Magnus Kessler for a correction to the
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# implementation of step 4.
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if kappa <= 1e-6:
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return TWOPI * random()
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a = 1.0 + sqrt(1.0 + 4.0 * kappa * kappa)
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b = (a - sqrt(2.0 * a))/(2.0 * kappa)
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r = (1.0 + b * b)/(2.0 * b)
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while 1:
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u1 = random()
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z = cos(pi * u1)
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f = (1.0 + r * z)/(r + z)
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c = kappa * (r - f)
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u2 = random()
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if not (u2 >= c * (2.0 - c) and u2 > c * exp(1.0 - c)):
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break
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u3 = random()
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if u3 > 0.5:
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theta = (mu % TWOPI) + acos(f)
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else:
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theta = (mu % TWOPI) - acos(f)
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return theta
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# -------------------- gamma distribution --------------------
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LOG4 = log(4.0)
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verify('LOG4', 1.38629436111989)
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def gammavariate(alpha, beta):
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# beta times standard gamma
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ainv = sqrt(2.0 * alpha - 1.0)
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return beta * stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
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SG_MAGICCONST = 1.0 + log(4.5)
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verify('SG_MAGICCONST', 2.50407739677627)
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def stdgamma(alpha, ainv, bbb, ccc):
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# ainv = sqrt(2 * alpha - 1)
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# bbb = alpha - log(4)
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# ccc = alpha + ainv
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if alpha <= 0.0:
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raise ValueError, 'stdgamma: alpha must be > 0.0'
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if alpha > 1.0:
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# Uses R.C.H. Cheng, "The generation of Gamma
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# variables with non-integral shape parameters",
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# Applied Statistics, (1977), 26, No. 1, p71-74
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while 1:
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u1 = random()
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u2 = random()
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v = log(u1/(1.0-u1))/ainv
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x = alpha*exp(v)
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z = u1*u1*u2
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r = bbb+ccc*v-x
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if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= log(z):
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return x
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elif alpha == 1.0:
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# expovariate(1)
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u = random()
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while u <= 1e-7:
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u = random()
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return -log(u)
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else: # alpha is between 0 and 1 (exclusive)
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# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
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while 1:
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u = random()
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b = (e + alpha)/e
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p = b*u
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if p <= 1.0:
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x = pow(p, 1.0/alpha)
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else:
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# p > 1
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x = -log((b-p)/alpha)
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u1 = random()
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if not (((p <= 1.0) and (u1 > exp(-x))) or
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((p > 1) and (u1 > pow(x, alpha - 1.0)))):
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break
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return x
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# -------------------- Gauss (faster alternative) --------------------
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gauss_next = None
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def gauss(mu, sigma):
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# When x and y are two variables from [0, 1), uniformly
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# distributed, then
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#
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# cos(2*pi*x)*sqrt(-2*log(1-y))
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# sin(2*pi*x)*sqrt(-2*log(1-y))
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#
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# are two *independent* variables with normal distribution
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# (mu = 0, sigma = 1).
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# (Lambert Meertens)
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# (corrected version; bug discovered by Mike Miller, fixed by LM)
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# Multithreading note: When two threads call this function
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# simultaneously, it is possible that they will receive the
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# same return value. The window is very small though. To
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# avoid this, you have to use a lock around all calls. (I
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# didn't want to slow this down in the serial case by using a
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# lock here.)
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global gauss_next
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z = gauss_next
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gauss_next = None
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if z is None:
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x2pi = random() * TWOPI
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g2rad = sqrt(-2.0 * log(1.0 - random()))
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z = cos(x2pi) * g2rad
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gauss_next = sin(x2pi) * g2rad
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return mu + z*sigma
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# -------------------- beta --------------------
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def betavariate(alpha, beta):
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# Discrete Event Simulation in C, pp 87-88.
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y = expovariate(alpha)
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z = expovariate(1.0/beta)
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return z/(y+z)
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# -------------------- Pareto --------------------
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def paretovariate(alpha):
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# Jain, pg. 495
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u = random()
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return 1.0 / pow(u, 1.0/alpha)
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# -------------------- Weibull --------------------
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def weibullvariate(alpha, beta):
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# Jain, pg. 499; bug fix courtesy Bill Arms
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u = random()
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return alpha * pow(-log(u), 1.0/beta)
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# -------------------- shuffle --------------------
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# Not quite a random distribution, but a standard algorithm.
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# This implementation due to Tim Peters.
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def shuffle(x, random=random, int=int):
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"""x, random=random.random -> shuffle list x in place; return None.
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Optional arg random is a 0-argument function returning a random
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float in [0.0, 1.0); by default, the standard random.random.
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Note that for even rather small len(x), the total number of
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permutations of x is larger than the period of most random number
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generators; this implies that "most" permutations of a long
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sequence can never be generated.
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"""
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for i in xrange(len(x)-1, 0, -1):
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# pick an element in x[:i+1] with which to exchange x[i]
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j = int(random() * (i+1))
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x[i], x[j] = x[j], x[i]
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# -------------------- test program --------------------
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def test(N = 200):
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print 'TWOPI =', TWOPI
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print 'LOG4 =', LOG4
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print 'NV_MAGICCONST =', NV_MAGICCONST
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print 'SG_MAGICCONST =', SG_MAGICCONST
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test_generator(N, 'random()')
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test_generator(N, 'normalvariate(0.0, 1.0)')
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test_generator(N, 'lognormvariate(0.0, 1.0)')
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test_generator(N, 'cunifvariate(0.0, 1.0)')
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test_generator(N, 'expovariate(1.0)')
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test_generator(N, 'vonmisesvariate(0.0, 1.0)')
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test_generator(N, 'gammavariate(0.5, 1.0)')
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test_generator(N, 'gammavariate(0.9, 1.0)')
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test_generator(N, 'gammavariate(1.0, 1.0)')
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test_generator(N, 'gammavariate(2.0, 1.0)')
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test_generator(N, 'gammavariate(20.0, 1.0)')
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test_generator(N, 'gammavariate(200.0, 1.0)')
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test_generator(N, 'gauss(0.0, 1.0)')
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test_generator(N, 'betavariate(3.0, 3.0)')
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test_generator(N, 'paretovariate(1.0)')
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test_generator(N, 'weibullvariate(1.0, 1.0)')
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def test_generator(n, funccall):
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import time
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print n, 'times', funccall
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code = compile(funccall, funccall, 'eval')
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sum = 0.0
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sqsum = 0.0
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smallest = 1e10
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largest = -1e10
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t0 = time.time()
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for i in range(n):
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x = eval(code)
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sum = sum + x
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sqsum = sqsum + x*x
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smallest = min(x, smallest)
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largest = max(x, largest)
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t1 = time.time()
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print round(t1-t0, 3), 'sec,',
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avg = sum/n
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stddev = sqrt(sqsum/n - avg*avg)
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print 'avg %g, stddev %g, min %g, max %g' % \
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(avg, stddev, smallest, largest)
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if __name__ == '__main__':
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test()
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