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- # R A N D O M V A R I A B L E G E N E R A T O R S
- #
- # distributions on the real line:
- # ------------------------------
- # normal (Gaussian)
- # lognormal
- # negative exponential
- # gamma
- # beta
- #
- # distributions on the circle (angles 0 to 2pi)
- # ---------------------------------------------
- # circular uniform
- # von Mises
-
- # Translated from anonymously contributed C/C++ source.
-
- # Multi-threading note: the random number generator used here is not
- # thread-safe; it is possible that two calls return the same random
- # value. See whrandom.py for more info.
-
- import whrandom
- from whrandom import random, uniform, randint, choice, randrange # For export!
- from math import log, exp, pi, e, sqrt, acos, cos, sin
-
- # Interfaces to replace remaining needs for importing whrandom
- # XXX TO DO: make the distribution functions below into methods.
-
- def makeseed(a=None):
- """Turn a hashable value into three seed values for whrandom.seed().
-
- None or no argument returns (0, 0, 0), to seed from current time.
-
- """
- if a is None:
- return (0, 0, 0)
- a = hash(a)
- a, x = divmod(a, 256)
- a, y = divmod(a, 256)
- a, z = divmod(a, 256)
- x = (x + a) % 256 or 1
- y = (y + a) % 256 or 1
- z = (z + a) % 256 or 1
- return (x, y, z)
-
- def seed(a=None):
- """Seed the default generator from any hashable value.
-
- None or no argument returns (0, 0, 0) to seed from current time.
-
- """
- x, y, z = makeseed(a)
- whrandom.seed(x, y, z)
-
- class generator(whrandom.whrandom):
- """Random generator class."""
-
- def __init__(self, a=None):
- """Constructor. Seed from current time or hashable value."""
- self.seed(a)
-
- def seed(self, a=None):
- """Seed the generator from current time or hashable value."""
- x, y, z = makeseed(a)
- whrandom.whrandom.seed(self, x, y, z)
-
- def new_generator(a=None):
- """Return a new random generator instance."""
- return generator(a)
-
- # Housekeeping function to verify that magic constants have been
- # computed correctly
-
- def verify(name, expected):
- computed = eval(name)
- if abs(computed - expected) > 1e-7:
- raise ValueError, \
- 'computed value for %s deviates too much (computed %g, expected %g)' % \
- (name, computed, expected)
-
- # -------------------- normal distribution --------------------
-
- NV_MAGICCONST = 4*exp(-0.5)/sqrt(2.0)
- verify('NV_MAGICCONST', 1.71552776992141)
- def normalvariate(mu, sigma):
- # mu = mean, sigma = standard deviation
-
- # Uses Kinderman and Monahan method. Reference: Kinderman,
- # A.J. and Monahan, J.F., "Computer generation of random
- # variables using the ratio of uniform deviates", ACM Trans
- # Math Software, 3, (1977), pp257-260.
-
- while 1:
- u1 = random()
- u2 = random()
- z = NV_MAGICCONST*(u1-0.5)/u2
- zz = z*z/4.0
- if zz <= -log(u2):
- break
- return mu+z*sigma
-
- # -------------------- lognormal distribution --------------------
-
- def lognormvariate(mu, sigma):
- return exp(normalvariate(mu, sigma))
-
- # -------------------- circular uniform --------------------
-
- def cunifvariate(mean, arc):
- # mean: mean angle (in radians between 0 and pi)
- # arc: range of distribution (in radians between 0 and pi)
-
- return (mean + arc * (random() - 0.5)) % pi
-
- # -------------------- exponential distribution --------------------
-
- def expovariate(lambd):
- # lambd: rate lambd = 1/mean
- # ('lambda' is a Python reserved word)
-
- u = random()
- while u <= 1e-7:
- u = random()
- return -log(u)/lambd
-
- # -------------------- von Mises distribution --------------------
-
- TWOPI = 2.0*pi
- verify('TWOPI', 6.28318530718)
-
- def vonmisesvariate(mu, kappa):
- # mu: mean angle (in radians between 0 and 2*pi)
- # kappa: concentration parameter kappa (>= 0)
- # if kappa = 0 generate uniform random angle
-
- # Based upon an algorithm published in: Fisher, N.I.,
- # "Statistical Analysis of Circular Data", Cambridge
- # University Press, 1993.
-
- # Thanks to Magnus Kessler for a correction to the
- # implementation of step 4.
-
- if kappa <= 1e-6:
- return TWOPI * random()
-
- a = 1.0 + sqrt(1.0 + 4.0 * kappa * kappa)
- b = (a - sqrt(2.0 * a))/(2.0 * kappa)
- r = (1.0 + b * b)/(2.0 * b)
-
- while 1:
- u1 = random()
-
- z = cos(pi * u1)
- f = (1.0 + r * z)/(r + z)
- c = kappa * (r - f)
-
- u2 = random()
-
- if not (u2 >= c * (2.0 - c) and u2 > c * exp(1.0 - c)):
- break
-
- u3 = random()
- if u3 > 0.5:
- theta = (mu % TWOPI) + acos(f)
- else:
- theta = (mu % TWOPI) - acos(f)
-
- return theta
-
- # -------------------- gamma distribution --------------------
-
- LOG4 = log(4.0)
- verify('LOG4', 1.38629436111989)
-
- def gammavariate(alpha, beta):
- # beta times standard gamma
- ainv = sqrt(2.0 * alpha - 1.0)
- return beta * stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
-
- SG_MAGICCONST = 1.0 + log(4.5)
- verify('SG_MAGICCONST', 2.50407739677627)
-
- def stdgamma(alpha, ainv, bbb, ccc):
- # ainv = sqrt(2 * alpha - 1)
- # bbb = alpha - log(4)
- # ccc = alpha + ainv
-
- if alpha <= 0.0:
- raise ValueError, 'stdgamma: alpha must be > 0.0'
-
- if alpha > 1.0:
-
- # Uses R.C.H. Cheng, "The generation of Gamma
- # variables with non-integral shape parameters",
- # Applied Statistics, (1977), 26, No. 1, p71-74
-
- while 1:
- u1 = random()
- u2 = random()
- v = log(u1/(1.0-u1))/ainv
- x = alpha*exp(v)
- z = u1*u1*u2
- r = bbb+ccc*v-x
- if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= log(z):
- return x
-
- elif alpha == 1.0:
- # expovariate(1)
- u = random()
- while u <= 1e-7:
- u = random()
- return -log(u)
-
- else: # alpha is between 0 and 1 (exclusive)
-
- # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
-
- while 1:
- u = random()
- b = (e + alpha)/e
- p = b*u
- if p <= 1.0:
- x = pow(p, 1.0/alpha)
- else:
- # p > 1
- x = -log((b-p)/alpha)
- u1 = random()
- if not (((p <= 1.0) and (u1 > exp(-x))) or
- ((p > 1) and (u1 > pow(x, alpha - 1.0)))):
- break
- return x
-
-
- # -------------------- Gauss (faster alternative) --------------------
-
- gauss_next = None
- def gauss(mu, sigma):
-
- # When x and y are two variables from [0, 1), uniformly
- # distributed, then
- #
- # cos(2*pi*x)*sqrt(-2*log(1-y))
- # sin(2*pi*x)*sqrt(-2*log(1-y))
- #
- # are two *independent* variables with normal distribution
- # (mu = 0, sigma = 1).
- # (Lambert Meertens)
- # (corrected version; bug discovered by Mike Miller, fixed by LM)
-
- # Multithreading note: When two threads call this function
- # simultaneously, it is possible that they will receive the
- # same return value. The window is very small though. To
- # avoid this, you have to use a lock around all calls. (I
- # didn't want to slow this down in the serial case by using a
- # lock here.)
-
- global gauss_next
-
- z = gauss_next
- gauss_next = None
- if z is None:
- x2pi = random() * TWOPI
- g2rad = sqrt(-2.0 * log(1.0 - random()))
- z = cos(x2pi) * g2rad
- gauss_next = sin(x2pi) * g2rad
-
- return mu + z*sigma
-
- # -------------------- beta --------------------
-
- def betavariate(alpha, beta):
-
- # Discrete Event Simulation in C, pp 87-88.
-
- y = expovariate(alpha)
- z = expovariate(1.0/beta)
- return z/(y+z)
-
- # -------------------- Pareto --------------------
-
- def paretovariate(alpha):
- # Jain, pg. 495
-
- u = random()
- return 1.0 / pow(u, 1.0/alpha)
-
- # -------------------- Weibull --------------------
-
- def weibullvariate(alpha, beta):
- # Jain, pg. 499; bug fix courtesy Bill Arms
-
- u = random()
- return alpha * pow(-log(u), 1.0/beta)
-
- # -------------------- test program --------------------
-
- def test(N = 200):
- print 'TWOPI =', TWOPI
- print 'LOG4 =', LOG4
- print 'NV_MAGICCONST =', NV_MAGICCONST
- print 'SG_MAGICCONST =', SG_MAGICCONST
- test_generator(N, 'random()')
- test_generator(N, 'normalvariate(0.0, 1.0)')
- test_generator(N, 'lognormvariate(0.0, 1.0)')
- test_generator(N, 'cunifvariate(0.0, 1.0)')
- test_generator(N, 'expovariate(1.0)')
- test_generator(N, 'vonmisesvariate(0.0, 1.0)')
- test_generator(N, 'gammavariate(0.5, 1.0)')
- test_generator(N, 'gammavariate(0.9, 1.0)')
- test_generator(N, 'gammavariate(1.0, 1.0)')
- test_generator(N, 'gammavariate(2.0, 1.0)')
- test_generator(N, 'gammavariate(20.0, 1.0)')
- test_generator(N, 'gammavariate(200.0, 1.0)')
- test_generator(N, 'gauss(0.0, 1.0)')
- test_generator(N, 'betavariate(3.0, 3.0)')
- test_generator(N, 'paretovariate(1.0)')
- test_generator(N, 'weibullvariate(1.0, 1.0)')
-
- def test_generator(n, funccall):
- import time
- print n, 'times', funccall
- code = compile(funccall, funccall, 'eval')
- sum = 0.0
- sqsum = 0.0
- smallest = 1e10
- largest = -1e10
- t0 = time.time()
- for i in range(n):
- x = eval(code)
- sum = sum + x
- sqsum = sqsum + x*x
- smallest = min(x, smallest)
- largest = max(x, largest)
- t1 = time.time()
- print round(t1-t0, 3), 'sec,',
- avg = sum/n
- stddev = sqrt(sqsum/n - avg*avg)
- print 'avg %g, stddev %g, min %g, max %g' % \
- (avg, stddev, smallest, largest)
-
- if __name__ == '__main__':
- test()
-