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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
#
# distributions on the circle (angles 0 to 2pi)
# ---------------------------------------------
# circular uniform
# von Mises
# Translated from anonymously contributed C/C++ source.
from whrandom import random, uniform, randint, choice # Also for export!
from math import log, exp, pi, e, sqrt, acos, cos
# 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)
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
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*pi
verify('TWOPI', 6.28318530718)
def vonmisesvariate(mu, kappa):
# mu: mean angle (in radians between 0 and 180 degrees)
# kappa: concentration parameter kappa (>= 0)
# if kappa = 0 generate uniform random angle
if kappa <= 1e-6:
return TWOPI * random()
a = 1.0 + sqrt(1 + 4 * kappa * kappa)
b = (a - sqrt(2 * a))/(2 * kappa)
r = (1 + b * b)/(2 * b)
while 1:
u1 = random()
z = cos(pi * u1)
f = (1 + 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 + 0.5*acos(f)
else:
theta = mu - 0.5*acos(f)
return theta % pi
# -------------------- gamma distribution --------------------
LOG4 = log(4)
verify('LOG4', 1.38629436111989)
def gammavariate(alpha, beta):
# beta times standard gamma
ainv = sqrt(2 * alpha - 1)
return beta * stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
SG_MAGICCONST = 1+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-u1))/ainv
x = alpha*exp(v)
z = u1*u1*u2
r = bbb+ccc*v-x
if r + SG_MAGICCONST - 4.5*z >= 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
# -------------------- test program --------------------
def test():
print 'TWOPI =', TWOPI
print 'LOG4 =', LOG4
print 'NV_MAGICCONST =', NV_MAGICCONST
print 'SG_MAGICCONST =', SG_MAGICCONST
N = 100
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)')
def test_generator(n, funccall):
import sys
print '%d calls to %s:' % (n, funccall),
sys.stdout.flush()
code = compile(funccall, funccall, 'eval')
sum = 0.0
sqsum = 0.0
for i in range(n):
x = eval(code)
sum = sum + x
sqsum = sqsum + x*x
avg = sum/n
stddev = sqrt(sqsum/n - avg*avg)
print 'avg %g, stddev %g' % (avg, stddev)
if __name__ == '__main__':
test()
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