mirror of
https://github.com/python/cpython.git
synced 2024-11-24 17:47:13 +01:00
261 lines
6.2 KiB
Python
261 lines
6.2 KiB
Python
# 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.
|
|
|
|
from whrandom import random, uniform, randint, choice # Also for export!
|
|
from math import log, exp, pi, e, sqrt, acos, cos, sin
|
|
|
|
# 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 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(1.0 + 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 + 0.5*acos(f)
|
|
else:
|
|
theta = mu - 0.5*acos(f)
|
|
|
|
return theta % pi
|
|
|
|
# -------------------- 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)*log(1-y)
|
|
# sin(2*pi*x)*log(1-y)
|
|
#
|
|
# are two *independent* variables with normal distribution
|
|
# (mu = 0, sigma = 1).
|
|
# (Lambert Meertens)
|
|
|
|
global gauss_next
|
|
|
|
if gauss_next != None:
|
|
z = gauss_next
|
|
gauss_next = None
|
|
else:
|
|
x2pi = random() * TWOPI
|
|
log1_y = log(1.0 - random())
|
|
z = cos(x2pi) * log1_y
|
|
gauss_next = sin(x2pi) * log1_y
|
|
|
|
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)
|
|
|
|
# -------------------- 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)')
|
|
|
|
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()
|