def gauss(self, 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.)
random = self.random
z = self.gauss_next
self.gauss_next = None
if z is None:
x2pi = random() * TWOPI
g2rad = _sqrt(-2.0 * _log(1.0 - random()))
z = _cos(x2pi) * g2rad
self.gauss_next = _sin(x2pi) * g2rad
return mu + z*sigma
def vonmisesvariate(self, 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.
random = self.random
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
def _test_generator(n, funccall):
import VS
print n, 'times', funccall
code = compile(funccall, funccall, 'eval')
sum = 0.0
sqsum = 0.0
smallest = 1e10
largest = -1e10
t0 = VS.timeofday()
for i in range(n):
x = eval(code)
sum = sum + x
sqsum = sqsum + x*x
smallest = min(x, smallest)
largest = max(x, largest)
t1 = VS.timeofday()
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)
def _test_generator(n, funccall):
import VS
debug.info(n+' times '+funccall)
code = compile(funccall, funccall, 'eval')
sum = 0.0
sqsum = 0.0
smallest = 1e10
largest = -1e10
t0 = VS.timeofday()
for i in range(n):
x = eval(code)
sum = sum + x
sqsum = sqsum + x*x
smallest = min(x, smallest)
largest = max(x, largest)
t1 = VS.timeofday()
debug.info(round(t1-t0, 3) + ' sec,')
avg = sum/n
stddev = _sqrt(sqsum/n - avg*avg)
debug.info('avg %g, stddev %g, min %g, max %g' % \
(avg, stddev, smallest, largest))
def gammavariate(self, alpha, beta):
# beta times standard gamma
ainv = _sqrt(2.0 * alpha - 1.0)
return beta * self.stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
from VS import log as _log, exp as _exp
from VS import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
__all__ = ["Random","seed","random","uniform","randint","choice",
"randrange","shuffle","normalvariate","lognormvariate",
"cunifvariate","expovariate","vonmisesvariate","gammavariate",
"stdgamma","gauss","betavariate","paretovariate","weibullvariate",
"getstate","setstate","jumpahead","whseed"]
def _verify(name, computed, expected):
if abs(computed - expected) > 1e-7:
raise ValueError(
"computed value for %s deviates too much "
"(computed %g, expected %g)" % (name, computed, expected))
NV_MAGICCONST = 4 * _exp(-0.5)/_sqrt(2.0)
_verify('NV_MAGICCONST', NV_MAGICCONST, 1.71552776992141)
TWOPI = 2.0*_pi
_verify('TWOPI', TWOPI, 6.28318530718)
LOG4 = _log(4.0)
_verify('LOG4', LOG4, 1.38629436111989)
SG_MAGICCONST = 1.0 + _log(4.5)
_verify('SG_MAGICCONST', SG_MAGICCONST, 2.50407739677627)
del _verify
# Translated by Guido van Rossum from C source provided by
# Adrian Baddeley.
def gammavariate(self, alpha, beta):
# beta times standard gamma
ainv = _sqrt(2.0 * alpha - 1.0)
return beta * self.stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)
"Random", "seed", "random", "uniform", "randint", "choice", "randrange",
"shuffle", "normalvariate", "lognormvariate", "cunifvariate",
"expovariate", "vonmisesvariate", "gammavariate", "stdgamma", "gauss",
"betavariate", "paretovariate", "weibullvariate", "getstate", "setstate",
"jumpahead", "whseed"
]
def _verify(name, computed, expected):
if abs(computed - expected) > 1e-7:
raise ValueError("computed value for %s deviates too much "
"(computed %g, expected %g)" %
(name, computed, expected))
NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0)
_verify('NV_MAGICCONST', NV_MAGICCONST, 1.71552776992141)
TWOPI = 2.0 * _pi
_verify('TWOPI', TWOPI, 6.28318530718)
LOG4 = _log(4.0)
_verify('LOG4', LOG4, 1.38629436111989)
SG_MAGICCONST = 1.0 + _log(4.5)
_verify('SG_MAGICCONST', SG_MAGICCONST, 2.50407739677627)
del _verify
# Translated by Guido van Rossum from C source provided by
# Adrian Baddeley.
