def rwiener(self, tau, xmin=float('-inf'), xmax=float('inf'), \
pmin=0.0, pmax=1.0):
"""
Generates random numbers corrsponding to a Wiener process (the
intergral of white noise (Langevin's function)), inverse variant.
The Wiener process is W(t+tau) - W (t) = N(0, sqrt(tau))
where tau is the time increment and N(0, sqrt(tau)) is a
normally distributed random variable having zero mean and
sqrt(tau) as its standard deviation.
This method returns W(t+tau) - W(t) given tau and allows
tau to be negative.
"""
self._checkminmax(xmin, xmax, pmin, pmax, 'rwiener')
mu = 0.0
sigma = sqrt(abs(tau)) # abs(tau) is used
pmn = pmin
pmx = pmax
if xmin > float('-inf'): pmn = max(pmin, cnormal(mu, sigma, xmin))
if xmax < float('inf'): pmx = min(pmax, cnormal(mu, sigma, xmax))
p = pmn + (pmx-pmn)*self.runif01()
w = inormal(p, mu, sigma)
return w
def rnormal(self, mu, sigma, xmin=float('-inf'), xmax=float('inf'), \
pmin=0.0, pmax=1.0):
"""
Generator of normally distributed random variates using an inverse
method, claimed to give a maximum relative error less than 2.6e-9
(cf. statlib.invcdf.inormal for details).
"""
self._checkminmax(xmin, xmax, pmin, pmax, 'rnormal')
pmn = pmin
pmx = pmax
if xmin > float('-inf'): pmn = max(pmin, cnormal(mu, sigma, xmin))
if xmax < float('inf'): pmx = min(pmax, cnormal(mu, sigma, xmax))
p = pmn + (pmx-pmn)*self.runif01()
x = inormal(p, mu, sigma)
return x
def rlognormal(self, mulg, sigmalg, xmax=float('inf'), pmax=1.0):
"""
Generator of lognormally distributed random variates, inverse variant.
The log10-converted form is assumed for mulg and sigmalg:
mulg is the mean of the log10 (and the log10 of the median) of
the random variate, NOT the log10 of the mean of the non-logged
variate!, and sigmalg is the standard deviation of the log10 of
the random variate, NOT the log10 of the standard deviation of
the non-logged variate!!
sigmalg > 0.0
"""
assert xmax >= 0.0, "xmax must be a non-negative float in rlognormal!"
# sigmalg is checked in rnormal
self._checkpmax(pmax, 'rlognormal')
if xmax < float('inf'): \
pmx = min(pmax, pow(10.0, cnormal(mulg, sigmalg, xmax)))
pmn = 0.0
x = pow(10.0, self.rnormal(mulg, sigmalg, pmn, pmx))
return x