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 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 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