Example #1
0
    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
Example #2
0
    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
Example #3
0
    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
Example #4
0
    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