예제 #1
0
    def stdgamma(self, alpha, ainv, bbb, ccc):
        # ainv = sqrt(2 * alpha - 1)
        # bbb = alpha - log(4)
        # ccc = alpha + ainv

        random = self.random
        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
예제 #2
0
    def stdgamma(self, alpha, ainv, bbb, ccc):
        # ainv = sqrt(2 * alpha - 1)
        # bbb = alpha - log(4)
        # ccc = alpha + ainv

        random = self.random
        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
예제 #3
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    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
예제 #4
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    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
예제 #5
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    def expovariate(self, lambd):
        # lambd: rate lambd = 1/mean
        # ('lambda' is a Python reserved word)

        random = self.random
        u = random()
        while u <= 1e-7:
            u = random()
        return -_log(u)/lambd
예제 #6
0
    def expovariate(self, lambd):
        # lambd: rate lambd = 1/mean
        # ('lambda' is a Python reserved word)

        random = self.random
        u = random()
        while u <= 1e-7:
            u = random()
        return -_log(u) / lambd
예제 #7
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    def normalvariate(self, 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.

        random = self.random
        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
예제 #8
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    def normalvariate(self, 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.

        random = self.random
        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
예제 #9
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    def weibullvariate(self, alpha, beta):
        # Jain, pg. 499; bug fix courtesy Bill Arms

        u = self.random()
        return alpha * pow(-_log(u), 1.0/beta)
예제 #10
0
           "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.

class Random:

    VERSION = 1     # used by getstate/setstate

    def __init__(self, x=None):
예제 #11
0
    def weibullvariate(self, alpha, beta):
        # Jain, pg. 499; bug fix courtesy Bill Arms

        u = self.random()
        return alpha * pow(-_log(u), 1.0 / beta)
예제 #12
0

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.


class Random:

    VERSION = 1  # used by getstate/setstate