Lib/random.py

"""Random variable generators.

    distributions on the real line:
    ------------------------------
           normal (Gaussian)
           lognormal
           negative exponential
           gamma
           beta

    distributions on the circle (angles 0 to 2pi)
    ---------------------------------------------
           circular uniform
           von Mises

Translated from anonymously contributed C/C++ source.

Multi-threading note: the random number generator used here is not
thread-safe; it is possible that two calls return the same random
value.  See whrandom.py for more info.
"""

import whrandom
from whrandom import random, uniform, randint, choice, randrange # For export!
from math import log, exp, pi, e, sqrt, acos, cos, sin

# Interfaces to replace remaining needs for importing whrandom
# XXX TO DO: make the distribution functions below into methods.

def makeseed(a=None):
    """Turn a hashable value into three seed values for whrandom.seed().

    None or no argument returns (0, 0, 0), to seed from current time.

    """
    if a is None:
        return (0, 0, 0)
    a = hash(a)
    a, x = divmod(a, 256)
    a, y = divmod(a, 256)
    a, z = divmod(a, 256)
    x = (x + a) % 256 or 1
    y = (y + a) % 256 or 1
    z = (z + a) % 256 or 1
    return (x, y, z)

def seed(a=None):
    """Seed the default generator from any hashable value.

    None or no argument seeds from current time.

    """
    x, y, z = makeseed(a)
    whrandom.seed(x, y, z)

class generator(whrandom.whrandom):
    """Random generator class."""

    def __init__(self, a=None):
        """Constructor.  Seed from current time or hashable value."""
        self.seed(a)

    def seed(self, a=None):
        """Seed the generator from current time or hashable value."""
        x, y, z = makeseed(a)
        whrandom.whrandom.seed(self, x, y, z)

def new_generator(a=None):
    """Return a new random generator instance."""
    return generator(a)

# Housekeeping function to verify that magic constants have been
# computed correctly

def verify(name, expected):
    computed = eval(name)
    if abs(computed - expected) > 1e-7:
        raise ValueError, \
'computed value for %s deviates too much (computed %g, expected %g)' % \
(name, computed, expected)

# -------------------- normal distribution --------------------

NV_MAGICCONST = 4*exp(-0.5)/sqrt(2.0)
verify('NV_MAGICCONST', 1.71552776992141)
def normalvariate(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.

    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

# -------------------- lognormal distribution --------------------

def lognormvariate(mu, sigma):
    return exp(normalvariate(mu, sigma))

# -------------------- circular uniform --------------------

def cunifvariate(mean, arc):
    # mean: mean angle (in radians between 0 and pi)
    # arc:  range of distribution (in radians between 0 and pi)

    return (mean + arc * (random() - 0.5)) % pi

# -------------------- exponential distribution --------------------

def expovariate(lambd):
    # lambd: rate lambd = 1/mean
    # ('lambda' is a Python reserved word)

    u = random()
    while u <= 1e-7:
        u = random()
    return -log(u)/lambd

# -------------------- von Mises distribution --------------------

TWOPI = 2.0*pi
verify('TWOPI', 6.28318530718)

def vonmisesvariate(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.

    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

# -------------------- gamma distribution --------------------

LOG4 = log(4.0)
verify('LOG4', 1.38629436111989)

def gammavariate(alpha, beta):
    # beta times standard gamma
    ainv = sqrt(2.0 * alpha - 1.0)
    return beta * stdgamma(alpha, ainv, alpha - LOG4, alpha + ainv)

SG_MAGICCONST = 1.0 + log(4.5)
verify('SG_MAGICCONST', 2.50407739677627)

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

    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


# -------------------- Gauss (faster alternative) --------------------

gauss_next = None
def gauss(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.)

    global gauss_next

    z = gauss_next
    gauss_next = None
    if z is None:
        x2pi = random() * TWOPI
        g2rad = sqrt(-2.0 * log(1.0 - random()))
        z = cos(x2pi) * g2rad
        gauss_next = sin(x2pi) * g2rad

    return mu + z*sigma

# -------------------- beta --------------------

def betavariate(alpha, beta):

    # Discrete Event Simulation in C, pp 87-88.

    y = expovariate(alpha)
    z = expovariate(1.0/beta)
    return z/(y+z)

# -------------------- Pareto --------------------

def paretovariate(alpha):
    # Jain, pg. 495

    u = random()
    return 1.0 / pow(u, 1.0/alpha)

# -------------------- Weibull --------------------

def weibullvariate(alpha, beta):
    # Jain, pg. 499; bug fix courtesy Bill Arms

    u = random()
    return alpha * pow(-log(u), 1.0/beta)

# -------------------- shuffle --------------------
# Not quite a random distribution, but a standard algorithm.
# This implementation due to Tim Peters.

def shuffle(x, random=random, int=int):
    """x, random=random.random -> shuffle list x in place; return None.

    Optional arg random is a 0-argument function returning a random
    float in [0.0, 1.0); by default, the standard random.random.

    Note that for even rather small len(x), the total number of
    permutations of x is larger than the period of most random number
    generators; this implies that "most" permutations of a long
    sequence can never be generated.
    """

    for i in xrange(len(x)-1, 0, -1):
    # pick an element in x[:i+1] with which to exchange x[i]
        j = int(random() * (i+1))
        x[i], x[j] = x[j], x[i]

# -------------------- test program --------------------

def test(N = 200):
    print 'TWOPI         =', TWOPI
    print 'LOG4          =', LOG4
    print 'NV_MAGICCONST =', NV_MAGICCONST
    print 'SG_MAGICCONST =', SG_MAGICCONST
    test_generator(N, 'random()')
    test_generator(N, 'normalvariate(0.0, 1.0)')
    test_generator(N, 'lognormvariate(0.0, 1.0)')
    test_generator(N, 'cunifvariate(0.0, 1.0)')
    test_generator(N, 'expovariate(1.0)')
    test_generator(N, 'vonmisesvariate(0.0, 1.0)')
    test_generator(N, 'gammavariate(0.5, 1.0)')
    test_generator(N, 'gammavariate(0.9, 1.0)')
    test_generator(N, 'gammavariate(1.0, 1.0)')
    test_generator(N, 'gammavariate(2.0, 1.0)')
    test_generator(N, 'gammavariate(20.0, 1.0)')
    test_generator(N, 'gammavariate(200.0, 1.0)')
    test_generator(N, 'gauss(0.0, 1.0)')
    test_generator(N, 'betavariate(3.0, 3.0)')
    test_generator(N, 'paretovariate(1.0)')
    test_generator(N, 'weibullvariate(1.0, 1.0)')

def test_generator(n, funccall):
    import time
    print n, 'times', funccall
    code = compile(funccall, funccall, 'eval')
    sum = 0.0
    sqsum = 0.0
    smallest = 1e10
    largest = -1e10
    t0 = time.time()
    for i in range(n):
        x = eval(code)
        sum = sum + x
        sqsum = sqsum + x*x
        smallest = min(x, smallest)
        largest = max(x, largest)
    t1 = time.time()
    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)

if __name__ == '__main__':
    test()