American Osteopathic Ass…tion Yearbook 2005 & 2006/American Osteopathic Association Yearbook 2005 & 2006.iso/mac/app/random.pyc

Python Compiled Bytecode | 2004-07-22 | 26.1 KB | 678 lines

# Source Generated with Decompyle++
# File: in.pyc (Python 2.3)

'''Random variable generators.

    integers
    --------
           uniform within range

    sequences
    ---------
           pick random element
           pick random sample
           generate random permutation

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

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

General notes on the underlying Mersenne Twister core generator:

* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence
* Without a direct way to compute N steps forward, the
  semantics of jumpahead(n) are weakened to simply jump
  to another distant state and rely on the large period
  to avoid overlapping sequences.
* The random() method is implemented in C, executes in
  a single Python step, and is, therefore, threadsafe.

'''
from math import log as _log, exp as _exp, pi as _pi, e as _e
from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from math import floor as _floor
__all__ = [
    'Random',
    'seed',
    'random',
    'uniform',
    'randint',
    'choice',
    'sample',
    'randrange',
    'shuffle',
    'normalvariate',
    'lognormvariate',
    'cunifvariate',
    'expovariate',
    'vonmisesvariate',
    'gammavariate',
    'stdgamma',
    'gauss',
    'betavariate',
    'paretovariate',
    'weibullvariate',
    'getstate',
    'setstate',
    'jumpahead']
NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0)
TWOPI = 2.0 * _pi
LOG4 = _log(4.0)
SG_MAGICCONST = 1.0 + _log(4.5)
import _random

class Random(_random.Random):
    """Random number generator base class used by bound module functions.

    Used to instantiate instances of Random to get generators that don't
    share state.  Especially useful for multi-threaded programs, creating
    a different instance of Random for each thread, and using the jumpahead()
    method to ensure that the generated sequences seen by each thread don't
    overlap.

    Class Random can also be subclassed if you want to use a different basic
    generator of your own devising: in that case, override the following
    methods:  random(), seed(), getstate(), setstate() and jumpahead().

    """
    VERSION = 2

    def __init__(self, x = None):
        '''Initialize an instance.

        Optional argument x controls seeding, as for Random.seed().
        '''
        self.seed(x)
        self.gauss_next = None


    def seed(self, a = None):
        '''Initialize internal state from hashable object.

        None or no argument seeds from current time.

        If a is not None or an int or long, hash(a) is used instead.
        '''
        super(Random, self).seed(a)
        self.gauss_next = None


    def getstate(self):
        '''Return internal state; can be passed to setstate() later.'''
        return (self.VERSION, super(Random, self).getstate(), self.gauss_next)


    def setstate(self, state):
        '''Restore internal state from object returned by getstate().'''
        version = state[0]
        if version == 2:
            (version, internalstate, self.gauss_next) = state
            super(Random, self).setstate(internalstate)
        else:
            raise ValueError('state with version %s passed to Random.setstate() of version %s' % (version, self.VERSION))


    def __getstate__(self):
        return self.getstate()


    def __setstate__(self, state):
        self.setstate(state)


    def __reduce__(self):
        return (self.__class__, (), self.getstate())


    def randrange(self, start, stop = None, step = 1, int = int, default = None):
        """Choose a random item from range(start, stop[, step]).

        This fixes the problem with randint() which includes the
        endpoint; in Python this is usually not what you want.
        Do not supply the 'int' and 'default' arguments.
        """
        istart = int(start)
        if istart != start:
            raise ValueError, 'non-integer arg 1 for randrange()'

        if stop is default:
            if istart > 0:
                return int(self.random() * istart)

            raise ValueError, 'empty range for randrange()'

        istop = int(stop)
        if istop != stop:
            raise ValueError, 'non-integer stop for randrange()'

        if step == 1 and istart < istop:
            return int(istart + int(self.random() * (istop - istart)))

        if step == 1:
            raise ValueError, 'empty range for randrange()'

        istep = int(step)
        if istep != step:
            raise ValueError, 'non-integer step for randrange()'

        if istep > 0:
            n = ((istop - istart) + istep - 1) / istep
        elif istep < 0:
            n = ((istop - istart) + istep + 1) / istep
        else:
            raise ValueError, 'zero step for randrange()'
        if n <= 0:
            raise ValueError, 'empty range for randrange()'

        return istart + istep * int(self.random() * n)


    def randint(self, a, b):
        '''Return random integer in range [a, b], including both end points.
        '''
        return self.randrange(a, b + 1)


    def choice(self, seq):
        '''Choose a random element from a non-empty sequence.'''
        return seq[int(self.random() * len(seq))]


    def shuffle(self, x, random = None, 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.
        '''
        if random is None:
            random = self.random

        for i in xrange(len(x) - 1, 0, -1):
            j = int(random() * (i + 1))
            (x[i], x[j]) = (x[j], x[i])



    def sample(self, population, k):
        '''Chooses k unique random elements from a population sequence.

        Returns a new list containing elements from the population while
        leaving the original population unchanged.  The resulting list is
        in selection order so that all sub-slices will also be valid random
        samples.  This allows raffle winners (the sample) to be partitioned
        into grand prize and second place winners (the subslices).

        Members of the population need not be hashable or unique.  If the
        population contains repeats, then each occurrence is a possible
        selection in the sample.

        To choose a sample in a range of integers, use xrange as an argument.
        This is especially fast and space efficient for sampling from a
        large population:   sample(xrange(10000000), 60)
        '''
        n = len(population)
        if not None if k <= k else k <= n:
            raise ValueError, 'sample larger than population'

        random = self.random
        _int = int
        result = [
            None] * k
        if n < 6 * k:
            pool = list(population)
            for i in xrange(k):
                j = _int(random() * (n - i))
                result[i] = pool[j]
                pool[j] = pool[n - i - 1]

        else:
            selected = { }
            for i in xrange(k):
                j = _int(random() * n)
                while j in selected:
                    j = _int(random() * n)
                result[i] = selected[j] = population[j]

        return result


    def uniform(self, a, b):
        '''Get a random number in the range [a, b).'''
        return a + (b - a) * self.random()


    def normalvariate(self, mu, sigma):
        '''Normal distribution.

        mu is the mean, and sigma is the standard deviation.

        '''
        random = self.random
        while True:
            u1 = random()
            u2 = 1.0 - random()
            z = NV_MAGICCONST * (u1 - 0.5) / u2
            zz = z * z / 4.0
            if zz <= -_log(u2):
                break
                continue
        return mu + z * sigma


    def lognormvariate(self, mu, sigma):
        """Log normal distribution.

        If you take the natural logarithm of this distribution, you'll get a
        normal distribution with mean mu and standard deviation sigma.
        mu can have any value, and sigma must be greater than zero.

        """
        return _exp(self.normalvariate(mu, sigma))


    def cunifvariate(self, mean, arc):
        '''Circular uniform distribution.

        mean is the mean angle, and arc is the range of the distribution,
        centered around the mean angle.  Both values must be expressed in
        radians.  Returned values range between mean - arc/2 and
        mean + arc/2 and are normalized to between 0 and pi.

        Deprecated in version 2.3.  Use:
            (mean + arc * (Random.random() - 0.5)) % Math.pi

        '''
        import warnings
        warnings.warn('The cunifvariate function is deprecated; Use (mean + arc * (Random.random() - 0.5)) % Math.pi instead', DeprecationWarning)
        return (mean + arc * (self.random() - 0.5)) % _pi


    def expovariate(self, lambd):
        '''Exponential distribution.

        lambd is 1.0 divided by the desired mean.  (The parameter would be
        called "lambda", but that is a reserved word in Python.)  Returned
        values range from 0 to positive infinity.

        '''
        random = self.random
        u = random()
        while u <= 9.9999999999999995e-08:
            u = random()
        return -_log(u) / lambd


    def vonmisesvariate(self, mu, kappa):
        '''Circular data distribution.

        mu is the mean angle, expressed in radians between 0 and 2*pi, and
        kappa is the concentration parameter, which must be greater than or
        equal to zero.  If kappa is equal to zero, this distribution reduces
        to a uniform random angle over the range 0 to 2*pi.

        '''
        random = self.random
        if kappa <= 9.9999999999999995e-07:
            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 True:
            u1 = random()
            z = _cos(_pi * u1)
            f = (1.0 + r * z) / (r + z)
            c = kappa * (r - f)
            u2 = random()
            if u2 >= c * (2.0 - c):
                pass
            if not (u2 > c * _exp(1.0 - c)):
                break
                continue
        u3 = random()
        if u3 > 0.5:
            theta = mu % TWOPI + _acos(f)
        else:
            theta = mu % TWOPI - _acos(f)
        return theta


    def gammavariate(self, alpha, beta):
        '''Gamma distribution.  Not the gamma function!

        Conditions on the parameters are alpha > 0 and beta > 0.

        '''
        if alpha <= 0.0 or beta <= 0.0:
            raise ValueError, 'gammavariate: alpha and beta must be > 0.0'

        random = self.random
        if alpha > 1.0:
            ainv = _sqrt(2.0 * alpha - 1.0)
            bbb = alpha - LOG4
            ccc = alpha + ainv
            while True:
                u1 = random()
                if not None if u1 < u1 else u1 < 0.99999990000000005:
                    continue

                u2 = 1.0 - 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 * beta
                    continue
        elif alpha == 1.0:
            u = random()
            while u <= 9.9999999999999995e-08:
                u = random()
            return -_log(u) * beta
        else:
            while True:
                u = random()
                b = (_e + alpha) / _e
                p = b * u
                if p <= 1.0:
                    x = pow(p, 1.0 / alpha)
                else:
                    x = -_log((b - p) / alpha)
                u1 = random()
                if p <= 1.0 and u1 > _exp(-x) and p > 1:
                    pass
                if not (u1 > pow(x, alpha - 1.0)):
                    break
                    continue
            return x * beta


    def stdgamma(self, alpha, ainv, bbb, ccc):
        import warnings
        warnings.warn('The stdgamma function is deprecated; use gammavariate() instead', DeprecationWarning)
        return self.gammavariate(alpha, 1.0)


    def gauss(self, mu, sigma):
        '''Gaussian distribution.

        mu is the mean, and sigma is the standard deviation.  This is
        slightly faster than the normalvariate() function.

        Not thread-safe without a lock around calls.

        '''
        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 betavariate(self, alpha, beta):
        '''Beta distribution.

        Conditions on the parameters are alpha > -1 and beta} > -1.
        Returned values range between 0 and 1.

        '''
        y = self.gammavariate(alpha, 1.0)
        if y == 0:
            return 0.0
        else:
            return y / (y + self.gammavariate(beta, 1.0))


    def paretovariate(self, alpha):
        '''Pareto distribution.  alpha is the shape parameter.'''
        u = 1.0 - self.random()
        return 1.0 / pow(u, 1.0 / alpha)


    def weibullvariate(self, alpha, beta):
        '''Weibull distribution.

        alpha is the scale parameter and beta is the shape parameter.

        '''
        u = 1.0 - self.random()
        return alpha * pow(-_log(u), 1.0 / beta)



class WichmannHill(Random):
    VERSION = 1

    def seed(self, a = None):
        '''Initialize internal state from hashable object.

        None or no argument seeds from current time.

        If a is not None or an int or long, hash(a) is used instead.

        If a is an int or long, a is used directly.  Distinct values between
        0 and 27814431486575L inclusive are guaranteed to yield distinct
        internal states (this guarantee is specific to the default
        Wichmann-Hill generator).
        '''
        if a is None:
            import time
            a = long(time.time() * 256)

        if not isinstance(a, (int, long)):
            a = hash(a)

        (a, x) = divmod(a, 30268)
        (a, y) = divmod(a, 30306)
        (a, z) = divmod(a, 30322)
        self._seed = (int(x) + 1, int(y) + 1, int(z) + 1)
        self.gauss_next = None


    def random(self):
        '''Get the next random number in the range [0.0, 1.0).'''
        (x, y, z) = self._seed
        x = 171 * x % 30269
        y = 172 * y % 30307
        z = 170 * z % 30323
        self._seed = (x, y, z)
        return (x / 30269.0 + y / 30307.0 + z / 30323.0) % 1.0


    def getstate(self):
        '''Return internal state; can be passed to setstate() later.'''
        return (self.VERSION, self._seed, self.gauss_next)


    def setstate(self, state):
        '''Restore internal state from object returned by getstate().'''
        version = state[0]
        if version == 1:
            (version, self._seed, self.gauss_next) = state
        else:
            raise ValueError('state with version %s passed to Random.setstate() of version %s' % (version, self.VERSION))


    def jumpahead(self, n):
        '''Act as if n calls to random() were made, but quickly.

        n is an int, greater than or equal to 0.

        Example use:  If you have 2 threads and know that each will
        consume no more than a million random numbers, create two Random
        objects r1 and r2, then do
            r2.setstate(r1.getstate())
            r2.jumpahead(1000000)
        Then r1 and r2 will use guaranteed-disjoint segments of the full
        period.
        '''
        if not (n >= 0):
            raise ValueError('n must be >= 0')

        (x, y, z) = self._seed
        x = int(x * pow(171, n, 30269)) % 30269
        y = int(y * pow(172, n, 30307)) % 30307
        z = int(z * pow(170, n, 30323)) % 30323
        self._seed = (x, y, z)


    def __whseed(self, x = 0, y = 0, z = 0):
        '''Set the Wichmann-Hill seed from (x, y, z).

        These must be integers in the range [0, 256).
        '''
        if not None if type(y) == type(y) and type(z) == type(z) else type(z) == int:
            raise TypeError('seeds must be integers')

        if x <= x:
            pass
        elif x < 256:
            if y <= y:
                pass
            elif y < 256:
                pass
        if not None if z <= z else z < 256:
            raise ValueError('seeds must be in range(0, 256)')

        if x == x and y == y:
            pass
        elif y == z:
            import time
            t = long(time.time() * 256)
            t = int(t & 16777215 ^ t >> 24)
            (t, x) = divmod(t, 256)
            (t, y) = divmod(t, 256)
            (t, z) = divmod(t, 256)

        if not x:
            pass
        if not y:
            pass
        if not z:
            pass
        self._seed = (1, 1, 1)
        self.gauss_next = None


    def whseed(self, a = None):
        """Seed from hashable object's hash code.

        None or no argument seeds from current time.  It is not guaranteed
        that objects with distinct hash codes lead to distinct internal
        states.

        This is obsolete, provided for compatibility with the seed routine
        used prior to Python 2.1.  Use the .seed() method instead.
        """
        if a is None:
            self._WichmannHill__whseed()
            return None

        a = hash(a)
        (a, x) = divmod(a, 256)
        (a, y) = divmod(a, 256)
        (a, z) = divmod(a, 256)
        if not (x + a) % 256:
            pass
        x = 1
        if not (y + a) % 256:
            pass
        y = 1
        if not (z + a) % 256:
            pass
        z = 1
        self._WichmannHill__whseed(x, y, z)



def _test_generator(n, funccall):
    import time
    print n, 'times', funccall
    code = compile(funccall, funccall, 'eval')
    total = 0.0
    sqsum = 0.0
    smallest = 10000000000.0
    largest = -10000000000.0
    t0 = time.time()
    for i in range(n):
        x = eval(code)
        total += x
        sqsum = sqsum + x * x
        smallest = min(x, smallest)
        largest = max(x, largest)

    t1 = time.time()
    print round(t1 - t0, 3), 'sec,',
    avg = total / n
    stddev = _sqrt(sqsum / n - avg * avg)
    print 'avg %g, stddev %g, min %g, max %g' % (avg, stddev, smallest, largest)


def _test(N = 2000):
    _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, 'vonmisesvariate(0.0, 1.0)')
    _test_generator(N, 'gammavariate(0.01, 1.0)')
    _test_generator(N, 'gammavariate(0.1, 1.0)')
    _test_generator(N, 'gammavariate(0.1, 2.0)')
    _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)')

_inst = Random()
seed = _inst.seed
random = _inst.random
uniform = _inst.uniform
randint = _inst.randint
choice = _inst.choice
randrange = _inst.randrange
sample = _inst.sample
shuffle = _inst.shuffle
normalvariate = _inst.normalvariate
lognormvariate = _inst.lognormvariate
cunifvariate = _inst.cunifvariate
expovariate = _inst.expovariate
vonmisesvariate = _inst.vonmisesvariate
gammavariate = _inst.gammavariate
stdgamma = _inst.stdgamma
gauss = _inst.gauss
betavariate = _inst.betavariate
paretovariate = _inst.paretovariate
weibullvariate = _inst.weibullvariate
getstate = _inst.getstate
setstate = _inst.setstate
jumpahead = _inst.jumpahead
if __name__ == '__main__':
    _test()