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python中uniform的源代码

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[已解决问题] 解决于 2019-03-10 18:17

请问大家,python中用于生成随机数的uniform函数的源代码在哪可以找到,或者直接分享给我也行。谢谢大家

Ts归零者的主页 Ts归零者 | 初学一级 | 园豆:185
提问于:2019-03-08 20:49
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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.

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(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.

"""

VERSION = 3     # used by getstate/setstate

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, version=2):
    """Initialize internal state from hashable object.

    None or no argument seeds from current time or from an operating
    system specific randomness source if available.

    If *a* is an int, all bits are used.

    For version 2 (the default), all of the bits are used if *a* is a str,
    bytes, or bytearray.  For version 1 (provided for reproducing random
    sequences from older versions of Python), the algorithm for str and
    bytes generates a narrower range of seeds.

    """

    if version == 1 and isinstance(a, (str, bytes)):
        a = a.decode('latin-1') if isinstance(a, bytes) else a
        x = ord(a[0]) << 7 if a else 0
        for c in map(ord, a):
            x = ((1000003 * x) ^ c) & 0xFFFFFFFFFFFFFFFF
        x ^= len(a)
        a = -2 if x == -1 else x

    if version == 2 and isinstance(a, (str, bytes, bytearray)):
        if isinstance(a, str):
            a = a.encode()
        a += _sha512(a).digest()
        a = int.from_bytes(a, 'big')

    super().seed(a)
    self.gauss_next = None

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

def setstate(self, state):
    """Restore internal state from object returned by getstate()."""
    version = state[0]
    if version == 3:
        version, internalstate, self.gauss_next = state
        super().setstate(internalstate)
    elif version == 2:
        version, internalstate, self.gauss_next = state
        # In version 2, the state was saved as signed ints, which causes
        #   inconsistencies between 32/64-bit systems. The state is
        #   really unsigned 32-bit ints, so we convert negative ints from
        #   version 2 to positive longs for version 3.
        try:
            internalstate = tuple(x % (2**32) for x in internalstate)
        except ValueError as e:
            raise TypeError from e
        super().setstate(internalstate)
    else:
        raise ValueError("state with version %s passed to "
                         "Random.setstate() of version %s" %
                         (version, self.VERSION))

---- Methods below this point do not need to be overridden when

---- subclassing for the purpose of using a different core generator.

-------------------- pickle support -------------------

# Issue 17489: Since __reduce__ was defined to fix #759889 this is no
# longer called; we leave it here because it has been here since random was
# rewritten back in 2001 and why risk breaking something.
def __getstate__(self): # for pickle
    return self.getstate()

def __setstate__(self, state):  # for pickle
    self.setstate(state)

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

-------------------- integer methods -------------------

def randrange(self, start, stop=None, step=1, _int=int):
    """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.

    """

    # This code is a bit messy to make it fast for the
    # common case while still doing adequate error checking.
    istart = _int(start)
    if istart != start:
        raise ValueError("non-integer arg 1 for randrange()")
    if stop is None:
        if istart > 0:
            return self._randbelow(istart)
        raise ValueError("empty range for randrange()")

    # stop argument supplied.
    istop = _int(stop)
    if istop != stop:
        raise ValueError("non-integer stop for randrange()")
    width = istop - istart
    if step == 1 and width > 0:
        return istart + self._randbelow(width)
    if step == 1:
        raise ValueError("empty range for randrange() (%d,%d, %d)" % (istart, istop, width))

    # Non-unit step argument supplied.
    istep = _int(step)
    if istep != step:
        raise ValueError("non-integer step for randrange()")
    if istep > 0:
        n = (width + istep - 1) // istep
    elif istep < 0:
        n = (width + istep + 1) // istep
    else:
        raise ValueError("zero step for randrange()")

    if n <= 0:
        raise ValueError("empty range for randrange()")

    return istart + istep*self._randbelow(n)

def randint(self, a, b):
    """Return random integer in range [a, b], including both end points.
    """

    return self.randrange(a, b+1)

def _randbelow(self, n, int=int, maxsize=1<<BPF, type=type,
               Method=_MethodType, BuiltinMethod=_BuiltinMethodType):
    "Return a random int in the range [0,n).  Raises ValueError if n==0."

    random = self.random
    getrandbits = self.getrandbits
    # Only call self.getrandbits if the original random() builtin method
    # has not been overridden or if a new getrandbits() was supplied.
    if type(random) is BuiltinMethod or type(getrandbits) is Method:
        k = n.bit_length()  # don't use (n-1) here because n can be 1
        r = getrandbits(k)          # 0 <= r < 2**k
        while r >= n:
            r = getrandbits(k)
        return r
    # There's an overridden random() method but no new getrandbits() method,
    # so we can only use random() from here.
    if n >= maxsize:
        _warn("Underlying random() generator does not supply \n"
            "enough bits to choose from a population range this large.\n"
            "To remove the range limitation, add a getrandbits() method.")
        return int(random() * n)
    rem = maxsize % n
    limit = (maxsize - rem) / maxsize   # int(limit * maxsize) % n == 0
    r = random()
    while r >= limit:
        r = random()
    return int(r*maxsize) % n

-------------------- sequence methods -------------------

def choice(self, seq):
    """Choose a random element from a non-empty sequence."""
    try:
        i = self._randbelow(len(seq))
    except ValueError:
        raise IndexError('Cannot choose from an empty sequence') from None
    return seq[i]

def shuffle(self, x, random=None):
    """Shuffle list x in place, and return None.

    Optional argument random is a 0-argument function returning a
    random float in [0.0, 1.0); if it is the default None, the
    standard random.random will be used.

    """

    if random is None:
        randbelow = self._randbelow
        for i in reversed(range(1, len(x))):
            # pick an element in x[:i+1] with which to exchange x[i]
            j = randbelow(i+1)
            x[i], x[j] = x[j], x[i]
    else:
        _int = int
        for i in reversed(range(1, len(x))):
            # 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]

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

    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 range as an argument.
    This is especially fast and space efficient for sampling from a
    large population:   sample(range(10000000), 60)
    """

    # Sampling without replacement entails tracking either potential
    # selections (the pool) in a list or previous selections in a set.

    # When the number of selections is small compared to the
    # population, then tracking selections is efficient, requiring
    # only a small set and an occasional reselection.  For
    # a larger number of selections, the pool tracking method is
    # preferred since the list takes less space than the
    # set and it doesn't suffer from frequent reselections.

    if isinstance(population, _Set):
        population = tuple(population)
    if not isinstance(population, _Sequence):
        raise TypeError("Population must be a sequence or set.  For dicts, use list(d).")
    randbelow = self._randbelow
    n = len(population)
    if not 0 <= k <= n:
        raise ValueError("Sample larger than population or is negative")
    result = [None] * k
    setsize = 21        # size of a small set minus size of an empty list
    if k > 5:
        setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
    if n <= setsize:
        # An n-length list is smaller than a k-length set
        pool = list(population)
        for i in range(k):         # invariant:  non-selected at [0,n-i)
            j = randbelow(n-i)
            result[i] = pool[j]
            pool[j] = pool[n-i-1]   # move non-selected item into vacancy
    else:
        selected = set()
        selected_add = selected.add
        for i in range(k):
            j = randbelow(n)
            while j in selected:
                j = randbelow(n)
            selected_add(j)
            result[i] = population[j]
    return result

def choices(self, population, weights=None, *, cum_weights=None, k=1):
    """Return a k sized list of population elements chosen with replacement.

    If the relative weights or cumulative weights are not specified,
    the selections are made with equal probability.

    """
    random = self.random
    if cum_weights is None:
        if weights is None:
            _int = int
            total = len(population)
            return [population[_int(random() * total)] for i in range(k)]
        cum_weights = list(_itertools.accumulate(weights))
    elif weights is not None:
        raise TypeError('Cannot specify both weights and cumulative weights')
    if len(cum_weights) != len(population):
        raise ValueError('The number of weights does not match the population')
    bisect = _bisect.bisect
    total = cum_weights[-1]
    return [population[bisect(cum_weights, random() * total)] for i in range(k)]

-------------------- real-valued distributions -------------------

-------------------- uniform distribution -------------------

def uniform(self, a, b):
    "Get a random number in the range [a, b) or [a, b] depending on rounding."
    return a + (b-a) * self.random()

-------------------- triangular --------------------

def triangular(self, low=0.0, high=1.0, mode=None):
    """Triangular distribution.

    Continuous distribution bounded by given lower and upper limits,
    and having a given mode value in-between.

    http://en.wikipedia.org/wiki/Triangular_distribution

    """
    u = self.random()
    try:
        c = 0.5 if mode is None else (mode - low) / (high - low)
    except ZeroDivisionError:
        return low
    if u > c:
        u = 1.0 - u
        c = 1.0 - c
        low, high = high, low
    return low + (high - low) * (u * c) ** 0.5

-------------------- normal distribution --------------------

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

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

    """
    # 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 = 1.0 - 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(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))

-------------------- exponential distribution --------------------

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

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

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

    # we use 1-random() instead of random() to preclude the
    # possibility of taking the log of zero.
    return -_log(1.0 - self.random())/lambd

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

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.

    """
    # 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()

    s = 0.5 / kappa
    r = s + _sqrt(1.0 + s * s)

    while 1:
        u1 = random()
        z = _cos(_pi * u1)

        d = z / (r + z)
        u2 = random()
        if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d):
            break

    q = 1.0 / r
    f = (q + z) / (1.0 + q * z)
    u3 = random()
    if u3 > 0.5:
        theta = (mu + _acos(f)) % TWOPI
    else:
        theta = (mu - _acos(f)) % TWOPI

    return theta

-------------------- gamma distribution --------------------

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

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

    The probability distribution function is:

                x ** (alpha - 1) * math.exp(-x / beta)
      pdf(x) =  --------------------------------------
                  math.gamma(alpha) * beta ** alpha

    """

    # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2

    # Warning: a few older sources define the gamma distribution in terms
    # of alpha > -1.0
    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:

        # Uses R.C.H. Cheng, "The generation of Gamma
        # variables with non-integral shape parameters",
        # Applied Statistics, (1977), 26, No. 1, p71-74

        ainv = _sqrt(2.0 * alpha - 1.0)
        bbb = alpha - LOG4
        ccc = alpha + ainv

        while 1:
            u1 = random()
            if not 1e-7 < u1 < .9999999:
                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

    elif alpha == 1.0:
        # expovariate(1)
        u = random()
        while u <= 1e-7:
            u = random()
        return -_log(u) * beta

    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 = p ** (1.0/alpha)
            else:
                x = -_log((b-p)/alpha)
            u1 = random()
            if p > 1.0:
                if u1 <= x ** (alpha - 1.0):
                    break
            elif u1 <= _exp(-x):
                break
        return x * beta

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

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.

    """

    # 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

-------------------- beta --------------------

See

http://mail.python.org/pipermail/python-bugs-list/2001-January/003752.html

for Ivan Frohne's insightful analysis of why the original implementation:

def betavariate(self, alpha, beta):

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

y = self.expovariate(alpha)

z = self.expovariate(1.0/beta)

return z/(y+z)

was dead wrong, and how it probably got that way.

def betavariate(self, alpha, beta):
    """Beta distribution.

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

    """

    # This version due to Janne Sinkkonen, and matches all the std
    # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
    y = self.gammavariate(alpha, 1.0)
    if y == 0:
        return 0.0
    else:
        return y / (y + self.gammavariate(beta, 1.0))

-------------------- Pareto --------------------

def paretovariate(self, alpha):
    """Pareto distribution.  alpha is the shape parameter."""
    # Jain, pg. 495

    u = 1.0 - self.random()
    return 1.0 / u ** (1.0/alpha)

-------------------- Weibull --------------------

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

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

    """
    # Jain, pg. 499; bug fix courtesy Bill Arms

    u = 1.0 - self.random()
    return alpha * (-_log(u)) ** (1.0/beta)
奖励园豆:5
一个烂程序员 | 菜鸟二级 |园豆:207 | 2019-03-09 23:00

谢谢。

Ts归零者 | 园豆:185 (初学一级) | 2019-03-10 18:05
其他回答(1)
0

python的标准库大多数是python实现的。
在random.py中可以看到,或者在github上搜索python的项目

https://github.com/python/cpython

墨镜带佬星 | 园豆:2294 (老鸟四级) | 2019-03-08 22:12

谢谢

 

支持(0) 反对(0) Ts归零者 | 园豆:185 (初学一级) | 2019-03-10 18:05
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