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r""" Random Numbers with Python API
AUTHORS: -- Carl Witty (2008-03): new file
This module has the same functions as the Python standard module \module{random}, but uses the current \sage random number state from \module{sage.misc.randstate} (so that it can be controlled by the same global random number seeds).
The functions here are less efficient than the functions in \module{random}, because they look up the current random number state on each call.
If you are going to be creating many random numbers in a row, it is better to use the functions in \module{sage.misc.randstate} directly.
Here is an example:
(The imports on the next two lines are not necessary, since \function{randrange} and \function{current_randstate} are both available by default at the \code{sage:} prompt; but you would need them to run these examples inside a module.) ::
sage: from sage.misc.prandom import randrange sage: from sage.misc.randstate import current_randstate sage: def test1(): ....: return sum([randrange(100) for i in range(100)]) sage: def test2(): ....: randrange = current_randstate().python_random().randrange ....: return sum([randrange(100) for i in range(100)])
Test2 will be slightly faster than test1, but they give the same answer::
sage: with seed(0): test1() 5169 sage: with seed(0): test2() 5169 sage: with seed(1): test1() 5097 sage: with seed(1): test2() 5097 sage: timeit('test1()') # random 625 loops, best of 3: 590 us per loop sage: timeit('test2()') # random 625 loops, best of 3: 460 us per loop
The docstrings for the functions in this file are mostly copied from Python's \file{random.py}, so those docstrings are "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007 Python Software Foundation; All Rights Reserved" and are available under the terms of the Python Software Foundation License Version 2. """
# We deliberately omit "seed" and several other seed-related functions... # setting seeds should only be done through sage.misc.randstate .
from sage.misc.randstate import current_randstate
def _pyrand(): r""" A tiny private helper function to return an instance of random.Random from the current \sage random number state. Only for use in prandom.py; other modules should use current_randstate().python_random().
EXAMPLES::
sage: from sage.misc.prandom import _pyrand sage: _pyrand() <random.Random object at 0x...> sage: _pyrand().getrandbits(10) 114L """
def getrandbits(k): r""" getrandbits(k) -> x. Generates a long int with k random bits.
EXAMPLES::
sage: getrandbits(10) 114L sage: getrandbits(200) 1251230322675596703523231194384285105081402591058406420468435L sage: getrandbits(10) 533L """
def randrange(start, stop=None, step=1): r""" 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.
EXAMPLES::
sage: randrange(0, 100, 11) 11 sage: randrange(5000, 5100) 5051 sage: [randrange(0, 2) for i in range(15)] [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1] sage: randrange(0, 1000000, 1000) 486000 sage: randrange(-100, 10) -56 """
def randint(a, b): r""" Return random integer in range [a, b], including both end points.
EXAMPLES::
sage: [randint(0, 2) for i in range(15)] [0, 1, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2] sage: randint(-100, 10) -46 """
def choice(seq): r""" Choose a random element from a non-empty sequence.
EXAMPLES::
sage: [choice(list(primes(10, 100))) for i in range(5)] [17, 47, 11, 31, 47] """
def shuffle(x, random=None): r""" 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 sage.misc.random.random.
EXAMPLES::
sage: shuffle([1 .. 10]) """
def sample(population, k): r""" Choose k unique random elements from a population sequence.
Return 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 (in Python 2) or range (in Python 3). This is especially fast and space efficient for sampling from a large population: sample(range(10000000), 60)
EXAMPLES::
sage: sample(["Here", "I", "come", "to", "save", "the", "day"], 3) ['Here', 'to', 'day'] sage: from six.moves import range sage: sample(range(2^30), 7) [357009070, 558990255, 196187132, 752551188, 85926697, 954621491, 624802848] """
def random(): r""" Get the next random number in the range [0.0, 1.0).
EXAMPLES::
sage: [random() for i in [1 .. 4]] [0.111439293741037, 0.5143475134191677, 0.04468968524815642, 0.332490606442413] """
def uniform(a, b): r""" Get a random number in the range [a, b).
Equivalent to \code{a + (b-a) * random()}.
EXAMPLES::
sage: uniform(0, 1) 0.111439293741037 sage: uniform(e, pi) 0.5143475134191677*pi + 0.48565248658083227*e sage: RR(_) 2.93601069876846 """
def betavariate(alpha, beta): r""" Beta distribution.
Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1.
EXAMPLES::
sage: betavariate(0.1, 0.9) 9.75087916621299e-9 sage: betavariate(0.9, 0.1) 0.941890400939253 """
def expovariate(lambd): r""" 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.
EXAMPLES::
sage: [expovariate(0.001) for i in range(3)] [118.152309288166, 722.261959038118, 45.7190543690470] sage: [expovariate(1.0) for i in range(3)] [0.404201816061304, 0.735220464997051, 0.201765578600627] sage: [expovariate(1000) for i in range(3)] [0.0012068700332283973, 8.340929747302108e-05, 0.00219877067980605] """
def gammavariate(alpha, beta): r""" Gamma distribution. Not the gamma function!
Conditions on the parameters are alpha > 0 and beta > 0.
EXAMPLES::
sage: gammavariate(1.0, 3.0) 6.58282586130638 sage: gammavariate(3.0, 1.0) 3.07801512341612 """
def gauss(mu, sigma): r""" Gaussian distribution.
mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function, but is not thread-safe.
EXAMPLES::
sage: [gauss(0, 1) for i in range(3)] [0.9191011757657915, 0.7744526756246484, 0.8638996866800877] sage: [gauss(0, 100) for i in range(3)] [24.916051749154448, -62.99272061579273, -8.1993122536718...] sage: [gauss(1000, 10) for i in range(3)] [998.7590700045661, 996.1087338511692, 1010.1256817458031] """
def lognormvariate(mu, sigma): r""" 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.
EXAMPLES::
sage: [lognormvariate(100, 10) for i in range(3)] [2.9410355688290246e+37, 2.2257548162070125e+38, 4.142299451717446e+43] """
def normalvariate(mu, sigma): r""" Normal distribution.
mu is the mean, and sigma is the standard deviation.
EXAMPLES::
sage: [normalvariate(0, 1) for i in range(3)] [-1.372558980559407, -1.1701670364898928, 0.04324100555110143] sage: [normalvariate(0, 100) for i in range(3)] [37.45695875041769, 159.6347743233298, 124.1029321124009] sage: [normalvariate(1000, 10) for i in range(3)] [1008.5303090383741, 989.8624892644895, 985.7728921150242] """
def vonmisesvariate(mu, kappa): r""" 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.
EXAMPLES::
sage: [vonmisesvariate(1.0r, 3.0r) for i in range(1, 5)] # abs tol 1e-12 [0.898328639355427, 0.6718030007041281, 2.0308777524813393, 1.714325253725145] """
def paretovariate(alpha): r""" Pareto distribution. alpha is the shape parameter.
EXAMPLES::
sage: [paretovariate(3) for i in range(1, 5)] [1.0401699394233033, 1.2722080162636495, 1.0153564009379579, 1.1442323078983077] """
def weibullvariate(alpha, beta): r""" Weibull distribution.
alpha is the scale parameter and beta is the shape parameter.
EXAMPLES::
sage: [weibullvariate(1, 3) for i in range(1, 5)] [0.49069775546342537, 0.8972185564611213, 0.357573846531942, 0.739377255516847] """ |