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stdrandom.py
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stdrandom.py
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# code based on https://introcs.cs.princeton.edu/python/code/stdlib-python.zip as downloaded in dec 2017
"""
stdrandom.py
The stdrandom module defines functions related to pseudo-random
numbers.
"""
#-----------------------------------------------------------------------
import math
import random
#-----------------------------------------------------------------------
def seed(i=None):
"""
Seed the random number generator as hash(i), where i is an int.
If i is None, then seed using the current time or, quoting the
help page for random.seed(), "an operating system specific
randomness source if available."
"""
random.seed(i)
#-----------------------------------------------------------------------
def uniform(hi):
"""
Return an integer chosen uniformly from the range [0, hi).
"""
return random.randrange(0, hi)
#-----------------------------------------------------------------------
def uniformInt(lo, hi):
"""
Return an integer chosen uniformly from the range [lo, hi).
"""
return random.randrange(lo, hi)
#-----------------------------------------------------------------------
def uniformFloat(lo, hi):
"""
Return a number chosen uniformly from the range [lo, hi).
"""
return random.uniform(lo, hi)
#-----------------------------------------------------------------------
def bernoulli(p=0.5):
"""
Return True with probability p.
"""
return random.random() < p
#-----------------------------------------------------------------------
def binomial(n, p=0.5):
"""
Return the number of heads in n coin flips, each of which is
heads with probability p.
"""
heads = 0
for i in range(n):
if bernoulli(p):
heads += 1
return heads
#-----------------------------------------------------------------------
def gaussian(mean=0.0, stddev=1.0):
"""
Return a float according to a standard Gaussian distribution
with the given mean (mean) and standard deviation (stddev).
"""
# Approach 1:
# return random.gauss(mu, sigma)
# Approach 2: Use the polar form of the Box-Muller transform.
x = uniformFloat(-1.0, 1.0)
y = uniformFloat(-1.0, 1.0)
r = x*x + y*y
while (r >= 1) or (r == 0):
x = uniformFloat(-1.0, 1.0)
y = uniformFloat(-1.0, 1.0)
r = x*x + y*y
g = x * math.sqrt(-2 * math.log(r) / r)
# Remark: x * math.sqrt(-2 * math.log(r) / r)
# is an independent random gaussian
return mean + stddev * g
#-----------------------------------------------------------------------
def discrete(a):
"""
Return a float from a discrete distribution: i with probability
a[i]. Precondition: the elements of array a sum to 1.
"""
r = uniformFloat(0.0, sum(a))
subtotal = 0.0
for i in range(len(a)):
subtotal += a[i]
if subtotal > r:
return i
#return len(a) - 1
#-----------------------------------------------------------------------
def shuffle(a):
"""
Shuffle array a.
"""
# Approach 1:
# for i in range(len(a)):
# j = i + uniformInt(len(a) - i)
# temp = a[i]
# a[i] = a[j]
# a[j] = temp
# Approach 2:
random.shuffle(a)
#-----------------------------------------------------------------------
def exp(lambd):
"""
Return a float from an exponential distribution with rate lambd.
"""
# Approach 1:
# return random.expovariate(lambd)
# Approach 2:
return -math.log(1 - random.random()) / lambd
#-----------------------------------------------------------------------
def _main():
"""
For testing.
"""
import sys
from itu.algs4.stdlib import stdio
seed(1)
n = int(sys.argv[1])
for i in range(n):
stdio.writef(' %2d ' , uniformInt(10, 100))
stdio.writef('%8.5f ' , uniformFloat(10.0, 99.0))
stdio.writef('%5s ' , bernoulli())
stdio.writef('%5s ' , binomial(100, .5))
stdio.writef('%7.5f ' , gaussian(9.0, .2))
stdio.writef('%2d ' , discrete([.5, .3, .1, .1]))
stdio.writeln()
if __name__ == '__main__':
_main()
#-----------------------------------------------------------------------
# python stdrandom.py 5
# 27 60.65914 False 41 9.01682 0
# 55 46.88378 True 48 8.90171 0
# 58 92.96468 True 52 9.12770 0
# 79 64.41387 False 47 9.49241 0
# 29 32.30299 True 45 8.77630 1