5. Python Modules

Module

A module is a file containing Python definitions and statements intended for use in other Python programs.

There are many Python modules that come with Python as part of the standard library.

Once we import the module, we can use things that are defined inside.

import turtle   # use the turtle library

wn = turtle.Screen()     
alex = turtle.Turtle()   

alex.forward(150)        
alex.left(90)            
alex.forward(75)         
wn.exitonclick()
In [ ]:
from IPython.display import IFrame
IFrame('https://docs.python.org/3/library/turtle.html', width='100%', height=350)

Exercise

In Python a module is:
(A) A file containing Python definitions and statements intended for use in other Python programs.
(B) A separate block of code within a program.
(C) One line of code in a program.
(D) A file that contains documentation about functions in Python.

The math module

In [1]:
import math

print(math.pi)
print(math.e)
print(math.inf)
print(math.nan)

print(math.sqrt(2.0))
print(math.sin(math.radians(90))) # sin of 90 degree
3.141592653589793
2.718281828459045
inf
nan
1.4142135623730951
1.0
In [2]:
import math

print(math.factorial(20)) # 20!
print(math.gcd(100,25)) # greatest common divisor
print(math.fsum([.1, .1, .1, .1, .1, .1, 
                 .1, .1, .1, .1]))
print(math.frexp(134.567)) 
# return (m,e), x == m * 2**e 
2432902008176640000
25
1.0
(0.52565234375, 8)

Discussion

对于5008, 只移动两根火柴,能得到的最大数是多少?

The random module

We often want to use random numbers in programs.

Python provides a module random that helps with tasks like this.

In [3]:
import random

prob = random.random()
print(prob)

diceThrow = random.randrange(1, 7)       
# return an int, one of 1,2,3,4,5,6
print(diceThrow)
0.17722082806890382
6

The randrange function generates an integer between its lower and upper argument, using the same semantics as range — so the lower bound is included, but the upper bound is excluded. All the values have an equal probability of occurring (i.e. the results are uniformly distributed).

The random() function returns a floating point number in the range [0.0, 1.0)

  • Random number generators are based on a deterministic algorithm — repeatable and predictable.

  • So they’re called pseudo-random generators — they are not genuinely random.

  • They start with a seed value.

  • Each time you ask for another random number, you’ll get one based on the current seed attribute

In [7]:
import random
print(random.choice(range(10)))
print(random.sample(range(10),2))
2
[3, 6]
In [8]:
help(random)
Help on module random:

NAME
    random - Random variable generators.

MODULE REFERENCE
    https://docs.python.org/3.7/library/random
    
    The following documentation is automatically generated from the Python
    source files.  It may be incomplete, incorrect or include features that
    are considered implementation detail and may vary between Python
    implementations.  When in doubt, consult the module reference at the
    location listed above.

DESCRIPTION
        integers
        --------
               uniform within range
    
        sequences
        ---------
               pick random element
               pick random sample
               pick weighted random sample
               generate random permutation
    
        distributions on the real line:
        ------------------------------
               uniform
               triangular
               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.
    * The random() method is implemented in C, executes in a single Python step,
      and is, therefore, threadsafe.

CLASSES
    _random.Random(builtins.object)
        Random
            SystemRandom
    
    class Random(_random.Random)
     |  Random(x=None)
     |  
     |  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.
     |  
     |  Method resolution order:
     |      Random
     |      _random.Random
     |      builtins.object
     |  
     |  Methods defined here:
     |  
     |  __getstate__(self)
     |      # 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.
     |  
     |  __init__(self, x=None)
     |      Initialize an instance.
     |      
     |      Optional argument x controls seeding, as for Random.seed().
     |  
     |  __reduce__(self)
     |      Helper for pickle.
     |  
     |  __setstate__(self, state)
     |  
     |  betavariate(self, alpha, beta)
     |      Beta distribution.
     |      
     |      Conditions on the parameters are alpha > 0 and beta > 0.
     |      Returned values range between 0 and 1.
     |  
     |  choice(self, seq)
     |      Choose a random element from a non-empty sequence.
     |  
     |  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.
     |  
     |  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.
     |  
     |  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
     |  
     |  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.
     |  
     |  getstate(self)
     |      Return internal state; can be passed to setstate() later.
     |  
     |  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.
     |  
     |  normalvariate(self, mu, sigma)
     |      Normal distribution.
     |      
     |      mu is the mean, and sigma is the standard deviation.
     |  
     |  paretovariate(self, alpha)
     |      Pareto distribution.  alpha is the shape parameter.
     |  
     |  randint(self, a, b)
     |      Return random integer in range [a, b], including both end points.
     |  
     |  randrange(self, start, stop=None, step=1, _int=<class '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.
     |  
     |  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)
     |  
     |  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.
     |  
     |  setstate(self, state)
     |      Restore internal state from object returned by getstate().
     |  
     |  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.
     |  
     |  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
     |  
     |  uniform(self, a, b)
     |      Get a random number in the range [a, b) or [a, b] depending on rounding.
     |  
     |  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.
     |  
     |  weibullvariate(self, alpha, beta)
     |      Weibull distribution.
     |      
     |      alpha is the scale parameter and beta is the shape parameter.
     |  
     |  ----------------------------------------------------------------------
     |  Data descriptors defined here:
     |  
     |  __dict__
     |      dictionary for instance variables (if defined)
     |  
     |  __weakref__
     |      list of weak references to the object (if defined)
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes defined here:
     |  
     |  VERSION = 3
     |  
     |  ----------------------------------------------------------------------
     |  Methods inherited from _random.Random:
     |  
     |  __getattribute__(self, name, /)
     |      Return getattr(self, name).
     |  
     |  getrandbits(...)
     |      getrandbits(k) -> x.  Generates an int with k random bits.
     |  
     |  random(...)
     |      random() -> x in the interval [0, 1).
     |  
     |  ----------------------------------------------------------------------
     |  Static methods inherited from _random.Random:
     |  
     |  __new__(*args, **kwargs) from builtins.type
     |      Create and return a new object.  See help(type) for accurate signature.
    
    class SystemRandom(Random)
     |  SystemRandom(x=None)
     |  
     |  Alternate random number generator using sources provided
     |  by the operating system (such as /dev/urandom on Unix or
     |  CryptGenRandom on Windows).
     |  
     |   Not available on all systems (see os.urandom() for details).
     |  
     |  Method resolution order:
     |      SystemRandom
     |      Random
     |      _random.Random
     |      builtins.object
     |  
     |  Methods defined here:
     |  
     |  getrandbits(self, k)
     |      getrandbits(k) -> x.  Generates an int with k random bits.
     |  
     |  getstate = _notimplemented(self, *args, **kwds)
     |  
     |  random(self)
     |      Get the next random number in the range [0.0, 1.0).
     |  
     |  seed(self, *args, **kwds)
     |      Stub method.  Not used for a system random number generator.
     |  
     |  setstate = _notimplemented(self, *args, **kwds)
     |  
     |  ----------------------------------------------------------------------
     |  Methods inherited from Random:
     |  
     |  __getstate__(self)
     |      # 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.
     |  
     |  __init__(self, x=None)
     |      Initialize an instance.
     |      
     |      Optional argument x controls seeding, as for Random.seed().
     |  
     |  __reduce__(self)
     |      Helper for pickle.
     |  
     |  __setstate__(self, state)
     |  
     |  betavariate(self, alpha, beta)
     |      Beta distribution.
     |      
     |      Conditions on the parameters are alpha > 0 and beta > 0.
     |      Returned values range between 0 and 1.
     |  
     |  choice(self, seq)
     |      Choose a random element from a non-empty sequence.
     |  
     |  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.
     |  
     |  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.
     |  
     |  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
     |  
     |  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.
     |  
     |  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.
     |  
     |  normalvariate(self, mu, sigma)
     |      Normal distribution.
     |      
     |      mu is the mean, and sigma is the standard deviation.
     |  
     |  paretovariate(self, alpha)
     |      Pareto distribution.  alpha is the shape parameter.
     |  
     |  randint(self, a, b)
     |      Return random integer in range [a, b], including both end points.
     |  
     |  randrange(self, start, stop=None, step=1, _int=<class '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.
     |  
     |  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)
     |  
     |  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.
     |  
     |  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
     |  
     |  uniform(self, a, b)
     |      Get a random number in the range [a, b) or [a, b] depending on rounding.
     |  
     |  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.
     |  
     |  weibullvariate(self, alpha, beta)
     |      Weibull distribution.
     |      
     |      alpha is the scale parameter and beta is the shape parameter.
     |  
     |  ----------------------------------------------------------------------
     |  Data descriptors inherited from Random:
     |  
     |  __dict__
     |      dictionary for instance variables (if defined)
     |  
     |  __weakref__
     |      list of weak references to the object (if defined)
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes inherited from Random:
     |  
     |  VERSION = 3
     |  
     |  ----------------------------------------------------------------------
     |  Methods inherited from _random.Random:
     |  
     |  __getattribute__(self, name, /)
     |      Return getattr(self, name).
     |  
     |  ----------------------------------------------------------------------
     |  Static methods inherited from _random.Random:
     |  
     |  __new__(*args, **kwargs) from builtins.type
     |      Create and return a new object.  See help(type) for accurate signature.

FUNCTIONS
    betavariate(alpha, beta) method of Random instance
        Beta distribution.
        
        Conditions on the parameters are alpha > 0 and beta > 0.
        Returned values range between 0 and 1.
    
    choice(seq) method of Random instance
        Choose a random element from a non-empty sequence.
    
    choices(population, weights=None, *, cum_weights=None, k=1) method of Random instance
        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.
    
    expovariate(lambd) method of Random instance
        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.
    
    gammavariate(alpha, beta) method of Random instance
        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
    
    gauss(mu, sigma) method of Random instance
        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.
    
    getrandbits(...) method of Random instance
        getrandbits(k) -> x.  Generates an int with k random bits.
    
    getstate() method of Random instance
        Return internal state; can be passed to setstate() later.
    
    lognormvariate(mu, sigma) method of Random instance
        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.
    
    normalvariate(mu, sigma) method of Random instance
        Normal distribution.
        
        mu is the mean, and sigma is the standard deviation.
    
    paretovariate(alpha) method of Random instance
        Pareto distribution.  alpha is the shape parameter.
    
    randint(a, b) method of Random instance
        Return random integer in range [a, b], including both end points.
    
    random(...) method of Random instance
        random() -> x in the interval [0, 1).
    
    randrange(start, stop=None, step=1, _int=<class 'int'>) method of Random instance
        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.
    
    sample(population, k) method of Random instance
        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)
    
    seed(a=None, version=2) method of Random instance
        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.
    
    setstate(state) method of Random instance
        Restore internal state from object returned by getstate().
    
    shuffle(x, random=None) method of Random instance
        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.
    
    triangular(low=0.0, high=1.0, mode=None) method of Random instance
        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
    
    uniform(a, b) method of Random instance
        Get a random number in the range [a, b) or [a, b] depending on rounding.
    
    vonmisesvariate(mu, kappa) method of Random instance
        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.
    
    weibullvariate(alpha, beta) method of Random instance
        Weibull distribution.
        
        alpha is the scale parameter and beta is the shape parameter.

DATA
    __all__ = ['Random', 'seed', 'random', 'uniform', 'randint', 'choice',...

FILE
    /Users/caodg/Projects/miniconda3/lib/python3.7/random.py


Exercise

1. Which of the following is the correct way to reference the value pi within the math module. Assume you have already imported the math module.
(A) math.pi
(B) math(pi)
(C) pi.math
(D) math->pi
2. The correct code to generate a random number between 1 and 100 (inclusive) is:
(A) prob = random.randrange(1, 101)
(B) prob = random.randrange(1, 100)
(C) prob = random.randrange(0, 101)
(D) prob = random.randrange(0, 100)
3. One reason that lotteries don’t use computers to generate random numbers is:
(A) There is no computer on the stage for the drawing.
(B) Because computers don't really generate random numbers, they generate pseudo-random numbers.
(C) They would just generate the same numbers over and over again.
(D) The computer can't tell what values were already selected, so it might generate all 5's instead of 5 unique numbers.
4. Use a for statement to print 10 random numbers between 25 and 35.

The End

In [ ]:
import this

Glossary

deterministic

A process that is repeatable and predictable.

documentation

A place where you can go to get detailed information about aspects of your programming language.

module

A file containing Python definitions and statements intended for use in other Python programs. The contents of a module are made available to the other program by using the import statement.

pseudo-random number

A number that is not genuinely random but is instead created algorithmically.

random number

A number that is generated in such a way as to exhibit statistical randomness.

random number generator

A function that will provide you with random numbers, usually between 0 and 1.

standard library

A collection of modules that are part of the normal installation of Python.