Part 1: Mapping Functions

In many situations you would like to apply the same function to lots of different pieces of data. For example, lets create two arrays of numbers, and use our add function to add pairs of numbers together. In ipython type;

a = [ 1, 2, 3, 4, 5 ]
b = [ 6, 7, 8, 9, 10 ]

result = []

for i in range(0, len(a)):
    result.append( sum(a[i], b[i]) )


This should print

[7, 9, 11, 13, 15]

The above code has looped over every pair of numbers in the lists a and b, and has called the function sum for each pair. Each result is appended to the list result, which is printed at the end of the loop.

Applying the same function to every item in a list (or pair of lists) of data is really common. For example, in a molecular simulation, you may want to loop over a list of every molecule and call a calculate_energy function for each one. In a fluid dynamics simulation, you may want to loop over a list of grid points and call a solve_gridpoint function for each one. This pattern, of calling the same function for each element of a list (or set of lists) of data, is called mapping. In the above example, we have mapped the function sum onto the lists a and b, returning result.

The above code mapped the function sum. How about if we wanted to map our diff or multiply functions? One option would be to copy out this code again. A better solution would be to use functional programming to write our own mapping function.

Type into ipython

def mapper( func, arg1, arg2 ):
    """This will map the function 'func' to each pair
       of arguments in the list 'arg1' and 'arg2', returning
       the result"""

    nargs = min( len(arg1), len(arg2) )

    res = []

    for i in range(0, nargs):
        res.append( func(arg1[i], arg2[i]) )

    return res

result = mapper( sum, a, b )


This should print out

[7, 9, 11, 13, 15]

Now type

result = mapper( multiply, a, b )

This should print out

[6, 14, 24, 36, 50]

Can you see how this works?

The mapper function takes as its first argument the function to be mapped. The other arguments are the two lists of data for the mapping. The line

    nargs = min( len(arg1), len(arg2) )

works out the number of pairs of data that can be mapped, using the smallest size of the two lists. The mapper function then loops through each of these pairs of data, calling func for each pair, and storing the result in the list res. This is then returned at the end.

Because the mapper function calls the mapped function using the argument func, it can map any function that is passed to it, as long as that function accepts two arguments. For example, let us now create a completely different function to map. Type into ipython

import math

def calc_distance( point1, point2 ):
    """Function to calculate and return the distance between
       two points"""

    dx2 = (point1[0] - point2[0])**2
    dy2 = (point1[1] - point2[1])**2
    dz2 = (point1[2] - point2[2])**2

    return math.sqrt( dx2 + dy2 + dz2 )

This has created a function that calculates the distance between two points. Let’s now create two lists of points and use mapper to control the calculation of distances between points. Type into ipython;

points1 = [ (1.0,1.0,1.0), (2.0,2.0,2.0), (3.0,3.0,3.0) ]
points2 = [ (4.0,4.0,4.0), (5.0,5.0,5.0), (6.0,6.0,6.0) ]

distances = mapper( calc_distance, points1, points2 )


This should print

[5.196152422706632, 5.196152422706632, 5.196152422706632]

Standard Map

Mapping is so common and useful that it is built in as a standard python function, called map. For example, please type

distances = map( calc_distance, points1, points2 )


You should see that your calc_distances function has been mapped to all of the pairs of points, with the following then printed to the screen.

[5.196152422706632, 5.196152422706632, 5.196152422706632]

The standard map function behaves exactly like your hand-written mapper function, returing a list containing the result of applying your function to each item of data.

One advantage of map is that it knows how to handle multiple arguments. For example, let’s create a function that only maps a single argument. Type into ipython

def square(x):
    """Simple function to return the square of
       the passed argument"""
    return x*x

Now, let’s try to use your handwritten mapper function to map square onto a list of numbers. Type into ipython;

numbers = [ 1, 2, 3, 4, 5 ]

result = mapper(square, numbers)

This should fail, with an error message that looks something like

mapper() takes exactly 3 arguments (2 given)

We wrote our mapper function so that it mapped functions that expected two arguments. That meant that our mapper function needs three arguments; the mapped function plus two lists of arguments.

The standard map function can handle different numbers of arguments. Type into ipython

result = map(square, numbers)

print( result )

You should see that this works, and that you see printed

[1, 4, 9, 16, 25]

The standard map function can work with mapping functions that accept any number of arguments. If the mapping function accepts n arguments, then you must pass n+1 arguments to map, i.e. the mapped function, plus n lists of arguments.

For example, type this into ipython

def find_smallest(arg1, arg2, arg3):
    """Function used to return the smallest value out 
       of 'arg1', 'arg2' and 'arg3'"""

    return min(arg1, min(arg2,arg3))

a = [1, 2, 3, 4, 5]
b = [5, 4, 3, 2, 1]
c = [1, 2, 1, 2, 1]

result = map( find_smallest, a, b, c )

print( result )

This should print

[1, 2, 1, 2, 1]

Is this what you expect?


Download and unpack the file shakespeare.tar.bz2, e.g. type

tar -jxvf shakespeare.tar.bz2

This has created a directory called shakespeare that contains the full text of many of Shakespeare’s plays.

Your task is to write a Python script, called, that will count the total number of lines in each of these Shakespeare plays, e.g. by using the command line call

python shakespeare/*

To do this, first write a function that counts the number of lines in a file.

Then, use the standard map function to count the number of lines in each Shakespeare play, printing the result as a list.

If you get stuck or want some inspiration, a possible answer is given here.

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