Repeating Actions with Loops

Last updated on 2024-12-02 | Edit this page

Overview

Questions

  • How can I do the same operations on many different values?

Objectives

  • Explain what a for loop does.
  • Correctly write for loops to repeat simple calculations.
  • Trace changes to a loop variable as the loop runs.
  • Trace changes to other variables as they are updated by a for loop.

Iterating over lists

An example task that we might want to repeat is accessing numbers in a list, which we will do by printing each number on a line of its own.

PYTHON 

odds = [1, 3, 5, 7]

In Python, a list is basically an ordered collection of elements, and every element has a unique number associated with it — its index. This means that we can access elements in a list using their indices. For example, we can get the first number in the list odds, by using odds[0]. One way to print each number is to use four print statements:

PYTHON 

print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

OUTPUT 

1
3
5
7

This is a terrible approach for three reasons:

  1. Not scalable. Imagine you need to print a list that has \(N\) elements.

  2. Difficult to maintain. If we want to format each printed element with an asterisk or any other character, we would have to change four lines of code. While this might not be a problem for small lists, it would definitely be a problem for longer ones.

  3. Fragile. If we use it with a list that has more elements than what we initially envisioned, it will only display part of the list’s elements. A shorter list, on the other hand, will cause an error because it will be trying to display elements of the list that do not exist.

PYTHON 

odds = [1, 3, 5]
print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

OUTPUT 

1
3
5

ERROR 

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-3-7974b6cdaf14> in <module>()
      3 print(odds[1])
      4 print(odds[2])
----> 5 print(odds[3])

IndexError: list index out of range

Here’s a better approach: a for loop

PYTHON 

odds = [1, 3, 5, 7]
for odd_number in odds:
    print(odd_number)

OUTPUT 

1
3
5
7

This is shorter — certainly shorter than something that prints every number in a hundred-number list — and more robust as well:

PYTHON 

odds = [1, 3, 5, 7, 9, 11]
for odd_number in odds:
    print(odd_number)

OUTPUT 

1
3
5
7
9
11

The improved version uses a for loop to repeat an operation — in this case, printing — once for each thing in a sequence. The general form of a loop is:

PYTHON 

for variable in collection:
    # do things using variable, such as print

Using the odds example above, the loop might look like this:

Loop variable 'num' being assigned the value of each element in the list odds in turn andthen being printed

where each number (num) in the variable odds is looped through and printed one number after another. The other numbers in the diagram denote which loop cycle the number was printed in (1 being the first loop cycle, and 6 being the final loop cycle).

We can call the loop variable anything we like, but there must be a colon at the end of the line starting the loop, and we must indent anything we want to run inside the loop. Unlike many other languages, there is no command to signify the end of the loop body (e.g. end for); everything indented after the for statement belongs to the loop.

What’s in a name?

In the example above, the loop variable was given the descriptive name odd_number. We can choose any name we want for these loop variables. We might just as easily have chosen the name banana for the loop variable, as long as we use the same name when we invoke the variable inside the loop:

PYTHON 

odds = [1, 3, 5, 7, 9, 11]
for banana in odds:
    print(banana)

OUTPUT 

1
3
5
7
9
11

It is a good idea to choose variable names that are meaningful, otherwise it would be more difficult to understand what the loop is doing.

Here’s another loop that repeatedly updates a variable:

PYTHON 

length = 0
names = ['Curie', 'Noether', 'Turing']
for value in names:
    length = length + 1
print(f'There are {length} names in the list.')

OUTPUT 

There are 3 names in the list.

It’s worth tracing the execution of this little program step by step. Since there are three names in names, the statement on line 4 will be executed three times. The first time around, length is zero (the value assigned to it on line 1) and value is Curie. The statement adds 1 to the old value of length, producing 1, and updates length to refer to that new value. The next time around, value is Darwin and length is 1, so length is updated to be 2. After one more update, length is 3; since there is nothing left in names for Python to process, the loop finishes and the print function on line 5 tells us our final answer. We and Python know the loop is over by line 5 because of the indenting of the code block.

Note that a loop variable is a variable that is being used to record progress in a loop. It still exists after the loop is over, and we can re-use variables previously defined as loop variables as well:

PYTHON 

name = 'Rosalind'
for name in ['Curie', 'Noether', 'Turing']:
    print(name)
print(f'After the loop, `name` is set to {name}')

OUTPUT 

Curie
Noether
Turing
After the loop, `name` is set to Turing

Recall also that finding the length of an object is such a common operation that Python actually has a built-in function to do it called len:

PYTHON 

print(len([0, 1, 2, 3]))

OUTPUT 

4

len is much faster than any function we could write ourselves, and much easier to read than a two-line loop; it will also give us the length of many other things that we haven’t met yet, so we should always use it when we can.

Iterating over ranges

Python has a built-in function called range that generates a sequence of numbers. range can accept 1, 2, or 3 parameters.

  • If one parameter is given, range generates a sequence of that length, starting at zero and incrementing by 1. For example, range(3) produces the numbers 0, 1, 2.
  • If two parameters are given, range starts at the first and ends just before the second, incrementing by one. For example, range(2, 5) produces 2, 3, 4.
  • If range is given 3 parameters, it starts at the first one, ends just before the second one, and increments by the third one. For example, range(3, 10, 2) produces 3, 5, 7, 9.

From 1 to N

Using range, write a loop that prints the first 3 non-zero integers:

PYTHON 

1
2
3

PYTHON 

for number in range(1, 4):
    print(number)

Computing Powers With Loops

Exponentiation is built into Python:

PYTHON 

print(5 ** 3)

OUTPUT 

125

Write a loop that calculates the same result as 5 ** 3 using multiplication (and without exponentiation).

PYTHON 

result = 1
for number in range(0, 3):
    result *= 5
print(result)

Summing a list

Write a loop that calculates the sum of elements in a list by adding each element and printing the final value, so [124, 402, 36] prints 562

PYTHON 

numbers = [124, 402, 36]
summed = 0
for num in numbers:
    summed += num
print(summed)

Alternatively, we could have used the built-in sum function,

PYTHON 

numbers = [124, 402, 36]
summed = sum(numbers)
print(summed)

Iterating over strings

In Python, any iterable object may be looped over. This, for example, includes the characters in a string.

Understanding the loops

Given the following loop:

PYTHON 

word = 'oxygen'
for letter in word:
    print(letter)

How many times is the body of the loop executed?

  • 3 times
  • 4 times
  • 5 times
  • 6 times

The body of the loop is executed 6 times.

Using enumerate to iterate over lists

The built-in function enumerate takes a sequential container object (e.g., a list) and generates a new sequence of the same length. Each element of the new sequence is a pair composed of the index (0, 1, 2,…) and the value from the original sequence:

PYTHON 

odds = [1,3,5,7]
for index, odd in enumerate(odds):
    print(f'list_index={index} :: list_value={odd}')

OUTPUT 

list_index=0 :: list_value=1
list_index=1 :: list_value=3
list_index=2 :: list_value=5
list_index=3 :: list_value=7

The code above loops through odds, assigning the index to index and the value to odd.

Computing the Value of a Polynomial

Suppose you have encoded a polynomial as a list of coefficients in the following way: the first element is the constant term, the second element is the coefficient of the linear term, the third is the coefficient of the quadratic term, where the polynomial is of the form \(ax^0 + bx^1 + cx^2\).

PYTHON 

x = 5
coefs = [2, 4, 3]
y = coefs[0] * x**0 + coefs[1] * x**1 + coefs[2] * x**2
print(y)

OUTPUT 

97

Write a loop using enumerate(coefs) which computes the value y of any polynomial, given x and coefs.

PYTHON 

y = 0
for idx, coef in enumerate(coefs):
    y += coef * x**idx

List comprehensions

Often times we want to quickly generate a container object, like a list. So far, our only method involves the append internal method. Suppose we want to generate a list of the first five positive odd numbers:

PYTHON 

# create an empty list
odds = []
# loop over integers \in [0,4], append associated odd to odds list
for i in range(5):
    odds.append(2*i+1)
# enumerate over the odds, which provides two loop variables, the
# incremental count from zero `i` and the associated list value `odd`
for i,odd in enumerate(odds): 
    print(f'{i} : {odd}')

OUTPUT 

0 : 1
1 : 3
2 : 5
3 : 7
4 : 9

This is such a common task that most high-level languages — and even some low-level ones like Fortran — provide a syntactical sugar for quickly creating the same list, via list comprehension:

PYTHON 

odds = [2*i+1 for i in range(5)]
for i,odd in enumerate(odds): 
    print(f'{i} : {odd}')

OUTPUT 

0 : 1
1 : 3
2 : 5
3 : 7
4 : 9

Dictionary comprehension

Similarly, if we wanted to create a dictionary via repetition, we have the implied method of instantiating an empty object and appending to it. But there is a nuance when comparing to list iteration: dictionary objects do not work as expected with the enumerate method. Instead we must access the items() sub-method of the dictionary object,

PYTHON 

squares = {}
for i in range(5):
    squares[i] = i**2
for key,square in squares.items():
    print(f'The square of {key} is {square}')

OUTPUT 

The square of 0 is 0
The square of 1 is 1
The square of 2 is 4
The square of 3 is 9
The square of 4 is 16

A dictionary comprehension makes this all the more syntactically sweet:

PYTHON 

squares = {i:i**2 for i in range(5)}
for key,square in squares.items():
    print(f'The square of {key} is {square}')

OUTPUT 

The square of 0 is 0
The square of 1 is 1
The square of 2 is 4
The square of 3 is 9
The square of 4 is 16

There are also the submethods of keys() and values() for times when both pairs are unneeded.

Monitoring loop progress

Often times in scientific computing, the majority of a program’s execution will occur within a loop. For example, when solving a system of partial or ordinary differential equations, solvers typically must iteratively step forward in time. Without periodic reporting or indication of the loop’s status, it may feel like the program will never end. (We will see examples of this after the upcoming numpy and plotting lessons.) But for now it’s important to emphasize the existence of an extremely convenient external third-party module that provides rich progress bars for loops, tqdm:

PYTHON 

import tqdm
a = 0
for i in tqdm.tqdm(range(10**4)):
    for j in range(10**4):
        a += j
print(a)

OUTPUT 

42%|████████████                | 4233/10000 [00:03<00:04, 1183.17it/s]]

Key Points

  • Use for variable in sequence to process the elements of a sequence one at a time.
  • The body of a for loop must be indented.
  • Use len(thing) to determine the length of something that contains other values.
  • Use enumerate to obtain loop variables for a sequential object’s indices and values.
  • List and dictionary comprehensions provide a fast and convent way to initialize those objects.
  • Use the tqdm module to create rich progress bars that give a better indication of the loop’s status and provide rough benchmarks.