Foundations of computer programming in MATLAB — Loops

The idea of loops

Loops allow us to repeat the same snippet of code. Of course, we could just copy/paste it a bunch of times, but that has two major limitations:

1. we have to hard-wire in the number of times to repeat it and
2. it looks like 💩.

And remember: if it looks like 💩, it probably is 💩.

The for loop

We consider first the for loop, which repeats the same snippet of code a pre-determined number of times. The syntax is shown in the following “pseudocode.””

for INDEX = ARRAY
    SNIPPET OF CODE
end

Here’s a specific example.

for i = 2:2:10
    disp(['i equals ',num2str(i)])
end

The interpreter first assigns i = 2, then executes the snippet, which prints 'i equals 2'. Then it it assigns i = 4, then it executes the snippet again, which prints 'i equals 4'. Et cetera. The snippet will be executed length(2:2:10) times.

This is wildly useful. Let’s actually do something in a for loop.

v = zeros(9,1);     % preallocate v
for i = 2:length(v)
  v(i) = v(i-1) + 5;
end
disp(v)

Loops are not the most efficient choice for some tasks. When efficiency matters, we try to eliminate loops, especially for loops, by using “vectorized” operations. For instance, we could have obtained the same v from the loop above with the following code.

v = 0:5:40;

But sometimes we must compute something that is not so easily constructed otherwise. In these cases, we often just use it. Here’s one such example.

v_rand = randi(10,50,1);    % vector of random integers between 1 and 10
for i = 1:length(v_rand)
  if v_rand(i) > 5
    disp('big')
  else
    disp('little')
  end
end

In this loop, there was no simple substitute for going through each value of v_rand and testing it.

Exercises

• Use a for loop to create a 10 by 1 array that has its first value equal to 10 and each consecutive value thereafter equal to the square root of the previous.
• Use a for loop to perform a simulation to estimate the probability of rolling a 1 on a six-sided die on two consecutive rolls. How many trials did you need to get close to the true probability?

The while loop

The while loop evaluates a conditional statement at the beginning of each loop to determine whether or not to evaluate the contained snippet. Here’s the pseudocode.

while CONDITION
  SNIPPET OF CODE
end

If CONDITION evaluates to 1 (true), the snippet is evaluated. After the snippet is evaluated, CONDITION is evaluated again to see if it is still true. Et cetera.

Here’s an example.

secret_number = randi(5);
not_yet_guessed = true;
while not_yet_guessed
  guess = input('Guess an integer between 1 and 5: ');
  if guess == secret_number
    disp('you win!')
    not_yet_guessed = false;
  else
    disp('Nope. Try again: ')
  end
end

Notice that if we never guess correctly, we just keep repeating the loop! While loops can do that. It’s nice because we don’t have to know beforehand how many times we need to repeat the loop, but it can also be dangerous. What if you enter had made it an integer between 1 and 1e5? You’d be guessing a while! Or, worse yet, you might make a while loop that never stops running. For instance, see the following example.

i_am_awesome = true;
while i_am_awesome
  disp('Yes, so awesome.')
end

This loop never ends because it never changes the condition: i_am_awesome is always true. If you happen to start running such a loop, you can exit it in the Command Window by typing control+c (Windows) or command+. (OS X).

Exercise

Use a while loop to test the probability of rolling snake eyes (two 1s), again. This time, simulate until the estimate changes less than $1\ \%$ from the previous estimate.