LESSON 9: Program control questions

FOCUS QUESTION: How can I execute different code depending on the data?

Contents

EXAMPLE 1: Simulate tossing a coin (selection using if-else)

    toss = rand(1, 1);            % Pick a value at random between 0 and 1
    if toss <= 0.5                % Test against the value 0.5
        fprintf('Tossed heads\n'); % Say its heads if toss is less 0.5
    else
        fprintf('Tossed tails\n'); % Say its tails if toss is less 0.5
    end;

Tossed tails

Questions Answers
Why does the output change when I execute this cell multiple times? The if statement gives alternative paths of execution, and only one of the two fprintf statements executes each time. The branch is determined by the "random" value generated by rand.
Does rand produce truly "random" values? The rand function generates "pseudorandom" values that are distributed uniformly in (0, 1). The values are not correlated and so they can simulate picking numbers at random or tossing a coin. However, they appear in a well-defined, repeatable sequence so they are not truly random. The fact that the sequence is repeatable is very useful for repeating experiments.
Does rand ever generate a value that is exactly 0 or exactly 1? No, the output of rand is strictly between 0 and 1, exclusive.
What do the parameters of the rand function do? The rand function generates an array of random numbers and the parameters specify the size of the array. In this example, rand generates a single value (i.e., a 1 x 1 array). The call rand(2, 3) generates an array with 2 rows and 3 columns.
Can each branch of the if contain more than one statement? Yes, you can put any number of statements in each section.
What happens after the selected branch of the if executes? MATLAB continues execution with the statement after the end.

EXAMPLE 2: Output the square roots of first 3 integers (simple for loop)

    for k = 1:3               % The loop index k takes values 1, 2, 3
      fprintf('sqrt(%g) = %g\n', k, sqrt(k));
    end;

sqrt(1) = 1
sqrt(2) = 1.41421
sqrt(3) = 1.73205

Questions Answers
How many times is this loop executed? MATLAB executes statements between the for and the end 3 times. Each time, the loop variable k takes on one of the values in the list: 1, 2, 3.
Does a loop body always contain just one statement? No, you can put as many statements as you want between the for and the end.
Do I always have to use k for the loop variable? No, you can use any loop variable name that you want.
Does the loop variable have to take on consecutive integral values? No, you can specify any list of values (e.g., for x = [1.3, 2.2, 4.2, 5.1]).
Can I modify the loop variable inside the loop? Technically you can. However, it is highly recommended that you do not.
What is the value of the loop variable after the loop completes? Assuming that you following good programming practice and do not modify the loop variable inside the loop, the loop variable will have the last value in the list. For this example, the loop variable k will have the value 3.
What happens after the loop finishes? MATLAB continues execution with the statement after the end.

EXAMPLE 3: Sum the square roots of the first 10 integers (accumulation using a for loop )

    sumSqrts = 0;               % Need a variable to accumulate sum
    for k = 1:10                % Loop over the values k = 1, 2, ... 10
      sumSqrts = sumSqrts + sqrt(k);  % Add the next sqrt root to total
    end;
    fprintf('Sum of square roots is %g\n', sumSqrts);

Sum of square roots is 22.4683

Questions Answers
What does the statement sumSqrts = sumSqrts + sqrt(k) mean? Recall that the equals (=) is the assignment operator, not test for equality. This statement evaluates the right hand side by adding the current value of sumSqrts and the square root of k. MATLAB assigns the result to the variable on the left of the =. In this case sumSqrts receives the result.
What does the statement sumSqrts = sumSqrts + sqrt(k) actually do? This statement accumulates a sum (of the square roots of the first 10 integers).
What happens if I remove the sumSqrts = 0 statement? MATLAB will terminate with an error the first time through the loop because the assignment statement requires that sumSqrts have a value.
What happens if I move the sumSqrts = 0 statement inside the body of the for loop? MATLAB sets sumSqrts to 0 each time and so instead of accumulating a sum, sumSqrts only has the square root of 10 on loop completion.
Why was the area under the square root curve relevant in this example? Summing up values of a function at integer valuse is equivalent to adding up the areas of rectangles that have height that is the function and width of 1. The result is a rough approximation to the area under the curve of the function. If you have taken integral calculus, the result will be meaningful. Otherwise, ignore it.

EXAMPLE 4: Simulate tossing coin 50 times (for loop with selection and accumulation)

    numTosses = 50;            % Number of times to toss the coin
    numHeads = 0;              % Need a variable to accumulate total heads
    for k = 1:numTosses        % Loop over the values k = 1, 2, ... numTosses
       if rand(1, 1) <= 0.5    % Add to head count if 'tossed a head'
           numHeads = numHeads + 1;
        end;
    end;
    fprintf('%g heads in %g tosses\n', numHeads, numTosses);

29 heads in 50 tosses

Questions Answers
How many times is this loop executed? MATLAB executes this loop 50 times, one for each value of k in the list 1, 2, ..., 50.
How many times is the statement numHeads = numHeads + 1 executed? MATLAB only executes this statement when the result of rand is less than 0.5. On average, this happens half the time. However, results will vary each time you execute the cell, just as the results of tossing a coin 50 times will vary.
Which end statement closes the loop? The last end statement closes the loop. The other end statement finishes the if.

EXAMPLE 5: Alternative implementation of coin toss simulation (vector indexing)

    timesToTosses = 50;                  % Number of times to toss the coin
    randTosses = rand(timesToTosses,1);  % Create vector of "tosses"
    numHeads = sum(randTosses <= 0.5);   % How many were heads?
    fprintf('%g heads in %g tosses\n', numHeads, numTosses);

27 heads in 50 tosses

Questions Answers
How big is randTosses? The randTosses variable has 50 rows and 1 column.
How big is randTosses <= 0.5? The result is a logical array with 50 rows and 1 column. The entries are 1's when the corresponding entries of randTosses are less than 0.5.
Why does sum(randTosses <= 0.5) give the number of heads? The result counts the number of values in randTosses that are less than 0.5. We have assigned the values of rand that are less than or equal to 0.5 to mean heads.
Could I choose heads to be sum(randTosses > 0.5) to mean heads? Yes, the assignment is arbitrary as long as you designate half of the values in (0, 1).

EXAMPLE 6: Load the sleep diary data

    load diaries.mat;                        % Load the sleep diaries

EXAMPLE 7: Output a message if any subjects awoke after 3:30 pm

    wakeHours = (wakeTimes - floor(wakeTimes))*24; % Calculate the wake-up hours
    lateWakeup = sum(sum(wakeHours > 15.5));       % How many late wake-ups?
    if  lateWakeup > 0                             % See if any late wake-ups
        fprintf('%g wake-ups after 3:30 pm\n', lateWakeup);
    end;

30 wake-ups after 3:30 pm

Questions Answers
What is the size of wakeHours? The wakeHours variable has 21 rows and 144 columns.
What is the size of wakeHours > 15.5? The variable holds an array that is the same size as wakeHours. It has 1's where the corresponding entries of wakeHours are greater than 15.5 and 0's elsewhere.
Why do I need two sum functions to find the total? Since wakeHours > 15.5 is a 21 x 144 array, sum(wakeHours > 15.5) is a row vector size 1 x 144 containing the column sums. To find the overall total, you need to add up these column sums. Hence, the nested sum functions.

EXAMPLE 8: Output subject number and gender for subjects with at least 1 wake-up after 3:30 pm

Create a new cell in which you type and execute:

    timesLate = sum(wakeHours > 15.5);  % Times each subject woke up late
    fprintf('Subjects who had a least one wake-up after 3:30 pm:\n');
    for k = 1:length(timesLate)
        if timesLate(k) > 0
          fprintf('Subject %g: a %s with %g late wake-ups\n', ...
            k, gender{k}, timesLate(k));
        end;
    end;

Subjects who had a least one wake-up after 3:30 pm:
Subject 2: a female with 1 late wake-ups
Subject 7: a male with 1 late wake-ups
Subject 8: a female with 1 late wake-ups
Subject 40: a female with 1 late wake-ups
Subject 46: a male with 3 late wake-ups
Subject 66: a male with 1 late wake-ups
Subject 70: a female with 1 late wake-ups
Subject 71: a female with 1 late wake-ups
Subject 73: a female with 1 late wake-ups
Subject 86: a female with 5 late wake-ups
Subject 101: a male with 4 late wake-ups
Subject 118: a female with 3 late wake-ups
Subject 125: a male with 2 late wake-ups
Subject 134: a female with 3 late wake-ups
Subject 142: a female with 2 late wake-ups

EXAMPLE 9: Output the subject number and gender of the first student in section 3 (break)

    sect3 = section == 3;            % True (1) for subjects in section 3
    for k = 1:length(sect3)          % Here k = 1, 2, ... subject number
       if sect3(k)                   % If subject is in section 3
            fprintf('First subject in section 3 is a %s with subject number %g\n', ...
                gender{k}, k);
            break;                   % Get out of the loop, we done
       end;
    end;

First subject in section 3 is a female with subject number 2

Questions Answers
What does the break do? The break provides a controlled way to get out of a loop without going through all of the iterations. The break causes the statement after the innermost enclosing loop to be the next one executed.
Does break transfer control out of all loops? No, break only "breaks" out of the innermost enclosing loop.
Does it matter that the break appears in an if-else? No, the break is not affected by if-else. However, you will often see break as part of an if-else because you will usually only want to "break" out of the loop under certain circumstances.

EXAMPLE 10: Using find to perform same task as EXAMPLE 8

    pFirst = find(section == 3, 1, 'first'); % Find position of first subject in section 3
    fprintf('First subject in section 3 is a %s with subject number %g\n', ...
                gender{pFirst}, pFirst);

First subject in section 3 is a female with subject number 2

Questions Answers
Is the find better for solving this problem than the loop of EXAMPLE 8? Generally, indexing code is shorter and clearer than loops. MATLAB also has optimized indexing operations. However, in general the approach you choose is up to you. Often, it is possible to solve the problem either way.
What does the second argument of find represent? The second argument of find specifies the number of items to be returned. The find statement of this example finds the first subject in section 3. You have the option of returning the k first items, where k is a positive integer.
What if there are no items satisfying find's condition? The find function returns an empty array in this case.

EXAMPLE 11: Output sections that have subjects with late wake-ups (continue)

    wakeHour = 12;                     % Wake hour to check
    averWake = mean(wakeHours);        % Compute the average wake up time for all subjects
    for s = 0:3                         % Check each section (0, 1, 2, 3)
       sectWake = averWake(section==s); % Pick out wakeups for section s
       numLate = sum(sectWake >= wakeHour);   % How many are after wakeHour?
       if numLate == 0                  % Skip this section if no late ones
           continue;
       end;
       fprintf('Section %g has %g subjects with mean wake-up after %g\n', ...
               s, numLate, wakeHour);
    end;

Section 2 has 2 subjects with mean wake-up after 12
Section 3 has 3 subjects with mean wake-up after 12

Questions Answers
What does the continue function do? The continue function skips the remaining statements in the loop and goes on to the next loop iteration.
What if the continue is the last statement in the loop so there is nothing to be skipped? The continue doesn't hurt anything.
What happens when continue is encountered on the last iteration of the loop? Control transfers to the first statement outside the loop.

EXAMPLE 12: Output a table of early wake-ups using a loop

    earlyWake = 6;
    fprintf('\n\n\tEarly wake-ups\n');
    fprintf('Subj\tSect\tGender\tAver Wakeup\n');    % Print out a title
    for k = 1:length(averWake)           % Here k = 1, 2, ... subject number
       if averWake(k) >= earlyWake       % Skip subjects who awoke later
           continue;
       end;
       fprintf(' %g\t  %g\t%s\t  %g\n', k, section(k), gender{k}, averWake(k));
    end;


	Early wake-ups
Subj	Sect	Gender	Aver Wakeup
 32	  1	male	  5.87253
 91	  2	female	  5.50243
 140	  3	female	  5.68481

This lesson was written by Kay A. Robbins of the University of Texas at San Antonio and last modified on 31-Dec-2010. Please contact krobbins@cs.utsa.edu with comments or suggestions. The image is a photo of a silver Dekadrachm (Greek) from about 400 B.C. taken by Carl Malamud on 12/14/05 and available at http://commons.wikimedia.org/wiki/File:Ancient_Greek_Silver_Coin_%28Dekadrachm%29,_rev,_about_400_B.C.E..jpg.


Published with MATLAB® 7.14