The goal of this tutorial is to introduce the fundamental ideas of programming in MATLAB. It requires no programming experience, but some familiarity with MATLAB is recomended. All background needed can be found on the tutorial Introduction to MATLAB.
The programming structures presented below apply to MATLAB. However, these structures look very similar in other computer languages, such as C, Java, Pascal, etc., so by understanding how loops, logical operations, etc., work in MATLAB, you will be well-prepared for beginning programming in other languages as well.
Many of the examples given may seem to be irrelevant to this course. However, by understanding the seemingly stupid and sometimes mathematically irrelevant examples and exercises in this tutorial, you will have all the background to write programs to solve all the homework problems.
A number of examples will be given below. They will be given as MATLAB code but the output which you will get when you run these programs will not be given. When going over this tutorial, you are recommended to implement the examples yourself and then run them in the MATLAB command window and carefully study the outcome and compare it to the code.
In case your code has errors, MATLAB will complain when you try to run the program in the command window. When this happens, try to interpret the error message and make necessary changes to you code in the editor. The error that is reported by MATLAB is hyperlinked to the line in the file that caused the problem. Using the mouse you can thus jump right to the line in your program that has caused the error. After you have made the changes, make sure you save your file before trying to run the program again in the command window.
Let's say that we want the user to enter some value that we want the program to work with. This can be done using the input command with the syntax
variable=input('text');
This command will print out text on the screen and then wait for the user to enter a number. The variable will now be assigned the number that the user entered. (Using this command for reading letters instead of numbers is slightly more complicated and will not be covered in this tutorial.)
Now it is time for our first example. The following program asks the user for an amount in dollars, and returns the value of this amount in a foreign currency.
Example 1.
clear exchange_rate = 0.5; amount = input('Give amount in dollars: '); amount_in_foreign_currency = exchange_rate*amount |
A good practice is to begin your code with clear, which erases all variables. If you do not do this, you can get errors when you run your program that are very hard to discover.
Logical operators
Operation: | MATLAB command: |
Logical and | & |
Logical or | | |
Negate | ~ |
Relational operators
Operation: | MATLAB command: |
Strictly less than | < |
Less than or equal to | <= |
Strictly greater than | > |
Greater than or equal to | >= |
Equal to | == |
Not equal to | ~= |
It is important to know the difference between = and ==. The former, =, is used when assigning a number to a variable, e.g., x=3;. The latter, ==, is used to check if two expressions are equal. This is illustrated in the examples below, but first we need to know what an if-statement is. When programming we often want the computer to check whether a statement is true or false and perform different operations depending on the result of this test. This can be done using a so-called if-statement. The syntax is given below.
if logical expression
commandselse commandsend |
Note that for each if, you need to "close" the if-statement with an end. Make sure the if:s and end:s always match! (This is a common source for programming errors.)
The content of this paragraph may have seemed abstract but by carefully studying the following three examples and doing Exercise 1 it will hopefully become clearer.
Example 2.
clear N = input('Give numerator: '); D = input('Give denominator: '); if D==0 'Sorry, cannot divide by zero'else ratio = N/Dend |
In the next example, we make MATLAB write something depending on which test our month "passes". To make MATLAB write text as output, use single quote ' around the text.
Example 3.
clear month = input('Give month number (1-12): ' ); if month==1 | month==3 | month ==5 | month==7 | month==10 | month==12 'Your month has 31 days'else if month==2end |
In the next example we use the command rem (remainder). The syntax is
rem(x,y)
and returns the remainder after the division of the two integers x and y.
Example 4.
clear number = input('Give an integer: ' ); remainder2 = rem(number,2); remainder3 = rem(number,3); if remainder2==0 & remainder3==0 'Your number is divisible by both 2 and 3'else if remainder2==0end |
Exercise 1. Write a "currency exchange program" similar to the one in Example 1 which can handle two different exchange rates, exchange_rate1 = 0.5 and exchange_rate2 = 0.25. Design the program to first ask for the amount in dollars and then ask the user which rate (represented by the numbers 1 and 2 respectively) he/she wants. Let the program return the amount in the requested foreign currency. |
for loop variable = startvalue : endvalue commandsend |
This loop will initate loop variable as start value, increment loop variable by 1 each step until end value is reached. Below follows a few examples of how to use for-loops.
Example 5.
clear for i=1:20 x(i)=i/7;end x |
In the following example we see a so-called nested for-loop. This is nothing else then a "loop within a loop". Note how we must "close" each for with an end. Make sure you understand how this example works!
Example 6.
clear for i=1:5 for j=1:5endA(i,j)=10*i+j;end A |
In the following example, make sure you understand the purpose of the variable mysum. This is a common way of performing summations when programming.
Example 7.
clear mysum = 0; for k=0:10 mysum = mysum+1/gamma(k+1);end e_approximation = mysum e_exact = exp(1) |
In the next example, notice how we have to "shift" the indexing of the vector. MATLAB must have non-zero, positive integers as vector- or matrix-indices! One of the most common mistakes when programming in MATLAB is that your program begins indexing at zero instead of one. Also note how by typing a percent sign (%) before text in the code, MATLAB does not interpret this text as code. It just serves as a comment for any person using the code. Commenting your code is essential when writing programs.
Example 8.
clear for k=0:70 x(k+1)=0.1*k; % Indices of vectors must be NON-ZERO!end semilogy(x,e) title('Approximation of e^x for x between 0 and 7') xlabel('x') ylabel('e^x') |
Exercise 2. Write a program that approximates PI by computing the sum . The more terms (i.e., the larger m) you keep in the summation, the more accurate your answer will be. (In fact, the series converges to PI as m goes to infinity.) See how many terms you need to approximate PI with 5 decimals. (Note: This is by no means the most efficient way to approximate PI, but the formula is quite beautiful...) |
Exercise 3. Use the sum given in Exercise 2 to approximate PI using 10, 100, 1000, 10000 and 100000 terms. For each of these number, compute the error of the approximation. Plot the error as a function of the number of terms used in the sum. |