Basic Programming Control : Decision Making                                 (last updated  9/9/99)

The information in this tutorial is located in the MATLAB manual. Any page or section numbers refer to the following:

The Student Edition of MATLAB, Version 5, The MATH WORKS Inc. Prentice-Hall, 1997.

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This tutorial contains the following sections;

Introduction

for Loops

while Loops

Example Problem - while Loop

Breaking Out of for and while Loops

if-else-end Statements

Example Problem - for Loop and if-else-end Statement

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Introduction

Like other programming languages, MATLAB allows the control of command execution based on a decision making structure. MATLAB has three structures to control decision making:

for loops
while loops
if-else-end structures

Each of these structures often involves numerous commands. Therefore, they should always be put in m-files.

Information related to the use of these commands is located in Chapter 11 of the MATLAB manual.

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for Loops - Section 11.1

for loops allow for a group of MATLAB commands to be repeated a fixed, predetermined number of times. The general form is:

for x = array
         group of commands
end
 

The commands are executed once for every column of the array. At each iteration, x is assigned to the next column of the array. It is best to use an integer counter array.

for n = 1:6
     x(n) = 2^n (Note that the MATLAB prompt ( >> ) doesn't appear.)
end

x =
     2
x =
    2   4
x =
   2   4   8
x =
   2   4   8   16
x =
   2   4   8   16   32
x =
   2   4   8   16   32   64
 

Notice that MATLAB prints x at every loop. You should suppress printing during the calculation, then print x after exiting the loop.

Write the simple m-file given here.
for n = 1:6
     x(n) = 2^n;
end
 x

The Command Window output looks like this
x =
   2   4   8   16   32   64

You cannot short-circuit the loop by reassigning the loop variable, n, within the loop.
 

While using an array such as n = 1:6 is the most common way of using a for loop, any array can be used.  Here is a short m-file.

data = [ 3 9 45 6 ];
for n = data
     result = n*3
end

Here is the output

result =
    9
result =
    27
result =
    135
result =
    18
 

While this is possible, it is not recommended.  Use the following structure to accomplish the same calculation.

data = [ 3 9 45 6 ];
for n = 1:4
    result(n) = data(n)*3;
end

>> result
result =
   9   27   135   18

By keeping 'n' as an integer loop counter it is much easier to organize and access arrays.
 

for loops can be nested, ie. stacked within each other.

for n = 1:4

    for m = 1:3
        c(n,m) = 2*n + 3*m;
   end

end

>> c
c =
   5    8   11
  7   10  13
  9   12  15
11   14  17
 

Note that for loops are not necessary for all repeated calculations. In some cases the element-by-element dot notation can be used.

 n = 1:6;
 x = 2 .^ n        % Note the ( .^ ) notation.

x =
   2   4   8   16   32   64

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while Loops - Section 11.2

As opposed to for loops which execute a fixed number of times, while loops evaluate a group of commands an indefinite number of times. The general form of the while loop is:

while expression
     commands
end

The commands between the while and end statements are executed as long as all elements in expression are True.

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Example Problem - while Loop

The following example increases a number by 50 percent until the value exceeds 100.

• Click on FILE / NEW / M-FILE. If you are editing a previously created m-file click on FILE / OPEN M-FILE, then select the file from the list. Alternately you can choose the file from the quick list at the bottom of the FILE menu.
• Type the following list of MATLAB commands They aren't started with >> because the MATLAB prompt doesn't appear in an m-file.

Here is the m-file
___________________________________________________________________________________________________________________________

clear n t value             %  This statement clears any old values. (not required, but a good idea
n = 1;                        %  n and t are initialized
t =1;
value(n) = t;

while t<100              %  The indenting is only to clarify where the while loop begins and ends
   t = t*1.5;
   n = n + 1;
   value(n) = t;
end

value'                     %  This statement displays the created array of values
__________________________________________________________________________________________________

• Save the m-file to the any directory with any name you want.
• Return to the MATLAB workspace, change to the proper directory and enter the following:

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Breaking Out of for and while loops

You can jump out of loops by using the break command. Inside the loop you would use a section of code looking something like this;

if t > 100
   break
end

If your not in a loop the break command stops execution of the program.

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if-else-end Structures - Section 5.13.3

This structure causes a sequence of commands to be conditionally evaluated based on a relational test. In the simplest form we decide whether or not to evaluate a list of commands. In more advanced structures we can choose which of many command lists to evaluate.

The simplest if-else-end structure is:

if expression
     commands
end

The commands are evaluated if all elements of expression are True.
 

For two alternatives the structure is:

if expression
     commands evaluated if expression is True
else
     commands evaluated if expression is False
end
 

For three or more alternatives:

if expression1
     commands evaluated if expression1 is True
elseif expression2
     commands evaluated if expression2 is True
elseif expression3
     commands evaluated if expression3 is True
else
     commands evaluated if no expression is True
end

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Example Problem - for Loop and if-else-end Statement

Type the following commands into an m-file. Remember to use semi-colons to suppress display until the calculations are complete. Indenting is not necessary, but helps the readability.

for n = 1:20

    if n < 6
         x(n) = n;
    elseif n < 11
        x(n) = 2*n;
    elseif n < 16
        x(n) = 3*n;
    else
        x(n) = 4*n;
    end

end

x
____________________________________________________________

Save the file as test.m. and return to the Command Window.

>> test
x =
Columns 1 through 12
   1   2   3   4   5   12   14   16   18   20   33   36

Columns 13 through 20
   39   42   45   64   68   72   76   80

Note that once an expression is True, all following expressions are ignored even if they are also True. When n < 6 the n < 11, n < 16 etc. expressions are ignored. Note that you need an end statement for both the if structure and the outer for loop.