After you have written a program, you can execute it. In most cases this is done by typing the name of the (script) m-file in the Command Window, pressing the F5 key or selecting the symbol \includegraphics[width=.4cm]{ch6_run}. Sometimes you will then get error messages, i.e. red lines in the command prompt, warnings, or something you do not expect happens.

In most cases, a MATLAB error message is clear enough to enable you to improve your program. This is especially the case with syntax errors, a forgotten end command or operations with matrices that do not have the correct size (e.g., you have forgotten to transpose). When you do not understand the error or if the program does run but gives unexpected results, you will have to debug the program.

The simplest way of debugging is to look at intermediate results. You can have these printed on your screen by omitting the semicolon at the ends of the corresponding lines. For example, this enables you to keep track of what happens to a certain variable in a loop.

Another, somewhat more intricate option, is to use the MATLAB Debugger. This is built into the Editor, and allows you to go through the program step by step, so that you can see where the error occurs. You can also indicate so-called break points. The program then runs from break point to break point and pauses at these break points. Type doc debug for more info, the link under "GUI Alternatives" may be helpful as well.

Example 6.7: Suppose you want to create an $ 10 \times 8$ array $ B$ , where each element $ b_{ij}$ is chosen randomly, with uniform distribution in [0,1]. Afterwards, create an array $ C$ , such that $ c_{ij}=1$ if $ b_{ij}<\sqrt{\bar{B}}$ , and $ c_{ij}=0$ otherwise, where $ \bar{B}$ represents the mean of the squared elements of $ B$ , i.e. $ \displaystyle \bar{B}=\frac{1}{mn}\sum_{i=1}^m\sum_{j=1}b_{ij}^2.$

Hereto, first the following program is written, where the first two characters of each line represent the line numbering:

 1 %Program to create B with random elements, and C according to the text
 3 %% give size of matrices, initialise matrices C
 4 sh=8;    %horizontal size
 5 sv=10;   %vertical size
 7 B=zeros(sv,sh);
 8 C=zeros(sv,sh);
10 %% compute random elements of B
11 B=rand(sv,sh)
13 %% Show outputs of B in command window
14 B
15 Bbar=mean(B.^2)
17 %% Create C
18 for m=1:sv;
19     for n=1:sh
20         if B(n,m)<sqrt(Bbar);
21             C(n,m)=1;
22         else
23             C(n,m)=0;
24         end
25     end
26 end
28 %% Show C
29 C
However, running this file in MATLAB yields outputs for $ B$ and $ Bbar$ and the following error message:
??? Attempted to access B(1,9); index out of bounds because size(B)=[10,8].

Error in ==> Untitled at 20
        if B(n,m)<sqrt(Bbar);
Apparently, the element $ B_{1,9}$ is not defined, although MATLAB tries to read it. Since $ B$ was supposed to be a $ 10 \times 8$ matrix, this element $ B_{1,9}$ should not be attempted to read. Thus, in the above m-file the indices $ n$ and $ m$ are interchanged in line 20,21 and 23. To repair this bug, these lines are changed to:
20         if B(m,n)<sqrt(Bbar);
21             C(m,n)=1;
23             C(m,n)=0;

Now, MATLAB indeed returns a $ B$ , $ Bbar$ and $ C$ . This does not mean this answer is correct!

Checking the intermediate outputs, $ Bbar$ is not correct, since:

Bbar =
    0.2960    0.1812    0.4881    0.3324    0.3646...
is not a scalar, though an row vector with 8 elements. With help mean we find:
.. For matrices, MEAN(X) is a row vector containing the mean
value of each column...
Thus, we have to change line 15 to:
15 Bbar=mean(mean(B.^2)')
Note, that this command takes the mean of elements of the previously found vector mean(B.^2). Hereto, this row vector is first transposed with '. Now, the m-file is working properly.

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Esteur 2010-03-22