\chapter{Debugging}

\centerline{\includegraphics[width=0.7\textwidth]{xkcd_debugger}\rotatebox{90}{\footnotesize\url{www.xkcd.com}}}\vspace{4ex}


When writing a program from scratch we almost always make
mistakes. Accordingly, a quite substantial amount of time is invested
into finding and fixing errors. This process is called
\entermde{Debugging}{debugging}. Don't be frustrated that a
self-written program does not work as intended and produces errors. It
is quite exceptional if a program appears to be working on the first
try and, in fact, should leave you suspicious.

In this chapter we will talk about typical mistakes, how to read and
understand error messages, how to actually debug your program code and
some hints that help to minimize errors.

\section{Types of errors and error messages}

There are a number of different classes of programming errors and it
is good to know the common ones. Some of your programming errors will
will lead to violations of the syntax or to invalid operations that
will cause \matlab{} to \code{throw} an error. Throwing an error
ends the execution of a program and there will be an error messages
shown in the command window. With such messages \matlab{} tries to
explain what went wrong and to provide a hint on the possible cause.

Bugs that lead to the termination of the execution may be annoying but
are generally easier to find and to fix than logical errors that stay
hidden and the results of, e.g. an analysis, are seemingly correct.

\begin{important}[Try --- catch]
  There are ways to \code{catch} errors during \enterm{runtime}
  (\determ{Laufzeit}, i.e. when the program is executed) and handle
  them in the program.

\begin{lstlisting}[label=trycatch, caption={Try catch clause}]
  try
     y = function_that_throws_an_error(x);
  catch
     y = 0;
  end
\end{lstlisting}

This way of solving errors may seem rather convenient but is
risky. Having a function throwing an error and catching it in the
\code{catch} clause will keep your command line clean but may obscure
logical errors! Take care when using the \code{try}-\code{catch}
clause.
\end{important}


\subsection{Syntax errors}\label{syntax_error}
The most common and easiest to fix type of error. A
\entermde[error!syntax]{Fehler!Syntax@Syntax\texttildelow}{syntax error} violates the
rules (spelling and grammar) of the programming language. For example
every opening parenthesis must be matched by a closing one or every
\code{for} loop has to be closed by an \code{end}. Usually, the
respective error messages are clear and the editor will point out and
highlight most syntax errors.

\begin{lstlisting}[label=syntaxerror, caption={Unbalanced parenthesis error.}]
>> mean(random_numbers
                      |
Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.

Did you mean:
>>   mean(random_numbers)
\end{lstlisting}

\subsection{Indexing error}\label{index_error}
Second on the list of common errors are the
\entermde[error!indexing]{Fehler!Index@Index\texttildelow}{indexing errors}. Usually
\matlab{} gives rather precise infromation about the cause, once you
know what they mean. Consider the following code.

\begin{lstlisting}[label=indexerror, caption={Indexing errors.}]
>> my_array = (1:100);
>> % first try: index 0
>> my_array(0)
Subscript indices must either be real positive integers or logicals.

>> % second try: negative index
>> my_array(-1)
Subscript indices must either be real positive integers or logicals.

>> % third try: a floating point number
>> my_array(5.7)
Subscript indices must either be real positive integers or logicals.

>> % fourth try: a character
>> my_array('z')
Index exceeds matrix dimensions.

>> % fifth try: another character
>> my_array('A')
ans =
     65 % wtf ?!?
\end{lstlisting}

The first two indexing attempts in listing \ref{indexerror} are rather
clear. We are trying to access elements with indices that are
invalid. Remember, indices in \matlab{} start with 1. Negative numbers
and zero are not permitted.  In the third attemp we index using a
floating point number. This fails because indices have to be 'integer'
values.  Using a character as an index (fourth attempt) leads to a
different error message that says that the index exceeds the matrix
dimensions. This indicates that we are trying to read data behind the
length of our variable \varcode{my\_array} which has 100 elements.
One could have expected that the character is an invalid index, but
apparently it is valid but simply too large. The fith attempt finally
succeeds. But why? \matlab{} implicitely converts the character to a
number and uses this number to address the element in
\varcode{my\_array}. The character \varcode{'A'} has the ASCII code 65
and thus the 65th element of \varcode{my\_array} is returned.

\subsection{Assignment error}
Related to the indexing error, an
\entermde[error!assignment]{Fehler!Zuweisungs@Zuweisungs\texttildelow}{assignment
  error} occurs when we want to write data into a variable, that does
not fit into it. Listing \ref{assignmenterror} shows the simple case
for 1-d data but, of course, it extents to n-dimensional data. The
data that is to be filled into a matrix hat to fit in all
dimensions. The command in line 7 works due to the fact, that matlab
automatically extends the matrix, if you assign values to a range
outside its bounds.

\begin{lstlisting}[label=assignmenterror, caption={Assignment errors.}]
>> a = zeros(1, 100);
>> b = 0:10;

>> a(1:10) = b;
     In an assignment  A(:) = B, the number of elements in A and B must be the same.

>> a(100:110) = b;
>> size(a)
ans =
     110    1
\end{lstlisting}

\subsection{Dimension mismatch error}
Similarly, some arithmetic operations are only valid if the variables
fulfill some size constraints. Consider the following commands
(listing\,\ref{dimensionmismatch}). The first one (line 3) fails
because we are trying to add two vectors of different lengths
elementwise. The matrix multiplication in line 6 also fails since for
this operations to succeed the inner matrix dimensions must agree (for
more information on the matrixmultiplication see
box\,\ref{matrixmultiplication} in chapter\,\ref{programming}). The
elementwise multiplication issued in line 10 fails for the same reason
as the addition we tried earlier. Sometimes, however, things
apparently work but the result may be surprising. The last operation
in listing\,\ref{dimensionmismatch} does not throw an error but the
result is something else than the expected elementwise multiplication.

% XXX Some arithmetic operations make size constraints, violating them leads to dimension mismatch errors.
\begin{lstlisting}[label=dimensionmismatch, caption={Dimension mismatch errors.}]
  >> a = randn(100, 1);
  >> b = randn(10, 1);
  >> a + b
  Matrix dimensions must agree.

  >> a * b      % The matrix multiplication!
  Error using  *
  Inner matrix dimensions must agree.

  >> a .* b
  Matrix dimensions must agree.

  >> c = a .* b';  % works but the result may not be what you expected!
  >> size(c)
  ans =
       100    10
\end{lstlisting}



\section{Logical error}
Sometimes a program runs smoothly and terminates without any
complaint. This, however, does not necessarily mean that the program
is correct. We may have made a
\entermde[error!logical]{Fehler!logischer}{logical error}. Logical
errors are hard to find, \matlab{} has no chance to detect such errors
since they do not violate the syntax or cause the throwing of an
error. Thus, we are on our own to find and fix the bug. There are a
few strategies that should we can employ to solve the task.

\begin{enumerate}
\item Be sceptical: especially when a program executes without any
  complaint on the first try.
\item Clean code: Structure your code that you can easily read
  it. Comment, but only where necessary. Correctly indent your
  code. Use descriptive variable and function names.
\item Keep it simple.
\item Test your code by writing \entermde[unit test]{Modultest}{unit tests} that test every
  aspect of your program (\ref{unittests}).
\item Use scripts and functions and call them from the command
  line. \matlab{} can then provide you with more information. It will
  then point to the line where the error happens.
\item If you still find yourself in trouble: Apply debugging
  strategies to find and fix bugs (\ref{debugging}).
\end{enumerate}


\section{Avoiding errors}
It would be great if we could just sit down, write a program, run it,
and be done with the task. Most likely this will not happen. Rather,
we will make mistakes and have to bebug the code. There are a few
guidelines that help to reduce the number of errors.


\subsection{Keep it small and simple}

\shortquote{Debugging time increases as a square of the program's
  size.}{Chris Wenham}

\shortquote{Everyone knows that debugging is twice as hard as writing
  a program in the first place. So if you're as clever as you can be
  when you write it, how will you ever debug it?}{Brian Kernighan}

Break down your programming problems into small parts (functions) that
do exactly one thing and are thus easily testable. This has already
been discussed in the context of writing scripts and functions. In
parts this is just a matter of feeling overwhelmed by 1000 lines of
code. Further, with each task that you incorporate into the same
script the probability of naming conflicts (same or similar names for
variables) increases. Remembering the meaning of a certain variable
that was defined in the beginning of the script is simply hard.

Many tasks within an analysis can be squashed into a single line of
code. This saves some space in the file, reduces the effort of coming
up with variable names and simply looks so much more competent than a
collection of very simple lines. Consider the following listing
(listing~\ref{easyvscomplicated}). Both parts of the listing solve the
same problem but the second one breaks the task down to a sequence of
easy-to-understand commands. Finding logical and also syntactic errors
is much easier in the second case. The first version is perfectly fine
but it requires a deep understanding of the applied functions and also
the task at hand.

% XXX Converting a series of spike times into the firing rate as a function of time. Many tasks can be solved with a single line of code. But is this readable?
\begin{lstlisting}[label=easyvscomplicated, caption={One-liner versus readable code.}]
% the one-liner
rate = conv(full(sparse(1, round(spike_times/dt), 1, 1, length(time))), kernel, 'same');

% easier to read
rate = zeros(size(time));
spike_indices = round(spike_times/dt);
rate(spike_indices) = 1;
rate = conv(rate, kernel, 'same');
\end{lstlisting}

The preferred way depends on several considerations. (i) How deep is
your personal understanding of the programming language?  (ii) What
about the programming skills of your target audience or other people
that may depend on your code? (iii) Is one solution faster or uses
less resources than the other? (iv) How much do you have to invest
into the development of the most elegant solution relative to its
importance in the project? The decision is yours.


\subsection{Unit tests}\label{unittests}

The idea of unit tests to write small programs that test \emph{all}
functions of a program by testing the program's results against
expectations.  The pure lore of test-driven development requires that
the tests are written \textbf{before} the actual program is
written. In parts the tests put the \enterm{functional
  specification}, the agreement between customer and programmer, into
code. This helps to guarantee that the delivered program works as
specified. In the scientific context, we tend to be a little bit more
relaxed and write unit tests, where we think them helpful and often
test only the obvious things. To write \emph{complete} test suits that
lead to full \enterm{test coverage} is a lot of work and is often
considered a waste of time. The first claim is true, the second,
however, may be doubted. Consider that you change a tiny bit of a
standing program to adjust it to the current needs, how will you be
able to tell that it is still valid for the previous purpose? Of
course you could try it out and be satisfied, if it terminates without
an error, but, remember, there may be logical errors hiding behind the
facade of a working program.

Writing unit tests costs time, but provides the means to guarantee
validity.

\subsubsection{Unit testing in \matlab{}}

Matlab offers a unit testing framework in which small scripts are
written that test the features of the program. We will follow the
example given in the \matlab{} help and assume that there is a
function \varcode{rightTriangle()} (listing\,\ref{trianglelisting}).

% XXX Slightly more readable version of the example given in the \matlab{} help system. Note: The variable name for the angles have been capitalized in order to not override the matlab defined functions \code{alpha, beta,} and \code{gamma}.
\begin{lstlisting}[label=trianglelisting, caption={Example function for unit testing.}]
function angles = rightTriangle(length_a, length_b)
    ALPHA = atand(length_a / length_b);
    BETA = atand(length_a / length_b);
    hypotenuse = length_a / sind(ALPHA);
    GAMMA = asind(hypotenuse * sind(ALPHA) / length_a);

    angles = [ALPHA BETA GAMMA];
end
\end{lstlisting}

This function expects two input arguments that are the length of the
sides $a$ and $b$ and assumes a right angle between them. From this
information it calculates and returns the angles $\alpha, \beta,$ and
$\gamma$.

Let's test this function: To do so, create a script in the current
folder that follows the following rules.
\begin{enumerate}
\item The name of the script file must start or end with the word
  'test', which is case-insensitive.
\item Each unit test should be placed in a separate section/cell of the script.
\item After the \mcode{\%\%} that defines the cell, a name for the
  particular unit test may be given.
\end{enumerate}

Further there are a few things that are different in tests compared to normal scripts.
\begin{enumerate}
\item The code that appears before the first section is the in the so
  called \emph{shared variables section} and the variables are available to
  all tests within this script.
\item In the \emph{shared variables section}, one can define
  preconditions necessary for your tests. If these preconditions are
  not met, the remaining tests will not be run and the test will be
  considered failed and incomplete.
\item When a script is run as a test, all variables that need to be
  accessible in all test have to be defined in the \emph{shared
    variables section}.
\item Variables defined in other workspaces are not accessible to the
  tests.
\end{enumerate}

The test script for the \varcode{rightTriangle()} function
(listing\,\ref{trianglelisting}) may look like in
listing\,\ref{testscript}.

\begin{lstlisting}[label=testscript, caption={Unit test for the \varcode{rightTriangle()} function stored in an m-file testRightTriangle.m}]
tolerance = 1e-10;

% preconditions
angles = rightTriangle(7, 9);
assert(angles(3) == 90, 'Fundamental problem: rightTriangle is not producing a right triangle')

%% Test 1: sum of angles
angles = rightTriangle(7, 7);
assert((sum(angles) - 180) <= tolerance)

angles = rightTriangle(7, 7);
assert((sum(angles) - 180) <= tolerance)

angles = rightTriangle(2, 2 * sqrt(3));
assert((sum(angles) - 180) <= tolerance)

angles = rightTriangle(1, 150);
assert((sum(angles) - 180) <= tolerance)

%% Test: isosceles triangles
angles = rightTriangle(4, 4);
assert(abs(angles(1) - 45) <= tolerance)
assert(angles(1) == angles(2))

%% Test: 30-60-90 triangle
angles = rightTriangle(2, 2 * sqrt(3));
assert(abs(angles(1) - 30) <= tolerance)
assert(abs(angles(2) - 60) <= tolerance)
assert(abs(angles(3) - 90) <= tolerance)

%% Test: Small angle approx
angles = rightTriangle(1, 1500);
smallAngle = (pi / 180) * angles(1); % radians
approx = sin(smallAngle);
assert(abs(approx - smallAngle) <= tolerance, 'Problem with small angle approximation')
\end{lstlisting}

In a test script we can execute any code. The actual test whether or
not the results match our predictions is done using the
\code{assert()} function. This function basically expects a
boolean value and if this is not true, it raises an error that, in the
context of the test does not lead to a termination of the program. In
the tests above, the argument to assert is always a boolean expression
which evaluates to \code{true} or \code{false}. Before the first unit
test (``Test 1: sum of angles'', that starts in line 5,
listing\,\ref{testscript}) a precondition is defined. The test assumes
that the $\gamma$ angle must always be 90$^\circ$ since we aim for a
right triangle. If this is not true, the further tests, will not be
executed. We further define a \varcode{tolerance} variable that is
used when comparing double values (Why might the test on equality of
double values be tricky?).

\begin{lstlisting}[label=runtestlisting, caption={Run the test!}]
result = runtests('testRightTriangle')
\end{lstlisting}

During the run, \matlab{} will put out error messages onto the command
line and a summary of the test results is then stored within the
\varcode{result} variable. These can be displayed using the function
\code[table()]{table(result)}.

\begin{lstlisting}[label=testresults, caption={The test results.}, basicstyle=\ttfamily\scriptsize]
table(result)
ans =
  4x6 table

            Name                    Passed  Failed  Incomplete  Duration   Details
_________________________________   ______  ______  ___________  ________  ____________

'testR.../Test_SumOfAngles'          true   false   false        0.011566   [1x1 struct]
'testR.../Test_IsoscelesTriangles'   true   false   false        0.004893   [1x1 struct]
'testR.../Test_30_60_90Triangle'     true   false   false        0.005057   [1x1 struct]
'testR.../Test_SmallAngleApprox'     true   false   false        0.0049     [1x1 struct]
\end{lstlisting}

So far so good, all tests pass and our function appears to do what it
is supposed to do. But tests are only as good as the programmer who
designed them. The attentive reader may have noticed that the tests
only check a few conditions. But what if we passed something else than
a numeric value as the length of the sides $a$ and $b$? Or a negative
number, or zero?



\section{Debugging strategies}\label{debugging}

If you still find yourself in trouble you can apply a few strategies
that help to solve the problem.

\begin{enumerate}
\item Lean back and take a breath.
\item Read the error messages and identify the line or command where
  the error happens. Unfortunately, the position that breaks is not
  always the line or command that really introduced the bug. In some
  instances the actual error hides a few lines above.
\item No idea what the error message is trying to say? Google it!
\item Read the program line by line and understand what each line is
  doing.
\item Use \code{disp()} to print out relevant information on the command
  line and compare the output with your expectations.  Do this step by
  step and start at the beginning.
\item Use the \matlab{} debugger to stop execution of the code at a
  specific line and proceed step by step. Be sceptical and test all
  steps for correctness.
\item Call for help and explain the program to someone else. When you
  do this, start at the beginning and walk through the program line by
  line. Often, it is not necessary that the other person is a
  programmer or exactly understands what is going on. Rather, it is the
  own reflection on the problem and the chosen approach that helps
  finding the bug (this strategy is also known as \enterm{Rubber
    ducking}).
\end{enumerate}


\subsection{Debugger}

The \matlab{} editor (figure\,\ref{editor_debugger}) supports
interactive debugging. Once you save an m-file in the editor and it
passes the syntax check, i.e. the little box in the upper right corner
of the editor window is green or orange, you can set one or several
\entermde[break point]{Haltepunkt}{break points}. When the program is
executed by calling it from the command line it will be stopped at the
line with the breakpoint. In the editor this is indicated by a green
arrow. The command line will change to indicate that we are now
stopped in debug mode (listing\,\ref{debuggerlisting}).

\begin{figure}
  \centering
  \includegraphics[width=\linewidth]{editor_debugger.png}
  \titlecaption{\label{editor_debugger} Setting
    breakpoints.}{Screenshot of the \matlab{} m-file editor. Once a
    file is saved and passes the syntax check (the indicator in the
    top-right corner of the editor window turns green or orange), a
    breakpoint can be set. Breakpoints can be set either using the
    dropdown menu on top or by clicking the line number on the left
    margin. An active breakpoint is indicated by a red dot. The line
    at which the program execution was stopped is indicated by the
    green arrow.}
\end{figure}


\begin{lstlisting}[label=debuggerlisting, caption={Command line when the program execution was stopped in the debugger.}]
>> simplerandomwalk
6   for run = 1:num_runs
K>>
\end{lstlisting}

When stopped in the debugger we can view and change the state of the
program at this point, we can also issue commands to try the next
steps etc. Beware however, the state of a variable can be altered or
even deleted which might affect the execution of the remaining code.

The toolbar of the editor offers now a new set of tools for debugging:
\begin{enumerate}
\item \textbf{Continue} --- simply move on until the program terminates or the
  execution reaches the next breakpoint.
\item \textbf{Step} --- Execute the next command and stop.
\item \textbf{Step in} --- If the next command is a
  function call, step into it and stop at the first command.
\item \textbf{Step out} --- Suppose you entered a function with
  \emph{step in}. \emph{Step out} will continue with the execution and
  stop once you are back in the calling function.
\item \textbf{Run to cursor} --- Execute all statements up to the
  current cursor position.
\item \textbf{Quit debugging} --- Immediately stop the debugging
  session and stop further code execution.
\end{enumerate}

The debugger offers some more (advanced) features but the
functionality offered by the basic tools is often enough to debug a
program.


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