ABSTRACT
We are now familiar with some of the most essential
elements of MATLAB® and Octave, namely, vectors and
matrices. We have learned how to manipulate them and
carry out important operations with them such as addition,
substraction, multiplication and, within the definition in the
software, even division. Similarly, we know how to address
and extract individual elements as well as sequences of
In this chapter we turn our attention to one of the distin-
guishing features of MATLAB and Octave, i.e. the plotting
and visualisation capabilities integrated with the devel-
opment environment itself. Whereas other programming
environments do not include a way to produce plots and
graphs, MATLAB and Octave enable us to merge data visu-
a
and Octave. In this chapter we are going to see how to
y(x) = cos(4x), (4.1)
and imagine that we are interested in creating a graph of
this function in the interval 0 ≤ x ≤ pi. This can be easily done by
A common and simple approach is to take equally spaced
points along the x values. We can thus have n + 1 points a distance h apart from each other; for example, in the case of n = 20 we can write:
This will therefore create a set of points stored in the vari-
able x. We could also use the command linspace, whose
which generates a vector with n points at an equal distance
and the case
It is now possible to evaluate y at the various points given by the values stored in the vector x:
Finally the plot of the points calculated above can be ob-
The result of the commands above is shown in Figure 4.1,
where it is clear that the number of points used is small
Note that we need to specify N − 1 so that the colon notation generates a vector with N elements. All we need to do now is repeat the calculations and recreate the plot with the
As we can see, the curve is now much smoother and closer
to what we imagine as a plot for the cosine function. The
number of points can further be increased, but care must
be taken when dealing with larger and more complicated
problems, as an increased number of points may result in a
Although we have now been able to create a plot for the
desired function, we know that appropriate labels and
deal with
The plots shown in Figures 4.1 and 4.2 do show the
main characteristics of the function depicted, but they can
be made more useful by adding further information such as
a helpful and explanatory title, labels for the axes used and
perhaps even a legend for the functions plotted. Further-
more, we can increase or decrease the fonts, manipulate the
this can be
4.2.1 Titles and Labels
It is very useful to add a title that describes the plot as
well as information about what it is that is being plotted
along each of the axes. In order to add a title and label
the axes in the plot, we use the commands title, xlabel
and ylabel. Try out the following commands for the plot
generated in the previous section; the result can be seen in
The strings enclosed in single quotes can be (almost) any-
thing we choose. Some simple LATEX commands are avail-
able for formatting mathematical expressions and Greek
characters. More information about this can be seen in
4.2.2 Grids
Sometimes it is useful to show a grid that helps guide
the eye when looking at a plot. For example, a dotted grid
removed
with a blue solid line. A more general command to create a
From the discussion in the previous sections we know the
meaning of the first two arguments passed to the plot com-
is a
tation marks): the first character of the string specifies the
colour of the line to be plotted, and the second corresponds
to the type of line style. In the example above, b stands for
blue, and - represents a solid line. The options for colours
and styles are shown in Table 4.1. Please note that we can
In some cases it may be desirable to present several
plots in the same figure, provided that there is enough
space to show the plots. We can easily achieve this with the
Notice that the single plot command is taking two plot
specifications, i.e. six arguments in total, three per plot. In
the example above we are asking MATLAB and Octave
to plot the y = x function in a blue solid line and the y = sin(4x) in a black dashed line.
