Basic 2-d Plot Commands

Basic 2-d Plot Commands

The basic command for plotting in Matlab is: plot(x,y). The important thing to remember is that in Matlab, variables such as x and y are matrices, which must be of the same size. The plot command simply creates a figure window and plots the data in the variable x versus those in y and interpolates linearly between the points. If x is a vector and y are a matrix, then plot(x,y) will plot the rows or columns of y versus the vector x, depending on whether the row or column length matches the length of x.

We are interested in using Matlab to plot functions. The important point is: all built in functions in Matlab are vectorized. This means that if x is a matrix, then the command sin(x) will create a matrix of the same size whose entries are computed by taking the sine of each entry of x. Hence, to create a plot of sin(x) on say the interval [-pi,pi] we would use:

>>x=-pi:pi/20:pi;
>>plot(x,sin(x))

The first line creates a vector of data for the independent variable; the step size is pi/20. To find out how long the vector is type

>>length(x) % no semicolon produces output

ans = 41 % this is the form of output

Alternatively, we could type

>>size(x)

ans = 1 41 % x is a row vector of length 41

Multiple plots on the same axis can be done in two ways.

>>x=-pi:pi/20:pi;
>>plot(x,sin(x))
>>hold on % this command forces the same set of axis for further plots
>>plot(x,cos(x))
>>grid on % places a grid on the axis
>>hold off % future plot commands will go to a new set of axis

Alternatively, the same thing can be accomplished with the command

>>plot(x,sin(x),x,cos(x))

Either way produces something like the following output.



Alternatively, one may wish to plot the two functions in the same figure window but on a different set of axes. The command is

>>subplot(1,2,1),plot(x,sin(x))
>>grid on
>>subplot(1,2,2),plot(x,cos(x))
>>grid on

NOTE: If you forget to type grid on, or any other axis command below after the first plot, simply click on the axis region and then type the command.

The output looks like:



Several observations are in order:

The x-axis ranges from -4 to 4, not matching the original data.
Except for color, we cannot distinguish between the graphs.
The axes are not labeled.
Are there other line styles?
There is no title on the figure.
Can we control the tick mark positions on the x and y axes?
Axis commands:

axis tight (Sets axis limits to the range of the plotted data).
axis([xmin xmax ymin ymax]) (Used before the plot command, sets the limits as given in the vector)
axis equal (Set the aspect ratio so that equal tick mark increments have the same size on each axis)
axis normal (Restore the axis box to full size and removes any restriction on scaling)
axis off (Turn off the axis, tick marks, and background)
axis on (Turn on the axis, tick marks, and background)
Line styles. The curves depicted in a given set of axis can have a variety of line styles. For example

>>plot(x,sin(x),x,cos(x),'--') % plots sin(x) and cos(x) on the same axis with cosine plotted with a dashed line

>>plot(x,sin(x),'LineWidth',2) % plots sin(x) with line thickness of 2 points; default is 0.5; possible choices 2,3,4.

Labeling the axis:

xlabel('string') % string represents the desired label
ylabel('string')
zlabel('string') % For use in 3-d plots
Annotating the plot:

legend('string1','string2',.....,m)
The strings string1, string2, etc are the desired labels for the different functions plotted. The variable m placed at the end specifies the position of the legend box: m=1, upper right hand corner, m=2 upper left hand corner, m=3 lower left hand corner, m=4 lower right hand corner, m=-1 to the right of the axis, without m specified the default is m=1.
gtext('string')
This command transforms the mouse pointer into crosshairs over the plot, when clicked over a desired position, the string will appear on the plot.
Plot title command:

title('string') % places string above the plot
gtext can be used as above for manual positioning of a title.
Tick mark values can be set with the command:

set(gca,'xtick',[vector of values])
gca means : get current axis object
'xtick' : could be 'ytick' or 'ztick'
[vector of values] : you specify the numerical values for the ticks.

Example: Sine & Cosine Plots

This example makes use of a variety of the above commands.

>>x=-pi:pi/20:pi;
>>plot(x,sin(x),x,cos(x),'--',2)
>>axis tight
>>legend('sin(x)','cos(x)',2)
>>title('An Example Plot')
>>xlabel('x'); ylabel('y')
>>set(gca,'xtick',[-3 0 3])
>>grid on

The output should look something like:



NOTE: Many of the plot refinements can be done from the figure window. Look under the Tool menu in the figure window. The tool bar also offers a variety of ways to edit the plot.

Example: Roots of an equation

Here we will obtain a plot of tan(pi*x) and -x. This is a graphical depiction of the roots of the equation tan(pi*x)=-x.

» x=-0.495:0.005:0.495; % vector for x
» x=[x x+1 x+2 x+3 x+4]; % making use of periodicity and avoiding singularities
» plot(x,tan(pi*x),'LineWidth',2)
» hold on
» axis([0 4.5 -6 4]) % adjusting the axis limits
» plot(x,-x) % plotting the line
» plot(x,zeros(length(x))) % plotting a horizontal line
» title('tan\pi\lambda = -\lambda')
» title('tan\pi\lambda = -\lambda : Graphical Depiction of Roots')
» gtext('\lambda_{1}')
» gtext('\lambda_{2}')
» gtext('\lambda_{3}')
» gtext('\lambda_{4}')

NOTE: In the last five lines we have used a LaTex interpreter built into Matlab for writing Greek letters. The backslash \ invokes the interpreter, LaTex command for Greek letters is to spell them, and the _{k} forces a subscript. The output looks as follows.



WARNING: In Matlab, the operand +, -, *, / are all matrix operations.

There is no problem with the first two: if x is a matrix, then x+5 simply adds 5 to every entry in x. However, if x and y are matrices of the same size, x*y performs matrix multiplication. If you want multiplication to be done element by element, the command is x.*y.

For example, if you want to plot the polynomial function (x^4-1)(x+3) on the interval [-4,2] one could write

>>x=-4:0.1:2;
>>plot(x,(x.^4-1).*(x+3))