Plotting Fundamentals: (Attaway Ch 2.5, (10))
How long would it take you to walk to the moon (assuming there
was a footpath)? A day? a week? a month? a year? a lifetime? more?
- We only need simple plotting in 160. Attaway Section
2.5 is really enough.
But if you want to have fun,
Matlab has super-sophisticated plotting (Attaway Chapter 10 is a start).
Back in 1996 the hardcopy manual for plotting and graphics was 200 pages long.
Functionality we need for the rest of this course is all mentioned in
Sect. 2.5 but it's a terse treatment.
Matlab help and examples (templates)
are useful tools (too much to remember otherwise).
The following help request is enough to get all sorts of pointers
to useful Matlab functions. More help is available for each individually.
>> help graph2d
Elementary X-Y graphs.
plot - Linear plot.
loglog - Log-log scale plot.
semilogx - Semi-log scale plot.
semilogy - Semi-log scale plot.
axis - Control axis scaling and appearance.
zoom - Zoom in and out on a 2-D plot.
grid - Grid lines.
plotedit - Tools for editing and annotating plots.
title - Graph title.
xlabel - X-axis label.
ylabel - Y-axis label.
Hardcopy and printing.
print - Print graph or Simulink system;
or save graph to M-file.
printopt - Printer defaults.
See also graph3d, specgraph.
The Minimum You Need to Know
- A few built-in functions:
- How to control how the plot-line looks using
arguments to plot.
- The basic appearance and functionality of the
Figure Window (where plots show up).
Basic Built-in Plot Functions
plot, surf produce 2-D line
and 3-D surface plots in the figure window.
create and clear plot-windows.
allows several plots to be drawn into one figure.
Calling hold alone is a 'toggle'.
hold on to start accumulating plots in the current figure and
hold off to start replacing the current figure with each
new plot command.
grid with various suffixes is used to control the appearance of
grid lines in the plot.
xlabel, ylabel, title, and legend
label your plot in various ways for
inclusion into a report so your reader knows what the axes mean, what
the plot is supposed to show, and what data is represented by the
different lines on the plot.
Use help to discover more about these functions!!
There is no substitute for
help plot, (unless you want to find out even more
by reading the online manual)
Plots vector Y versus vector X. Various OK things happen if X or Y is
a matrix or scalar.
Plots vector Y versus vector X. The short (usually 2 or 3-character,
1 to 4 characters possible) option
the color, plot-markers, or line-types in the plot.
For example, 'r-' produces a red line.
Plot Trivial but Useful Special Case:
Plots elements of vector Y versus their index. So if Y is an N-vector,
X axis is 1, 2, 3,...., N.
To produce log-log and semi-log plots, use
loglog(), semilogx(), and semilogy(),
which have the same syntax as plot().
There are all sorts of additional commands and arguments that
allow you to change the viewpoint, the mode of display, the
shading, the colors, etc., etc. Some of this can be tracked down
using help. Other parts of it require knowing something
about 3D visualization and graphics, and more complete reading in the manual.
A lot more possible complexity, having an extra dimension to visualize.
help is still some help. "Surf" is short for "surface"
Here think of a function
z(x,y), and think of visualizing z as a height above the x-y plane.
Surf Easy Special Case
Displays a surface corresponding to the values in the 2-D array A,
where the row is considered to correspond to the y coordinate,
the column to the x coordinate, and the array value to the z coordinate.
With beautiful false-color height coding. And grid lines.
It may be necessary to make the call view(3) to
get a nice 3-D view.
surf(xrange, yrange, A)
This call takes a vector of x values (the xrange) a vector
of y values (the yrange), and a 2-D array of z values of size(yrange)
rows by size(xrange) cols, and produces a visualization of the surface.
plot() Option Strings
The options string sent as a last argument to plot
(and discussed in Attaway 220.127.116.11)
controls how your "plot line" looks, for example:
'bo' plot points as blue circles
'mx' plot points as magenta x's
'r-' connect data points, plot as red solid line
'g-.' connect data points, plot as green dash-dot line
'r-o' red line AND circles.
Data = [1 3 4 5];
Attaway shows at end of 2.5.2 a little 9-line script that
creates an x-range, plots sin(x) and cos(x) on same axes,
and illustrates the use of legend and title
commands. Check it out for yourselves.
Saving a Plot as a File
You will be featuring plots in your project writeups as a major
tool in helping yourself and your readers understand ('visualize')
- Make sure you have informative title, legend, x and y axis
- Make sure your axis and data ranges show the phenomena
you want to illustrate.
- Pick colors, line styles, and plot symbols
that maximally clarify your results.
In the resulting Figure window with your gorgeous plot,
- Go to File
- Go to Save As...
- Type a descriptive name into the File Name box, no suffix.
- Go to Files of Type drop-down and pick a type. I like JPEG
image (*.jpg) -- pretty universal, but sometimes has compression
artifacts; *.png is a compressionless alternative.
When you pick a type the proper suffix appears on your file name
- Klik on Save
- New file appears in your working directory. Use it in your word
processor to create final .PDF file for handing in.
Some Real-Life Situations
Suppose I generate answers y(x) for x = [1 10 100 1000 10000]
and want to plot y against x, but don't want 10000-long vectors
99.95% full of zeros?
How do I put two or more graphs on same axes in one plot?
How do I generate more than one plot at once? Add legends? Colors?
This page shows
about 2% of Matlab's plotting power but it's all we really need.
% Set up some data
xdata = zeros(1,10);
ydata = zeros(1,10);
for elt= 1:10
xdata(elt) = elt;
ydata(elt) = elt*elt;
plot(ydata); % defaults to plot(ydata, 'b-')
title('1. line graph of i versus i*i');
figure; % create a new plot window...
%we'll wind up with 10 of em
title('2. i versus i*i, with red diamonds');
plot(ydata, 'c'); % cyan
plot(ydata+13, 'm'); % magenta
title('3. hold on to superimpose 2 plots');
hold off % else the rest will be superimposed
Spaced-out equally-spaced X data points:
xdata = [20 40 60 80];
ydata = zeros(1,4);
yindex = 1;
for n = 1:4
ydata(n) = xdata(n) * xdata(n);
plot(ydata, '-*'); % plot line and *
title('4. x versus x*x for sparse x, squeezed');
plot(xdata,ydata,'-d'); % due to autoscale
% and equally-spaced X
% values, graph looks same
title('5. n versus n*n, sparse n, unsqueezed');
Spaced-out UNequally-spaced X data points:
Plotting power functions
like x = y2, Volume =
The log-log plot.
xdata = [2 4 8 16 32 64 ];
ydata = zeros(1,6);
for n = 1:length(xdata)
ydata(n) = xdata(n) ^ 2; % power law
plot(ydata, '-o'); % plot with line and circle,
title('6. y = x*x, unequally spaced xs, squeezed');
plot(xdata,ydata,'r-o'); % now graphs different
title('7. y = x*x, unequally spaced xs unsqueezed');
% log-log plot for power relationship
% yields straight line no matter how x values spaced
title('8. y = x*x, log-log plot');
Plotting Exponential relationships like
y =ex, DecayingVal = InitVal(-.1*t)
The semi-log plot.
xdata = linspace(1,10,10);
ydata = zeros(1,10);
for n = 1:10
ydata(n) = 100 ^ (-.1 * xdata(n)); % exponential
plot(xdata, ydata, 'm-');
title('9. exponential function');
semilogy(xdata, ydata, 'g-*'); % semi-log plot
title('10. exponential function, semi-log plot');
Fun with Surface Plots
Making 2-D plots using surf can be neat.
It can get complicated, but there are some defaults that can be used
to generate some pretty cool graphics without a lot of trouble.
a = -1 : .05 : 1; % a 41 element vector from -1 to 1
b = a .* a; % a^2 pointwise
c = linspace(1, 1, 41); % a 41 element vector of 1s
x2 = c' * b; % array representing z(x,y) = x^2
y2 = b' * c; % array representing z(x,y) = y^2
view(3); % default 3-D view
surf(x2); % plot the x2 array as a surface
surf(y2); % plot the y2 array as a surface
Produces the following figure windows (note the toolbar!).
These were produced by a window-grab, not by "Save As..."
(Note: The window produced by surf may need
to be closed before another surface plot can be made)
We can add x^2 and y^2 to get a paraboloid (illustrating the squared
Euclidean distance function / 2),
x2_y2 = (x2 + y2) / 2; % z(x,y) = (x^2 + y^2) / 2
or take the outer product of a^2 with itself to get a
particular 4th order function
x2y2 = 1 - b' * b; % z(x,y) = 1 - x^2 * y^2
For even more fun we can combine the last two,
z4 = x2y2 + x2_y2;
or make our own function using for loops.
z = zeros(41,41);
for m = 1:41
for n = 1:41
y = (m - 21) / 20;
x = (n - 21) / 20;
z(m,n) = (x*x + y*y) * ...
sin(1.7*pi*x) * cos(2.7*pi*y);
Last update: 04/20/2011: RN