Nomenclature for a Typical xy Plot (Review)
Example
Problem T5.2-7, Page 238
3
y
=
8
x
Write a program that plots the function
for
1 x 1 with a tick spacing of 0.25 on the x-axis
and 2 on the y-axis.
Solution
Plot the function y = 8 x for 1 x 1 with a tick spacing
of 0.25 on the x-axis and 2 on the y-axis.
3
x=-1:0.01:1;
y=8*x.^3;
plot(x,y),set(gca,'xtick',-1:0.25:1,'ytick',-8:2:8)
xlabel('x'),ylabel('y')
gca: Get Current Axes
Labeling Curves and Data
The legend command automatically obtains from the
plot the line type used for each data set and displays a
sample of this line type in the legend box next to the
string you selected.
The following script file plots two functions with the
corresponding legends (see next slide).
x = 0:0.01:2;
y = sinh(x);
z = tanh(x);
plot(x,y,x,z,--),xlabel(x), ...
ylabel(Hyperbolic Sine and Tangent), ...
legend(sinh(x),tanh(x))
Application of the legend Command
Application of the hold Command
x = -1:0.01:1;
y1 = 3+exp(-x).*sin(6*x);
y2 = 4+exp(-x).*cos(6*x);
plot((0.1+0.9i).^(0:0.01:10)),hold
plot(y1,y2),gtext('y2 versus y1'),gtext('Imag(z) versus Real(z)')
Why Use Log Scales?
Rectilinear scales
cannot properly
display variations
over wide ranges.
Next plot shows the
missing information
for the x-range of
0.1 to 10.
Rectangular Plot
Why Use Log Scales? (cont.)
A log-log plot can
display wide
variations in data
values.
This plot shows the
same information as
in the last plot for the
small x-range of 0.1
to 10.
Logarithmic Plot
Logarithmic Plots
1. You cannot plot negative
numbers on a log scale,
because the logarithm of a
negative number is not
defined.
2. You cannot plot the number 0
on a log scale, because log10
0 = ln 0 = . You must
choose an appropriate small
number (e.g. 0.01) as the
lower limit on the plot.
Logarithmic Plots (cont.)
3. The tick-mark labels on
a log scale are the
actual values being
plotted; they are not the
logarithms of the
numbers.
For example, the range of
x values in this plot is from
101 = 0.1 to 102 = 100.
0.1
100
Logarithmic Plots (cont.)
4. Gridlines and tick marks
within a decade are
unevenly spaced.
If 8 gridlines or tick marks
occur within the decade,
they correspond to values
equal to 2, 3, 4, . . . , 8, 9
times the value
represented by the first
gridline or tick mark of the
decade.
2 x101
3 x101
4 x101
Logarithmic Plots (cont.)
5. Equal distances on a
log scale correspond to
multiplication by the
same constant (as
opposed to addition of
the same constant on a
rectilinear scale).
For example, all numbers that differ by a factor of 10 are separated
by the same distance on a log scale. That is, the distance between
0.2 and 2 is the same as the distance between 3 and 30. This
separation is referred to as a decade or cycle.
Types of Logarithmic Plots
1. Use the loglog(x,y) command to have both
scales logarithmic.
2. Use the semilogx(x,y) command to have the
x scale logarithmic and the y scale rectilinear.
3. Use the semilogy(x,y) command to have the
y scale logarithmic and the x scale rectilinear.
The appropriate command depends on which axis must have a log
scale.
Example y = 25e0.5 x , y = 40(1.7) x and
y = 15 x 0.37
Exponential and Power Functions Plotted on Log Scales
x1 = 0:0.01:3;
y1 = 25*exp(0.5*x1); y2 = 40*(1.7.^x1);
x2 = logspace(-1,1,500); y3 = 15*x2.^(0.37);
subplot(1,2,1),semilogy(x1,y1,x1,y2, '--'),...
legend ('y = 25e^{0.5x}', 'y = 40(1.7) ^x'), ....
xlabel('x'),ylabel('y'),grid on
subplot(1,2,2),loglog(x2,y3),legend('y = 15x^{0.37}'), ...
xlabel('x'),ylabel('y'), grid on
y = 25e0.5 x
120
110
100
90
y1
80
70
60
50
40
30
20
0.5
1.5
x1
2.5
Interactive Plotting in MATLAB
The interactive plotting environment in MATLAB is a set of
tools for:
Creating different types of graphs,
Selecting variables to plot directly from the Workspace Browser,
Creating and editing subplots,
Adding annotations such as lines, arrows, text, rectangles, and
ellipses, and
Editing properties of graphics objects, such as their color, line weight,
and font.
For details, see textbook pages 241-246.
The Figure and Plot Editor Toolbars
The Figure Editor Toolbars (Cont.)
The Plot View interface includes the following three
panels associated with a given figure.
The Figure Palette: Use this to create and arrange
subplots, to view and plot workspace variables, and to add
annotations.
The Plot Browser: Use this to select and control the
visibility of the axes or graphics objects plotted in the figure,
and to add data for plotting.
The Property Editor: Use this to set basic properties of
the selected object and to obtain access to all properties
through the Property Inspector.
Exercise
Create the following plot:
>> t=1:0.1:100;
>>y=sin(t);
>>plot(t,y)
Use the Plot View tools to:
a) Add labels to the axes
b) Change the color and thickness of the plot
c) Generate and save the m-file for the modified plot
Exercise (Cont.)
5. File > Generate Code.
The result is a function file (createfigure.m) that can be
executed in the Command Window as:
>> t=0:.1:10;
>> y=sin(t);
>>createfigure(t,y)
3. Click on the graph
to activate the
window for
color/thickness
1. Click on the
axes to activate
the window for
labeling
2. Click on the
tabs to
add/change the
axes labels
4. Click on the
available options
to change
color/thickness
Surface Plots (3D) Example
The following shows how to
generate the surface plot of the
function z = xe [(x y 2)2+y 2] , for
2 x 2 and 2 y 2, with a
spacing of 0.1.
[X,Y]= meshgrid(-2:0.1:2);
Z = X.*exp(-((X-Y.^2).^2+Y.^2));
mesh(X,Y,Z),xlabel(x) ,...
ylabel(y) zlabel(z)
Test Your Understanding
P. 232: T5.2-2 through T5.2-5
P. 238: T5.2-6
P. 250: T5.4-1
