Programming with matlab session 6

SESSION-6 :MATLAB
PLOTTING-2D, 3D
By: Prof. Ganesh Ingle

Session objective
Introdcution
Plotting basic 2-D plots.
The plot command
The fplot command
Plotting multiple graphs in the same plot
Formatting plots
SUMMARY

MAKING X-Y PLOTS
MATLAB has many functions and commands that can be used to create
various types of plots.
In our class we will only create two dimensional x – y plots.

8 10 12 14 16 18 20 22 24
0
200
400
600
800
1000
1200
DISTANCE (cm)
INTENSITY(lux)
Light Intensity as a Function of Distance
Comparison between theory and experiment.
Theory
Experiment
Plot title
y axis
label
x axis
label
Text
Tick-mark label
EXAMPLE OF A 2-D PLOT
Data symbol
Legend
Tick-mark
Plotting

TWO-DIMENSIONAL plot() COMMAND
where x is a vector (one dimensional array), and y is a vector.
Both vectors must have the same number of elements.
 The plot command creates a single curve with the x values on
the abscissa (horizontal axis) and the y values on the ordinate
(vertical axis).
 The curve is made from segments of lines that connect the
points that are defined by the x and y coordinates of the
elements in the two vectors.
The basic 2-D plot command is:
plot(x,y)
Plotting

 If data is given, the information is entered as the elements of the
vectors x and y.
 If the values of y are determined by a function from the values
of x, than a vector x is created first, and then the values of y
are calculated for each value of x. The spacing (difference)
between the elements of x must be such that the plotted curve
will show the details of the function.
CREATING THE X AND Y VECTORS
Plotting

PLOT OF GIVEN DATA
Given data:
>> x=[1 2 3 5 7 7.5 8 10];
>> y=[2 6.5 7 7 5.5 4 6 8];
>> plot(x,y)
A plot can be created by the commands shown below. This can be done
in the Command Window, or by writing and then running a script file.
Once the plot command is executed, the Figure Window opens with the
following plot.
x
y
1 2 3 5 7 7.5 8
6.5 7 7 5.5 4 6 8
10
2
Plotting

LINE SPECIFIERS IN THE plot() COMMAND
Line specifiers can be added in the plot command to:
 Specify the style of the line.
 Specify the color of the line.
 Specify the type of the markers (if markers are desired).
plot(x,y,’line specifiers’)
Plotting

Line Specifier Line Specifier Marker Specifier
Style Color Type
Solid - red r plus sign +
dotted : green g circle o
dashed -- blue b asterisk *
dash-dot -. Cyan c point .
magenta m square s
yellow y diamond d
black k
plot(x,y,‘line specifiers’)
Plotting

 The specifiers are typed inside the plot() command as strings.
 Within the string the specifiers can be typed in any order.
 The specifiers are optional. This means that none, one, two, or
all the three can be included in a command.
EXAMPLES:
plot(x,y) A solid blue line connects the points with no markers.
plot(x,y,’r’) A solid red line connects the points with no markers.
plot(x,y,’--y’) A yellow dashed line connects the points.
plot(x,y,’*’) The points are marked with * (no line between the
points.)
plot(x,y,’g:d’) A green dotted line connects the points which are
marked with diamond markers.
Plotting

Year
Sales (M)
1988 1989 1990 1991 1992 1993 1994
127 130 136 145 158 178 211
PLOT OF GIVEN DATA USING LINE
SPECIFIERS IN THE plot() COMMAND
>> year = [1988:1:1994];
>> sales = [127, 130, 136, 145, 158, 178, 211];
>> plot(year,sales,'--r*')
Line Specifiers:
dashed red line and
asterisk markers.
Plotting

PLOT OF GIVEN DATA USING LINE
SPECIFIERS IN THE plot() COMMAND
Dashed red line and
asterisk markers.
Plotting

% A script file that creates a plot of
% the function: 3.5^(-0.5x)*cos(6x)
x = [-2:0.01:4];
y = 3.5.^(-0.5*x).*cos(6*x);
plot(x,y)
CREATING A PLOT OF A FUNCTION
Consider: 42for)6cos(5.3 5.0
 
xxy x
A script file for plotting the function is:
Creating a vector with spacing of 0.01.
Calculating a value of y
for each x.
Once the plot command is executed, the Figure Window opens with the
following plot.
Plotting

A PLOT OF A FUNCTION
42for)6cos(5.3 5.0
 
xxy x
Plotting

CREATING A PLOT OF A FUNCTION
If the vector x is created with large spacing, the graph is not accurate.
Below is the previous plot with spacing of 0.3.
x = [-2:0.3:4];
y = 3.5.^(-0.5*x).*cos(6*x);
plot(x,y)
Plotting

THE fplot COMMAND
fplot(‘function’,limits)
The fplot command can be used to plot a function
with the form: y = f(x)
 The function is typed in as a string.
 The limits is a vector with the domain of x, and optionally with limits
of the y axis:
[xmin,xmax] or [xmin,xmax,ymin,ymax]
 Line specifiers can be added.
Plotting

PLOT OF A FUNCTION WITH THE fplot() COMMAND
>> fplot('x^2 + 4 * sin(2*x) - 1', [-3 3])
33for1)2sin(42
 xxxyA plot of:
Plotting

PLOTTING MULTIPLE GRAPHS IN THE SAME PLOT
Plotting two (or more) graphs in one plot:
1. Using the plot command.
2. Using the hold on, hold off commands.
Plotting

USING THE plot() COMMAND TO PLOT
MULTIPLE GRAPHS IN THE SAME PLOT
Plots three graphs in the same plot:
y versus x, v versus u, and h versus t.
 By default, MATLAB makes the curves in different colors.
 Additional curves can be added.
 The curves can have a specific style by adding specifiers after
each pair, for example:
plot(x,y,u,v,t,h)
plot(x,y,’-b’,u,v,’—r’,t,h,’g:’)
Plotting

42  x
Plot of the function, and its first and second
derivatives, for , all in the same plot.
10263 3
 xxy
42  x
x = [-2:0.01:4];
y = 3*x.^3-26*x+6;
yd = 9*x.^2-26;
ydd = 18*x;
plot(x,y,'-b',x,yd,'--r',x,ydd,':k')
vector x with the domain of the function.
Vector y with the function value at each x.
42  x
Vector yd with values of the first derivative.
Vector ydd with values of the second derivative.
Create three graphs, y vs. x (solid blue line),
yd vs. x (dashed red line), and ydd vs. x
(dotted black line) in the same figure.
Plotting

-2 -1 0 1 2 3 4
-40
-20
0
20
40
60
80
100
120
Plotting

hold on Holds the current plot and all axis properties so that
subsequent plot commands add to the existing plot.
hold off Returns to the default mode whereby plot commands
erase the previous plots and reset all axis properties
before drawing new plots.
USING THE hold on, hold off, COMMANDS
TO PLOT MULTIPLE GRAPHS IN THE SAME PLOT
This method is useful when all the information (vectors) used for the
plotting is not available a the same time.
Plotting

Plot of the function, and its first and second
derivatives, for all in the same plot.
10263 3
 xxy
42  x
x = [-2:0.01:4];
y = 3*x.^3-26*x+6;
yd = 9*x.^2-26;
ydd = 18*x;
plot(x,y,'-b')
hold on
plot(x,yd,'--r')
plot(x,ydd,':k')
hold off
Two more graphs are created.
First graph is created.
USING THE hold on, hold off, COMMANDS
TO PLOT MULTIPLE GRAPHS IN THE SAME PLOT
Plotting

8 10 12 14 16 18 20 22 24
0
200
400
600
800
1000
1200
DISTANCE (cm)
INTENSITY(lux)
Light Intensity as a Function of Distance
Comparison between theory and experiment.
Theory
Experiment
Plot title
y axis
label
x axis
label
Text
EXAMPLE OF A FORMATTED 2-D PLOT
Data symbol
Legend
Tick-mark
Tick-mark label
Plotting

FORMATTING PLOTS
A plot can be formatted to have a required appearance.
With formatting you can:
 Add title to the plot.
 Add labels to axes.
 Change range of the axes.
 Add legend.
 Add text blocks.
 Add grid.
Plotting

FORMATTING PLOTS
There are two methods to format a plot:
1. Formatting commands.
In this method commands, that make changes or additions to
the plot, are entered after the plot() command. This can be
done in the Command Window, or as part of a program in a
script file.
2. Formatting the plot interactively in the Figure Window.
In this method the plot is formatted by clicking on the plot and
using the menu to make changes or add details.
Plotting

FORMATTING COMMANDS
title(‘string’)
Adds the string as a title at the top of the plot.
xlabel(‘string’)
Adds the string as a label to the x-axis.
ylabel(‘string’)
Adds the string as a label to the y-axis.
axis([xmin xmax ymin ymax])
Sets the minimum and maximum limits of the x- and y-axes.
Plotting

FORMATTING COMMANDS
legend(‘string1’,’string2’,’string3’)
Creates a legend using the strings to label various curves (when
several curves are in one plot). The location of the legend is
specified by the mouse.
text(x,y,’string’)
Places the string (text) on the plot at coordinate x,y relative to
the plot axes.
gtext(‘string’)
Places the string (text) on the plot. When the command
executes the figure window pops and the text location is clicked
with the mouse.
Plotting

EXAMPLE OF A FORMATTED PLOT
Below is a script file of the formatted light intensity plot (2nd slide).
(Some of the formatting options were not covered in the lectures, but
are described in the book)
x=[10:0.1:22];
y=95000./x.^2;
xd=[10:2:22];
yd=[950 640 460 340 250 180 140];
plot(x,y,'-','LineWidth',1.0)
hold on
plot(xd,yd,'ro--','linewidth',1.0,'markersize',10)
hold off
Creating a vector with
light intensity from data.
Creating a vector with coordinates of data points.
Creating vector x for plotting the theoretical curve.
Creating vector y for plotting the theoretical curve.
Plotting

Formatting of the light intensity plot (cont.)
xlabel('DISTANCE (cm)')
ylabel('INTENSITY (lux)')
title('fontname{Arial}Light Intensity as a Function of
Distance','FontSize',14)
axis([8 24 0 1200])
text(14,700,'Comparison between theory and
experiment.','EdgeColor','r','LineWidth',2)
legend('Theory','Experiment',0)
Creating text.
Creating a legend.
Title for the plot.
Setting limits of the axes.
Labels for the axes.
The plot that is obtained is shown again in the next slide.
Plotting

Plotting

FORMATTING A PLOT IN THE FIGURE WINDOW
Once a figure window is open, the figure can be formatted interactively.
Use Figure, Axes,
and Current
Object-
Properties in the
Edit menu
Click here to start the
plot edit mode.
Use the insert menu to
Plotting

MATLAB PROGRAM TO PLOT VI CHARACTERISTICS OF A DIODE
%Matlab program to plot VI characteristics of a diode
clc;
close all;
clear all;
a=input('Enter the temperatre in degree centigrade '); %40
b=input('Enter the reverse saturation current at room temperature '); %25
q=1.6e-19;
k=1.38e-23;
t=a+273;
v=-0.2:0.01:0.25;
i=b*(exp(q*v/(k*t))-1);
plot(v,i)
xlabel('Voltage -->')
ylabel('Current -->')
grid on;
Plotting

DIFFERENT PLOT CODE FOR PRACTISE
Plotting
%%
x=[10:0.1:22];
y=95000./x.^2;
xd=[10:2:22];
yd=[950 640 460 340 250 180 140];
plot(x,y,'-','LineWidth',1.0)
hold on
plot(xd,yd,'ro--','linewidth',1.0,'markersize',10)
hold off
xlabel('DISTANCE (cm)')
ylabel('INTENSITY (lux)')
title('fontname{Arial}Light Intensity as a Function of Distance','FontSize',14)
axis([8 24 0 1200])
text(14,700,'Comparison between theory and experiment.','EdgeColor','r','LineWidth',2)
legend('Theory','Experiment',0)
%%
clear all;
x = randn(1,1000);
hist(x,100);
%%
figure(2);
t=-4:.1:4;
y = exp(-t.^2);
plot(t,y);
%%
t = 0:pi/20:2*pi;
x = sin(t);
y = cos(t);
figure(1);
plot(x);
figure(2);
plot(t,y);
figure(3);
plot(x,y);

DIFFERENT PLOT CODE FOR PRACTISE
Plotting
%%
sys = tf([2 5 1],[1 2 3]);
rlocus(sys)
sys = tf([0.5 -1],[4 0 3 0 2]);
k = (1:0.5:5);
r = rlocus(sys,k);
size(r)
rlocus(sys,k)
%%
[x,y] = meshgrid(-2:.1:2, -2:.1:2);
z = x.*exp(-x.^2 - y.^2);
mesh(z);
%%
%Matlab program to plot VI characteristics of a diode
clc;
close all;
clear all;
a=input('Enter the temperatre in degree centigrade ');
b=input('Enter the reverse saturation current at room temperature ');
q=1.6e-19;
k=1.38e-23;
t=a+273;
v=-0.2:0.01:0.25;
i=b*(exp(q*v/(k*t))-1);
plot(v,i)
xlabel('Voltage -->')
ylabel('Current -->')
grid on;

THANK YOU
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Programming with matlab session 6

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