Getting_Start_MATLAB_BVM1.pptx

MATLAB – Selection and Repetition Structure
Mechanical Engineering Department
Sardar Vallabhbhai National Institute of Technology, Surat,
Gujarat, India.
mkr@med.svnit.ac.in
Dr. Manish K Rathod
1

 It is developed by The Mathworks, Inc.
(http://www.mathworks.com)
• It is an integrated technical computing environment that
combines numeric computation, advanced graphics and
visualization, and a high-level programming language.
– Interpreted language
– Scientific programming environment
– Very good tool for the manipulation of matrices
– Great visualisation capabilities
– Loads of built-in functions
– Easy to learn and simple to use
– slow (compared with FORTRAN or C) because it is interpreted.
– automatic memory management; no need to declare arrays.
What is MATrix LABoratory ?
Dr. Manish K Rathod, Assistant Professor, MED, SVNIT,
Surat
2

Surat
3

vast collection of computational algorithms ranging from
elementary functions to more sophisticated functions
high-level matrix/array language with Control flow
statements, functions, data structures, input/output, and
object-oriented programming features.
Mathematical Function Library
MATLAB Language
Surat
4

5
Computer program
• One way to think of a computer program (not
just MATLAB®) is to consider how the
statements that compose it are organized.
• Usually, sections of computer code can be
categorized as sequences , selection
structures , and repetition structures.
Dr. Manish K Rathod, Assistant Professor, MED, Surat

Computer program
Sequence
• List of commands
that are executed
one after another.
Selection Structure
• Allows the
programmer to
execute one / more
commands if some
criterion is true and
a second command
if the criterion is
false.
Repetition Structure
• A group of
statements to be
executed multiple
times.
• Depends on either a
counter or the
evaluation of a
logical condition.
Dr. Manish K Rathod, Assistant Professor, MED, Surat 6

• Plan your program
– Two common approach
• Graphical approach (Flowchart)
• Verbal description (Pseudocode)
• For simple program, Psdeudocode is best.
– Outline a set of statements describing the steps to
solve a problem
– Convert these steps into an M-file using
appropriate code
Flowchart and pseudo code

1. Wake-up at 7:00 a.m., except Sunday
2. Get ready and reach office before 8:45 a.m.
3. If it is late; take auto, else go by bus
4. Work from 9.00 a.m. to 12.00 a.m.
5. Go to lunch for all days except fast
6. Between 4:00 p.m. to 6:00 p.m. conduct Weekly Meeting
Marketing meeting on Mon, Wed, Fri and
Production meeting on Tue, Thu, Sat
7. On every 1st , check for salary & release important dues
8. Go back to residence
Schedule of an executive

Read Time, Day and Date from watch & calendar
For Day == Mon, Tue, Wed, Thu, Fri and Sat
if (Time > or = 7:00), wake-up (brake)
else go to sleep and check again after some time
% Get ready and reach office before 8:45
while not reached in office hurry up!!!
if it is late; pickup an auto, (i.e. Time > or = 8:00)
else wait for bus until bus arrives
while Time < or = 12:00 work in office (from 9.00 to 12.00)
while (Time == 12:00) & (NOT fast) go to lunch end
while Time ~= 4:00 work in office (from 12.00 to 4.00 PM)
if (Day == Mon) or (Day == Wed) or (Day == Fri)
Conduct Marketing Meeting, end at 6:00
if (Day == Tue) or (Day == Thu) or (Day == Sat)
Conduct Production Meeting, end at 6:00
if Date == 1st Get salary and release important dues
Go back to residence and end the day
Schedule of an executive (pseudo-code)

MATLAB Functions - Basic Features
Gujarat, India.
mkr@med.svnit.ac.in
Dr. Manish K Rathod
10

• Programming often requires repeating a set of tasks over
and over again.
• For example, the sin function in MATLAB is a set of
tasks (i.e., mathematical operations) that computes an
approximation for sin(x).
• Rather than having to retype or copy these instructions
every time you want to use the sin function, it is useful
to store this sequence of instruction as a function that
you can call over and over again.
11
Motivations

• A function is a group of statements that together
perform a task. In MATLAB, functions are defined in
separate files.
• MATLAB functions are similar to C functions or
Fortran subroutines.
• Two types: Inbuilt Functions and, User Defined
Function
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Motivations

• You decide to paint your house by some one (which you also can do)
– Main code can perform the required task but for the simplicity outside
party is preferred
• Identifying someone who can do this
– Give a name and write a separate file
• Giving possession of the house to him/them
– Command of the program will be shifted to the function
• Providing them with required material (color containers, brush, etc)
– Submit your variable to function from your control to there control
this may required that variable will be identified by different name
• Observe successful completion of task
– Halt the main program execution till your function will executed
• Get cleaned the floor and other parts of house & take possession
– Delete all the variable & workspace generated by function & get
control back
• Pay the persons and send off them
– Spend required CPU time and terminate the function call 13

• MATLAB® has an extensive library of built-in functions to
allow to perform mathematical functions, including
logarithms, trigonometric functions, and statistical analysis
functions.
• Many of the names for MATLAB® ’s built-in functions are the
same as those defined not only in the C programming
language, but in Fortran and Java as well. For example,
• To take the square root of the variable x ,
b = sqrt(x)
• A big advantage of MATLAB ® is that function arguments can
generally be either scalars or matrices.
14
Built-in function

All functions can be thought of as having three components:
a name, input, and output.
• In the preceding example, the name of the function is sqrt , the
required input (also called the argument) goes inside the
parentheses and can be a scalar or a matrix, and the output is a
calculated value or values.
Some functions require multiple inputs.
• For example, the remainder function,
rem , requires two inputs: a dividend and a divisor, i.e. rem(x,y)
rem(10,3) %calculates the remainder of 10 divided by 3:
ans = 1
15
Built-in function

• The size function is an example of a function that returns
two outputs, which are stored in a single array. It determines
the number of rows and columns in a matrix. Thus,
d = [1, 2, 3; 4, 5, 6];
f = size(d) %returns the 1 X 2 result matrix
f = 2 3
• You can also assign variable names to each of the answers by
representing the left-hand side of the assignment statement
as a matrix. For example,
[rows,cols] = size(d)
rows =
2
cols =
3 16
Built-in function

• You can create more complicated expressions by nesting
functions. For instance,
g = sqrt(sin(x))
• Finds the square root of the sine of whatever values are
stored in the matrix named x .
• If x is assigned a value of 2,
x = 2;
• the result is
g =
0.9536
17
Built-in function

• MATLAB ® includes extensive help tools, which are especially
useful in understanding how to use functions.
• There are two ways to get help from within MATLAB® :
– A command-line help function ( help ) and
– an HTML-based set of documentation available by
selecting Help from the menu bar
• For example, to get help on the tangent function, type
help tan
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Built-in function

• Common Computations
19
ELEMENTARY MATH FUNCTIONS

• As a rule, the function log in all computer languages means
the natural logarithm .
• If you want logarithms to the base 10, you’ll need to use the
log10 function.
• The mathematical notation and MATLAB ® syntax for raising e
to a power are not the same. To raise e to the third power, the
mathematical notation would be e3.
• However, the MATLAB ® syntax is exp(3) .
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Built-in function

21
Rounding functions
For example, suppose you want to buy apples at the grocery store. The apples
cost 15 Rs. a piece. You have 55 Rs. How many apples can you buy?
fix (55/15)
ans =
3

22
Discrete Mathematics

23
TRIGONOMETRIC FUNCTIONS

24
DATA ANALYSIS FUNCTIONS
• max(x)
Finds the largest value in a vector x.
x[1, 5, 3];
max(x)
ans =
5
If x[1, 5, 3; 2, 4, 6];…..????
• [a,b]=max(x)
Finds both the largest value in a vector x and its location in vector x.
x[1, 5, 3];
[a,b]= max(x)
a =
5
b =
2

25
• max(x,y)
Creates a matrix the same size as x and y. (Both x and y must
have the same number of rows and columns.) Each element in
the resulting matrix contains the maximum value from the
corresponding positions in x and y.
x[1, 5, 3; 2, 4, 6]; y[10,2,4; 1, 8, 7];
max(x,y)
• Same as min(x);
[a,b]=min(x);
min(x,y)

26
• sum(x)
Sums the elements in vector x.
• prod(x)
Computes the product of the
elements of a vector x.
• sort(x)
sorting the elements
• diff(x)
differences between
adjacent elements

27
• cumsum(x)
Computes a vector of the same size as, and containing
cumulative sums of the elements of, a vector x.
For example, if x = [1 5 3], the resulting vector is x=[1 6 9].
• cumprod(x)
Computes a vector of the same size as, and containing
cumulative products of the elements of, a vector x .
For example, if x = [1 5 3], the resulting vector is x=[1 5 15].
• sortrows(x,n)
Sorts the rows in a matrix on the basis of the values in column
n. If n is negative, the values are sorted in descending order. If
n is not specified, the default column used as the basis for
sorting is column 1.

28
skating_results = [ 1.0000 42.0930
2.0000 42.0890
3.0000 41.9350
4.0000 42.4970
5.0000 42.0020]
>> sortrows(skating_results)
>> sortrows(skating_results,2)
>> sortrows(skating_results,-2)

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Special function

30
User defined function
• A company requires some of its assembly drawings are to be drawn by an
AutoCad operator as an out side party
– Main program ‘Company’ performs the task of doing assembly drawing
• Calls an AutoCad operator, explains the drawing and the details of parts
– Main program ‘Company’ requires a function name ‘AutoCad_Operator’
• Company also provides operator with a zerox copy of drawing of all the parts
– Program ‘Company’ supplies a copy of all details (i. e. variables) to
function ‘AutoCad_Operator’, any modification by ‘AutoCad_Operator’ in
the drawing will not affect the performance of company.
• Company fixes the date and wait for completion of consignment
– Program ‘Company’ waits for the ‘AutoCad_Operator’ to complete job
• Company gets work done in time in the form of an assembly drawing
– Main program ‘Company’ gets work done from function name
‘AutoCad_Operator’ in the form of an assembly drawing, without
submitting the zerox he received by the ‘Company’, which he may destroy.

31
• A function file is also an M-file, like a script file, except that the
variables in a function file are all local .
• Both built-in MATLAB® functions and user-defined MATLAB®
functions have the same structure. Each consists of a name, user-
provided input, and calculated output.
• For example, the function cos(x)
• is named cos ,
• takes the user input inside the parentheses (in this case, x ), and
• calculates a result.
• The user does not see the calculations performed, but just accepts
the answer.

32
• Imagine that you have created a function called my_function .
Using my_function(x)
• in a program or from the command window will return a
result, as long as x is defined and the logic in the function
definition works.
• User-defined functions are created in M-files. Each must start
with a function definition line that contains:
• The word ‘function’
• A variable that defines the function output
• A function name
• A variable used for the input argument

33
• For example,
function [output variables] = my_function(x)
• The first word, function, is mandatory, and tells MATLAB this m-
file in a function file.
• On the lefthand side of the equals sign is a list of the output
variables that the function will return. When there is more than
one output variable, then they are enclosed in square brackets.
• On the righthand side of the equals sign is the name of the
function. The name used to save a function file must match the
function name.
• Lastly, within the round brackets after the function name, is a
comma separated list of the input variables.

35
• It is good practice to put some comments after the function
definition line to explain what task the function performs and
how you should use the input and output variables.

36
When x and y are defined in the command window and the function g is called, a
vector of output values is returned:

37
When x and y are defined in the command window and the function g is called, a
vector of output values is returned:

38
• You can also create functions that return more than one output
variable. Make the output a matrix of answers instead of a single
variable
function [dist, vel, accel] = motion(t)
% This function calculates the distance, velocity, and
% acceleration of a particular car for a given value of t
% assuming all 3 parameters are initially 0.
accel = 0.5 .*t;
vel = t.^2/4;
dist = t.^3/12;
• Once saved as motion in the current folder, you can use the
function to find values of distance , velocity , and acceleration at
specified times:

39
[distance, velocity, acceleration] = motion(10)
distance =
83.33
velocity =
25
acceleration =
5
• If you call the motion function without specifying all three outputs,
only the first output will be returned:
motion(10)
ans =
83.333

40
• EXAMPLE
• Produce a conversion table for Celsius and Fahrenheit
temperatures.
• The input to the function should be two numbers: Tlower and Tupper
which define the lower and upper range, in Celsius, for the table.
• The output of the function should be a two column matrix with
the first column showing the temperature in Celsius, from Tlower
and Tupper with an increment of 1 C, and the second column
showing the corresponding temperature in Fahrenheit.

A user interface is the point of contract or method
of interactions between a person and a computer
or computer program.
A Graphical user interface, or GUI is a user interface
incorporating graphical objects such as window , icons,
buttons, menus, and text.
The user communicates with the computer using input
devices such as a keyboard, mouse, trackball, drawing
pad, and microphone.
GRAPHICAL USER INTERFACE

Some well known GUI’s
WORD, Network Configuration and Control Panel offer functionality for
controlling the computer and data without need for system level commands
and scripts. Most operations on data can be done with icon presses.

Some simple interface commands
Simplest user interface command is the message
box. This is common in Windows programs and
VB. Matlab msgbox is configured as follows.
The result of calling this in the command line is a
little box with a message displayed and a single
‘ok’ button that clears the box. 43

As you can imagine you could use the msgbox to output
the result of your program.
Ie.
Some simple interface commands
44

An error message
• an error message
• Errordlg(‘string’,’DBName’)
errordlg('you got that wrong','error message')

Questdlg
It provides a question and a series of possible
answers. The user presses a key and that key
name is returned from the questdlg function. The
example below uses switch to effect an operation
based on the choice.
%syntax
%ButtonName=questdlg(Question,Title
,Btn1,Btn2,OPTIONS);
46

• Print dlg Box:-
• Syntax:- printdlg
printdlg prints the current figure.
48

• Help dlg Box:
• Syntax:- helpdlg('helpstring')
helpdlg('helpstring','dlgname')
• helpdlg('helpstring')
displays a dialog box named 'Help Dialog'
containing the string specified by
'helpstring'.
• helpdlg('helpstring','dlgname')
displays a dialog box named 'dlgname'
containing the string 'helpstring'

• Example:-
helpdlg('Choose 10 points from the
figure','Point Selection');

MATLAB – Graphics Capability (Plots)
Gujarat, India.
mkr@med.svnit.ac.in
Dr. Manish K Rathod
51

x a b
10 1 2
15 3 4
25 5 8
32 7 11
Introduction - plot
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35
Series1
Series2

• Large tables of data are difficult to interpret.
• Engineers use graphing techniques to make the
information easier to understand.
• With a graph, it is easy to identify trends, pick out
highs and lows, and isolate data points that may be
measurement or calculation errors.
• Graphs can also be used as a quick check to
determine whether a computer solution is yielding
expected results.
Introduction - plot

OBJECTIVE
• Create and label two dimensional plots
• Adjust the appearance of your plots
• Divide the plotting window into subplots
• Use the interactive MATLAB ® plotting tools

55
Introduction - plot
linear plots
line plots
logarithmic plots on both scales
logarithmic plots on one scale
stem plots
bar graphs
three-dimensional plots
MATLAB has the capability to generate plots of many types.

• The xy plot is the most commonly used plot
by engineers
• The independent variable is usually called x
• The dependent variable is usually called y
56
Two Dimensional Plots
A very important fact that should be emphasized at the outset is
that to plot one vector against another, the vectors must have
the same number of elements.
One can plot either a column vector or a row vector versus either
a column vector or a row vector provided they have the same
number of values.

57
•If the vectors have different lengths, it is possible to
use a portion of the longer one as one of the
variables.
•For example, suppose y has 200 values and x has
120 values. One could define y1 by the following
command:
>> y1 = y(1:120)
•The variable y1 now has the same number of
points as x and the two could be plotted together.
Two Dimensional Plots

Command for producing a simple plot is
plot (x values, y values, 'style-options’)
x values and y values – Vector
Style-option - Optional argument
Creating a plot

59
Time, sec Distance, Ft
0 0
2 0.33
4 4.13
6 6.29
8 6.85
10 11.19
12 13.19
14 13.96
16 16.33
18 18.17
Time is the independent
variable and distance is
the dependent variable
example

Define x and y and call the plot function
60
Any variable name that is convenient for the dependent and independent
variables can be used.
time, sec Distance,
Ft
0 0
1 0.33
3 4.13
5 6.29
7 6.85
9 11.19
11 13.19
13 13.96
15 16.33
17 18.17
example

61
Once the plot command is executed, the Figure Window opens with the following
plot.

• If the plot command with a single matrix is used,
MATLAB plots the values versus the index number
• Usually this type of data is plotted on a bar graph
• When plotted on an xy grid, it is often called a line
graph.
62
Variations

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’)

• The appearance of the plots by selecting user defined can be
changed
– line styles
– color
– mark styles
• Try using “help plot” for a list of available styles

 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.

Table 5. 2 Line, Mark and Color Options
Line Type Indicator Point Type Indicato
r
Color Indicator
solid - point . blue b
dotted : circle o green g
dash-dot -. x-mark x red r
dashed -- plus + cyan c
star * magenta m
square s yellow y
diamond d black k
triangle
down
v
triangle up ^
triangle left <
triangle
right
>
pentagram p
hexagram h

Year
Sales (M)
1988 1989 1990 1991 1992 1993 1994
127 130 136 145 158 178 211
>> year = [1988:1:1994];
>> sales = [127, 130, 136, 145, 158, 178, 211];
>> plot(year,sales,'--r*')
Line Specifiers:
dashed red line and
asterisk markers.

Dashed red line and
asterisk markers.

plot(x,y,':ok')
• In this command
– the : means use a dotted line
– the o means use a circle to mark each point
– the letter k indicates that the graph should
be drawn in black
69

70
dotted line
circles
black

• MATLAB overwrites the figure window every
time you request a new plot
• To open a new figure window use the figure
function – for example
figure(2)
71
Creating Multiple Plots

• hold on
– Freezes the current plot, so that an additional plot
can be overlaid
• When you use this approach the additional line is
drawn in blue – the default drawing color
72
MULTIPLE GRAPHS IN A SAME PLOT
The first plot is drawn in blue

73
The hold on command
freezes the plot
The second line
is also drawn in
blue, on top of
the original plot
The second line
is also drawn in
blue, on top of
the original plot

Using hold command
Invoking hold on at any
point freezes the plot in the
graphics window
Subsequent plots are added
to existing plot

• Multiple lines on a single graph with one command
can also be created.
76
Plots three graphs in the same plot:
yversus x, vversus u, and hversus 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:’)

4
2 

 x
Plot of the function, and its first and second derivatives, for
, all in the same plot.
10
26
3 3


 x
x
y
4
2 

 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.
4
2 

 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.

-2 -1 0 1 2 3 4
-40
-20
0
20
40
60
80
100
120
USING THE plot() COMMAND TO PLOT
MULTIPLE GRAPHS IN THE SAME PLOT

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.

FORMATTING PLOTS
MATLAB SUPPORTS TWO WAYS TO EDIT THE PLOTS :
Using the mouse to select and edit objects interactively
(Interactive Plot Editing)
Using MATLAB functions at command-line or in an M-file
(Using Functions to Edit Graphs)

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.

FORMATTING COMMANDS
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.
legend(‘string1’,’string2’,’string3’)
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.

 legend (…., pos) :
pos = -1 places the legend outside the axes boundary on the right
side.
pos = 0 places the legend inside the axes boundary, obscuring as
few points as possible.
pos = 1 places the legend in the upper-right corner of the axes
(default).
pos = 2 places legend in the upper-left corner of axes.
pos = 3 places legend in the lower-left corner of axes.
pos = 4 places legend in the lower-right corner of axes.
 legend off: deletes the legend from plot
FORMATTING COMMANDS

-1
0
1
3 4

EXAMPLE OF A FORMATTED PLOT
Below is a script file of the formatted light intensity plot
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.

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.

88

You can use Greek letters in your labels by putting a
backslash () before the name of the letter.
For example:
title(‘alpha beta gamma’)
creates the plot title α β γ
To create a superscript use curly brackets
title(‘x^{2}’) Gives x2
89
IMPROVING LABELS

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

SAVING A FIGURE
Save from File menu saves the a figure
To save figure using a graphics format
(*.bmp,*.jpg, etc) , select Export from
the File menu

Subplots
94
• The subplot command allows to subdivide the
graphing window into a grid of m rows and n
columns
• subplot(m,n,p)
rows columns location
2 rows
2 columns
1 2
3 4
-2
0
2
-2
0
2
-5
0
5
x
Peaks
y
subplot(2,2,1)

95
2 rows and 1 column
Subplots

Other Types of 2-D Plots
• Polar Plots
• Logarithmic Plots
• Bar Graphs
• Pie Charts
• Histograms
• X-Y graphs with 2 y axes
• Function Plots
96
MATLAB supports a variety of graph types that enable to present information
effectively. The type of graph selected depends, to a large extent on the nature
of the data

Logarithmic Plots
• A logarithmic scale (base 10) is convenient when
– a variable ranges over many orders of magnitude, because
the wide range of values can be graphed, without
compressing the smaller values.
– data varies exponentially.
• plot – uses a linear scale on both axes
• semilogy – uses a log10 scale on the y axis
• semilogx – uses a log10 scale on the x axis
• loglog – use a log10 scale on both axes
97

98
Logarithmic Plots

99
Logarithmic Plots

• Bar graphs are useful to view results over
time, comparing results, and displaying
individual contribution to a total amount.
• Pie charts show individual contribution to a
total amount.
• Histograms show the distribution of data
values.
Bar Graphs and Pie Charts

Bar Graphs and Pie Charts
• MATLAB includes a whole family of bar graphs and
pie charts
– bar(x) – vertical bar graph
– barh(x) – horizontal bar graph
– bar3(x) – 3-D vertical bar graph
– bar3h(x) – 3-D horizontal bar graph
– pie(x) – pie chart
– pie3(x) – 3-D pie chart
101

102

103

Histograms
• A histogram is a plot showing the distribution
of a set of values
104

Stem and stair step plots
display discrete data.
Stem and Stair
105

Polar Plots
• Some functions are easier to specify using
polar coordinates than by using rectangular
coordinates
• For example the equation of a circle is
– y=sin(x) in polar coordinates
106

107

X-Y Graphs with Two Y Axes
• Scaling Depends on the largest value plotted
• Its difficult to see how the blue line behaves, because
the scale isn’t appropriate
108

109
The plotyy function
allows you to use two
scales on a single
graph
X-Y Graphs with Two Y Axes

Function Plots
110
• Function plots allow you to use a function as
input to a plot command, instead of a set of
ordered pairs of x-y values
• fplot('sin(x)',[-2*pi,2*pi])
function input as a
string
range of the independent
variable – in this case x

111
Function Plots

• Compass, feather, and quiver plots display
direction and velocity vectors.
• Contour plots show equivalued regions in
data.
• Interactive plotting enable to select data
points to plot with the pointer.
Other Plots

3 D Graphs
Elementary 3-D plots
• plot3 - Plot lines and points in 3-D space.
• mesh - 3-D mesh surface.
• surf - 3-D colored surface.
• fill3 - Filled 3-D polygons.
plot3(x,y,z) - generates a line in 3-space through the
points whose coordinates are the elements of x, y, z.

• These plots require a set of order triples ( x-y-z values) as input
114
The z-axis is labeled the
same way the x and y
axes are labeled
3 D Graphs

115
MATLAB uses a
coordinate
system
consistent with
the right hand
rule
3 D Graphs

Creating a grid in the x-y plane:
X and Y are the matrix of the x and y
coordinates of the grid points
respectively.
x and y are vectors that divides the
domain of the x and y respectively.
(-1,1)
(-1,4) (3,4)
(3,1)
3 D Graphs

For Example, if
z=xy2/(x2 + y2)
The value of z at
each point of the
grid is calculated
3 D Graphs

• Controls the direction from which the plot is
viewed.
• Done by specifying a direction in terms of
azimuth and elevation angles.
• View (az,el) or view([az,el])
Angle in the x-y plane measured
relative to the negative y axis
direction and positive in counter
clockwise direction
Angle of elevation from
x-y plane.
3 D Graphs - View Command

Printing the Figure
 using option Print under File menu
 using print command
 The Export option under File menu to
export figure to a variety of standard
graphics file format
 Using print command

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