WELCOME
EF 105
Fall 2006
Week 11
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Topics:
1. Plotting with MATLAB
2. Program Flows
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MATLAB Plotting: Basic Commands
•Graphing in MATLAB
•Several types of graphs can be created in MATLAB,
including:
• x-y charts
• column charts (or histograms)
• contour plots
• surface plots
•x-y charts are most commonly used in engineering courses,
so we will focus on these.
•x-y Charts in MATLAB
•The table on the next page shows several commands that are
available in MATLAB for plotting x-y graphs.
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Table of MATLAB Plotting Commands
MATLAB Command
Description
plot(x,y)
Plots y values versus x values
(x and y values stored in vectors).
plot(x,y,S)
Similar to plot(x,y) except the character
string S can be used to specify various line
types, symbols, and colors as shown in the
table on the next page.
loglog(x,y)
Like plot(x,y) but uses log-log axes
semilogx(x,y)
Like plot(x,y) but uses log scale for x-axis
semilogy(x,y)
Like plot(x,y) but uses log scale for y-axis
hold
Plot the next set of data on the same chart
title(‘text’)
Adds a title to the top of the graph.
xlabel(‘text’)
Adds a label to the x-axis.
ylabel(‘text’)
Adds a label to the y-axis.
grid on (or grid)
Turns on the grid lines.
grid off
Turns off the grid lines.
grid minor
Turns on the minor grid lines.
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Table of S Options for the MATLAB plot(x,y,S) Command
S
Color
S
Data
Symbol
S
Line
Type
b
Blue
.
Point
-
Solid
g
Green
O
Circle
:
Dotted
r
Red
x
x-mark
-.
Dash-dot
c
Cyan
+
Plus
--
Dashed
m
Magenta
*
Star
y
Yellow
s
Square
k
Black
d
Diamond
v
Triangle (down)
^
Triangle (up)
<
Triangle (left)
>
Triangle (right)
Note: Many of these options can be set using the Graph Property
Editor (illustrated in the following pages)
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Examples of using S options in the plot command:
plot(x, y, ‘k*-’) - Plot y versus x using a solid black line with an *
marker shown for each point
plot(x, y, ‘gd:’) - Plot y versus x using a dotted green line with a diamond
marker shown for each point
plot(x, y, ‘r+--’) - Plot y versus x using a dashed red line with a +
marker shown for each point
Example – MATLAB program to plot an x-y graph:
Enter the name of the program (Graph) in the MATLAB Command Window
and the graph (Figure 1) on the following page appears.
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Note that certain
features of the
graph may be
edited from this
window (called
the Graph
Property Editor).
See next page.
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Editing a graph
Changing Line
Series Properties
Begin by
pressing this
button to
enter “picking
mode”.
Double-click
on a graph
line or point
to open the
Property
Editor –
Lineseries
shown below.
You can
change
various line
series
properties
here. 8
Editing a graph
Changing Axes
Properties
Double-click
on an axis (or
a point on an
axis) to open
the Property
Editor – Axes
shown below.
Note that the
x-axis was
changed to a
log scale.
You can
change
various axes
properties
here.
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Editing a graph
Using features on
the Insert menu.
Use Insert –
Text Arrow to
add the arrow
and text
shown on the
graph.
Use Insert –
Text Box to
add the text
box shown on
the graph.
Note that various other features of graphs can be changed using the
Graph Properties Editor above.
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Graphing data points
Graphing data points is similar to graphing functions. The data points simply need to
be stored in vectors.
Example: Suppose that the power, P, dissipated by a resistor was measured in lab for
a variety of resistance, R, values using a constant voltage of 50 V. The measured
results are shown below. Graph P versus R.
Resistance
R (k)
Power
P (W)
10
248.3
22
110.2
47
50.4
68
36.1
100
24.2
220
11.0
470
5.25
680
3.85
1000
2.75
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Example: Try the following example in class:
• Calculate the area of a circle for a radius of 10, 15, 20, … , 75 (inches).
• Display the results in a table.
• Graph area versus radius.
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MATLAB Environment
Enter the following:
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Mathematics Example:Linear Systems
• Solve the system:
5 x  2 y  3 z  3
4 y  3 z  2
x  y  9 z  60
• A*S=B
• Enter the following MATLAB Code:
>> A=[5,-2,-3;0,4,3;1,-1,9];
>> B=[-3,-2,60]'; % Note vector transpose (‘)
>> S=linsolve(A,B)
• You should see:
S=
1.0000
-5.0000
6.0000
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Mathematics Example: Polynomial Roots
• Find the roots of the following system:
y  12 x 2  x  8
• Enter the following MATLAB code:
>> roots([12 -1 -8])
ans =
0.8592
-0.7759
Now enter the following:
>>
>>
>>
>>
>>
>>
a=12;
b=-1;
c=-8;
x=-1:0.1:1;
y=a*x.^2+b*x+c;
plot(x,y)
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Physics Example:
Graphical Solution of a Trajectory
• Problem:
A football kicker can give the ball an initial
speed of 25 m/s. Within what two elevation
angles must he kick the ball to score a field
goal from a point 50 m in front of goalposts
whose horizontal bar is 3.44 m above the
ground?
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Physics Example:
Field Goal Problem
Solution: The general solution is the “trajectory equation.”
gx 2
y  x tan( 0 )  2
2v0 cos 2 ( 0 )
where y = height, x = distance from goal, v0 = take-off speed, θ0 =
take-off angle. Given the take-off speed of 25 m/s, the
problem requires the solutions for θ0 that result in a minimum
height of y = 3.44 m at a distance of x = 50 m from the goal
post. Although an analytical solution is possible, a graphical
solution provides more physical insight.
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Physics Example:Field Goal Problem
• Enter the following MATLAB code for a graphical
solution:
>> v0=25;
>> x=50;
>> g=9.8;
>> y=3.44;
>> theta=5:.1:70;
>> theta_r=theta*pi/180;
>> z=y*ones(1,length(theta));
>> zz=x*tan(theta_r)-g*x^2./(2*v0^2*(cos(theta_r)).^2);
>> plot(theta,zz)
>> hold
Current plot held
>> plot(theta,z)
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Physics Example:
MATLAB Results
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Outputting a Table with Headings
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MATLAB Program Flows
Command
Command
Command
Command
Command
False
Test
Commands
to execute
if False
True
Commands
to execute
if True
Setup
Done
Commands
Command
Command
Straight Line Control
Command
Conditional Control
(branching structure)
Command
Iterative Control
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(looping structure)
MATLAB Program Flows (cont.)
Since conditional structures involve branching based on the result of logical tests
(such as a program that branches if x > 2), it is important to first introduce logical
expressions.
Logical Expressions
Logical variables in MATLAB can have values of true or false.
To create a logical variable, a logical values simply needs to be assigned to it.
For example:
A = true;
B = false;
Note that logical values also have a numerical equivalent:
true = 1
false = 0
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MATLAB Program Flows (cont.)
Logical Operators
Logical operators are used in MATLAB between two logical operands to yield a logical
result. The general form for logical expression with the 5 available binary operators is:
L1 logical operator L2
(for example: x > 2 AND x < 8)
where L1 and L2 are logical expressions or variables.
The general form for logical expression with the one available unary operators is:
logical operator L1
(for example: ~x > 2)
Logical Operators
Operator
Operation
Binary or unary
&
Logical AND
Binary
&&
Logical AND with
shortcut evaluation
Binary
|
Logical OR
Binary
||
Logical OR with
shortcut evaluation
Binary
xor
Logical Exclusive OR
Binary
~
Logical NOT
Unary
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MATLAB Program Flows (cont.)
Truth Tables for Logical Operators
L1
L2
L1 & L2 L1 | L2
AND
OR
xor(L1,L2)
Exclusive-OR
~L1
NOT
false
false
false
false
false
true
false
true
false
true
true
true
true
false
false
true
true
false
true
true
true
true
false
false
Precedence of Operations (1 = highest precedence, 5 = lowest precedence)
Precedence
Operator
1
Arithmetic operators (as described previously)
2
Relational operators (= =, ~=, >, >=, <, <=) from left to right
3
Unary NOT operator (~)
4
Logical AND operators (&, &&) from left to right
5
Logical OR and Exclusive OR operators (|, ||, xor) from left to right
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MATLAB Program Flows (cont.)
Examples of Logical Expressions
Logical Expression
(for x = 2, y = 5)
Result
x<4&x>1
true (1)
1<x<4
invalid expression
x==1|x==3
false (0)
~x < y
false (0)
xor(x > 3, y > 3)
true (1)
x = = 2| y = = 3 & x < 0
true (1)
Shortcut evaluation (a minor point)
What is the difference between Logical AND (&) and Logical AND with shortcut
evaluation (&&)? The difference is illustrated below:
L1 & L2
% L1 and L2 are both evaluated, then the results are ANDed
L1 && L2
% L1 is evaluated. If it is false, the result of the entire expression is
% false, so L2 is never evaluated.
Also note that && works only with scalars, where & works with either scalar or array
values.
The differences are between Logical OR (|) and Logical OR with shortcut
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evaluation (||) are similar to those described above for & and &&.
MATLAB Program Flows (cont.)
Conditional Control Structures in MATLAB
MATLAB offers three types of conditional control structures:
• IF – THEN – ELSE structure
• SWITCH structure
• TRY/CATCH structure
We will only cover the IF – THEN – ELSE structure as it is the most common.
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MATLAB Program Flows (cont.)
if relational/logical test
<commands to execute if test is true>
end
IF – THEN – ELSE structure
There are four versions of this
structure as shown.
if relational/logical test
<commands to execute if test is true>
else
<commands to execute if test is false>
end
if relational/logical test #1
<commands to execute if test #1 is true>
elseif relational/logical test #2
<commands to execute if test #2 is true>
end
Note that an unlimited number
of elseif statements could be
added to the last two structures.
if relational/logical test #1
<commands to execute if test #1 is true>
elseif relational/logical test #2
<commands to execute if test #2 is true>
else
<commands to execute if all tests above are false>
end
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MATLAB Program Flows (cont.)
% IF - THEN - ELSE structure - Example 1
% EF105
% filename: if1.m
% Sample program to calculate weekly pay. Overtime paid for over 40 hours.
format compact
Hours = input('Enter number of hours worked this week: ');
Rate = input('Enter amount paid per hour: $');
Pay = Hours*Rate;
if Hours > 40
disp('You earned overtime pay.')
Pay = Pay + (Hours-40)*Rate/2;
end
fprintf('Your pay is $%0.2f\n',Pay)
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MATLAB Program Flows (cont.)
% IF - THEN - ELSE structure - Example 2
% EF 105
% filename: if2.m
% Sample program to calculate weekly pay. Overtime paid for over 40 hours.
format compact
Hours = input('Enter number of hours worked this week: ');
Rate = input('Enter amount paid per hour: $');
if Hours <= 40
disp('No overtime earned.')
Pay = Hours*Rate;
else
disp('You earned overtime pay.')
Pay = 40*Rate + (Hours-40)*Rate*1.5;
end
fprintf('Your pay is $%0.2f\n',Pay)
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MATLAB Program Flows (cont.)
Function y(x) is defined as follows :
 0,
 4x,

y(x)  
  4x  80,
0,
x0
0  x  10
10  x  20
20  x
y
40
x
0
10
20
% IF - THEN - ELSE structure - Example 3
% EF 105
% filename: if3.m
% Sample program to calculate y(x) defined
% over several ranges of x.
format compact
x = input('Enter value of x: ');
y = 0; % This value will be replaced if
% x is between 0 and 20.
if 0 <= x & x < 10
y = 4*x;
elseif 10 <= x & x < 20
y = -4*x+80;
end
fprintf('y(x) = %0.2f\n',y)
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MATLAB Program Flows (cont.)
% IF - THEN - ELSE structure - Example 4
% EF 105
% filename: if4.m
% Sample program to display letter grade for an input
% numerical grade using a standard 10 point scale.
% Display error message if grades are from 0 to 100.
format compact
Grade = input('Enter numerical grade (0 to 100): ');
if Grade < 0 | Grade > 100
disp('Invalid grade')
elseif Grade >= 90
disp('Grade = A')
elseif Grade >= 80
disp('Grade = B')
elseif Grade >= 70
disp('Grade = C')
elseif Grade >= 60
disp('Grade = D')
else
disp('Grade = F')
end
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MATLAB Flow Control
The “for” statement
for index = start : [increment :] end
statements
end
index, start, increment, and end do not need to be integer valued
increment is optional, if increment is not specified
increment defaults to 1
index can be incremented positive (increment > 0) or
negative (increment < 0)
loop stops when index > end (or index < end)
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MATLAB PLOTTING
Adding a Legend for multiple graphs
“legend” remembers
the order the graphs
were plotted
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MATLAB Program Flows (cont.)
for loopVar = loopVector
Command 1
Command 2
…
Command n
end
The for loop
The for loop is used to execute a block of
statements a specified number of times. It has
the form shown to the right.
Example
Evaluate the following summation:
Sum 
10
3
i

i 1
% filename: for1.m
% Example: Use a for loop to find sum(i^3) for i = 1 to 10.
Sum = 0;
%Initialize variable to zero
for i = 1:1:10
Sum = Sum + i^3;
end
fprintf('Sum = %0.0f\n',Sum);
% filename: for2.m
% Example: Use a for loop to find sum(i^3) for i = 1 to 10.
Sum = 0;
%Initialize variable to zero
for i = [1,2,3,4,5,6,7,8,9,10]
Sum = Sum + i^3;
end
fprintf('Sum = %0.0f\n',Sum);
Results:
>> for1
Sum = 3025
>> for2
Sum = 3025
>>
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MATLAB Program Flows (cont.)
Example
Write a program to determine the balance after N years on an account that contains
an initial deposit D and earns a simple interest of I percent. Prompt the user to
enter values for N, D, and I.
% Sample program to determine the final balance in a savings account where
% D = initial deposit
% I = interest rate (percent)
% N = number of years
% Filename: Interest.m
D = input('Enter the amount of the initial deposit: $');
I = input('Enter the percent interest rate: ');
N = input('Enter the number of years: ');
Balance = D; %Initial value in the account
for years = 1:N
Balance = Balance*(1+I/100);
end
fprintf('Final balance = $%0.2f\n',Balance);
>> Interest
Enter the amount of the initial deposit: $1000
Enter the percent interest rate: 6
Enter the number of years: 10
Final balance = $1790.85
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MATLAB Program Flows (cont.)
Nested for loops
For loops can occur within other for loops as shown in the examples below. Note that
while indenting loops is not required, it helps to make them more readable.
for loopVar1 = loopVector1
Command 1
for loopVar2 = loopVector2
Command A1
Command A2
…
Command An
end
Command 2
…
Command n
end
What value for Sum is printed
in the program below?
Sum = 0;
for I = 1:10
for J = 1:15
Sum = Sum + 1;
end
End
fprintf(‘\nSum = %0.0f’,Sum);
Example:
The example program on the following slide:
• Prompts the user to enter each value of a 2D array
• Calculates the maximum value of the array (and the row/column where the max
37
occurs)
MATLAB Program Flows (cont.)
% Program to prompt the user to enter values in a matrix
% by row and column number.
% Also find the max value in the matrix.
% Filename: Matrixmax.m
format compact
Rows = input('Enter the number of rows in the matrix: ');
Columns = input('Enter the number of columns in the matrix: ');
for i = 1:Rows
for j = 1:Columns
fprintf('Enter A(%0.0f,%0.0f):',i,j);
A(i,j) = input(' ');
end
end
A
% find the max value in the matrix
Max = A(1,1);
%Set max to first value in array
MaxRow = 1;
MaxCol = 1;
for i = 1:Rows
for j = 1:Columns
if A(i,j)> Max
Max = A(i,j);
MaxRow = i;
MaxCol = j;
end
end
end
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fprintf('Max value in array A is A(%0.0f,%0.0f) = %0.2f\n',MaxRow,MaxCol,Max);
MATLAB Program Flows (cont.)
>> Matrixmax
Enter the number of rows in the matrix: 2
Enter the number of columns in the matrix: 3
Enter A(1,1): 12
Enter A(1,2): 14
Enter A(1,3): 17
Enter A(2,1): 23
Enter A(2,2): 11
Enter A(2,3): -8
A =
12
14
17
23
11
-8
Max value in array A is A(2,1) = 23.00
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MATLAB Exercise 2
• See the Word document for this
exercise and perform at end of
class on your own!!
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