1. Class 9.1 Chapter 4 Sections: 4.1, 4.2, 4.3
MatLab – Palm Chapter 4, Part 1 Relational Operators, Logical Operators and Conditional Statements
Class 9.1
Chapter 4
Sections: 4.1, 4.2, 4.3
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ENGR 111A – Fall 2004

2. RAT 9.1
Take out a piece of paper, write your name and team number, today’s date and RAT 9.1.
In 2-minutes, Individually translate the following English logical statement into MATLAB and write the MATLAB statement on your paper.
Assign the variable named Z with the value that results from: x greater than 5 or x less than 1
Assume that x exists in the workspace
Keep for your own notes.
Answer: Z = x>5|x<1
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ENGR 111A – Fall 2004

3. Learning Objectives Students should be able to:
Use relational operators to develop relational expressions (i.e., x<y).
Use logical operators to develop logical expressions (i.e., (x<y) & (a>b) ).
Use logical functions given in Table (p. 198).
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ENGR 111A – Fall 2004

4. 4.2 Relational Operators (p. 191)
MATLAB has 6 relational operators to make comparisons between variables. See Table (p. 191).
< less than
> greater than
<= less than or equal to
>= greater than or equal to
== equal to (You will get this one wrong in the exam!)
~= not equal to
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ENGR 111A – Fall 2004

5. RELATIONAL OPERATORS Results of comparison using relational operators:
ZERO, if comparison is false.
False = 0
ONE, if comparison if true.
True = 1
If comparing numbers, any non-zero is considered “true”
1/3/2019
ENGR 111A – Fall 2004

6. EXAMPLE >> x=2; >> y=3;
>> z=x<y; % same as z = (x<y)
>> u=x==y; % same as u = (x==y)
>> z,u
z = 1
u =
Here z and u are “logical” variables (p. 192).
1/3/2019
ENGR 111A – Fall 2004

7. 4.3 Logical Operators
MATLAB has five logical operators ( also called Boolean operators) shown in Table (p. 194):
~ (NOT): z = ~x.
& (AND): used to link logical expressions:
z =(x<y) & (a>b).
| (OR): used to link logical expressions:
q =(x<y) | (a>b).
&& (Short-Circuit AND): used for operations on 2 scalar logical expressions.
|| (Short-Circuit OR): used for operations on 2 scalar logical expressions.
(Note | is the shift-\ key, above Enter).
xor (exclusive OR) is used to link logical expressions:
w = xor(A, B).
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ENGR 111A – Fall 2004

8. ORDER OF PRECEDENCE SEE TABLE 4.3-2 (p. 195)
First: parenthesis, innermost first.
Second: arithmetic operators and logical NOT (~)
Evaluated from left to right.
Third: relational operators
Fourth: logical AND.
Fifth: logical OR.
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ENGR 111A – Fall 2004

9. THE NOT OPERATOR ( ~ ) Given an array A:
~A returns an array of the same dimension.
~A has ones where A is zero and zeros where A is nonzero.
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ENGR 111A – Fall 2004

10. EXAMPLE of the ~ Operator
>> x = [6, 3, 9]; y = [14, 2, 9];
>>z = ~x
z =
[0, 0, 0]
>>z = ~x > y % same as z = (~x) > y
>>z = ~( x > y)
[1, 0, 1]
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ENGR 111A – Fall 2004

11. EXAMPLE continued What would z = (x>~y) return?
How about z = (x~>y)?
How about z = (x~=y)?
After you write down what you think they return, type them into Matlab
(Recall x = [6, 3, 9]; y = [14, 2, 9])
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ENGR 111A – Fall 2004

12. Practice
For the arrays x and y in the previous example, show using MATLAB that
z = ~( x > y) is equivalent to
z = ( x <= y )
(Recall x = [6, 3, 9]; y = [14, 2, 9])
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ENGR 111A – Fall 2004

13. THE AND OPERATOR ( & )
The & operator compares two arrays A and B of the same dimension and returns an array of the same dimension.
Returns ONE when both of the corresponding elements of A and B are non-zero.
Returns ZERO when either or both of the corresponding elements of A and B are zero.
1/3/2019
ENGR 111A – Fall 2004

14. EXAMPLE of the & Operator
z = 0 & 3 returns z = 0.
z = 2 & 3 returns z = 1.
z = 0 & 0 returns z = 0.
z = [ 5, -3, 0, 0] & [ 2, 4, 0, 5] returns z = [1, 1, 0, 0].
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ENGR 111A – Fall 2004

15. ORDER OF PRECEDENCE FOR OPERATOR TYPES (AGAIN)
SEE TABLE (p. 195)
First: parenthesis, innermost first.
Second: arithmetic operators and logical NOT (~)
Evaluated from left to right.
Third: relational operators
Fourth: logical AND.
Fifth: logical OR.
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ENGR 111A – Fall 2004

16. INDIVIDUAL EXERCISE (3 min).
Show that
(a) z1 = 1&2 + 3
is equivalent to
z2 = 1&( 2 + 3) and,
(b) z3 = 5 < 6&1
z4 = ( 5 < 6) &1
What about z5 = 5 < (6&1)? Are these parentheses necessary?
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ENGR 111A – Fall 2004

17. THE OR OPERATOR ( | )
The | operator compares two arrays A and B of the same dimension and returns an array of the same dimension.
Returns ONE when either or both of the corresponding elements of A and B are non-zero.
Returns ZERO when both of the corresponding elements of A and B are zero.
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ENGR 111A – Fall 2004

18. EXAMPLE of the | OPERATOR
z = 0|3 returns z = 1.
z = 0|0 returns z = 0.
z = [ 5, -3, 0, 0] | [2, 4, 0, 5] returns z = [ 1, 1, 0, 1].
What value does the expression below assign to z? z = 3 < 5 | 4 ==7
Test in Matlab. Write out how to solve this problem by hand.
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ENGR 111A – Fall 2004

19. XOR (Exclusive OR)
xor(A,B) return zeros where A and B are either both nonzero or both zero. It returns ones where either A or B is nonzero, but not both.
This can be written as a function:
function z = xor(A,B)
z = (A|B) & ~(A&B);
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ENGR 111A – Fall 2004

20. Example of xor and | Operators
z = xor([3,0,6], [5,0,0]);
Returns z = [0,0,1].
z = ([3,0,6] | [5,0,0]);
Returns z = [1,0,1].
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ENGR 111A – Fall 2004

21. RELATIONAL AND LOGICAL FUNCTIONS
MATLAB provides additional relational and logical functions:
any(x)
all(x)
find(x)
finite(x)
etc.
SEE TABLE (p. 198)
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ENGR 111A – Fall 2004

22. Comparisons
Note: Truth Table in Table (p. 196). A good way to deal with complex logic problems. Some people do not use it much and prefer to combine switch, if and while structures.
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ENGR 111A – Fall 2004

23. Example
Average daytime highs in College Station for this week are: t_ave = [ ]
Forecasted highs are: t_now = [ ]
How many days will the temperature be above average or average?
How many days will the temperature be either below or above average?
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ENGR 111A – Fall 2004

24. Example 4.3-1 & T4.3-2 REVIEW Example 4.3-1 (p. 199)
Work T4.3-2 (p. 200) as a script file:
Do the plot if you can.
Don’t forget the comments at the top to identify your work, etc.
Make the format compact and short.
Make sure you check the answers.
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ENGR 111A – Fall 2004

25. T4.3-2 Solution % Program TYU4p3_2.m
% Solves Test Your Understanding problem T4.3-2 on p. 200.
% Set the values for initial speed, gravity, and angle.
v0 = 20; g = 9.81; A = 40*pi/180;
% Compute the time to hit.
t_hit = 2*v0*sin(A)/g;
% Compute the arrays containing time, height, and speed.
t = 0 : t_hit/100 : t_hit;
h = v0*t*sin(A) - 0.5*g*t.^2;
v = sqrt(v0^2 - 2*v0*g*sin(A)*t + g^2*t.^2);
% Determine when the height is less than 4m or the speed is greater than
% 17m/s.
u = find(~(h<4 | v>17));
% Compute the corresponding times.
t_1 = (u(1) - 1)*(t_hit/100);
t_2 = u(length(u) - 1)*(t_hit/100);
% Plot to check your answer.
figure(1) ; plot(t,h) ; figure(2) ; plot(t,v)
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ENGR 111A – Fall 2004

26. Assessment
Take out a sheet of paper and Individually, write a brief description of the MATLAB topic that is the “muddiest” to you so far in Chapter 4.
Then, as a team, agree on a topic you would like for me to cover in more detail next time.
Turn in your paper with your team number
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ENGR 111A – Fall 2004

27. Assignment #8 Individual assignment.
Palm Chapter 4: (starting on p. 241)
Problems #5, 10, 11 & 13.
Submit a clear write-up of your problems
DUE: Nov. 2, 2004
Reading Assignment: Sections 4.4 and 4.6.
1/3/2019
ENGR 111A – Fall 2004