1. MATLAB Logical Expressions
Topics:
1. Relational and Logical Operators
Instructor notes:
This lecture basically covers branching in Matlab by looking at if-end, if-else-end, and if-elseif-else-end conditional statements. For students who have not done any prior programming this will be a fairly large concept to become comfortable with since they need to get used not only to the idea of a program taking different paths, but also the syntax of setting up the conditions.
Instructional objectives:
Acquire basic concepts of programming including evaluation of conditions
Acquire knowledge about relational and logical operators.
Use conditional statements (if–end/if-else–end/if-elseif-else–end) in MATLAB
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2. Examples >> 5 > 8 ans = This statement is FALSE, so ans = 0
This statement is FALSE, so ans = 0
>> 5 < 8
ans = 1
This statement is TRUE, so ans = 1
Instructor notes:
Here some quick examples. In the first Matlab asks “Is 5 greater than 8?”. Since the answer is false, the “5>8” relationship evaluates to FALSE, which is 0. So, Matlab returns a 0 for this relationship.
In the next example Matlab asks, “Is 5 less than 8?”. Since the answer is true, the “5<8” relationship evaluates to TRUE, which is 1.
In the third example, the result of the comparison from example 2 is assigned to the variable res. As a result res has the value 1.
>> q = 5 < 8
q = 1
Assigns the result of the conditional operation to the variable name 'q'
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3. The Logical Operators In MatLab: 1 is TRUE 0 is FALSE
Operator Name Example Meaning
& AND A & B TRUE when both A and B are true
| OR A | B TRUE if either A or B are true
~ NOT ~ A TRUE if A is false.
In MatLab:
1 is TRUE
0 is FALSE
Actually, any number is true, except for 0, which is false.
Instructor notes:
In addition to the relational operators, we also have logical operators that evaluate operands to determine if a specific combination of the operands is true or false. The ampersand (&) is the operator used to evaluate if A AND B are true. For the AND condition to be true, both operands in the AND evaluate to true. A vertical bar (|) is used to evaluate if A OR B are true. For the OR condition to be true, either one or both of the operands in the OR must evaluate to true. The tilde (~) is the NOT operator. It negates the state of the operand. So, for ~(operand) to be TRUE, the operand must be false, and for ~(operand) to be FALSE, the operand must be false. Because some students may have experience with C/C++, it might be a good idea to point out that the NOT operator is different in Matlab than it is in C/C++ where NOT is represented by a “!”.
It’s important to point out that nonzero numbers evaluate to TRUE and zero evaluates to FALSE. This can be difficult to get a grasp of, that the number 8, for example, would evaluate to TRUE, which is 1. There will be examples of this on the next slide.
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4. Examples of logical operations
3 and 7 are both TRUE.
So (3 & 7) is evaluated as (1 & 1)
which is TRUE (= 1)
a = 1
>> b = 5 | 0
b = 1
Instructor notes:
These are very simple examples of logical operators which show the students the concept. They can read more from the book.
5 is TRUE and 0 is FALSE
So (5 OR 0) is TRUE (= 1)
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5. Math, Relational and Logical Operators Order of Precedence
Name
Highest 1
( )
Parentheses 2 ^
Exponent 3 ~
Negation (Logical "NOT") 4
* /
Multiply, Divide 5
+ –
Add, Subtract 6
< > <= >= == ~=
Relational Operators 7
&
Logical "AND"
Lowest 8 |
Logical "OR"
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6. Order of precedence example
>> y = 6 < == 20/2
>> y = (6 < 10) + (10 == 20/2)
= 6 < == 10
= 6 < 20 == 10
TRUE
TRUE
TRUE +
= 1
= 1
Instructor Notes:
This example shows them how logical operators and the order of precedence works. == 1 10
Solution :
y = 2
Solution :
y =
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7. RELATIONAL OPERATORS >> 5 + 4 > 8 ans = 1
>> 5 + (4>8) 5
>> y = ~1 & 0
y =
Addition is done first, so true (1)
4>8 is false, so add 0
~ is performed first, then &
Instructor notes:
Here some quick examples. In the first Matlab asks “Is 5 greater than 8?”. Since the answer is false, the “5>8” relationship evaluates to FALSE, which is 0. So, Matlab returns a 0 for this relationship.
In the next example Matlab asks, “Is 5 less than 10?”. Since the answer is true, the “5<10” relationship evaluates to TRUE, which is 1. The result of the comparison is then assigned to the variable a. As a result a has the value 1.
In the third example, three different relationships are evaluated. The first, “6<10”, evaluates to 1. The second, “7>8”, evaluates to 0. The third, “5*3==60/4” which becomes “15==15” evaluates to 1. The results of each of these relationships is summed and then the sum stored in y. .
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8. Arrays in Logical Expressions
Use of arrays in logical expressions will produce an array of 1s and 0s using element-by-element comparisons
T=[ ];
>>T>32
ans =
U=[ ];
>>T&U
>>~(T&U)
>>sum(T>32)
ans = 3
>> find(T>32)
>>find(T>32 & T<60)
2 5
Instructor notes:
In addition to the relational operators, we also have logical operators that evaluate operands to determine if a specific combination of the operands is true or false. The ampersand (&) is the operator used to evaluate if A AND B are true. For the AND condition to be true, both operands in the AND evaluate to true. A vertical bar (|) is used to evaluate if A OR B are true. For the OR condition to be true, either one or both of the operands in the OR must evaluate to true. The tilde (~) is the NOT operator. It negates the state of the operand. So, for ~(operand) to be TRUE, the operand must be false, and for ~(operand) to be FALSE, the operand must be false. Because some students may have experience with C/C++, it might be a good idea to point out that the NOT operator is different in Matlab than it is in C/C++ where NOT is represented by a “!”.
It’s important to point out that nonzero numbers evaluate to TRUE and zero evaluates to FALSE. This can be difficult to get a grasp of, that the number 8, for example, would evaluate to TRUE, which is 1. There will be examples of this on the next slide.
P. 8
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9. Tips for HW MAT-08 CH. 6 prob 1,3,and 6
Best to write out prob 1 & 3. Let’s look at
Problem 2d to prepare for HW
Keep Order of Precedence chart nearby! On page 178
Problem 6 – you’ll need to know sum( ) and find () functions.. Let’s look at sample prob. 6-1 on page Very Similar…