Relational & Logical Operators

Transcription

1 Relational & Logical Operators ELEC 206 Prof. Siripong Potisuk 1 Objectives Learn how to change the flow of execution of a MATLAB program through some kind of a decision-making process within that program The program makes these decisions by comparing values of some variables The comparison is done by using a combination of relational & logical operators 2 1

2 Relational Operator Compare two quantities (numbers, vectors, matrices, etc.) by determining whether a comparison statement (e.g., 5 < 8) is true or false If "true", MATLAB gives the comparison a value of one (1) If "false", MATLAB gives the comparison a value of zero (0) Can be used in mathematical expressions Used in combination with other commands to make decisions about the flow of the program 3 No space between characters for operators that have two of them Equal to comparison has two equal signs (==), not one 4 2

3 Relational Operator When comparing array to scalar, MATLAB compares scalar to every member of array. The result is an array of the same dimensions as the original but only contains 1's and 0's When comparing two arrays, - they must be of the same dimensions - element-by-element comparison - the result is an array of the same dimensions as the originals but only contains 1's and 0's To find the number of 1 s (true s), use the sum command 5 It helps to picture in your mind that the result of a logical comparison (a) is a vector (b) has a 0 or 1 corresponding to each original element >> x=8:12 x = >> x>10 ans = False False False True True 6 3

4 Example >> x=8:12 x = >> x>10 ans = >> x==11 ans = >> x>=7 ans = Precedence Relational operations have equal precedence and evaluated left to right When mixed with arithmetic operations, relational operations always have lower precedence than arithmetic operations 8 4

5 Logical Indexing (Subscripting) The result of performing relational operation is called a logical vector or array (a sequence of 0 s and 1 s) Can use logical vector to get actual values that satisfy relation, i.e., using logical vector as a vector of indices for the vector of values The technique doesn't quite work with arrays (matrices) 9 EXAMPLE: What are the numbers from 1-10 that are multiples of 3? >> x = 1:10 x = >> index = (rem(x,3)==0) index = >> multiplesof3 = x(index) multiplesof3 = Note: Think of x(index) as pulling out of x all elements that have a 1 in the corresponding element of index 10 5

6 Logical Operator Makes MATLAB perform a logical operation on one or two numbers or expressions Three logical operators: &,, ~ a&b does the logical AND operation on a and b a b does the logical OR operation on a or b ~a does the logical NOT operation on a Arguments to all logical operators are numbers: 0 is false and any non-zero number is true Result of logical operator is a logical one (true) or zero (false) according to the truth table 11 AND is true if both inputs are true, otherwise it is false OR is true if at least one input is true, otherwise it is false XOR (exclusive OR) is true if exactly one input is true; otherwise it is false NOT is true if the input is false, otherwise it is false 12 6

7 Logical Operator When operating on array and scalar, MATLAB does element-by-element operation on each array element with scalar resulting in an array of the same dimensions as the original with 1's and 0's When using & and on two arrays, - they must be of the same dimensions - element-by-element operation - the result is an array of the same dimensions as the originals but only contains 1's and 0's ~(not) only operates on one array 13 Can combine arithmetic, relational, and logical operators 14 7

8 EXAMPLE Given the following description and an array of ages: Child 12 or less years Teenager more than 12 and less than 20 years Adult 20 or more years >> age=[ ]; >> age>=13 & age<=19 % Who are teenagers? ans = These mark the two teenagers >> ~(age>=13 & age<=19) %Who is not a teenager? ans = >> age>19 age<13 %Who is an adult or a child? ans = Built-in logical functions MATLAB has some built-in functions or commands for doing logical operations and related calculations Three are equivalent to the logical operators and(a,b) same as A&B or(a,b) same as A B not(a) same as ~A 16 8

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10 EXAMPLE The daily maximum temperatures (in F) in Washington DC during the month of April 2002 were: 58, 73, 73, 53, 50, 48, 56, 73, 73, 66, 69, 63, 74, 82, 84, 91, 93, 89, 91, 80, 59, 69, 56, 64, 63, 66, 64, 74, 63, 69. Use relational and logical operations to determine a) number of days the temperature was above 75 b) number of days the temperature was between 65 and 80 c) the days of the month when the temperature was between 50 and >> T = [ ]; >> Ndays_Tabove75 = sum(t > 75) Ndays_Tabove75 = 7 >> T_65and80 = sum(t>=65 & T<=80) T_65and80 = 12 >> Dates_50and60 = find(t>=50 & T<=60) Dates_50and60 =