Chapter 4 Controlling Execution CSE 1010

22 Objectives Evaluate logical expressions –Boolean –Relational Change the flow of execution –Diagrams (e.g., flowcharts) –Selection: if and switch statements –Iteration: for and while loops

3 Suppose… Problem: Assign letter grades for course performance: avg >= 90 gets A 80 <= avg < 90 gets B 70 <= avg < 80 gets C 60 <= avg < 70 gets D avg < 60 gets F Input: list of student averages

4 Program Execution Recall Algorithm = a step-by-step sequence of instructions that leads to the solution of a specific problem Program = implementation of an algorithm in a programming language So far, all our scripts have executed the statements one-by-one in order, i.e., sequentially Is that always what we want to do?... If not, we need something new…

5 Example, cont’d if avg > = 90, then letter = ‘A’ else … i.e., if (expression is true) execute code for true else execute code for false avg >= 90? letter = ‘A’ true false do other

6 General Syntax of the IF statement if (logical expression 1 is true)  execute code block 1 else if (logical expression 2 is true)  execute code block 2 … else if (logical expr m is true)  execute code block m else execute code block for no conditions were true ONLY ONE code block ever runs Can only have ONE else

7 Logical Expressions Any collection of constants, variables, and operators whose result is a Boolean true or false value MATLAB prints 1 for true, 0 for false But you have to specify values as true or false Types: Boolean, relational

8 Relational Operators < strictly less than < = less than or equal to > strictly greater than > = greater than or equal to = = equal to ~ = not equal to

9 Relational Examples A = 3; B = 6; A < B ans 1 A > B ans 0 A == B ans 0 A ~= B ans 1 A = [ ]; B = [ ]; A < B ans A > B ans A == B ans A ~= B ans

10 Logical Operators &element-wise logical AND (vectors) |element-wise logical OR (vectors) && logical AND (scalar) || logical OR (scalar) ~unary NOT Generally, these are the ones most used in conditional expressions

11 Logical Examples A = 4; % Declaration B = -2; % Declaration A > 2 && B < 2 % Is A greater than 2 % and is B less than -2? ans 1 C = [ ]; D = [ ]; A > 2 && C > D ??? Operands to the || and && operators must be convertible to logical scalar values.

12 Truth Table ABA & BA | B~A~B False FalseFalseTrueTrue TrueFalseTrueTrueFalse FalseFalseTrueFalseTrue True TrueTrueFalseFalse

13 Example 1 A = 4; B = 8; C == (A && B > 2) ans = 1 C == ((A && B) > 2) ans = 0 Explanation 

Explanation

Let’s try that … A = 4; B = 8; C = true; A^2 = = B && C Ans ?

Explanation On first glance, one may be tempted to try it as (A^2) == (B && C) where one soon finds B && C would give an error. But the == has higher precedence than &&, so what one really has is (A^2 == B) && C which gives a false result.

17 Example 2 A = 4; B = 8; C = 1 % True A ^ 2 == B && C ans = ? % Can you explain? % Note: ans = 0!

Operator Precedence The precedence of operators governs the order in which operations are performed.  … on the next slide Operations listed on the same row are performed from left to right. The normal precedence of operators can be overruled by enclosing preferred operations in parentheses (...)  … recommended to avoid errors!

19 Matlab Precedence of Operators.’.^Scalar transpose and power ’ ^Matrix transpose and power + - ~Unary operators.*./.\ * / \Multiplication, division, left division + -Addition and subtraction :Colon operator = > == ~=Comparison &Element-wise AND |Element-wise OR &&Logical AND ||Logical OR The normal precedence of operators can be overruled by enclosing preferred operations in parentheses!

20 Try These: The test is run element-by-element on two row vectors, A and B: A = [ ], B = [ ] C = A < B  C = [ ] D = A < 5  D = [ ] E = B < 5  E = [ ] C & D % Try in Matlab ~ E% Try in Matlab

Short circuit Evaluation (on your own time) Evaluate only as much of the expression as needed to get the result A && condition short-circuits to false if the left operand evaluates to false A || condition short-circuits to true if the left operand evaluates to true Example: If n is not valid, the evaluation will stop and v(n) will cause an error n =Input('Enter a index value'); % check that n is a valid index if ( n 0 ) … 21

Flow Chart A graphical representation of your algorithm Show solution design (algorithm) independent of the code implementation Flow Chart elements: : to begin or end a section of code : indicates input or output processes : indicates a decision point : for general statements and calculations 22

Example Flow Chart Algorithm: Define a vector of mph values Convert mph to ft/s Combine the mph and ft/s vectors in to a matrix Create a table title Create column headings Display the table Flow Chart: Write a program to convert from mph to ft/s Start Define a vector of mph Convert mph to ft/s Create a table Output table End  Recommendation: Transfer the algorithm/flowchart steps to your m-file as comments and then add appropriate code between the comments 23

Flow of control Sequential is restrictive, does not help solve some problems ( e.g., decision problems, etc.) –Just as humans change their minds depending on circumstances, machines should too ;-)) Selection –Choosing to execute a particular set of statements depending on a condition Repetition –Executing a set of statements more than one time (loops). 24

Conditional Execution in General Basic conditional execution requires two things: 1) A logical expression, and 2) A code block If the expression is true, the code block is executed. Otherwise, execution is resumed at the instruction following the code block IF condition statements true false 25

Compound Conditional = Selection  By introducing elseif and else, we allow the possibility of either conditional or unconditional execution when a test returns false. 26 IF condition elseIF condition statements1 stmts2 elseIF condition stmtsNstmtsN+1 else end if

MATLAB if statements Every if statement must be completed with a companion end statement  Shows where to pick up after executing or not executing a conditional code block 27 IF condition elseIF condition statements1 stmts2 elseIF condition stmtsNstmtsN+1 else if end

What Executes? What Result? >> a = 16; >> b = 4; >> if (a > b && b > 6) c = 3; elseif (b > 5) c = 4; else c = 5; end; >> c 28

Does This Program Work? score = input(‘enter score: ’); if (score > 55) disp( ‘D’ ) elseif (score > 65) disp( ‘C’) elseif (score > 80) disp( ‘B’ ) elseif (score > 93) disp( ‘A’ ) else disp( ‘Not good…’ ) end 29

Vector Conditionals Because in Matlab the Focus is on arrays, let’s see what happens when we apply a conditional to an array In the following slide, we use the example of a very simple array: a row vector 

Vector Conditional Example >> x =[ ]; >> if x < 0 disp('some elements of x are negative') else y = sqrt(x) end ans y = i So... x < 0 must have been false!

Example, cont’d >> x =[ ]; >> if x > = 0 disp('some elements of x are negative') else y = sqrt(x) end ans y = i What’s happening?  So x > = 0 must have been false!

Conditionals and Arrays:... How it works When the test if logical expression is performed where the logical expression may be an array, the test returns the value “ true ” only if all the elements of the logical expression are true! >> x =[ ]; >> if x < 0 >> x =[ ]; >> if x >= 0 33 x < 0 results in [0 1 0] x >= 0 results in [1 0 1] But the if returns the value “false” in both cases!!

Matlab Logical Functions Function all(v) any(v) all(A) any(A) Operation Returns scalar = 1 if all elements of v have nonzero values, otherwise returns 0 Returns scalar = 1 if any element of v has a nonzero value, otherwise returns 0 Returns a row vector, same number of columns as matrix A, where value 1 indicates column had all nonzero values, 0 otherwise Returns a row vector, same number of columns as matrix A, where value 1 indicates column had any nonzero value, 0 otherwise 34

Switch Statement To select one from a set of alternatives  May be used in place of multiple if-else statements  Template: 35 switch case case … case otherwise end

If-else versus Switch code = 11; switch code case 10 disp(‘Turn equipment off’); case 11 disp(‘Caution – recheck’); case 13 disp(‘Turn on fan’); otherwise disp(‘Normal temperature’); end … code = 11; if(code == 10) disp(‘Turn equipment off’); elseif(code == 11) disp(‘Caution – recheck’); elseif(code == 13) disp(‘Turn on fan’); else disp(‘Normal temperature’); end … 36

The Switch Statement Formal Syntax must be a single value or a set enclosed in {…} Code block may contain any sequence of legal MATLAB code including if statement, switch, or iteration switch case case. case otherwise end 37

Example Write a program that converts a test score into its equivalent letter grade. score = input(‘Enter score out of 100: ’); score = floor(score/10); switch(score) case {10,9} letterGrade = ‘A’; case 8 letterGrade = ‘B’; case 7 letterGrade = ‘C’; case 6 letterGrade = ‘D’; otherwise letterGrade = ‘F’; end fprintf(‘Your Grade is %c\n’, letterGrade); % Cool! 38