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

RecallAlgorithm = 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

elseexecute code for false

avg >= 90?

letter = ‘A’

true

false

doother

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

elseexecute 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 falseBut 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

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Relational ExamplesA = 3;B = 6;A < Bans 1A > Bans 0A == Bans 0A ~= Bans 1

A = [3 2 1 7];B = [6 5 4 3];A < Bans 1 1 1 0A > Bans 0 0 0 1A == Bans 0 0 0 0A ~= Bans 1 1 1 1

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

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Logical ExamplesA = 4; % DeclarationB = -2; % DeclarationA > 2 && B < 2 % Is A greater than

2 % and is B less than

-2?ans

1C = [3 6 9 12];D = [2 4 8 16];A > 2 && C > D

??? Operands to the || and && operators must be convertible to logical scalar values.

12

Truth Table

A B A & B A | B ~A ~B

False False FalseFalse FalseFalse TrueTrue TrueTrue

False True FalseFalse TrueTrue TrueTrue FalseFalse

True False FalseFalse TrueTrue FalseFalse TrueTrue

True True TrueTrue TrueTrue FalseFalse FalseFalse

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.

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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 slideOperations 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!

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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 ORThe normal precedence of operators can be overruled by enclosing

preferred operations in parentheses!

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Try These:

The test is run element-by-element on two row vectors, A and B:

A = [2 4 6 8], B = [1 3 9 27]C = A < B C = [0 0 1 1] D = A < 5 D = [1 1 0 0]E = B < 5 E = [1 1 0 0]

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 indexif ( n <= length(v) && n > 0 )

…

21

Flow Chart

A graphical representation of your algorithmShow 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, and2) A code block

If the expression is true, the code block is executed.

Otherwise, execution is resumed at the instruction following the code block

IFcondition

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.

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IFcondition

elseIFcondition

statements1 stmts2

elseIFcondition

stmtsN stmtsN+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

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IFcondition

elseIFcondition

statements1 stmts2

elseIFcondition

stmtsN stmtsN+1

elseif

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

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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 =[4 -9 25];

>> if x < 0

disp('some elements of x are negative')

else

y = sqrt(x)

end

ans y =

2.0000 0 + 3.0000i 5.0000

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So . . . x < 0 must have been false!

Example, cont’d

>> x =[4 -9 25];

>> if x > = 0

disp('some elements of x are negative')

else

y = sqrt(x)

end

ans y =

2.0000 0 + 3.0000i 5.0000

32What’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 =[4 -9 25];

>> if x < 0

>> x =[4 -9 25];

>> if x >= 0

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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

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Switch StatementTo select one from a set of alternatives

May be used in place of multiple if-else statements

Template:

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switch <parameter>case <case specification 1>

<code block 1>case <case specification 2>

<code block 2>…case <case specification N>

<code block N>otherwise

<default code block>end

If-else versus Switchcode = 11;switch codecase 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…

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The Switch StatementFormal Syntax

<case specification> 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 <parameter> case <case spec 1> <code block 1> case <case spec 2> <code block 2> . . case <case spec N> <code block N> otherwise <default code block> end

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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