Computational Method Course CHEG 220

Week_3_Lec_1

Programming with MATLAB

Previously in CHEG220

• Structured MATLAB Programs

• Top-down Structure

• Built-in and user-defined Functions

Outline

• Designing and developing programs • Relational Operators and Logical Variables • Logical operators and Functions • Conditional Statements • Loops and Switch Structures • Application to programming

Logical Operators (1)

MATLAB has five logical or Boolean operators ~ NOT & AND | OR && Short circuit AND || Short circuit OR Logical operators have lower precedence than the arithmetic operators

Logical Operators (2)

Examples

1- A[1,0,1]. ~A[0,1,0]

2- A[1,0,1], B[0,0,1]. A & B = C[0,0,1]

3- A[1,0,1], B[0,0,1]. A | B = C[1,0,1]

Logical Operators (2)

Order of precedence for operator types

1- Parentheses, evaluated starting with the innermost pair 2- Arithmetic operators and logical NOT (~), evaluated from left to right 3- Relational operators, evaluated from left to right 4- Logical AND 5-Logical OR

Logical operators (3)

Examples x[0,3,9], y[14,-2,9] z=~x , z[1,0,0] u=~x>y, u[0,1,0] v=~(x>y), v[1,0,1] z =[5,-3,0,0]&[2,4,0,5] z=[1,1,0,0] x[6,3,9] ,y[14,2,9], a[4,3,12],z=(x>y)&a, z[0,1,0] z =[5,-3,0,0]|[2,4,0,5] z=[1,1,0,1]

Logical operators (4)

The exclusive OR function xor(A,B) is defined as the following:

z=xor(A,B) = (A|B) & ~(A&B)

z=xor([3,0,6],[5,0,0]) z[0,0,1]

z=[3,0,6]|[5,0,0] z[1,0,1]

Logical operators (5)

Table of truth x y ~x x|y x&y xor (x,y) true true false true true false True false false true false true false true true true false true false false true false false false

Logical operators (6)

find Function

The function find(x) computes an array containing the

indices of the nonzero elements of the array x

Example: x=[5,-3,0,0,8]; y[2,4,0,5,7]

z=find[x&y] z=[1,2,5]

Conditional statements(1)

The MATLAB conditional statements enable us to write programs that make decisions

Conditional statements contain one or more of the if, else, and else if statements.

The end statement denotes the end of a conditional statement.

Conditional statements(2)

The if statement

if logical expression if x >= 0

statements y = sqrt(x)

end end

Conditional statements(3)

Another example z=0;w=0; if (x>=0)&(y>=0) z=sqrt(x)+sqrt(y) w=log(x)-3*log(y) end

Conditional statements(4)

Nested if statements

if logical expression 1 if x<0 statement group 1 y=abs(x) if logical expression 2 if y>4 statement group 2 z=sqrt(y) end end end end

Conditional statements(7)

The if statement if logical expression 1 if logical expression 1 & logical expression 2 if logical expression 2 statements statements end end end

Conditional statements(5)

Flowchart

x<0?

y>4?

y=abs(x)

z=sqrt(y)

End

x

false

false

true

true

Conditional statements(6)

The else statement

if logical expression if x >= 0 statement group 1 y = sqrt(x) else else statement group 2 y=exp(x)-1 end end

Conditional statements(8)

The else statement

Logical

Expression

Statement Group 1 Statement Group 2

start

False

True

End

Conditional statements(9)

The elseif statement

if logical expression 1 if x >= 5 statement group 1 y = log(x) elseif logical expression 2 elseif x>=0 statement group 2 y=sqrt(x) else else statement group 3 y=exp(x)-1 end end

Conditional statements(10)

The elseif statement

Logical Expression 1

Logical

Expression 1

Statement Group 2

Statement Group 3

Statement Group 1

Start

False

True False

True

End

Conditional statements(12)

flowchart

x>10

y=5x z=7x

y=log(x)

z=4y z=2y

z=0

y≥2.5? y≥3?

x

No

Yes

No No

Yes Yes

y,z

Conditional statements(11)

The program describing the flowchart on the last slide : if x > 10 y=log(x) if y >= 3 z=4*y elseif y >= 2.5 z=2*y else z=0 end else y=5*x z=7*x end