Engr/Math/Physics 25
Chp4 MATLAB
Programming-2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Learning Goals
 Write MATLAB Programs That can
MAKE “Logical” Decisions that Affect
Program Output
 Write Programs that Employ
LOOPing Processes
• For → No. Loops know a priori
• while → Loop Terminates based on Logic
Criteria
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Large Program Development - 1
1. Writing and testing of individual modules
(the unit-testing phase).
2. Writing of the top-level program that uses
the modules (the build phase).
•
•
Not all modules are included in the initial testing.
As the build proceeds, more modules are added.
Develop Software as a Series of Incremental
Builds; i.e., Build-a-Little, Test-a-Little, Repeat
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Large Program Development - 2
3. Testing of the first complete program
(the alpha release phase).
•
This is usually done only in-house by technical
people closely involved with the program
development. There might be several alpha
releases as bugs are discovered and removed.
4. Testing of the final alpha release by in-house
personnel and by familiar and trusted outside
users, who often must sign a confidentiality
agreement. This is the beta release phase,
and there might be several beta releases.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Finding Programming Errors

Errors in Software Code are Called “Bugs”
•
Contrary to the Popular Notion, using the term
"bug" to describe inexplicable defects or flaws did
NOT originate with Computers
– “Bug” had been Used for Decades-Prior to describe
Mechanical Malfunctions; Consider this Letter from
Thomas Edison to a Associate in 1878
It has been just so in all of my inventions. The first step is an
intuition, and comes with a burst, then difficulties arise—this
thing gives out and [it is] then that “Bugs” - as such little faults
and difficulties are called - show themselves and months of
intense watching, study and labor are requisite before
commercial success or failure is certainly reached.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
1st Computer Bug – Circa 1945

attributed to Grace Hopper, who publicized the cause of a malfunction in an early
electromechanical computer
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Finding Errors (DeBugging)

Debugging a program is the process of
finding and removing the “bugs,” or errors,
in a software program.

Program errors usually fall into one
of the following categories.
1. Syntax errors such as omitting a
parenthesis or comma, or spelling a
command name incorrectly.
•
MATLAB usually detects the more obvious
errors and displays a message describing
the error and its location.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Types of Bugs cont
2. Errors due to an incorrect
mathematical procedure.
•
•
Called RUNtime errors.
They do not necessarily
occur every time the
program is executed; their
occurrence often depends
on the particular input data.
– A common example is
Division by Zero
– Another example is the
production of COMPLEX
results when not expected
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Locating RUNtime Errors
1. Always test your program with a
simple version of the problem, whose
answers can be checked by hand
calculations.
2. Display any intermediate
calculations by removing semicolons
at the end of statements
3. ADD & Display TEMPORARY
Intermediate results
•
Can Comment Out later if Desired
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Locating RUNtime Errors cont.
4. To test user-defined functions, try
commenting out the function line and
running the file as a script.
5. Use the debugging features of the
Editor/Debugger, as Discussed in §4.8
of the TextBook
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
ReCall RELATIONAL Operators
Symbol
<
<=
>
>=
==
~=
Meaning
Less than
Less than or equal to
Greater than
Greater than or equal to
Equal to
Not equal to
 Expressions Evaluated With Relational
Operators Produce a Quantitative Result
in BINARY form; either “1” or “0”
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Relational Operator Examples
 Given
x = [6,3,9] and
y = [14,2,9]
• A MATLAB Session
>> z = (x < y)
z =
1
0
0
>> z = (x ~= y)
z =
1
1
0
>> z = (x > 8)
z =
0
0
1
Engineering/Math/Physics 25: Computational Methods
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 relational operators
can be used for
array addressing
• With x & y as before
>> z = x(x<y)
z =
6
• finds all the elements in
x that are less than the
corresponding
elements in y
– e.g. x(1) = 6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Operator Precedence
 The arithmetic
operators +, -,
*, /, and \ have
precedence over the
relational operators
 Thus the statement
z = 5 > 2 + 7
• Is Equivalent to
z = 5 >(2+7)
• Returns Result
z = 0
Engineering/Math/Physics 25: Computational Methods
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 Parentheses Can
Change the Order of
Precedence; for
example
>> z = 5 > 2 + 7
z =
0
>> z = (5 > 2) + 7
z =
8
>> z = (5>2)
z =
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
The Logical Class
 When the RELATIONAL operators are used,
such as
x = (5 > 2)
they CREATE a LOGICAL variable,
in this case, x
 Logical variables may take only two values:
• 1 (true)
• 0 (false)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
The Logical Class cont
 Just because an array contains only 0s & 1s,
however, it is not necessarily a logical array.
• For example, in the following session k and w
appear the same, but k is a logical array and w is a
numeric array, and thus an error message is issued
>> x = [-2:2]; k = (abs(x)>1)
k =
1
0
0
0
1
>> z = x(k)
z =
-2
2
>> w = [1,0,0,0,1]; v = x(w)
??? Subscript indices must either be
real positive integers or logicals.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Accessing Arrays w/ Logicals
 When a logical array
is used to
ADDRESS another
array, it extracts
from that array the
ELEMENTS in the
locations where the
logical array has 1s.
Engineering/Math/Physics 25: Computational Methods
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 So typing A(B),
where B is a logical
array of the same
size as A, returns
the VALUES of A at
the indices
(locations) where
B is 1.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Accessing Arrays w/ Logicals cont
 Specifying array
subscripts with
logical arrays
extracts the
elements that
correspond to the
true (1) elements in
the logical array
 Given 3x3 array:
• A = [5,6,7;
8,9,10;
11,12,13]
• and
Engineering/Math/Physics 25: Computational Methods
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>> B =
logical(eye(3))
B =
1
0
0
1
0
0
0
0
1
 Extract the diagonal
elements of A
>> C = A(B)
C =
5
9
13
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Logical Operators for Arrays
Definition
Oper. Name
~
NOT
&
AND
|
OR
~A returns an array the same dimension as
A; the new array has ones where A is zero
and zeros where A is nonzero
A & B returns an array the same dimension
as A and B; the new array has ones where
both A and B have nonzero elements and
zeros where either A or B is zero
A | B returns an array the same dimension
as A and B; the new array has ones where at
least one element in A or B is nonzero and
zeros where A and B are both zero.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Boolean Logic

The Logical Operators Form The Basis of
BOOLEAN (Two Value, T & F, 1 & 0,
or Hi & Lo) Logic
•

Developed by George Boole (1815-1864)
The Action of the Boolean Operators are
Often Characterized with TRUTH Tables
AND (all high = high, else low)
NOT (inverter)
Input 1
Input 2
Output
Input 1
Input 2
Output
Input = 1 Output = 0
0
0
0
0
0
0
Input = 0 Output = 1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
Engineering/Math/Physics 25: Computational Methods
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OR (any high = high, else low)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Venn Diagrams for Booleans
 AND Operator
• ALL Terms are
Present
• ANY ONE of the
terms are present
• AND represents the
INTERSECTION (∩)
of Sets
• OR represents the
UNION (U) of Sets
Engineering/Math/Physics 25: Computational Methods
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 OR Operator
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Xor → EXCLUSIVE or
 MATLAB SynTax
C = xor(A, B)
 xor Evaluates as
TRUE Only If
EACTLY ONE of
A or B is True, but
NOT BOTH
• Xor Venn Diagram
Engineering/Math/Physics 25: Computational Methods
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 Xor Truth Table
XOR (different = high, same = low)
Input 1
Input 2
Output
0
0
0
0
1
1
1
0
1
1
1
0
“Logic Gate” Symbol
used in Electrical
Engineering
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Other Logic Gates
 NOR  ~|
 NAND  ~&
• “Not OR”
• “Not AND”
NAND (all high = low, else high)
NOR (any high = low, else high)
Input 1
Input 2
Output
Input 1
Input 2
Output
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
 NANDs & NORs are easier to implement in
HARDWARE than are ANDs & ORs
• i.e., They take Fewer Transistors
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Boolean Algebra
 Boolean Logic can be Mathematically
Formalized with the use of Math Operators
 The Math Operators Corresponding to
Boolean Logic Operations:
Operator
Usage
Notation
AND
A AND B
A.B or A·B
OR
NOT
A OR B
NOT A
A+B
~A or A
• A and B can only be TRUE or FALSE
• TRUE represented by 1; FALSE by 0
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Boolean Algebraic Properties
 Commutative: A.B = B.A and A+B = B+A
 Distributive:
• A.(B+C) = (A.B) + (A.C)
• A+(B.C) = (A+B).(A+C)
 Identity Elements: 1.A = A and 0 + A = A
 Inverse: A.A = 0 and A + A = 1
 Associative:
• A.(B.C) = (A.B).C and A+(B+C) = (A+B)+C
 DeMorgan's Laws:
• A.B = A + B and
• A+B = A.B
Engineering/Math/Physics 25: Computational Methods
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Verify
DeMorgan in
MATLAB
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
DeMorgan in MATLAB
 Work Problem 14 → Case-a:
A  B  A  B
?
>> % case-a
>> x = 7
x =
1
1
7
>> a1 = ~((x < 10)&(x >= 6))
a1 =
0
0
0
>> a2 = (~(x < 10))|(~(x >= 6))
a2 =
0
Engineering/Math/Physics 25: Computational Methods
25
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
DeMorgan in MATLAB
 Work Problem 14 → Case-b
A  B  A  B
?
>> % case-b
>> y = 3
y =
0
0
3
>> b1 = ~((y == 2)|(y > 5))
b1 =
1
1
1
>> b2 = (~(y == 2))&(~(y >5))
b2 =
1
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Logical Opers  Short-Circuit
Definition
Oper. Name
Operator for scalar logical expressions.
A&& B returns true if both A and B evaluate
to true, and false if they do not. Does NOT
evaluate the Second expression if the First
evaluates to FALSE (B does matter if A is
False → B-eval is Shorted)
&&
ShortCkt
AND
||
Operator for scalar logical expressions.
A||B returns true if either A or B or both
Short- evaluate to true, and false if they do not.
Ckt OR Does NOT evaluate the Second expression
if the First evaluates to TRUE (B does
matter if A is True → B-eval Shorted)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Short Circuit Example

Avoid Occasional Division-by-Zero
a =
b =
73
>> b = 3
b =
3
>> x = (b ~= 0) &
(a/b > 18.5)
x =
1
>> x = (b ~= 0) &&
(a/b > 18.5)
x =
1
0
>> x = (b ~= 0) & (a/b >
18.5)
Warning: Divide by zero.
x =
0
>> x = (b ~= 0) && (a/b >
18.5)
x =
0
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Precedence  Operator Types
Precedence
Operator Type
FIRST
Parentheses; evaluated starting with the
innermost pair
SECOND
Arithmetic operators and logical NOT (~);
evaluated from left to right.
THIRD
FOURTH
FIFTH
Relational operators (<, ==, etc.); evaluated
from left to right
Logical AND (&)
Logical OR (|)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Logical Functions
Logical
Function
Definition
all(x)
Returns a scalar, which is 1 if all the elements in the vector x are
nonzero and 0 otherwise.
all(A)
Returns a row vector having the same number of columns as the
matrix A and containing ones and zeros, depending on whether or not
the corresponding column of A has all nonzero elements.
any(x)
Returns a scalar, which is 1 if any of the elements in the vector x is
nonzero and 0 otherwise.
any(A)
Returns a row vector having the same number of columns as A and
containing ones and zeros, depending on whether or not the
corresponding column of the matrix A contains any nonzero elemnts
finite(A)
Returns an array of the same dimension as A with ones where the
elements of A are finite and zeros elsewhere.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
More Logical Functions
Logical
Function
Definition
Returns a 1 if A is a character array and 0
ischar(A)
otherwise.
Returns a 1 if A is an empty matrix and 0
isempty(A)
otherwise
Returns an array of the same dimension as A,
isinf(A) with ones where A has ‘inf’ and zeros
elsewhere.
Returns an array of the same dimension as A
with ones where A has ‘NaN’ and zeros
isnan(A)
elsewhere. (‘NaN’ stands for “not a number,”
which means an undefined result.)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
More Logical Functions
Logical
Function
Definition
Returns a 1 if A is a numeric array and 0
isnumeric(A)
otherwise.
Returns a 1 if A has no elements with
isreal(A)
imaginary parts and 0 otherwise.
Converts the elements of the array A into
logical(A)
logical values
Returns an array the same dimension as A
and B; the new array has ones where either A
xor(A,B)
or B is nonzero, but not both, and zeros where
A and B are either both nonzero or both zero
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
The find Function
 find(v)
 Computes an array
containing the indices of
the nonzero elements of
the vector v.
 [u,v,w]=find(A)  Computes the arrays u and
v containing the row and
column indices of the
nonzero elements of the
array A and computes the
array w containing the values
of the nonzero elements.
• The array w may
be omitted.
Engineering/Math/Physics 25: Computational Methods
33
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Logical Ops and find Function

For the Session
>> x = [5, -3, 0, 0, 8];y = [2, 4, 0, 5, 7];
>> z = find(x&y)
z =
1
2
5

Note that the find function returns the
indices, and not the values.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Logical Ops and find Fcn cont

Remember, the find function returns the
indices, and not the values. In the following
session, note the difference between the
result obtained by y(x&y) and the result
obtained by find(x&y) in the previous slide.
>>x = [5, -3, 0, 0, 8];y = [2, 4, 0, 5, 7];
>> values = y(x&y)
values =
2
4
7
>> how_many = length(values)
how_many =
3
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
All Done for Today
George Boole
(1815 - 1864)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Engr/Math/Physics 25
Appendix
f x   2 x  7 x  9 x  6
3
2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
37
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Find Demo
>> x = [5, -3, 0, 0, 8];y = [2, 4, 0, 5, 7];
>> u = x&y
u =
1
1
0
0
1
>> v = x(u)
v =
5
-3
8
>> w = y(u)
w =
2
4
7
>> z = find(x&y)
z =
1
2
5
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
DeMorgan in MATLAB
 Work Problem 14 → Case-a: ~  A  B   A  B
?
>> % case-a
>> x = 7
x =
1
1
7
>> a1 = ~((x < 10)&(x >= 6))
a1 =
0
0
0
>> a2 = (~(x < 10))|(~(x >= 6))
a2 =
0
Engineering/Math/Physics 25: Computational Methods
39
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
DeMorgan in MATLAB
 Work Problem 14 → Case-b ~  A  B   A  B
?
>> % case-b
>> y = 3
y =
0
0
3
>> b1 = ~((y == 2)|(y > 5))
b1 =
1
1
1
>> b2 = (~(y == 2))&(~(y >5))
b2 =
1
Engineering/Math/Physics 25: Computational Methods
40
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Software Class
 Defined: A software module that
provides both procedural and data
abstraction. It describes a set of similar
objects, called its instances
 A Software object is defined via its CLASS, which
determines everything about an object. Objects are
individual instances of a class. For example, you may
create an object call Spot from class Dog. The Dog
class defines what it is to be a Dog object, and all the
"dog-related" messages a Dog object can act upon.
Engineering/Math/Physics 25: Computational Methods
41
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt
Software Objects & Classes


http://www.softwaredesign.com/objects.html
Object-oriented software is all about OBJECTS. An object is a "black
box" which receives and sends messages. A black box actually
contains code (sequences of computer instructions) and data
(information which the instructions operates on). Traditionally, code and
data have been kept apart. For example, in the C language, units of
code are called functions, while units of data are called structures.
Functions and structures are not formally connected in C. A C function
can operate on more than one type of structure, and more than one
function can operate on the same structure.
•

Not so for object-oriented software! In o-o (object-oriented) programming,
code and data are merged into a single indivisible thing -- an object. This
has some big advantages, as you'll see in a moment. But first, here is why
SDC developed the "black box" metaphor for an object. A primary rule of
object-oriented programming is this: as the user of an object, you should
never need to peek inside the box!
How are objects defined? An object is defined via its CLASS, which
determines everything about an object. Objects are individual instances
of a class. For example, you may create an object call Spot from class
Dog. The Dog class defines what it is to be a Dog object, and all the
"dog-related" messages a Dog object can act upon.
Engineering/Math/Physics 25: Computational Methods
42
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Programming-2.ppt