[email protected] ENGR-25_Programming-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical

[email protected] • ENGR-25_Programming-2.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp4 MATLAB

Programming-2



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



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



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.



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.



1st Computer Bug – Circa 1945

attributed to Grace Hopper, who publicized the cause of a malfunction in an early electromechanical computer



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.



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



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



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



ReCall RELATIONAL OperatorsSymbol 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”



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

relational operators can be used for array addressing• With x & y as before

• finds all the elements in x that are less than the corresponding elements in y– e.g. x(1) = 6

>> z = x(x<y)z = 6



Operator Precedence

The arithmetic operators +, -, *, /, and \ have precedence over the relational operators

Thus the statement

z = 5 > 2 + 7

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

• Is Equivalent to

z = 5 >(2+7)

• Returns Result z = 0



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)



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.



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.

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.



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

>> B = logical(eye(3))B = 1 0 0 0 1 0 0 0 1

Extract the diagonal elements of A

>> C = A(B)C = 5 9 13



Logical Operators for Arrays

Oper. Name Definition

~ NOT~A returns an array the same dimension as A; the new array has ones where A is zero and zeros where A is nonzero

& AND

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

| OR

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.



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 NOT (inverter)

Input = 1 Output = 0

Input = 0 Output = 1

AND (all high = high, else low)

Input 1 Input 2 Output

0 0 0

0 1 0

1 0 0

1 1 1

OR (any high = high, else low)


0 0 0

0 1 1

1 0 1

1 1 1



Venn Diagrams for Booleans

AND Operator• ALL Terms are

Present

• AND represents the INTERSECTION (∩) of Sets

OR Operator• ANY ONE of the

terms are present

• OR represents the UNION (U) of Sets



Xor → EXCLUSIVE or

MATLAB SynTax

xor Evaluates as TRUE Only If EACTLY ONE of A or B is True, but NOT BOTH

Xor Truth TableC = xor(A, B) XOR (different = high, same = low)


0 0 0

0 1 1

1 0 1

1 1 0

“Logic Gate” Symbol used in Electrical

Engineering• Xor Venn Diagram



Other Logic Gates NAND ~&

• “Not AND”

NANDs & NORs are easier to implement in HARDWARE than are ANDs & ORs• i.e., They take Fewer Transistors

NOR ~|• “Not OR”

NAND (all high = low, else high)


0 0 1

0 1 1

1 0 1

1 1 0

NOR (any high = low, else high)


0 0 1

0 1 0

1 0 0

1 1 0



Boolean Algebra

Boolean Logic can be Mathematically Formalized with the use of Math Operators

The Math Operators Corresponding to Boolean Logic Operations:

• A and B can only be TRUE or FALSE• TRUE represented by 1; FALSE by 0

Operator Usage Notation

AND A AND B A.B or A·B

OR A OR B A+B

NOT NOT A ~A or A



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 Verify DeMorgan in

MATLAB

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



DeMorgan in MATLAB

Work Problem 14 → Case-a:

>> % case-a

>> x = 7x = 7>> a1 = ~((x < 10)&(x >= 6))a1 = 0>> a2 = (~(x < 10))|(~(x >= 6))a2 = 0

11

0 0

BABA ?



DeMorgan in MATLAB

Work Problem 14 → Case-b

>> % case-b

>> y = 3y = 3>> b1 = ~((y == 2)|(y > 5))b1 = 1>> b2 = (~(y == 2))&(~(y >5))b2 = 1

00

1 1

BABA ?



Logical Opers Short-CircuitOper. Name Definition

&&Short-

Ckt AND

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)

|| Short-Ckt OR

Operator for scalar logical expressions. A||B returns true if either A or B or both evaluate to true, and false if they do not. Does NOT evaluate the Second expression if the First evaluates to TRUE (B does matter if A is True → B-eval Shorted)



Short Circuit Example

Avoid Occasional Division-by-Zeroa = 73>> b = 3b = 3>> x = (b ~= 0) & (a/b > 18.5)x = 1>> x = (b ~= 0) && (a/b > 18.5)x = 1

b = 0>> x = (b ~= 0) & (a/b > 18.5)Warning: Divide by zero.x = 0>> x = (b ~= 0) && (a/b > 18.5)x = 0



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 Relational operators (<, ==, etc.); evaluated from left to right

FOURTH Logical AND (&)

FIFTH Logical OR (|)



Logical FunctionsLogical

FunctionDefinition

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.



More Logical FunctionsLogical

Function Definition

ischar(A) Returns a 1 if A is a character array and 0 otherwise.

isempty(A) Returns a 1 if A is an empty matrix and 0 otherwise

isinf(A)Returns an array of the same dimension as A, with ones where A has ‘inf’ and zeros elsewhere.

isnan(A)

Returns an array of the same dimension as A with ones where A has ‘NaN’ and zeros elsewhere. (‘NaN’ stands for “not a number,” which means an undefined result.)



More Logical Functions

LogicalFunction Definition

isnumeric(A)

Returns a 1 if A is a numeric array and 0 otherwise.

isreal(A) Returns a 1 if A has no elements with imaginary parts and 0 otherwise.

logical(A) Converts the elements of the array A into logical values

xor(A,B)

Returns an array the same dimension as A and B; the new array has ones where either A or B is nonzero, but not both, and zeros where A and B are either both nonzero or both zero



The find Function

find(v)

[u,v,w]=find(A)

Computes an array containing the indices of the nonzero elements of the vector v.

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.



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.



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



All Done for Today

George Boole(1815 - 1864)



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf



Find Demo>> x = [5, -3, 0, 0, 8];y = [2, 4, 0, 5, 7];>> u = x&yu = 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



DeMorgan in MATLAB

Work Problem 14 → Case-a:

>> % case-a

>> x = 7x = 7>> a1 = ~((x < 10)&(x >= 6))a1 = 0>> a2 = (~(x < 10))|(~(x >= 6))a2 = 0

11

0 0

BABA ?

~



DeMorgan in MATLAB

Work Problem 14 → Case-b

>> % case-b

>> y = 3y = 3>> b1 = ~((y == 2)|(y > 5))b1 = 1>> b2 = (~(y == 2))&(~(y >5))b2 = 1

00

1 1

BABA ?

~



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.



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.

Documents

[email protected] ENGR-25_Programming-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical