ENGR-25_Programming-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Chp4 MATLAB Programming-2

ENGR-25_Programming-2.ppt 2 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 3 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Large Program Development 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

ENGR-25_Programming-2.ppt 4 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Large Program Development 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.

ENGR-25_Programming-2.ppt 5 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 6 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 1st Computer Bug – Circa 1945  attributed to Grace Hopper, who publicized the cause of a malfunction in an early electromechanical computer

ENGR-25_Programming-2.ppt 7 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 8 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 9 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 10 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 11 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods ReCall RELATIONAL Operators SymbolMeaning <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”

ENGR-25_Programming-2.ppt 12 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Relational Operator Examples  Given x = [6,3,9] and y = [14,2,9] A MATLAB Session >> z = (x < y) z = >> z = (x ~= y) z = >> z = (x > 8) z =  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

ENGR-25_Programming-2.ppt 13 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Operator Precedence  The arithmetic operators +, -, *, /, and \ have precedence over the relational operators  Thus the statement z = 5 >  Parentheses Can Change the Order of Precedence; for example >> z = 5 > z = 0 >> z = (5 > 2) + 7 z = 8 >> z = (5>2) z = 1 Is Equivalent to z = 5 >(2+7) Returns Result z = 0

ENGR-25_Programming-2.ppt 14 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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)

ENGR-25_Programming-2.ppt 15 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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 = >> 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.

ENGR-25_Programming-2.ppt 16 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 17 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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 =  Extract the diagonal elements of A >> C = A(B) C =

ENGR-25_Programming-2.ppt 18 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 19 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Boolean Logic  The Logical Operators Form The Basis of BOOLEAN (Two Value, T & F, 1 & 0, or Hi & Lo) Logic Developed by George Boole ( )  The Action of the Boolean Operators are Often Characterized with TRUTH Tables

ENGR-25_Programming-2.ppt 20 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 21 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Xor → EXCLUSIVE or  MATLAB SynTax  xor Evaluates as TRUE Only If EACTLY ONE of A or B is True, but NOT BOTH  Xor Truth Table C = xor(A, B) “Logic Gate” Symbol used in Electrical Engineering Xor Venn Diagram

ENGR-25_Programming-2.ppt 22 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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”

ENGR-25_Programming-2.ppt 23 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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 OperatorUsageNotation ANDA AND BA.B or A·B ORA OR BA+B NOTNOT A ~A or A

ENGR-25_Programming-2.ppt 24 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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

ENGR-25_Programming-2.ppt 25 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods DeMorgan in MATLAB  Work Problem 14 → Case-a: >> % case-a >> x = 7 x = 7 >> a1 = ~((x < 10)&(x >= 6)) a1 = 0 >> a2 = (~(x < 10))|(~(x >= 6)) a2 =

ENGR-25_Programming-2.ppt 26 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods DeMorgan in MATLAB  Work Problem 14 → Case-b >> % case-b >> y = 3 y = 3 >> b1 = ~((y == 2)|(y > 5)) b1 = 1 >> b2 = (~(y == 2))&(~(y >5)) b2 =

ENGR-25_Programming-2.ppt 27 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Logical Opers  Short-Circuit Oper.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)

ENGR-25_Programming-2.ppt 28 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Short Circuit Example  Avoid Occasional Division-by-Zero a = 73 >> b = 3 b = 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

ENGR-25_Programming-2.ppt 29 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Precedence  Operator Types PrecedenceOperator 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 FOURTHLogical AND (&) FIFTHLogical OR (|)

ENGR-25_Programming-2.ppt 30 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 31 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods More Logical Functions Logical 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.)

ENGR-25_Programming-2.ppt 32 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods More Logical Functions Logical Function 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

ENGR-25_Programming-2.ppt 33 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 34 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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 =  Note that the find function returns the indices, and not the values.

ENGR-25_Programming-2.ppt 35 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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 = >> how_many = length(values) how_many = 3

ENGR-25_Programming-2.ppt 36 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods All Done for Today George Boole ( )

ENGR-25_Programming-2.ppt 37 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Appendix

ENGR-25_Programming-2.ppt 38 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Find Demo >> x = [5, -3, 0, 0, 8];y = [2, 4, 0, 5, 7]; >> u = x&y u = >> v = x(u) v = >> w = y(u) w = >> z = find(x&y) z = 1 2 5

ENGR-25_Programming-2.ppt 39 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods DeMorgan in MATLAB  Work Problem 14 → Case-a: >> % case-a >> x = 7 x = 7 >> a1 = ~((x < 10)&(x >= 6)) a1 = 0 >> a2 = (~(x < 10))|(~(x >= 6)) a2 =

ENGR-25_Programming-2.ppt 40 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods DeMorgan in MATLAB  Work Problem 14 → Case-b >> % case-b >> y = 3 y = 3 >> b1 = ~((y == 2)|(y > 5)) b1 = 1 >> b2 = (~(y == 2))&(~(y >5)) b2 =

ENGR-25_Programming-2.ppt 41 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods 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.

ENGR-25_Programming-2.ppt 42 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Software Objects & Classes   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.