Introduction to MATLAB 7 for Engineers - The University of Jordan

Lecture 6 Computer Applications 0933201 Chapter 4Effective documentation can beaccomplished with the use of1. Proper selection of variable names toreflect the quantities they represent.2. Use of comments within the program.3. Use of structure charts.4. Use of flowcharts.5. A verbal description of the program,often in pseudo-code. (in which naturallanguage and mathematical expressions areused to construct statements that look likecomputer statements but without detailedsyntax).Documenting with ChartsTwo types of charts aid in developing structuredprograms and in documenting them.These are structure charts and flowcharts.A structure chart is a graphical description showing howthe different parts of the program are connected together.4-6 Z.R.KZ.R.K4-7Structure chart of a game program. Figure 4.1–14-8Flowcharts are useful fordeveloping and documentingprograms that containconditional statements,because they can display thevarious paths (called“branches”) that a program cantake, depending on how theconditional statements areexecuted.Flowchart representationof the if statement.Figure 4.1–2Z.R.K4-9Finding BugsDebugging a program is the process of finding andremoving the “bugs,” or errors, in a program.Such errors usually fall into one of the followingcategories.1. Syntax errors such as omitting a parenthesis orcomma, or spelling a command name incorrectly.MATLAB usually detects the more obvious errorsand displays a message describing the error and itslocation.2. Errors due to an incorrect mathematical procedure.These are called runtime errors. They do notnecessarily occur every time the program isexecuted; their occurrence often depends on theparticular input data. A common example isdivision by zero.Z.R.K4-10To locate a runtime errors, try the following:1. Always test your program with a simpleversion of the problem, whose answers canbe checked by hand calculations.2. Display any intermediate calculations byremoving semicolons at the end ofstatements.3. To test user-defined functions, trycommenting out the function line andrunning the file as a script.4. Use the debugging features of theEditor/Debugger, which is discussed inSection 4.7.Z.R.KLogical operators Table 4.3–1Operator Name Definition~ NOT ~A returns an array the same dimension as A; thenew array has ones where A is zero and zeroswhere A is nonzero.& AND A & B returns an array the same dimension as Aand B; the new array has ones where both A and Bhave nonzero elements and zeros where either Aor B is zero.| OR A|Breturns an array the same dimension as Aand B; the new array has ones where at least oneelement in A or B is nonzero and zeros where Aand B are both zero.&& Short-Circuit Operator for scalar logical expressions. A&&BAND returns true if both A and B evaluate to true, andfalse if they do not.|| Short-Circuit Operator for scalar logical expressions. A ||BOR returns true if either A or B or both evaluate to true,4-11and false if they Z.R.Kdo not.Z.R.K. 2008 Page 2 of 7

Lecture 6 Computer Applications 0933201 Chapter 44-12Order of precedence for operator types Table 4.3–2PrecedenceOperator typeFirst Parentheses; evaluated starting withthe innermost pair.Second Arithmetic operators and logicalNOT (~); evaluated from left to right.Third Relational operators; evaluated fromleft to right.Fourth Logical AND ( & ).Fifth Logical OR ( | ).Z.R.KLogical functions Table 4.3–4Logical function Definitionall(x) Returns a scalar, which is 1 if all the elements inthe vector x are nonzero and 0 otherwise.all(A) Returns a row vector having the same number ofcolumns as the matrix A and containing ones andzeros, depending on whether or not the correspondingcolumn of A has all nonzero elements.any(x) Returns a scalar, which is 1 if any of the elementsin the vector x is nonzero and 0 otherwise.any(A) Returns a row vector having the same number ofcolumns as A and containing ones and zeros,depending on whether or not the correspondingcolumn of the matrix A contains any nonzeroelements.finite(A) Returns an array of the same dimension as A withones where the elements of A are finite and zeroselsewhere.4-13Z.R.K13 (continued …)Logical function Definitionischar(A) Returns a 1 if A is a character array and 0 therwise.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, withones where A has ‘inf’ and zeros elsewhere.isnan(A) Returns an array of the same dimension as A withones where A has ‘NaN’ and zeros elsewhere. (‘NaN’stands for “not a number,” which means anundefined result.)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 imaginaryparts and 0 otherwise.logical(A) Converts the elements of the array A into logicalvalues.xor(A,B) Returns an array the same dimension as A and B;the new array has ones where either A or B isnonzero, but not both, and zeros where A andB are either both nonzero or both zero.4-14Logical functions Table 4.3–4 (continued)Z.R.K4-15Logical Operators & and the find Function>>x = [5, -3, 0, 0, 8]; y = [2, 4, 0, 5, 7];>>z = find(x&y)z =1 2 5Note that the find function returns the indices, and notthe values.In the following session, note the difference betweenthe result obtained by y(x&y) and the result obtainedby find(x&y) in the previous example.>>values = y(x&y)values =2 4 7>>how_many = length(values)how_many =3Z.R.KThe if and else StatementThe if statement’s basic form isif logical expressionstatementsendEvery if statement must have anaccompanying end statement. Theend statement marks the end of thestatements that are to be executedif the logical expression is true.The basic structure for the use ofthe else statement isif logical expressionstatement group 1elsestatement group 2end4-16Z.R.KFlowchart of the elsestructure. Figure 4.4–2More? See pages 201-202.4-17When the test, if logical expression, isperformed, where the logical expression maybe an array, the test returns a value of true only if allthe elements of the logical expression are true!For example, if we fail to recognize how the test works,the following statements do not perform the way wemight expect.x = [4,-9,25];if x < 0disp(’Some elements of x are negative.’)elsey = sqrt(x)endBecause the test if x < 0 is false, when this programis run it gives the resulty = 2 0 + 3.000i 5Z.R.K. 2008 Page 3 of 7Z.R.K

Instead, consider what happens if we test for x positive.x = [4,-9,25];if x >= 0y = sqrt(x)elsedisp(’Some elements of x are negative.’)endWhen executed, it produces the following message:Some elements of x are negative.The test if x < 0 is false, and the test if x >= 0also returns a false value because x >= 0 returns thevector [1,0,1].4-18Lecture 6 Computer Applications 0933201 Chapter 4The following statementsif logical expression 1if logical expression 2statementsendendcan be replaced with the more concise programif logical expression 1 & logical expression 2statementsendThe elseif StatementThe general form of the if statement isif logical expression 1statement group 1elseif logical expression 2statement group 2elsestatement group 3endThe else and elseif statements may be omitted if not required. However,if both are used, the else statement must come after the elseif statementto take care of all conditions that might be unaccounted for.4-19Z.R.KZ.R.K18For example, suppose thaty = ln(x) for x >10,y = sqrt(x) for 0 = 0y = sqrt(x)elsey = exp(x) - 1end4-20Flowchart illustrating nestedif statements. Figure 4.4–4Z.R.K20 More? See pages 205-208.4-21Strings ‘ ‘A string is a variable that contains characters.Strings are useful for creating input prompts andmessages and for storing and operating on data suchas names and addresses. To create a string variable,enclose the characters in single quotes (’ ’). Forexample, the string variable name is created as follows:>>name = ’Omar Student’name =Omar StudentThe following string, number, is not the same as thevariable number created by typing number = 123.>>number = ’123’number =123Z.R.KStrings and the input StatementThe prompt program on the next slide uses theisempty(x) function, which returns a 1 if the array xis empty and 0 otherwise.It also uses the input function, whose syntax isx = input(’prompt’, ’string’)orx = input(’prompt’, ’s’)This function displays the string prompt on thescreen, waits for input from the keyboard, and returnsthe entered value in the string variable x.The function returns an empty matrix if you press theEnter key ( ) without typing anything.4-22Strings and Conditional StatementsThe following prompt program is a script file that allowsthe user to answer Yes by typing either Y or y or bypressing the Enter key. Any other response is treated asthe answer No.response = input(’Want to ...continue? Y/N [Y]: ’,’s’);if(isempty(response))|(response==’Y’)...|(response==’y’)response = ’Y’elseresponse = ’N’endZ.R.KZ.R.K224-23More? See pages 209-210.Z.R.K. 2008 Page 4 of 7

Lecture 6 Computer Applications 0933201 Chapter 4A simple example of a while loop isx = 5;k = 0;while x < 25k = k + 1;y(k) = 3*x;x = 2*x-1;endThe loop variable x is initially assigned the value 5,and it keeps this value until the statement x = 2*x - 1is encountered the first time. Its value then changes to9. Before each pass through the loop, x is checked tosee if its value is less than 25. If so, the pass is made.If not, the loop is skipped.4-30Another Example of a while LoopWrite a script file to determine how many terms arerequired for the sum of the series 5k 2 –2k, k = 1, 2, 3, …to exceed 10,000. What is the sum for this many terms?total = 0;k = 0;while total < 1e+4k = k + 1;total = 5*k^2 - 2*k + total;enddisp(’The number of terms is:’)disp(k)disp(’The sum is:’)disp(total)The sum is 10,203 after 18 terms.4-31Z.R.KZ.R.K30 31The switch StructureThe switch structure provides an alternative to using theif, elseif, and else commands. Anything programmedusing switch can also be programmed using if structures.However, for some applications the switch structure ismore readable than code using the if structure.switch input expression % which can be a scalar or stringcase value1statement group 1case value2statement group 2...otherwisestatement group nend4-32Z.R.K4-33The following switch block displays the pointon the compass that corresponds to that angle.switch anglecase 45disp(’Northeast’)case 135disp(’Northwest’)case 225disp(’Southwest’)case 315disp(’Southeast’)otherwisedisp(’Direction Unknown’)endZ.R.K33 More? See pages 225-227.The Editor/Debugger containing twoprograms to be analyzed. Figure 4.7–1Fourier Seriesx(t) ) = a 0 + n=1 ( a n cos n 0 t + b n sin n n 0 t )Evaluate the following function:x(t) ) = 0.5 + 2/ ( cost – 1/3 cos 3t + 1/5 cos5t– 1/7 cos7t + … ) for -10 < t < 10.By using different colors plot the following:1- The first two terms.2- On the same figure plot the first three terms.3- On the same figure plot the first four terms.4- On the same figure plot the first five terms.5- By using the general form of the function, and by using thefor or while or … loop. Set n as input variable, On thesame figure plot the first one-hundredterms.4-34 Z.R.KMore? See pages 228-234. 4-35Z.R.KZ.R.K. 2008 Page 6 of 7

Lecture 6 Computer Applications 0933201 Chapter 4End of Chapter 4Problems Page 241 - 257 !Solve: 2, 5, 11, 16, 23, 24, 25, 33.www.ju.edu.jo\zkhatibZ.R.J.KZ.R.J.K Z.R.KZ.R.K. 2008 Page 7 of 7