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1 Structure Array A structure array is a data type that groups related data using data containers called fields. Each field can contain any type of data. Access data in a structure using dot notation of the form structname.fieldname. For example, 1 >> student.name='arthur'; 2 >> student.id='d '; 3 >> student.scores=[80, 90, 100]; 4 >> student % show the content of student 5 >> 6 7 student = 8 9 name: 'Arthur' 1 / 50

2 Title 10 id: 'd ' 11 scores: [ ] fieldnames returns the names of the fields contained in a structure variable. rmfield removes a field from a structure. You can pass structures to functions. More details can be found here. They are extremely useful in applications such as MATLAB GUI and database management. 2 / 50

3 In Workspace 3 / 50

4 Basic Math Functions 1 1 See Table in Palm, p / 50

5 Trigonometric Functions 2 Recall that 1 rad = 180 π. 2 See Table in Palm, p / 50

6 括弧種類整理 3 Parentheses ( ) Arithmetic, e.g. (x + y)/z. Input arguments of a function, e.g. sin(1), exp(1). Array addressing, e.g. A(1) refers to the first element in array A. Square brackets [ ]: only used in array operations e.g. x = [ ]. Curly brackets { }: only used to declare a cell array e.g. A = { This is MATLAB class., x}. 3 Thanks to a lively class discussion (MATLAB-237) on April 16, / 50

7 1 >> Lecture 2 2 >> -- Programming Basics 7 / 50

8 Introduction of MATLAB Programming The MATLAB command mode is very useful for simple problems, but more complex problems require a script. The usefulness of MATLAB is greatly increased by the use of decision making functions in its programs. These functions enable you to write programs whose operations depend on the results of calculations made by the program. MATLAB can also repeat calculations a specified number of times or until some condition is satisfied. This feature enables engineers to solve problems of great complexity or requiring numerous calculations. 8 / 50

9 Program Design and Development Design of programs to solve complex problems needs to be done in a systematic manner from the start to avoid time-consuming and frustrating difficulties later in the process. An algorithm is an ordered sequence of precisely defined instructions that performs specific task in a finite amount of time and space. 9 / 50

10 Elements in Algorithms There are three categories of algorithmic operations: Sequential operations: These instructions are executed in order. selection/conditional operations: These control structures first ask a question to be answered with a true/false answer and then select the next instruction based on the answer. Iterative operations: These control structures repeat the execution of a block of instructions. Note that not every problem can be solved with an algorithm, so-called undecidable problems 4. Besides, some potential algorithmic solutions can fail because they take too long to find a solution. 5 4 See halting problem. 5 Recall that the finiteness is one property of algorithms. 10 / 50

11 Programming Structures 6 6 See Figure 8.1 in Moore, p / 50

12 Structured Programming An algorithm often must have the ability to alter the order of its instructions using what is called a control structure. Structured programming is a technique for designing programs in which a hierarchy of modules/functions is used. Core concept: divide and conquer. In MATLAB, these modules can be built-in or user-defined functions. Structured programming, if used properly, results in programs that are easy to write, understand, modify, and debug. 12 / 50

13 Steps of Developing A Computer Program 1. (Problem formulation) State the problem concisely. (Input) Specify the data to be used by the program. (Output) Specify the information to be generated by the program. 2. (Algorithm) Work through the solution steps by hand or with a calculator; use a simpler set of data if necessary. 3. (Programming) Write and debug the program. 4. (Verification) Check the output of the program with your hand solution. Make sense? 5. (Generalization) If you will use the program as a general tool in the future, test it by running it for a range of reasonable data values. 13 / 50

14 If debugging is the process of removing software bugs, then programming must be the process of putting them in. Edsger W. Dijkstra ( ) 14 / 50

15 Flowcharts Flowcharts make it easy to visualize the structure of a program. It can display the various paths (called branches) that a program can take, depending on how the conditional statements are executed. Why we need flowcharts? Help developing the algorithm and program. Documenting programs properly is very important, even if you never give your programs to other people. 流程圖 (Flow Chart) 常用符號教學 15 / 50

16 Design Elements in Flowchart See Table 8.3 Flowcharting for Designing Computer Programs in Moore, p. 16 / 50

17 Example 8 8 See Figure 8.2 in Moore, p / 50

18 Pseudocode We use pseudocode in which natural language and mathematical expressions are used to construct statements that look like computer statements but without detailed syntax. For example, 1 if (student's grade >= 60) 2 Print pass 3 else 4 Print failed 5 end 18 / 50

19 Relational Operators 9 MATLAB has six relational operators to make comparisons between arrays of equal size. Note that all of them are binary operators, which need two operands. 9 See Table 8.1 in Moore, p / 50

20 Boolean Variables Boolean variables contain only 0 and 1 for false and true, respectively. For example, 1 >> x=2; y=5; 2 >> z=x<y % Note that z is a logical variable. 3 4 z = >> w = (y > x) ~= 1 % Note that w is a logical... variable w = / 50

21 Equivalently, w = x([ ]). (Try.) 21 / 50 More Examples 1 >> x=0:1:10; 2 >> y=10:-1:0; 3 >> z=x<y % Note that z is a logical variable. 4 5 z = >> w=x((x-y>0)) 11 w = In the second example, (x y) > 0 return a logical vector. So, w((x y) > 0) returns a partial vector of vector x when the corresponding element in (x y) > 0 is 1.

22 Logical Operators 22 / 50

Precedence of Operators 10 10 See Table 1.

23 Precedence of Operators See Table 1.2 Operator Precedence Rules in Attaway, p / 50

24 & vs. && 1 clear all; 2 clc 3 % main 4 x=[ ]; % x is a numeric array 5 y=[ ]; 6 7 x>0 & y>0 % boolean array 8 sum(x-y)>0 && sum(y-x)>0 % boolean scalar The difference between and is similar except that and do or operation. 24 / 50

25 Exercise 11 : & vs. == 1 >> x=[ ]; 2 >> y=[ ]; 3 >> x==y 4 5 ans = >> x&y 11 ans = Thanks to a lively class discussion (MATLAB-237) on April 16, / 50

26 Example: Exclusive OR (XOR) The exclusive OR function, denoted by xor(x, y) returns 0s where x and y are either both nonzero or both 0, and 1s where either x or x is nonzero, but not both. We can use the truth table 12 to find the equivalent boolean expression. More interesting details of XOR can be found here. Please write a program to do XOR operation on two boolean variable x and y. Input: boolean variables x, y Output: xor(x,y) / 50

27 Truth Tables and Basic Logic Gates 27 / 50

28 1 >> x=[3 0 6]; 2 >> y=[5 0 0]; 3 >> z= (x y)& ~(x&y) 4 5 z = Note that the boolean expression of one specific statement is not unique. 28 / 50

29 Logical Functions NaN: Not A Number, caused by the math operation like and See NaN. 29 / 50

30 Conditional Statements MATLAB conditional statements enable us to write programs that make decisions. Conditional statements contain one or more of the if, else, and elseif statements. The end statement denotes the end of a conditional statement. 30 / 50

31 Example: if-else If x is a nonnegative real number, then y = x. input(prompt) gives the user the prompt (in string) and then waits for numeric input from the keyboard. 1 clear all; 2 clc 3 % main 4 x=input('enter a number? '); % input from keyboard 5 if x>=0 6 y=sqrt(x) % show y 7 else 8 disp([num2str(x),' is a negative number.']); 9 end Note that one if should be paired with one end. input(prompt, s ) waits for a string input. 31 / 50

32 Example: if-elseif-else 1 clear all; 2 clc 3 % main 4 x=input('enter any real number: '); 5 if isempty(x) 6 disp('no input.') 7 elseif x>=0 8 disp('it is a positive number.') 9 else 10 disp('it is a negative number.') 11 end 32 / 50

33 Exercise: Do you want to continue? Write a program which allows the user to answer Yes by typing either Y or y or by pressing the Enter key. Any other response is treated as a No answer. 33 / 50

34 1 clear all; 2 clc 3 % main 4 response = input('do you want to continue? Y/N... [Y]:','s'); 5 if (isempty(response)) ( response ==... 'Y') ( response == 'y') 6 response = 'Y' 7 else 8 response = 'N' 9 end 14 Note that logical operators cannot be applied to empty sets, so putting isempty(response) in the first place is a better way. 14 Contribution by Mr. Grant Huang (MAT24217) on July 23, / 50

35 Selection Structure: switch/case The switch/case structure is often used when a series of programming path options exists for a given variable, depending on its value. The code is a bit easier to read with switch/case, a structure that allows you to choose between multiple outcomes, based on specific criterion. 35 / 50

36 Example 1 clear all; 2 clc 3 % main 4 disp('welcome to Taiwan. I can show you the... ticket price.') 5 disp('you can choose Taipei, Taichung, or Tainan.') 6 city = input('enter the name of a city: ','s'); 7 switch city 8 case 'Taipei' 9 disp('price: $100') 10 case 'Taichung' 11 disp('price: $200') 12 case 'Tainan' 13 disp('price: $300') 14 otherwise 15 disp('not an option.') % default 16 end 36 / 50

37 Error Handling You can use a try-catch statement to execute code after your program encounters an error. try-catch can be useful if you: want to finish the program in another way that avoids errors; need to clean up unwanted side effects of the error; 1 try 2 try block; % normal execution code 3 catch 4 catch block; % error handling section 5 end lasterr returns the last error message. 37 / 50

38 Example: Combinations For all nonnegative integers n k, ( n k) is given by ( ) n n! = k k!(n k)!. Note that factorial(n) returns n!. 1 clear all; 2 clc; 3 % main 4 n=input('n=?'); 5 k=input('k=?'); 6 if n>=0 && k>=0 7 y=factorial(n)/(factorial(k)*factorial(n-k)) 8 else 9 disp('invalid inputs.') 10 end 38 / 50

39 Try n = 2, k = 5. factorial( 3) is not allowed! 1 clear all; 2 clc; 3 % main 4 n=input('n=?'); 5 k=input('k=?'); 6 if n>=0 && k>=0 7 try 8 y=factorial(n)/(factorial(k)*factorial(n-k)) 9 catch 10 lasterr 11 y=factorial(k)/(factorial(n)*factorial(k-n)) 12 end 13 else 14 disp('invalid inputs.') 15 end 39 / 50

40 Repetition Structures As a rule of thumb, if a section of code is repeated more than three times, it is a good candidate for a repetition structure. Repetition structures are often called loops. All loops consist of 5 basic parts: A parameter to be used in determining whether or not to end the loop. Initialization of this parameter. A way to change the parameter each time through the loop. 15 A comparison, using the parameter, to a criterion used to decide when to end the loop. Calculations to do inside the loop. 15 If not, then an infinite loop, that is, a loop never stops. 40 / 50

41 MATLAB supports two different types of loops: the for loop and the while loop. break, continue, and return can be used in the loop if some condition meets. break: to end the loop even when the loop does not finish. continue: to pass the loop once. return: to end the subroutine (function). 41 / 50

42 for Loops for loop is the easiest choice when you know how many times you need to repeat the loop. 1 for loop variable 2 statements 3 end 42 / 50

43 43 / 50

44 Example: for Loop 1 clear all; 2 clc 3 % main 4 for i=[1 3 5] % Can be a string. (Try.) 5 i 6 end 1 clear all; 2 clc 3 % main 4 for i=0:1:10 5 i 6 end 44 / 50

45 while Loops While loops are the easiest choice when you need to keep repeating the instructions until a criterion which is written in logical expression is met. 1 while (criterion) 2 statements 3 end Note that before while, the criterion will be checked. Can you replace a while loop with a for loop? (Try.) 45 / 50

46 46 / 50

47 Example: while Loop Write a program to determine the number of terms required for the sum of the series 5k 2 2k, k N to exceed What is the sum for this many terms? Note that N = {1, 2, }. 47 / 50

48 Solution 1 clear all; 2 clc 3 % main 4 sol=0; 5 k=0; 6 while sol < 1e4 7 k=k+1; 8 sol=sol+5*kˆ2-2*k; 9 end 10 sol 11 k 48 / 50

49 Example: A Simple Infinite Loop 1 while 1 2 fprintf('press ctrl+c to stop me!!!!\n'); 3 end In line 2, fprintf shows a string on the screen. Besides, \n is used to create a new line. Note that your can stop your program by pressing ctrl+c. 49 / 50

50 Example: Infinite Loop by for? 1 clear all; 2 clc 3 % main 4 for i=0:inf % inf is a special word for infinite... large number. 5 end 1 Warning: FOR loop index is too large. Truncating... to > In test at 5 3 Elapsed time is seconds. I cannot run an infinite loop using a for loop on my desktop MATLAB R2010a (32-bit) on Windows 7 (64-bit), i7 920 with 14G memory. 50 / 50

Variables and Assignments

Variables and Assignments ˆ A variable is used to keep a value or values. ˆ A box which contains something. ˆ In most languages, a statement looks like var = expression, where var is a variable and expression