Variables and Assignments

Transcription

1 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 is any arithmetic operation. 1 ˆ For example, suppose x = 0. ˆ Then run y = x + 1 and so y = 1. (Trivial.) ˆ How about x = x + 1? ˆ Actually, the assignment operator (=) is defined to assign a value to the variable, from right to left. 1 To the best of my knowledge, 1 = x is not allowed because the left-hand side of the assignment should be a space. Zheng-Liang Lu 51 / 111

2 ˆ For example, 1 >> a = 10; 2 >> b = 20; 3 >> a + b 4 5 ans = ˆ The variable ans is used by default if you don t assign one for the immediate result. ˆ If you drop the semicolon (;) in Line 2, then the immediate result will appear in the command window. 2 2 Note that you may not drop semicolons in other programming languages. For example, the semicolon is used as the end symbol of a statement in C, C++, and Java. Zheng-Liang Lu 52 / 111

3 Variable Naming ˆ Cannot begin with a number, e.g. 1x is wrong. ˆ Cannot have blanks, e.g. x 1 is wrong. ˆ Cannot contain +-*\%, e.g. x%1 ˆ Cannot be any of key words, e.g. for ˆ Cannot be the same name as any m-file ˆ Matlab is case-sensitive, e.g. A and a are two distinct letters. Zheng-Liang Lu 53 / 111

4 ˆ Variable names should always be mnemonic. 3 ˆ May use underscores ( ) or use CamelCase. 4 ˆ We avoid to use names of reserved words 5 and built-in functions. ˆ i = 1 and j = 1 by default. ˆ If you set i = 1, then i = 1 until you clear i. ˆ pi and sin are also the names which are not to be overloaded. 3 The length of name is limited to 63 characters. The function namelengthmax returns the maximum length in this machine. 4 See 5 Try iskeyword. Zheng-Liang Lu 54 / 111

5 Scalar Variables ˆ The variable x is said to be a scalar variable if x R 1 or C 1. ˆ The complex field, denoted by C, contains all the complex numbers a + bi, where i = 1, and a, b R. 6 ˆ Try x = 1 + i in the command window. ˆ Usually used for parameters of the problems. ˆ For example, pi is a default variable to store the ratio of a circle s circumference to its diameter. 6 In math, C 1 is equivalent to R 2. So x contains two double values. However, Matlab treats a complex number as an entity. Zheng-Liang Lu 55 / 111

6 Scalar Arithmetic Operators 7 7 See Table 2.1 Arithmetic Operations Between Two Scalars in Moore, p. 21. Zheng-Liang Lu 56 / 111

7 Arrays ˆ An array, is a linear data structure consisting of a collection of elements, each identified by one array index. ˆ For math, arrays could be ˆ row vectors: u R 1 n for any positive integer n ˆ column vectors: u R n 1 for any positive integer n ˆ matrices: A R n m for any positive integers n, m ˆ Arrays can be said the simplest one of data structures. Zheng-Liang Lu 57 / 111

8 Example 1 >> rowvector = [1 2 3] % [... ] is used in arrays 2 3 rowvector = >> colvector = [1; 2; 3] % semicolon used to... change rows colvector = Zheng-Liang Lu 58 / 111

9 17 18 >> A = [1 2 3; 4 5 6; 7 8 9] A = ˆ You can create an n m k matrix for n, m, k,... N. ˆ For example, a matrix takes MBytes in memory. 8 ˆ The number of dimensions of arrays is unlimited without regarding to the limit of the memory space. 8 More explicit, / 2 20 B = MB. Zheng-Liang Lu 59 / 111

10 Alternatives for Vector Creation ˆ The function linspace(start, end, npts) generates a vector of uniformly incremented values. 9 1 >> x = linspace(0, 10, 5) 2 3 x = Also try logspace. Zheng-Liang Lu 60 / 111

11 ˆ You can also create a vector by using the colon operator as follows: start : step size : end 1 >> x = 0 : 2 : x = ˆ This is widely used to create index arrays to manipulate arrays. 1 >> x = 1 : 5 % default step size = x = Zheng-Liang Lu 61 / 111

12 ˆ You could create a null vector, say: 1 >> x = 1 : -1 : x = 4 5 Empty matrix: 1-by-0 ˆ It will be useful later! Zheng-Liang Lu 62 / 111

13 ˆ Some special matrices can be initialized by the following functions: Zheng-Liang Lu 63 / 111

14 Array Addressing ˆ We often use subscripted indexing like the way in math. ˆ Rarely use linear indexing: column major order >> A(2, 3) % using subscripted indexing 2 3 ans = >> A(8) % using linear indexing 8 9 ans = How could a 1d memory store a 2d array? Zheng-Liang Lu 64 / 111

15 1 >> A([1 3], [1 3]) % range selection 2 3 ans = >> A(2, 2 : end - 1) 9 10 ans = Zheng-Liang Lu 65 / 111

16 1 >> A(:, 2) = [] % deletion (removing the second... column vector) 2 3 A = >> B = [A, A] % merge A and A 11 B = Zheng-Liang Lu 66 / 111

17 Cells and Cell Arrays 11 ˆ An array cannot contain data of different types correctly! ˆ A cell array is a data type with indexed data containers called cells, and each cell can contain any type of data. ˆ Cell arrays commonly contain either lists of text strings, combinations of text and numbers, or numeric arrays of different sizes. 11 Basically, cell arrays do not require completely contiguous memory because Matlab does not allocate any memory for the contents of each cell when the cell array is created. However, each cell requires contiguous memory, as does the cell array header that Matlab creates to describe the array. Zheng-Liang Lu 67 / 111

18 Example 12 1 >> stock = {'TSMC', 100; 2 'GOOG', 200; 3 'AAPL', 300} 4 5 stock = 6 7 3x2 cell array 8 9 {'TSMC'} {[100]} 10 {'GOOG'} {[200]} 11 {'AAPL'} {[300]} ˆ However, the arithmetic operators cannot be applied to the cell arrays! 12 Thanks to a lively class discussion (Matlab263) on March 3, Zheng-Liang Lu 68 / 111

19 Referring to Cell Arrays ˆ Using curly braces, { } will reference the contents of a cell. 1 >> A{3, 1} 2 3 ans = 4 5 AAPL ˆ More details can be found in here. Zheng-Liang Lu 69 / 111

20 Structures and Structure Arrays ˆ A structure can be used to group related data by meaningful names, called fields. ˆ We access these fields by the dot operator. ˆ For example, 1 >> stock = struct('name', {'TSMC', 'GOOG',... 'APPL'}, 'price', {100, 200, 300}) 2 3 stock = 4 5 1x3 struct array with fields: 6 7 name 8 price Zheng-Liang Lu 70 / 111

21 ˆ More details can be found here. ˆ Widely used in object-oriented applications, such as GUI design. ˆ The arithmetic operators cannot be applied to structures, either! Zheng-Liang Lu 71 / 111

22 Symbols for Common Data Structures Zheng-Liang Lu 72 / 111

23 Summary 13,14 ˆ Parentheses ( ) ˆ Arithmetic, e.g. (x + y)/z. ˆ Input arguments of functions, e.g. sin(1), exp(1). ˆ Array addressing, e.g. A(1) refers to the first element in array A. ˆ Square brackets [ ]: only used in array operations ˆ e.g. x = [ ]. ˆ Curly brackets { }: only used in cells ˆ e.g. A = { This is Matlab class., x}. 13 Thanks to a lively class discussion (Matlab237) on April 16, You can refer to this page for more details of special characters. Zheng-Liang Lu 73 / 111

24 More Data Structures ˆ See data-types_data-types.html Some of them may not be available if your version is out-of-date. Zheng-Liang Lu 74 / 111

25 Vectorization 16 ˆ Matlab favors array operations. ˆ When two arrays have the same dimensions, addition, subtraction, multiplication, and division apply on an element-by-element basis. ˆ For example, 1 >> x = [1 2 3]; 2 >> y = [4 5 6]; 3 >> x + y 4 5 ans = More about vectorization. Zheng-Liang Lu 75 / 111

26 Element-By-Element Operations ˆ The Left division is used in the inverse matrix problems We will visit this in the chapter of matrix computation. Zheng-Liang Lu 76 / 111

27 1 >> Lecture 2 2 >> 3 >> -- Programming Basics 4 >> Zheng-Liang Lu 77 / 111

28 If debugging is the process of removing software bugs, then programming must be the process of putting them in. Edsger W. Dijkstra ( ) Zheng-Liang Lu 78 / 111

29 Introduction ˆ Decision making facilitates the usefulness of programs. ˆ For example, Self Driving Cars by Google. 18 ˆ Also, some actions (functions) are repeated for a specified number of times or until the stopping condition is satisfied. ˆ An algorithm must have the ability to alter the order of its instructions using what is called a control structure. ˆ The first principle in designing algorithms is to divide and conquer. ˆ Recall the algorithm for max(a). ˆ This feature enables engineers to solve problems of great complexity or requiring numerous calculations. 18 See Zheng-Liang Lu 79 / 111

30 Building Blocks ˆ Sequential operations: be executed in order. ˆ Selections: check which condition is satisfied and then execute the actions accordingly. ˆ Repetitions: repeat some instructions and stop while the termination condition is satisfied. Zheng-Liang Lu 80 / 111

31 Pseudo Code ˆ The pseudo code is widely used to describe algorithms. ˆ They are a mixture of natural language and mathematical expressions with common structures of programming languages. ˆ For example, 1 for each student 2 if this student's final score >= 60, then 3 get 'PASS' 4 else 5 get 'FAIL' 6 end 7 end Zheng-Liang Lu 81 / 111

32 Relational Operators 19 ˆ Matlab provides relational operators to make comparisons between two arrays of equal size. 19 See Table 8.1 in Moore, p Zheng-Liang Lu 82 / 111

33 Boolean (Logical) Values ˆ Boolean values are only true and false. 20 ˆ The function true and false represent logical true and logical false, respectively. 21 ˆ Boolean variable contains a boolean value. ˆ For example, 1 >> x = 1; y = 2; 2 >> w = (y > x) ~= true 3 4 w = Note that the numeric number 0 can be regarded as false in general, and nonzero numbers are regarded as true in Matlab and some programming languages. 21 The usage of true and false is similar to zeros. Zheng-Liang Lu 83 / 111

34 Masks as Filters ˆ Boolean arrays are often used as masks to manipulate arrays as an alternative to index arrays. 1 >> scores = [ ]; 2 >> haspassed = scores >= haspassed = >> scores(haspassed) 9 10 ans = Zheng-Liang Lu 84 / 111

35 Logical Operators ˆ Assume x = 0; ˆ How about 1 < x < 3? (Surprising!) Zheng-Liang Lu 85 / 111

36 Truth Table ˆ Let A and B be two Boolean variables. ˆ Then the truth table for logical operators is as follows: A B A A&B A B xor(a, B) T T F T T F T F F F T T F T T F T T F F T F F F ˆ Note that the instructions of computers, such as arithmetic operations, are implemented by logic gates See any textbook for digital circuit design. Zheng-Liang Lu 86 / 111

37 Exercise: & vs. == 23 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, Zheng-Liang Lu 87 / 111

38 Quantifiers 24 ˆ The function all determines if all elements are true. 1 >> x = [ ]; 2 >> all(x >= 60) 3 ans = ˆ The function any determines if there is any true element in the array. 1 >> any(x >= 60) 2 ans = See Zheng-Liang Lu 88 / 111

39 More Logical Functions ˆ NaN: Not A Number, caused by and See NaN. Zheng-Liang Lu 89 / 111

40 Digress: Set Membership 27 ˆ Matlab provides useful functions such as intersect, union, unique, and setdiff. 26 ˆ For example, 1 >> x = [ ]; y = [ ]; 2 >> intersect(x, y) 3 4 ans = See 27 Thanks to a lively class discussion (Matlab263) on March 9, Zheng-Liang Lu 90 / 111

41 Logic is the anatomy of thought. John Locke ( ) This sentence is false. I know that I know nothing. anonymous Plato (In Apology, Plato relates that Socrates accounts for his seeming wiser than any other person because he does not imagine that he knows what he does not know.) Zheng-Liang Lu 91 / 111

42 Precedence of Operators See Table 1.2 Operator Precedence Rules in Attaway, p. 25. Zheng-Liang Lu 92 / 111

43 Selections ˆ Selection enables us to write programs that make decisions on. ˆ Selection structures contain one or more of the if, else, and elseif statements. ˆ The end statement denotes the end of selection structures. Zheng-Liang Lu 93 / 111

44 Example: if-else ˆ Write a program which takes a number as input. ˆ If the number is a nonnegative real number, then calculate its square root. ˆ We may use the function input which takes a number from the keyboard. 1 clear; clc; 2 3 x = input('enter a number? '); % input from keyboard 4 if x >= 0 5 sqrt(x) 6 else 7 disp([num2str(x),' is a negative number.']); 8 end Zheng-Liang Lu 94 / 111

45 Exercise: Nested Conditional Statements 1 clear; clc; 2 x = input('enter x?', 's'); 3 % Contribution by Mr. Curtis Yen on Sep. 10, w = str2num(x); 5 if isempty(w) % w is not empty if w is a number 6 disp([x, ' is not a number.']); 7 else 8 if w >= 0 9 sqrt(w) 10 else 11 disp([x ' is not a positive real number.']); 12 end 13 end ˆ Do not write a deeply nested conditional statement. Zheng-Liang Lu 95 / 111

46 Example: if-elseif-else 1 clear; clc; 2 x = input('enter x?', 's'); 3 w = str2num(x); 4 if isempty(w) % w is not empty if w is a number 5 disp([x ' is not a number.']); 6 elseif w >= 0 7 sqrt(w) 8 else 9 disp([x ' is not a positive real number.']); 10 end ˆ Can we change the order of the conditions? ˆ You can put w >= 0 in the first condition. 29 ˆ The empty set can be evaluated as false by the if statement. 29 Thanks to a lively class discussion (Matlab-260) on August 29, Zheng-Liang Lu 96 / 111

47 Example: GPA Conversion Problem 30 ˆ Write a program which converts centesimal points to GPA. ˆ Let x be the grade input. ˆ For simplicity, ˆ If 90 x 100, then x is converted to 4. ˆ If 80 x < 90, then 3. ˆ If 70 x < 80, then 2. ˆ If 60 x < 70, then 1. ˆ If x < 60, then See GPA. Zheng-Liang Lu 97 / 111

48 1 clear; clc; 2 x = input('enter points? '); 3 if x >= 90 && x <= disp('4'); 5 elseif x >= 80 && x < 90 6 disp('3'); 7 elseif x >= 70 && x < 80 8 disp('2'); 9 elseif x >= 60 && x < disp('1'); 11 else 12 disp('0'); 13 end ˆ Can we reverse the conditions? ˆ Can we place the conditions at your will? Zheng-Liang Lu 98 / 111

49 & vs. && 1 clear; clc; 2 3 x = [ ]; 4 y = [ ]; 5 6 x > 0 & y > 0 % return [ ] 7 all(x > 0) && any(y > 0) % return 0 ˆ Consider A && B. ˆ If A returns false, then B won t be evaluated. ˆ This is so-called the short-circuit operator, which facilitates time-saving. ˆ Note that the argument for if statements can be a scalar only! Zheng-Liang Lu 99 / 111

50 Another Selection Structure: switch-case ˆ The switch-case statements allow you to choose between multiple outcomes by checking the value of the target variable. ˆ For example, 1 clear; clc; 2 city = input('enter the name of a city: ', 's'); 3 switch city 4 case {'Taipei', 'New Taipei'} 5 disp('price: $100'); 6 case 'Taichung' 7 disp('price: $200'); 8 case 'Tainan' 9 disp('price: $300'); 10 otherwise 11 disp('not an option.'); % default option 12 end Zheng-Liang Lu 100 / 111

51 Why Not if? if strcmp(city, 'Taipei') strcmp(city, 'New... Taipei') 3 disp('price: $100'); 4 elseif strcmp(city, 'Taichung') 5 disp('price: $200'); 6 elseif strcmp(city, 'Tainan') 7 disp('price: $300'); 8 else 9 disp('not an option.'); 10 end ˆ Can you implement the strcmp function? 31 Thanks to a lively class discussion (Matlab-244) on August 20, Zheng-Liang Lu 101 / 111

52 Exercise ˆ We can try to replicate the functionality of strcmp by not calling it. ˆ You may use the function length to calculate the size of the string (or any arrays later) istaipei = length(city) == length('taipei') &&... 3 all(city == 'Taipei'); 4 isnewtaipei =... % Do the same thing below. 5 6 if istaipei isnewtaipei 7... % Show the ticket price. 8 elseif % Do the same thing below. 10 end Zheng-Liang Lu 102 / 111

53 Error and Error Handling ˆ You can issue an error if you do not allow the callee for some situations >> error('this is an error.'); ˆ Also, you can use a try-catch statement to handle errors. 1 try 2 % normal operations 3 catch 4 % handler operations 5 end 32 In other words, you can decide if the action can be performed. Zheng-Liang Lu 103 / 111

54 Example: Combinations ˆ For all nonnegative integers n k, ( n k) is given by ( ) n n! = k k!(n k)!. ˆ Note that factorial(n) returns n!. 1 clear; clc; 2 3 n = input('n =? '); 4 k = input('k =? '); 5 y = factorial(n) / (factorial(k) * factorial(n - k)) 6 disp('end of program.'); Zheng-Liang Lu 104 / 111

55 ˆ Try n = 2, k = 5. ˆ factorial( 3) is not allowed! ˆ So your program stops in Line 5, and terminates abnormally. ˆ The reason is that Line 5 produces an error and the program is not designed to handle it. ˆ Then Matlab takes over and kills this program try 3 y = factorial(n) / (factorial(k) *... factorial(n - k)) 4 catch e % capture the thrown exception 5 disp(['error: ' e.message]); 6 end 7 disp('end of program.'); Zheng-Liang Lu 105 / 111

56 Exercise: Divided by Zero ˆ Write a program which calculates x/y for any two real numbers x, y. ˆ The program restricts the user to do division by zero. ˆ Note that we don t use this error-handling mechanism for normal executions in regard to the performance! 1... % assume x = 1 any y = 0 2 if y == 0 3 error('divided by zero!'); 4 else 5 ans = x / y; 6 end 7... Zheng-Liang Lu 106 / 111

57 Repetitions ˆ If a group of instructions is potentially repeated, you should wrap those in a repetition structure, called loops. ˆ All loops consist of 3 parts: ˆ Find the repeated pattern for each iteration. ˆ Warp them by a loop. ˆ Set the continuation condition by defining a loop variable with some criterion. ˆ Matlab provides two different types: the for loops and the while loops. ˆ Use for loops if you know the number of iterations. ˆ Otherwise, use while loops. Zheng-Liang Lu 107 / 111

58 for Loops ˆ A for loop is the easiest choice when you know how many times you need to repeat the loop. 1 for loopvar = somearray 2 % body 3 end ˆ Particularly, we often use for loops to manipulate arrays! Zheng-Liang Lu 108 / 111

59 Zheng-Liang Lu 109 / 111

60 Example 1 for i = 1 : 10 2 disp(i); 3 end ˆ Can you show the odd integers from 1 to 9? 1 for student = {'Arthur', 'Alice'} 2 disp(cell2mat(student)); 3 % remember to take things out of cells 4 end ˆ Clearly, Matlab has for-each loops, which is an enhanced one compared to the naive one in C. ˆ Note that we use the function cell2mat so that a string stored in the cell can be extracted as a string. Zheng-Liang Lu 110 / 111

61 Example: Find Maximum (Revisited) 1 clear; clc; 2 3 x = [ ]; % input list 4 max = x(1); 5 for i = 2 : 7 6 if max < x(i) 7 max = x(i); 8 end 9 end 10 max ˆ Can you find the location of the maximum element? ˆ Try to find the minimum element and its location. Zheng-Liang Lu 111 / 111