Selections. Zheng-Liang Lu 91 / 120

Transcription

1 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 91 / 120

2 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 92 / 120

3 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 93 / 120

4 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. 1 ˆ The empty set can be evaluated as false by the if statement. 1 Thanks to a lively class discussion (Matlab-260) on August 29, Zheng-Liang Lu 94 / 120

5 Example: GPA Conversion Problem 2 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 0. 2 See GPA. Zheng-Liang Lu 95 / 120

6 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 96 / 120

7 & 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 97 / 120

8 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 98 / 120

9 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? 3 Thanks to a lively class discussion (Matlab-244) on August 20, Zheng-Liang Lu 99 / 120

10 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 if istaipei isnewtaipei 6... % Show the ticket price. 7 elseif % Do the same thing below. 9 end Zheng-Liang Lu 100 / 120

11 Error and Error Handling ˆ You can issue an error if you do not allow the callee for some situations. 4 1 >> 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 4 In other words, you can decide if the action can be performed. Zheng-Liang Lu 101 / 120

12 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 102 / 120

13 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 103 / 120

14 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 104 / 120

15 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 105 / 120

16 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 106 / 120

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18 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 108 / 120

19 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 109 / 120

20 Example: Running Sum ˆ Write a program which calculates the sum of array elements. 1 clear; clc; 2 3 x = 1 : 1 : 100; 4 s = 0; 5 for i = 1 : length(x) 6 s = s + x(i); % running sum 7 end 8 s ˆ Use length(x) instead of 100 in Line 5. ˆ Then the loop will do as many times as the number of elements in x. Zheng-Liang Lu 110 / 120

21 Exercise: Estimating π by Monte Carlo Simulation 5 ˆ Write a program which estimates π by generating a certain number of sample points (x, y) and calculating ˆπ = 4 m n, where m is the number of points falling in the region of the quarter circle shown in the next page, n is the total number of points, and ˆπ is the estimate of π. 5 Monte Carlo was a code word used in World War II to describe sampling-based methods for neutron scattering computations associated with Manhattan project. Zheng-Liang Lu 111 / 120

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23 1 clear; clc; 2 3 n = 1e5; 4 m = 0; 5 for i = 1 : n 6 x = rand(1); 7 y = rand(1); 8 if x ˆ 2 + y ˆ 2 < 1 9 m = m + 1; 10 end 11 end 12 estimated pi = 4 * m / n ˆ ˆπ π as n by the law of large numbers (LLN). 6 ˆ Try to vectorize this program. 6 See Zheng-Liang Lu 113 / 120

24 More Exercises ˆ Write a program to estimate 5 by Monte Carlo. ˆ Write a program to estimate 1 0 xdx by Monte Carlo. ˆ Write a program to estimate the call price of European option by Monte Carlo. Zheng-Liang Lu 114 / 120

25 while Loops ˆ The while loops are preferred when you need to keep repeating the instructions until a continuation criterion is not met. 1 while criterion 2 % body 3 end ˆ Note that before entering the while loop, the criterion will be checked. ˆ Also note that the if statement is similar to the while loop except that the if statement executes only once. Zheng-Liang Lu 115 / 120

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27 Example: Compounding ˆ Let x be the initial amount of some investment, and r be the annual interest rate. ˆ Write a program which calculates the holding years n so that this investment doubles it value. Zheng-Liang Lu 117 / 120

28 Solution ˆ In this case, we don t know how many iterations we need before the loop. 1 clear; clc; 2 3 balance = 100; 4 goal = 200; 5 r = 0.01; 6 years = 0; 7 8 while balance < goal 9 balance = balance * (1 + r); 10 years = years + 1; 11 end 12 n ˆ Note that the criterion is to continue the loop. Zheng-Liang Lu 118 / 120

29 Infinite Loops 1 while true 2 disp('press ctrl+c to stop me!!!'); 3 end ˆ Note that your program can terminate the program by pressing ctrl+c. Zheng-Liang Lu 119 / 120

30 More Exercises ˆ Let a > b be two any positive integers. ˆ Write a program which calculates the remainder of a divided by b. ˆ Do not use mod(a, b). ˆ Write a program which determines the greatest common divisor (GCD) of a and b. ˆ Do not use gcd(a, b). Zheng-Liang Lu 120 / 120