Chapter 4 Branching Statements & Program Design

Transcription

1 EGR115 Introduction to Computing for Engineers Branching Statements & Program Design from: S.J. Chapman, MATLAB Programming for Engineers, 5 th Ed Cengage Learning Topics Introduction: Program Design 4.1 Introduction to Top-Down Design Techniques 4.2 Use of Pseudocode 4.3 The Logical Data Type 4.4 Branches 4.5 More on Debugging MATLAB Programs

2 Slide 1 of 17 Introduction: Program Design Program Design So far, we developed simple MATLAB programs that were executed one after another in a fixed order: these programs are called sequential programs. Typically, these programs read input data, process it to produce desired results, and stop. As a next step in programming, we need to look at the ways to design and control the order in which statements are executed in a program. Two broad Categories of Program Code Structures 1. Branches: program code structures that are designed to execute selected specific sections of the code, based on specific logical conditions. (if and switch construct) 2. Loops: program code structures that are designed to repeat specific sections of the code, based on specific logical conditions. (while and for loops) Logical Data Type In order to construct and control branches and loops, we need to employ logical data types (true or false) for defining the logical conditions.

3 Slide 2 of Introduction to Top-Down Design Techniques Top-Down Design Process Develop: Pseudocode Convert: Pseudocode => MATLAB COMPILE MATLAB: Run/Debug Finished! Top-Down Program Design Top-down design is the process of starting with a large task and breaking it down into smaller, more easily understandable sub-tasks, which perform a portion of the desired task. Each sub-task may in turn be subdivided into smaller sub-tasks if necessary. Once the program is divided into small pieces, each piece can be coded and tested indepently. Traditional Program Design & Development Process 1. State the problem you are trying to solve/define required inputs and outputs 2. Design the algorithm 3. Convert algorithm into statements (compile) Repeat these processes (Debug) 4. Test Run the program MATLAB Program Design & Development Process 1. State the problem you are trying to solve/define required inputs and outputs 2. Develop MATLAB Pseudocode 3. Convert Pseudocode => MATLAB statements 4. Test Run/Debug (on the fly) <= no need to compile

4 Slide 3 of Use of Pseudocode EXAMPLE 4-1 (from EXAMPLE 2-4) Design a MATLAB program that reads an input temperature in degrees Fahrenheit, converts it to an absolute temperature in kelvin, and writes out the result. The relationship between temperature in degrees Fahrenheit (F) and temperature in kelvins (K) is: T 5 K F T 1. Prompt the user to enter an input temperature in F. 2. Read the input temperature. 3. Calculate the temperature in kelvin. 4. Write the result and stop. Let s create a simple Pseudocode for this example MATLAB Pseudocode A pseudocode is a conceptual algorithm to describe constructs (program structures). It is usually a hybrid mixture of MATLAB & English languages. It is structured like MATLAB (with a separate line for each distinct segment of code), but the descriptions on each line are written in English. You can just right click your computer s desktop, create a simple text file (new => text document) to get started (use notepad). Notepad MATLAB example_4_1.m 1. Prompt the user to enter an input temperature in degrees F 2. Read the input temperature temp_f <- input( Enter the temp in degrees F ) 3. Calculate the temperature in degrees K temp_k <- (5/9)*(temp_f 32) Write the result and stop fprintf (??? temp_f =??? temp_k) Next, the pseudocode is imported into MATLAB. Convert it to MATLAB script (m-file). Test run and debug in MATLAB (on the fly) using MATLAB symbolic debugger.

5 Slide 4 of Use of Pseudocode EXAMPLE 4-2 (from EXAMPLE 2-5) A voltage source V = 120 V with an internal resistance R S of 50 W is applied to a load of resistance R L. Find the value of load resistance R L that will result in the maximum possible power being supplied by the source to the load. How much power will be supplied in this case? Also, plot the power supplied to the load as a function of the load resistance R L. In this exercise, we need to vary the load resistance R L and compute the power supplied to the load at each value of R L. 2 The power supplied to the load resistance is given by: PL I RL where I is the current supplied to the load. The current supplied to the load can be calculated by Ohm s Law: V V I R R R TOT S L 1. Create an array of possible values for the load resistance. 2. Calculate the current for each value of R L. 3. Calculate the power supplied to the load. 4. Plot the power supplied to the load. Notepad MATLAB example_4_2.m 0. Must set the values of source voltage and internal resistance volts <- 120 / rs < Create an array of load resistances r1 <- from 1 to 100 with increment of 1 2. Calculate the current flow for each resistance amps <- volts/(rs+rl) 3. Calculate the power supplied to the load pl = (amps^2)*rl 4. Plot the power versus load resistance plot(rl,pl) with title, x&ylabels, grid

6 Slide 5 of The Logical Data Type Logical data type = true or false The Logical Data Type The logical data type is a special data that can have only two possible values (true or false). >> a1 = true; >> whos Command Window Name Size Bytes Class Attributes a1 1x1 1 logical If logical value is used in a place where a numerical value is expected, true is converted to 1 and false is converted to 0 (used as numerical values). Relational & Logical Operators Relational operators are operators that compare two numbers and produce a true or false result. Logical operators are operators that compare one or two logical values, and produce a true or false result. Command Window >> 3 < 4 Relational Operators ans = 1 (true) >> 3 <= 4 ans = 1 (true) >> 3 == 4 ans = 0 (false) >> 3 > 4 ans = 0 (false) >> 4 <= 4 ans = 1 (true) >> A < B ans = 1 (true)

7 Slide 6 of The Logical Data Type Logical data type = true or false Logical Operators Truth Tables for Logical Operations The general form of logic operations are: l1 op l2 op l1 Hierarchy of Operations 1. All arithmetic operators are evaluated first in the order previously described. 2. All relational operators (==, ~=, >, >=, <, <=) are evaluated, working from left to right. 3. All ~ operators are evaluated. 4. All & and && operators are evaluated, working from left to right. 5. All,, and xor operators are evaluated, working from left to right.

8 Slide 7 of The Logical Data Type EXAMPLE 4-3 Assuming that the following variables are initialized with the values shown, evaluate the result of the specified expressions: value1 = 1 value2 = 0 value3 = 1 value4 = -10 value5 = 0 value6 = [1 2; 0 1] (a)~value1 (b)~value3 (c)value1 value2 (d)value1 & value2 (e)value4 & value5 (f)~(value4 & value5) (g)value1 + value4 (h)value1 + (~value4) (i)value3 && value6 (j)value3 & value6 example_4_3.m example_4_3.m value1 = 1; value2 = 0; value3 = 1; value4 = -10; value5 = 0; value6 = [1 2; 0 1]; (a) a = ~value1 (b) b = ~value3 (c) c = value1 value2 (d) d = value1 & value2 (e) e = value4 & value5 (f) f = ~(value4 & value5) (g) g = value1 + value4 (h) h = value1 + (~value4) (i) i = value3 && value6 <= Illegal! (j) j = value3 & value6 >> example_4_3 a = 0 b = 0 c = 1 d = 0 e = 0 f = 1 g = -9 h = 1 j = NOTES) Command Window (i) The && operator must be used with scalar operands. (j) AND between a scalar and an array operand. The nonzero values of array value6 are treated as true (1).

9 Slide 8 of The Logical Data Type Do-It-Yourself (DIY) EXERCISE 4-1 Assuming that the following variables are initialized with the values shown, evaluate the result of the specified expressions: a = 20; b = -2; c = 0; d = 1; a = 2; b = ; 1. a > b 2. b > d 3. a > b && c > d 4. a == b 5. a && b > c 6. ~~b c = ; d = ; 7. ~(a > b) 8. a > c && b > c 9. c <= d 10. logical(d) 11. a * b > c 12. a * (b > c) exercise_4_1a.m Command Window exercise_4_1a.m a = 20; b = -2; c = 0; d = 1; ans1 = a > b ans2 = b > d ans3 = a > b && c > d ans4 = a == b ans5 = a && b > c ans6 = ~~b clear a = 2; b = [1-2; 0 10]; c = [0 1; 2 0]; d = [-2 1 2; 0 1 0]; ans7 = ~(a > b) ans8 = a > c && b > c <= Illegal! ans9 = c <= d <= Illegal! ans10 = logical(d) ans11 = a * b > c ans12 = a * (b > c) >> example_4_1a ans1 = 1 ans2 = 0 ans3 = 0 ans4 = 0 ans5 = 0 ans6 = 1 ans7 = ans10 = ans11 = ans12 = NOTES) (8) The && operator must be used with scalar operands. (9) Matrix dimensions must agree.

10 Slide 9 of The Logical Data Type Do-It-Yourself (DIY) EXERCISE 4-1 (continued) Assuming that the following variables are initialized with the values shown, evaluate the result of the specified expressions: a = 2; b = 3; c = 10; d = 0; a = 20; b = -2; c = 0; d = Test ; 13. a*b^2 > a*c 14. d b > a 15. (d b) > a 16. isinf(a/b) 17. isinf(a/c) 18. a > b && ischar(d) 19. isempty(c) 20. (~a) & b 21. (~a) + b Logical Functions exercise_4_1b.m Command Window exercise_4_1b.m a = 2; b = 3; c = 10; d = 0; ans13 = a > b ans14 = b > d ans15 = a > b && c > d clear a = 20; b = -2; c = 0; d = 'Test'; ans16 = isinf(a/b) ans17 = isinf(a/c) ans18 = a > b && ischar(d) ans19 = isempty(c) ans20 = (~a) & b ans21 = (~a) + b >> example_4_1b ans13 = 0 ans14 = 1 ans15 = 0 ans16 = 0 ans17 = 1 ans18 = 1 ans19 = 0 ans20 = 0 ans21 = -2

11 Slide 10 of Branches The if and switch Construct Branches Branches are MATLAB statements that permit us to select and execute specific sections of code (called blocks) while skipping other sections of code. There are two main construct types: (i) if construct and (ii) switch construct. The if Construct The control expressions (control_expr_1, control_expr_2,...) are logical expressions. If control_expr_1 is true, then the program executes the statements in Block 1, and skips to. Otherwise, the program checks for the status of control_expr_2. If control_expr_2 is true, then the program executes the statements in Block 2, and skips to. If all control expressions are zero (false), then the program executes the statements in the block associated with the clause. There can be any number of if clauses (0 or more) in an if construct, but there can be at most one clause. The switch Construct If the value of switch_expr is equal to case_expr_1, then the Block 1 will be executed, and the program will jump to. Similarly, if the value of switch_expr is equal to case_expr_2, then the Block 2 will be executed, and the program will jump to (and so forth). The code block otherwise is optional.

12 Slide 11 of Branches The if and switch Construct The try/catch Construct When a try/catch construct is reached, the statements in the try block will be executed. If no error occurs, the statements in the catch block will be skipped, and execution will continue. If an error occurs in the try block, the program will stop executing the statements in the try block, and immediately execute the statements in the catch block (then execution will continue). Flowchart (Block Diagram) Microsoft Word provides standard shapes with flowchart templates (Insert => Shapes => Flowchart). It is often quite effective to use flowchart, in order to understand how the program flows (visualizing sequences of program execution).

13 Slide 12 of Branches EXAMPLE 4-4 Write a program to solve for the roots of a quadratic equation, regardless of type. 2 (NOTE) the solution of the quadratic equation of the form of: ax bx c 0 can be given by: 2 b b 4ac x 2a MATLAB PSEUDOCODE if (b^2 4*a*c) < 0 Write msg that equation has two complex roots if (b^2 4*a*c) == 0 Write msg that equation has two identical real roots (means: b^2 4*a*c > 0, but no need to specify that) Write msg that equation has two distinct real roots calc_roots.m calc_roots.m disp ('This program solves for the roots of a quadratic '); disp ('equation of the form A*X^2 + B*X + C = 0. '); a = input ('Enter the coefficient A: '); b = input ('Enter the coefficient B: '); c = input ('Enter the coefficient C: '); Calculate discriminant discriminant = b^2-4 * a * c; Solve for the roots, deping on the value of the discriminant if discriminant > 0 there are two real roots, so... x1 = ( -b + sqrt(discriminant) ) / ( 2 * a ); x2 = ( -b - sqrt(discriminant) ) / ( 2 * a ); disp ('This equation has two real roots:'); fprintf ('x1 = f\n', x1); fprintf ('x2 = f\n', x2); if discriminant == 0 there is one repeated root, so... x1 = ( -b ) / ( 2 * a ); disp ('This equation has two identical real roots:'); fprintf ('x1 = x2 = f\n', x1); there are complex roots, so... real_part = ( -b ) / ( 2 * a ); imag_part = sqrt ( abs ( discriminant ) ) / ( 2 * a ); disp ('This equation has complex roots:'); fprintf('x1 = f +i f\n', real_part, imag_part ); fprintf('x1 = f -i f\n', real_part, imag_part );

14 Slide 13 of Branches EXAMPLE 4-5 Write a program to evaluate a function f (x, y) for any two user-specified values x and y. The function is defined as follows: MATLAB PSEUDOCODE f (x, y) = Input: x, y Output: f (x,y) Algorithm: 1. Read the input values of x and y 2. Calculate f (x, y) 3. Write out f (x, y) Prompt the user for the value x and y Read x and y (user keyboard inputs) if x >= 0 & y >= 0 function <- x + y if x >= 0 & y < 0 function <- x + y^2 if x < 0 & y >= 0 function <- x^2 + y function <- x^2 + y^2 Write out f(x,y) funxy.m Script file: funxy.m Prompt the user for the values x and y x = input ('Enter the x value: '); y = input ('Enter the y value: '); Calculate the function f(x,y) based upon the signs of x and y. if x >= 0 && y >= 0 fun = x + y; if x >= 0 && y < 0 fun = x + y^2; if x < 0 && y >= 0 fun = x^2 + y; fun = x^2 + y^2; Write the value of the function. disp (['The value of the function is ' num2str(fun)]);

15 multiple_if.m multiple_if.m grade = input('enter the score: '); if grade > 95 disp('the grade is A.') if grade >86 disp('the grade is B.') if grade >76 disp('the grade is C.') if grade >66 disp('the grade is D.') disp('the grade is F.') nested_if.m nested_if.m grade = input('enter the score: '); if grade > 95 disp('the grade is A.') if grade > 86 disp('the grade is B.') if grade > 76 disp('the grade is C.') if grade > 66 disp('the grade is D.') disp('the grade is F.')

16 exercise_4_2.m exercise_4_2.m part_select = input('select a, b, or c: ','s'); if part_select == 'a' (a) x = input('enter the value of x: '); if x >= 0 sqrt(x) error('negative SQRT error') if part_select == 'b' (b) numerator = input('enter the value of numerator: '); denominator = input('enter the value of denominator: '); if denominator >= 1.0E-300 numerator/denominator error('divide by zero error') if part_select == 'c' (c) miles = input('enter the miles: ') if miles <= 100 t_cost = 1.00 * miles a_cost = t_cost / miles if miles <= 200 t_cost = 1.00 * (100) * (miles - 100) a_cost = t_cost / miles t_cost = 1.00 * (100) * (200) * (miles - 300) a_cost = t_cost / miles error('input a, b, or c ONLY!')

17 exercise_4_3a.m exercise_4_3a.m volts = input('enter volts: '); if volts > 125 disp('warning: High voltage on line.') if volts < 105 disp('warning: High voltage on line.') disp('line voltage is within tolerances.') >> exercise_4_3a Error: At least one END is missing: the statement may begin here. exercise_4_3b.m exercise_4_3b.m NOTES) temperature = input('enter temperature: '); if temperature > 37 The script runs. However, if disp('human body temperature exceeded.') temperature is (for example) 110, if temperature > 100 this falls into true for both: disp('boiling point of water exceeded.') > 37 and > 100 Hence, it causes an error!

18 Debug a MATLAB Program MATLAB Code Analyzer The code analyzer provides an indicator in the top right of the MATLAB editor window. If the indicator is green, the analyzer did not detect code generation issues. If the indicator is red, the analyzer provides line by line error message with detailed explanations. Using the MATLAB The MATLAB editor provides many useful features for effective code development and debugging. FILE: new/open/save scripts & functions, find/compare files, and print files. NAVIGATE: Go To Line..., Set/Clear bookmarks, and find commands/words. EDIT: insert section, function, comment line and indent code. BREAKPOINTS: Set/Clear, Enable/Disable breakpoints and control error handling. RUN: run, run and advance, run section, and run and time. Publishing You can publish your MATLAB and Command Window in a single html file (and many other different publishing format style). PUBLISH => Publish