program design branching...

EGR115 Introduction to Computing for Engineers

Chapter 4

Branching Statements &Program Design

from: S.J. Chapman, MATLAB Programming for Engineers, 5th Ed.© 2016 Cengage Learning

Chapter 4 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

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.

Chapter 4Slide 1 of 17

Introduction: Program Design

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 independently. 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) 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


4.1 Introduction to Top-Down Design Techniques

Top-Down Design Process

Develop:Pseudocode

Convert:Pseudocode => MATLAB

MATLAB:Run/Debug

Finished!

COMPILE

Repeat these processes (Debug)

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).

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.



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:

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.

5

K F 32.0 273.159

T T

Let’s create a simple Pseudocode

for this example

% 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)+273.15

%

% 4. Write the result and stop

% fprintf (??? temp_f = ??? temp_k)

%

% end

Notepad



EXAMPLE 4-2 (from EXAMPLE 2-5)A voltage source V = 120 V with an internal resistance RS of 50 W is applied to a load of resistance RL. Find the value of load resistance RL 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 RL. In this exercise, we need to vary the load resistance RL and compute the power supplied to the load at each value of RL. The power supplied to the load resistance is given by:where I is the current supplied to the load. The current supplied to the load can be calculated by Ohm’s Law:

1. Create an array of possible values for the load resistance.2. Calculate the current for each value of RL.3. Calculate the power supplied to the load.4. Plot the power supplied to the load.

2

L LP I R

TOT S L

V VI

R R R

% MATLAB example_4_2.m

%

% 0. Must set the values of source voltage and internal resistance

% volts <- 120 / rs <- 50

%

% 1. 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

%

% end

Notepad

>> 3 < 4

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)

The Logical Data Type The logical data type is a special data that can have only two possible values (true or false).

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. Relational Operators



Logical data type = true or falsehttps://www.mathworks.com/help/matlab/operators-and-elementary-operations.html

>> a1 = true;

>> whos

Name Size Bytes Class Attributes

a1 1x1 1 logical

Command Window

Command Window

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.



Logical data type = true or falsehttps://www.mathworks.com/help/matlab/operators-and-elementary-operations.html

>> example_4_3

a = 0

b = 0

c = 1

d = 0

e = 0

f = 1

g = -9

h = 1

j =

1 1

0 1

NOTES) (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).

example_4_3.m



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

%

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

Editor Command Window

>> example_4_1a

ans1 = 1

ans2 = 0

ans3 = 0

ans4 = 0

ans5 = 0

ans6 = 1

ans7 =

0 0

0 1

ans10 =

1 1 1

0 1 0

ans11 =

1 0

0 1

ans12 =

2 0

0 2

NOTES) (8) The && operator must be used with scalar operands. (9) Matrix dimensions must agree.

exercise_4_1a.m



Do-It-Yourself (DIY) EXERCISE 4-1


a = 20; b = -2;

c = 0; d = 1;

1. a > b

2. b > d

3. a > b && c > d

4. a == b

5. a && b > c

6. ~~b

a = 2;

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

%

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)

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>> example_4_1b

ans13 = 0

ans14 = 1

ans15 = 0

ans16 = 0

ans17 = 1

ans18 = 1

ans19 = 0

ans20 = 0

ans21 = -2

Logical Functions

exercise_4_1b.m



Do-It-Yourself (DIY) EXERCISE 4-1 (continued)


a = 2; b = 3;

c = 10; d = 0;

13. a*b^2 > a*c

14. d || b > a

15. (d | b) > a

a = 20; b = -2;

c = 0; d = ’Test’;

16. isinf(a/b)

17. isinf(a/c)

18. a > b && ischar(d)

19. isempty(c)

20. (~a) & b

21. (~a) + b

% 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

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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 end.

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 end.

If all control expressions are zero (false), then the program executes the statements in the block associated with the else clause.

There can be any number of elseif clauses (0 or more) in an if construct, but there can be at most one else 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 end. 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 end (and so forth). The code block otherwise is optional.


4.4 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).


4.4 Branches

The if and switch Construct

calc_roots.m


4.4 Branches

EXAMPLE 4-4

Write a program to solve for the roots of a quadratic equation, regardless of type.(NOTE) the solution of the quadratic equation of the form of:

can be given by:

2 4

2

b b acx

a

2 0ax bx c

MATLAB PSEUDOCODEif (b^2 – 4*a*c) < 0

Write msg that equation has two complex roots

elseif (b^2 – 4*a*c) == 0

Write msg that equation has two identical real roots

else (means: b^2 – 4*a*c > 0, but no need to specify that)

Write msg that equation has two distinct real roots

end

% 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, depending 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);

elseif 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);

else % 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 );

end

Editor

funxy.m


4.4 Branches

EXAMPLE 4-5

Write a program to evaluate a function f (x, y) for any two user-specified values xand y. The function is defined as follows:

f (x, y) =

MATLAB PSEUDOCODE

Prompt the user for the value x and y

Read x and y (user keyboard inputs)

if x >= 0 & y >= 0

function <- x + y

elseif x >= 0 & y < 0

function <- x + y^2

elseif x < 0 & y >= 0

function <- x^2 + y

else

function <- x^2 + y^2

end

Write out f(x,y)

Input: x, yOutput: f (x,y)

Algorithm:1. Read the input values of x and y2. Calculate f (x, y)3. Write out f (x, y)

% 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;

elseif x >= 0 && y < 0

fun = x + y^2;

elseif x < 0 && y >= 0

fun = x^2 + y;

else

fun = x^2 + y^2;

end

% Write the value of the function.

disp (['The value of the function is ' num2str(fun)]);

Editor

multiple_elseif.m nested_if.m

% multiple_elseif.m

%

grade = input('Enter the score: ');

if grade > 95

disp('The grade is A.')

elseif grade >86

disp('The grade is B.')

elseif grade >76

disp('The grade is C.')

elseif grade >66

disp('The grade is D.')

else

disp('The grade is F.')

end

Editor % nested_if.m

%

grade = input('Enter the score: ');

if grade > 95

disp('The grade is A.')

else

if grade > 86

disp('The grade is B.')

else

if grade > 76

disp('The grade is C.')

else

if grade > 66

disp('The grade is D.')

else

disp('The grade is F.')

end

end

end

end

Editor

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)

else

error('negative SQRT error')

end

elseif 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

else

error('divide by zero error')

end

elseif part_select == 'c' %(c)

miles = input('Enter the miles: ')

if miles <= 100

t_cost = 1.00 * miles

a_cost = t_cost / miles

elseif miles <= 200

t_cost = 1.00 * (100) + 0.80 * (miles - 100)


else

t_cost = 1.00 * (100) + 0.80 * (200) + 0.70 * (miles - 300)


end

else

error('Input a, b, or c ONLY!')

end

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NOTES) The script runs. However, if temperature is (for example) 110, this falls into true for both: > 37 and > 100 Hence, it causes an error!

exercise_4_3a.m

exercise_4_3b.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.')

else

disp('Line voltage is within tolerances.')

end

>> exercise_4_3a

Error: At least one END is

missing: the statement may

begin here.

% exercise_4_3b.m

%

temperature = input('Enter temperature: ');

if temperature > 37

disp('Human body temperature exceeded.')

elseif temperature > 100

disp('Boiling point of water exceeded.')

end

Editor

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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 Editor 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 Editor and Command Window in a single html file (and many other different publishing format style). PUBLISH => Publish

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