Chapter 2 MATLAB Basics

Transcription

1 EGR115 Introduction to Computing for Engineers MATLAB Basics from: S.J. Chapman, MATLAB Programming for Engineers, 5 th Ed Cengage Learning Topics 2.1 Variables & Arrays 2.2 Creating & Initializing Variables in MATLAB 2.3 Multidimensional Arrays 2.4 Subarrays 2.5 Special Values 2.6 Displaying Output Data 2.7 Data Files 2.8 Scalar & Array Operations 2.9 Hierarchy of Operations 2.10 Built-in MATLAB Functions 2.11 Introduction to Plotting 2.12 Examples 2.13 Debugging MATLAB Programs

2 Slide 1 of Variables & Arrays m 1 m (m, Variables & Arrays The fundamental unit of data (variable) in MATLAB is the ARRAY: a collection of data values organized into rows (m) & columns (n) with a given single name. Scalar: 1 1 array (single value). Vector: 1-D array (either row vector or column vector). The MATLAB default is the row vector, but typically the column vector is used in mathematics (calculus): a TRNSPOSE ( ) of matrix (transforming row vector => column vector) is often necessary. Matrix: 2-D array with the size of m n (rows columns). The actual value stored within the matrix can be specified at the location of (row, column). Multidimensional array (3-D/4-D): you can define 3-D (even 4-D) arrays in MATLAB. User-Defined Variable Names MATLAB standard user-defined variables: use all lower case with underscores between words: (i.e., example_1_1_sin_x.m) The first 63 characters of user-defined variable name is significant: make sure that your variable names are unique in the first 63 characters (else, MATLAB will not be able to tell the difference between them).

3 Slide 2 of Variables & Arrays MATLAB Variable Assignment Examples: Creating (Initializing) Variables Usually, the very first programming instruction in any MATLAB session (or code) is to create (initialize) user-defined variables: Creating (new) variables: for a new MATLAB session. Initializing variables: when you run different scripts (multiple MATLAB m-files), you want to clear your workspace (initialize variables) for each different script run (unless you want to share same variables between them). 3 ways to create (initialize) MATLAB variables: (i) Assign data to the variable in an assignment statement (ii) Input data into the variable from the keyboard (iii) Read data from a file MATLAB Variables: double & char double: a variable class, consisting of scalars or arrays of 64-bit double-precision floating-point numbers (can be real, imaginary, or complex numbers). char: a variable class, consisting of scalars or arrays of 16-bit values, each representing a single character. Arrays of this type are used to hold character strings.

4 2.2 Creating & Initializing Variables in MATLAB Slide 3 of 27 (a) The simplest way to initialize a variable is to assign it one or more values in an assignment statement. var = expression ; EXAMPLE 2-1 (NOTE) The semicolon (;) means suppression of the automatic echoing of assigned values in the given statement. (b) Initializing the variables by keyboard inputs: var = input( Enter an input value: ) ; (c) Initializing the variables using shortcut expressions: [first:(incr):last] ( ) or [first:last ] ( ) (incr=1) (NOTE) The (optional) apostrophe ( ) means transpose operation (swapping the rows and columns of any array. (a) Assignment statement create_var_a.m Creating (new) variables Demo var1 = 10.5 var2 = 4i var3 = i var4 = 20; comment = This is a character string >> create_var_a var1 = var2 = 0 + 4i var3 = i comment = This is a character string (b) Keyboard inputs create_var_b.m Creating (new) variables Demo var = input( Enter an input value: ); var >> create_var_b Enter an input value: (c) Shortcut expressions >> [2:2:10] ans = >> a = [0 1+7] a = 0 8 >> [2:1:5] ans = >> b = [a(2) 7 a] b = >> [2:2:6] ans = >> e = [1 2 3; 4 5] error!

5 2.2 Creating & Initializing Variables in MATLAB Slide 4 of 27 EXAMPLE 2-1 (continued) (d) Initializing the variables using MATLAB built-in Functions. >> a = zeros(2) a = >> b = zeros(2,3) b = >> c = eye(3) c = >> length(c) ans = 3 >> size(c) ans = 3 3 >> d = ones(3) d = >> e = ones(3,2) >> f = 1:4 f = >> g = [f f ] g = Input Function The input function includes the character ( s ) argument option: >> in1 = input( Enter data: ); Enter data: 1.23 >> in2 = input( Enter data:, s ); Enter data: 1.23 in1 is double 1.23 in2 is char 1.23

6 2.2 Creating & Initializing Variables in MATLAB Slide 5 of 27 Do-It-Yourself (DIY) EXERCISE 2-1 Answer the followings: (a) What is the difference between an array, a matrix, and a vector? (b) Let: c = (b-1) What is the size of c? (b-2) What is the value of c(2,3)? (b-3) List the subscripts of all elements containing the value 0.6. (a) In MATLAB, an array is a collection of data values organized into rows (m) & columns (n) with a given single name. The array is the fundamental unit of data in any MATLAB program. A MATLAB array can be categorized into vector (1-D array) or matrix (2-D array). (b) exercise_2_1b.m exercise_2_1b.m >> exercise_2_1b c = c = [ ; ; ] b_1 = 3 4 b_1 = size(c) b_2 = c(2,3) b_2 = c_1_1 = c(1,1) c_1_1 = c_1_2 = c(1,2) c_1_2 = c_1_3 = c(1,3) c_1_3 = c_1_4 = c(1,4) c_1_4 = c_2_1 = c(2,1) c_2_1 = c_2_2 = c(2,2) c_2_2 = c_2_3 = c(2,3) c_2_3 = c_2_4 = c(2,4) c_2_4 = ) c_3_1 = c(3,1) c_3_1 = c_3_2 = c(3,2) c_3_2 = c_3_3 = c(3,3) c_3_3 = c_3_4 = c(3,4) c_3_4 = 0 c(1,4), c(2,1), and c(3,2) are the elements containing the value of 0.6

7 2.2 Creating & Initializing Variables in MATLAB Slide 6 of 27 Do-It-Yourself (DIY) EXERCISE 2-2 Determine the size of the following arrays, using MATLAB. Check your answers by entering the arrays into MATLAB and using whos command (or checking the Workspace Browser). Note that the later arrays may depend on the definitions of arrays defined earlier in this exercise. (a) u = [10 20*i 10+20]; (b) v = [-1; 20; 3]; (c) w = [1 0-9; 2-2 0; 1 2 3]; (d) x = [u v]; (e) y(3,3) = -7; (f) z = [zeros(4,1) ones(4,1) zeros(1,4) ]; (g) v(4) = x(2,1); exercise_2_2_var.m

8 2.2 Creating & Initializing Variables in MATLAB Slide 7 of 27 Do-It-Yourself (DIY) EXERCISE 2-2 (continued) exercise_2_2_var.m u = [10 20*i 10+20]; v = [-1; 20; 3]; w = [1 0-9; 2-2 0; 1 2 3]; x = [u v]; y(3,3) = -7; z = [zeros(4,1) ones(4,1) zeros(1,4) ]; v(4) = x(2,1); Create a MATLAB script (M-File: exercise_2_2_var.m) and execute a series of commands above. Answer the following questions: (a) What is the value of w(2,1)? (b) What is the value of x(2,1)? (c) What is the value of y(2,1)? (d) What is the value of v(3)? exercise_2_2_var.m exercise_2_2_var.m >> exercise_2_2_var u = [10 20*i 10+20]; w_2_1 = 2 v = [-1; 20; 3]; w = [1 0-9; 2-2 0; 1 2 3]; x_2_1 = 0 20i x = [u v]; y(3,3) = -7; y_2_1 = 0 z = [zeros(4,1) ones(4,1) zeros(1,4) ]; v_3 = 3 v(4) = x(2,1); w_2_1 = w(2,1) x_2_1 = x(2,1) y_2_1 = y(2,1) v_3 = v(3)

9 Slide 8 of /2.4 Multi-Dimensional Arrays/Subarrays Multi-Dimensional Arrays: Subarrays: Multi-Dimensional Arrays MATLAB allows as many dimensions as necessary for any given problem. The multi-dimensional arrays have one subscript for each dimension, and an individual element is selected by specifying a value for each subscript. create_md_array.m Create 3-D Array Demo c(:,:,1) = [1 2 3; 4 5 6]; c(:,:,2) = [7 8 9; ]; whos c c >> create_md_array Name Size Bytes Class Attributes c 2x3x2 96 double c(:,:,1) = c(:,:,2) = A colon (:) can be used (instead of an integer subscript) to represent ALL of the elements within a row or a column of a given array. Subarrays It is possible to select and use subsets of MATLAB arrays as though they were separate arrays (subarrays). To select a portion of an array, just include the list of the elements to be selected in the parentheses after the array name.

10 Slide 9 of Special Values MATLAB Special Values Type clock & date in command window... Subarrays (Example) create_subarray.m Create Subarray Demo arr1 = [ ]; arr1a = arr1(3) arr1b = arr1([1 4]) arr1c = arr1(1:2:5) arr2 = [1 2 3; ; 3 4 5]; arr2a = arr2(1,:) arr2b = arr2(:,1:2:3) arr3 = [ ]; arr3a = arr3(5:end) arr3b = arr3(end) arr4 = [ ; ; ]; arr4a = arr4(2:end, 2:end) arr4 arr4(1:2,[1 4]) = [20 21; 22 23] >> create_subarray arr1a = arr1b = arr1c = arr2a = arr2b = arr3a = arr3b = 8 arr4a = arr4 = arr4 = The last command: the elements: arr4(1,1) arr4(1,4) arr4(2,1), and arr4(2,4) were updated with new values. In order to make this command legal, the array shape (numbers of rows & columns) MUST be the same on both sides of the equal sign (else, MATLAB gives an error).

11 Slide 10 of Special Values Do-It-Yourself (DIY) EXERCISE 2-3 Determine the contents of the following subarrays: 1. Let: c = (a) c(2,:) (b) c(:,end) (c) c(1:2,2:end) (d) c(6) (e) c(4:end) (f) c(1:2,2:4) (g) c([1 3],2) (h) c([2 2],[3 3]) exercise_2_3_1.m >> exercise_2_3_1 exercise_2_3_1.m c_a = c = [ ; ; c_b = ]; c_a = c(2,:) c_c = c_b = c(:,end) c_c = c(1:2,2:end) c_d = c_e = c_d = c(6) c_e = c(4:end) c_f = c_f = c(1:2,2:4) c_g = c_g = c([1 3],2) c_h = c([2 2],[3 3]) c_h = (d): c(6) = c(3,2) WHY??? Since MATLAB (in fact) stores data in column major order, one can (actually) treat a multidimensional array as though it were a 1-D array whose length is equal to the number of elements in the multidimensional array... (NOTE) under normal circumstance, you should never use this feature of MATLAB!

12 Slide 11 of Special Values Do-It-Yourself (DIY) EXERCISE 2-3 (continued) 2. Determine the contents of array a after the following statements are executed : (a) a = [1 2 3; 4 5 6; 7 8 9]; a([3 1],:) = a([1 3],:); (b) a = [1 2 3; 4 5 6; 7 8 9]; a([1 3],:) = a([2 2],:); (c) a = [1 2 3; 4 5 6; 7 8 9]; a = a([2 2],:); 3. Determine the contents of array a after the following statements are executed : (a) (b) (c) a = eye(3,3); b = [1 2 3]; a(2,:) = b; a = eye(3,3); b = [4 5 6]; a(:,3) = b ; a = eye(3,3); b = [7 8 9]; a(3,:) = b([3 1 2]); exercise_2_3_2.m / exercise_2_3_3.m exercise_2_3_2.m a = [1 2 3; 4 5 6; 7 8 9]; a([3 1],:) = a([1 3],:); a_a = a a = [1 2 3; 4 5 6; 7 8 9]; a([1 3],:) = a([2 2],:); a_b = a a = [1 2 3; 4 5 6; 7 8 9]; a_c = a([2 2],:) >> exercise_2_3_2 a_a = a_b = a_b = exercise_2_3_3.m >> exercise_2_3_3 a_a = a = eye(3,3); b = [1 2 3]; a(2,:) = b; a_a = a a_b = a = eye(3,3); b = [4 5 6]; a(:,3) = b'; a_c = a_b = a a = eye(3,3); b = [7 8 9]; a(3,:) = b([3 1 2]); a_c = a

13 Slide 12 of Displaying Output Data MATLAB Output Display: format and fprintf MATLAB Default Format When data is echoed in the command window, integers, characters (strings), and other numerical values (real/imaginary) are displayed in default format. A user can change this default. The disp & fprintf Functions output_demo_a.m str = ['The value of pi = ' num2str(pi)]; disp(str); fprintf('the value of pi is f \n',pi); fprintf('the value of pi is 6.2f \n',pi); >> output_demo_a The value of pi = The value of pi is The value of pi is 3.14 d Display value as integer e Display value in exponential format f Display value in floating point format g Display value in either floating point or exponential format (whichever is shorter) \n Skip to a new line (same as: )

14 Slide 13 of Data Files MATLAB Data File Handling: save and load I/O The Limitation of fprintf The fprintf function only displays the real part of a complex value (imaginary part is ignored). output_demo_b.m x = 2 * (1-2i)^3; str = ['disp: x = ' num2str(x)]; disp(str); fprintf('fprintf: x = 8.4f \n',x); >> output_demo_b disp: x = -22+4i fprintf: x = The MATLAB Data Handling The save command saves data from the current MATLAB workspace into a disk file: save filename var1 var2 var3 The load command is opposite of the save command (loads data from a disk file into the current MATLAB workspace): load filename >> x = [1 2 3; 4 5 6] x = e e e e e e+000 x.dat save x.dat x -ascii y.dat >> load y.dat >> y y = MATLAB can load comma or space separated ASCII format files from other programs (typically the file extension.dat is given).

15 Slide 14 of Data Files Do-It-Yourself (DIY) EXERCISE 2-4 Answer the followings: 1. How would you tell MATLAB to display all real values in exponential format with 15 significant digits? 2. What do the following sets of statements do? What is the output from them? (a) (b) radius = input( Enter circle radius:\n ); area = pi * radius^2; str = [ The area is num2str(area)]; disp(str); value = int2str(pi); disp([ The value is value! ]); 3. What do the following sets of statements do? What is the output from them? value = e2; fprintf( value = e\n,value); fprintf( value = f\n,value); fprintf( value = g\n,value); fprintf( value = 12.4f\n,value); 1. format long e will display all real values in exponential format with 15 significant digits. 2. exercise_2_4_2.m exercise_2_4_2.m >> exercise_2_4_2 (a) radius = input('enter circle radius:\n'); Enter circle radius: area = pi*radius^2; 25 str = ['The area is ' num2str(area)]; The area is disp(str); disp(' '); Hit Enter to continue... disp('hit Enter to continue...'); disp(' '); The value is 3! pause (b) value = int2str(pi); disp(['the value is ' value '!']); 3. exercise_2_4_3.m exercise_2_4_3.m value = e2; fprintf('value = e\n',value); fprintf('value = f\n',value); fprintf('value = g\n',value); fprintf('value = 12.4f\n',value); >> exercise_2_4_3 value = e+04 value = value = value =

16 Slide 15 of Scalar & Array Operations MATLAB Array & Matrix Operations MATLAB Calculations (Operations) MATLAB performs calculations (like a calculator) with an assignment statement: variable_name = expression; (this is NOT math: store the value of expression into the location variable_name) MATLAB Arithmetic Operators (for Scalars) Addition (a b): Subtraction (a b): Multiplication (a b): Division (a b): Exponentiation (a b ): a + b a - b a * b a / b a ^ b MATLAB Array & Matrix Operators (for Vectors & Matrices) Array operations: operations performed between arrays on an element-by-element basis. Matrix operations: follow the normal rules of linear algebra (if you don t know what it means... see this: (NOTE: these are fundamentally very different mathematical operations: be very careful)

17 Slide 16 of Scalar & Array Operations Assume that the following variables are defined as: 1 0 a 2 1 What is the result of each of the following expressions? (a)a + b (b)a.* b (c)a * b (d)a * c (e)a + c (f)a + d (g)a.* d (h)a * d 1 2 b 0 1 EXAMPLE c 2 d 5 example_2_2.m example_2_2.m a = [1 0; 2 1]; b = [-1 2; 0 1]; c = [3 2]'; d = 5; ans_a = a + b ans_b = a.* b ans_c = a * b ans_d = a * c ans_e = a + c <= CANNOT DO THIS! >> example_2_2 ans_a = ans_b = ans_c = ans_d = 3 8 ans_f = a + d ans_g = a.* d ans_h = a * d ans_f = ans_g = ans_h =

18 Slide 17 of Hierarchy of Operations MATLAB Hierarchy of Operations MATLAB Operations (Hierarchy) Many arithmetic operations are combined into a single expression. In order to accurately represent mathematical expressions in MATLAB assignment statement, it is very important to exactly follow the hierarchy of operations. MATLAB Operations (Hierarchy) Basics distance = 0.5 * accel * time ^ 2 (operation1) = (time ^ 2) (operation2) = (0.5 * accel) (operation3) = (operation2) * (operation1) distance = (0.5 * accel * time) ^ 2 => This will produce the different result!!! (operation1) = (0.5 * accel * time) (operation2) = (operation1) ^ 2 distance = 0.5 * accel * (time ^ 2) => This will produce the same result (parentheses NOT required, but recommended: makes the order of operation crystal clear and can avoid confusion for the operation hierarchy)

19 Slide 18 of Hierarchy of Operations Variables a, b, c, and d have been initialized to the following vales: a = 3; b = 2; c = 5; d = 3; Evaluate the following MATLAB assignment statements, showing the details of hierarchy of operations. (a)output = a*b+c*d; (b)output = a*(b+c)*d; (c)output = (a*b)+(c*d); (d)output = a^b^d; (e)output = a^(b^d); EXAMPLE 2-3 MATLAB Operations (Hierarchy): Some Important Professional Practices It is extremely important that every expression in a program be made as clear as possible. Ask yourself a series of questions: Can I easily understand this expression if I come back to it in 6 month? Can another programmer look at my code and instantly understand what my instructions are? If you are not sure, use extra parentheses in the expression to make it sure. Alternatively, separate your expression into a few parts (avoid using extremely long mathematical expression in a single line). (a) output = a*b+c*d = 3*2+5*3 = (3 * 2) + (5 * 3) = 6 + (5 * 3) = = 21 (b) output = a*(b+c)*d = 3*(2+5)*3 = 3 * (2 + 5) * 3 = 3 * 7 * 3 = 21 * 3 = 63 (c) output = (a*b)+(c*d) = (3*2)+(5*3) = (3 * 2) + (5 * 3) = 6 + (5 * 3) = = 21 (d) output = a^b^d = 3^2^3 = (3 ^ 2) ^ 3 = 9 ^ 3 = 729 (e) output = a^(b^d) = 3^(2^3) = 3 ^ (2 ^ 3) = 3 ^ 8 = 6561

20 Slide 19 of Hierarchy of Operations Do-It-Yourself (DIY) EXERCISE 2-5 Assume that the following variables are defined as: 2 1 a b 3 1 Evaluate the following MATLAB assignment statements, showing the details of hierarchy of operations. (a) result = a.* c; (b) result = a * [c c]; (c) result = a.* [c c]; (d) result = a + b * c; (e) result = a + b.* c; 1 c 2 d 3 exercise_2_5.m exercise_2_5.m >> exercise_2_5 a = [2 1; -1 2]; result_b = b = [0-1; 3 1]; 4 4 c = [1 2]'; 3 3 d = -3; result_c = result_a = a.* c <= CANNOT DO THIS! result_b = a * [c c] result_c = a.* [c c] result_d = a + b * c <= CANNOT DO THIS! result_e = a + b.* c <= CANNOT DO THIS!

21 Slide 20 of Hierarchy of Operations Do-It-Yourself (DIY) EXERCISE 2-6 Solve for x in the equation Ax = B, where: A B Understand that you are solving a set of simultaneous linear equations: a x a x a x b a x a x a x b a x a x a x b a11 a12 a13 b1 x1 Ax B A a21 a22 a 23 B b x x 2 2 a 31 a32 a33 b 3 x 3 This can be solved by a multiplication of Matrix Inverse of A and B, as: 1 x A B In MATLAB, the Matrix Left Division will do the job... A \ B <= which is defined as: inv(a) * B exercise_2_6.m exercise_2_6.m >> exercise_2_6 Simultaneous Linear Equations Solver x = A = [1 2 1; 2 3 2; ]; B = [1 1 0]'; x = A \ B; x x1 = x2 = x = inv(a)*b x3 = x x1 = x(1) x2 = x(2) x3 = x(3)

22 Slide 21 of Built-in MATLAB Function MATLAB Built-in Functions MATLAB Functions One of the greatest strength of MATLAB is it comes with an incredible (very comprehensive) library of predefined built-in functions. (for example) Trigonometry Functions include... LIST GOES ON...

23 Slide 22 of Introduction to Plotting MATLAB Plotting Another great feature of MATLAB is its very powerful plotting capability. Plotting is extremely easy in MATLAB, yet MATLAB offers plenty of freedom for customizing the plot. A brif summary of MATLAB plotting includes: Simple xy plots to 3-D plots Manipulating the plot figure in a Figure Window: rotate, pan, crop, zoom, etc. Exporting and printing the plots as graphical images Multiple plots within a single figure Customize axis, line colors, line style, marker style, and legends Logarithmic scales and more... (It is most likely the best to learn MATLAB plotting by actually using it... try plotting something and customize the plot until it becomes exactly as you want it to be. MATLAB allows you great freedom and has enough capability to custom design your own plot, in order to meet your problem solution needs.)

24 Slide 23 of Introduction to Plotting Do-It-Yourself (DIY) EXERCISE 2-7 Starting from the Example 1-1 (plot of sin(x) function), modify this plot as shown below: Modify: line color/style and marker style Add: title, axis labels, and grid exercise_2_7_sin_x.m exercise_2_7_sin_x.m Based on: example_1_1_sin_x.m clc close all clear all x = 0:0.1:6; y = sin(x); plot(x,y,'k-',x,y,'bo'); title('plot of f(x)=sin(x)'); xlabel('x'); ylabel('sin(x)'); grid on axis equal

25 Slide 24 of Introduction to Plotting Do-It-Yourself (DIY) EXERCISE 2-8 Starting from the Example 1-2 (plot of sin(x) and cos(x) function), modify this plot as shown below: Modify: line color/style Add: title, axis labels, legend, and grid exercise_2_8_cos_x.m exercise_2_8_cos_x.m Based on: example_1_2_cos_x.m clc clear all close all x = 0:0.1:6; y1 = sin(x); y2 = cos(x); plot(x,y1,'b-',x,y2,'r--'); title('plot of sin(x) and cos(x)'); xlabel('x'); ylabel('f(x)'); legend ('f(x)=sin(x)','f(x)=cos(x)') grid on axis equal

26 Slide 25 of Examples 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. example_2_4_temp_conversion.m Script file: temp_conversion.m Purpose: To convert an input temperature from degrees Fahrenheit to an output temperature in kelvin. Record of revisions: Date Programmer Description of change ==== ========== ===================== 01/03/14 S. J. Chapman Original code Define variables: temp_f -- Temperature in degrees Fahrenheit temp_k -- Temperature in kelvin Prompt the user for the input temperature. temp_f = input('enter the temperature in degrees Fahrenheit: '); Convert to kelvin. temp_k = (5/9) * (temp_f - 32) ; Write out the result. fprintf('6.2f degrees Fahrenheit = 6.2f kelvin.\n',... temp_f,temp_k);

27 Slide 26 of Examples 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. example_2_5_calc_power.m Script file: calc_power.m Define variables: amps -- Current flow to load (amps) pl -- Power supplied to load (watts) rl -- Resistance of the load (ohms) rs -- Internal resistance of the power source (ohms) volts -- Voltage of the power source (volts) Set the values of source voltage and internal resistance volts = 120; rs = 50; Create an array of load resistances rl = 1:1:100; Calculate the current flow for each resistance amps = volts./ ( rs + rl ); Calculate the power supplied to the load pl = (amps.^ 2).* rl; Plot the power versus load resistance plot(rl,pl); title('plot of power versus load resistance'); xlabel('load resistance (ohms)'); ylabel('power (watts)'); grid on;

28 Slide 27 of Debugging MATLAB Programs Debug a MATLAB Program Debug a MATLAB Program MATLAB Errors 3 Types of erros in MATLAB: (i) Syntax error: errors in the MATLAB statement itself (spelling, punctuation, format, etc.) (ii) Run-time error: errors when an illegal mathematical operation is attempted during the program execution (i.e., attempting to divide by zero, producing the infinity). The program returns inf or Nan, which is then used for further calculations. (iii) Logical error: errors when the program compiles and runs successfully but produces wrong answer (the toughest one to discover... MATLAB cannot detect this type of error: the program appears to run OK, but produces wrong results). You must spend some time, trying to debug your code. The MATLAB Symbolic Debugger MATLAB offers a powerful tool for debugging, embedded into the MATLAB editor. The MATLAB symbolic editor allows you to: walk through the code execution one statement at a time and to examine the values of any variables at each step along the way. see all of the intermediate results without having to insert a lot of output statements into your code.