MATLAB: How do you work with data to solve problems?

1. MATLAB:  How do you work with data to solve problems? Fall 2012 Lecture # XX

2. Mathematical Tools for Quantitative Methods • In today’s technology world, every engineering and computer science discipline uses computers: • For computer scientists, as an aid in writing programs. • For engineers, as a tool to help in the design process, and also to help in solving complex equations. • In most scientific and engineering disciplines, the most useful mathematical equations normally do not have closed solutions. • Often, useful equations are non-linear, perhaps involving second-order differential equations, for which there is no general solution. • This means that many equations are solved using a numerical approach (a fancy way of saying that answers are tried until one works!). • For modern technologists, there are many useful computer tools, normally programs that aid in solving complex equations.

3. “Too many tools & too little time” • In a course such as ECS 1200, we simply do not have the time to examine many of the available tools. • However, there is one tool, readily available, that would be useful to all undergraduates in ECS that we can survey briefly. • MATLAB

4. So What Is MATLAB? • A high-performance tool for technical computing, integrating computation, visualization, and programming in such a way that problems and solutions are expressed in familiar mathematical notation. • an “interactive, matrix-based system for algorithm development, GUI Design, data analysis, data visualization, and numeric computation” • A recommended mathematical tool at UTD • Available at the UTD Tech Store

5. MATLAB High Level Languages such as C, Pascal etc. Assembly What is MATLAB? • MATLAB is an abbreviation for MATrixLABoratory • MATLAB is basically a high level language which has many specialized toolboxes for making things easier for us as engineers and computer scientists • How high?

6. Why Use MATLAB? • Used mainly for algorithm development and data visualization • Algorithms can be implemented and tested more quickly and easily than with traditional programming languages • Quickly get numerical and graphic answers to matrix and vector related math problems • A way to solve complex numerical problems without actually writing a program • Built-in tools • No complex programming knowledge needed • MATLAB focuses on ease of use and quick development

7. Some of MATLAB’s Toolboxes Math and Analysis Optimization Requirements Management Interface Statistics Neural Network Symbolic/Extended Math Partial Differential Equations PLS Toolbox Mapping Spline Data Acquisition and Import Data Acquisition Instrument Control Excel Link Portable Graph Object Signal & Image Processing Signal Processing Image Processing Communications Frequency Domain System Identification Higher-Order Spectral Analysis System Identification Wavelet Filter Design Control Design  Control System Fuzzy Logic Robust Control μ-Analysis and Synthesis Model Predictive Control

8. MATLAB’s Appeal • Interactive code development proceeds incrementally; excellent development and rapid prototyping environment • Basic data element is the auto-indexed array • This allows quick solutions to problems that can be formulated in vector or matrix form • Powerful GUI tools • Large collection of toolboxes: collections of topic-related MATLAB functions that extend the core functionality significantly

9. MATLAB Example 1 • MATLAB can easily solve families of linear equations. • For example, suppose you need to solve three linear equations for x, y, and z such that: 2x+3y+z=11 x+y+z=6 4x-3y+z=1 • The MATLAB command to solve the equations would be: >> [x,y,z]=solve('2*x+3*y+z=11','x+y+z=6','4*x-3*y+z=1')

10. MATLAB Example 2 • An even tougher set of equations – say, five linear equations, would be even easier, compared to manual solution: 2v+2w+2x+2y+2z=30 2v+2w+2x+y-z=19 4x+y-z=3 v+w+x-y-z=5 5v-w+2x+2y+2z=27 • The same “solve” function is used. Equations are written as before, using “*” to denote multiplication, quotes (‘’) to denote the range of each equation, and a comma separator.

11. MATLAB Summary • MATLAB is a complex program that is an excellent mathematical tool for solving complex science and engineering problems. • In general, it is so complex that it takes some “getting used to.” You cannot just plunge into it today and expect to be a master in about ten minutes. • However, with a little work, you can master its intricacies and become a MATLAB master. • Because the student price is so good, and because you will be using MATLAB in some of your advanced UG courses, it would be a good idea to start learning now!

12. MATLAB Screen Command Window type commands Current Directory View folders and m-files Workspace View program variables Double click on a variable to see it in the Array Editor Command History view past commands save a whole session using diary

13. Some MATLAB Development Windows • Command Window: where you enter commands • Command History: running history of commands which is preserved across MATLAB sessions • Current directory: current location for session • Workspace: GUI for viewing, loading and saving MATLAB variables • Array Editor: GUI for viewing and/or modifying contents of MATLAB variables (openvarvarname or double-click the array’s name in the Workspace) • Editor/Debugger: text editor, debugger; editor works with file types in addition to .m (MATLAB “m-files”)

14. Entering Commands and Expressions • MATLAB retains your previous keystrokes. • Use the up-arrow key to scroll back back through the commands. • Press the key once to see the previous entry, and so on. • Use the down-arrow key to scroll forward. Edit a line using the left- and right-arrow keys the Backspace key, and the Delete key. • Press the Enter key to execute the command.

15. A video introduction: • A Five Minute Introduction to MATLAB

16. Example Session >> 8/10 ans = 0.8000 >> 5*ans ans = 4 >> r=8/10 r = 0.8000 >> r r = 0.8000 >> s=20*r s = 16

17. More Examples >> 8 + 3*5 ans = 23 >> 8 + (3*5) ans = 23 >>(8 + 3)*5 ans = 55 >>4^2­12­8/4*2 ans = 0 >>4^2­12­ 8/(4*2) ans = 3

18. …and some more examples >> 3*4^2 + 5 ans = 53 >>(3*4)^2 + 5 ans = 149 >>27^(1/3) + 32^(0.2) ans = 5 >>27^(1/3) + 32^0.2 ans = 5 >>27^1/3 + 32^0.2 ans = 11

21. int a; double b; float c; Variables • No need for types. i.e., • All variables are created with double precision unless specified and they are matrices. • After these statements, the variables are 1x1 matrices with double precision Example: >>x=5; >>x1=2;

22. Variable Basics >> 16 + 24 ans = 40 >> product = 16 * 23.24 product = 371.84 >> product = 16 *555.24; >> product product = 8883.8 no declarations needed mixed data types semi-colon suppresses output of the calculation’s result

23. Variable Basics >> clear >> product = 2 * 3^3; >> comp_sum = (2 + 3i) + (2 - 3i); >> show_i = i^2; >> save three_things >> clear >> load three_things >> who Your variables are: comp_sum product show_i >> product product = 54 >> show_i show_i = -1 clear removes all variables; clear x y removes only x and y complex numbers (i or j) require no special handling save/load are used to retain/restore workspace variables use home to clear screen and put cursor at the top of the screen

24. Special variables and constants Numeric display formats

25. >> A = [16 3; 5 10] A = 16 3 5 10 Matrices & Vectors • All (almost) entities in MATLAB are matrices • Easy to define: • Use ‘,’ or ‘ ’ to separate row elements -- use ‘;’ to separate rows

26. Matrix: >> A=[1 2; 3 4]; >> A' ans = 1 3 2 4 Vector : >> a=[1 2 3]; >> a' 1 2 3 Creating Vectors and Matrices >> A = [16 3; 5 10] A = 16 3 5 10 >> B = [3 4 5 6 7 8] B = 3 4 5 6 7 8 • Define • Transpose

27. Creating Vectors Create vector with equally spaced intervals >> x=0:0.5:pi x = 0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 Create vector with n equally spaced intervals >> x=linspace(0, pi, 7) x = 0 0.5236 1.0472 1.5708 2.0944 2.6180 3.1416 Equal spaced intervals in logarithm space >> x=logspace(1,2,7) x = 10.0000 14.6780 21.5443 … 68.1292 100.0000 Note: MATLAB uses pi to represent , uses i or j to represent imaginary unit

28. Creating Matrices • zeros(m, n):matrix with all zeros • ones(m, n): matrix with all ones. • eye(m, n): the identity matrix • rand(m, n): uniformly distributed random • randn(m, n): normally distributed random • magic(m): square matrix whose elements have the same sum, along the row, column and diagonal. • pascal(m) : Pascal matrix.

29. Matrix operations • ^:exponentiation • *: multiplication • /: division • \: left division. The operation A\Bis effectively the same as INV(A)*B, although left division is calculated differently and is much quicker. • +: addition • -: subtraction

30. Matrices Operations Given A and B: Addition Subtraction Transpose Product

31. Array Operations • Evaluated element by element .' : array transpose (non-conjugated transpose) .^ : array power .* : array multiplication ./ : array division • Very different from Matrix operations >> A=[1 2;3 4]; >> B=[5 6;7 8]; >> A*B 19 22 43 50 But: >> A.*B 5 12 21 32

32. The use of “.” – “Element” Operation A = [1 2 3; 5 1 4;3 2 1] A = 1 2 3 5 1 4 3 2 -1 b = x .* y b= 3 8 -3 c = x . / y c= 0.33 0.5 -3 d = x .^2 d= 1 4 9 x = A(1,:) x= 1 2 3 y = A(3 ,:) y= 3 4 -1

33. Some Built-in functions • mean(A):mean value of a vector • max(A), min (A): maximum and minimum. • sum(A): summation. • sort(A): sorted vector • median(A): median value • std(A): standard deviation. • det(A) : determinant of a square matrix • dot(a,b): dot product of two vectors • Cross(a,b): cross product of two vectors • Inv(A): Inverse of a matrix A • length(A): number of values in an array

34. Operators (relational, logical) • == Equal to • ~= Not equal to • < Strictly smaller • > Strictly greater • <= Smaller than or equal to • >= Greater than equal to • & And operator • | Or operator

35. Indexing Matrices n A = 0.9501 0.6068 0.4231 0.2311 0.4860 0.2774 Given the matrix: Then: A(1,2) = 0.6068 A(:,1) = [0.9501 0.2311 ] A(1,2:3)=[0.6068 0.4231] m 1:m

36. Adding Elements to a Vector or a Matrix >> C=[1 2; 3 4] C= 1 2 3 4 >> C(3,:)=[5 6]; C= 1 2 3 4 5 6 >> D=linspace(4,12,3); >> E=[C D’] E= 1 2 4 3 4 8 5 6 12 >> A=1:3 A= 1 2 3 >> A(4:6)=5:2:9 A= 1 2 3 5 7 9 >> B=1:2 B= 1 2 >> B(5)=7; B= 1 2 0 0 7

37. Flow Control • if • for • while • break • ….

38. Some Dummy Examples if ((a>3) & (b==5)) Some MATLAB Commands; end if (a<3) Some MATLAB Commands; elseif (b~=5) Some MATLAB Commands; end if (a<3) Some MATLAB Commands; else Some MATLAB Commands; end Control Structures • If Statement Syntax if (Condition_1) MATLAB Commands elseif (Condition_2) MATLAB Commands elseif (Condition_3) MATLAB Commands else MATLAB Commands end

39. Some Dummy Examples for i=1:100 Some MATLAB Commands; end for j=1:3:200 Some MATLAB Commands; end for m=13:-0.2:-21 Some MATLAB Commands; end for k=[0.1 0.3 -13 12 7 -9.3] Some MATLAB Commands; end Control Structures • For loop syntax for i=Index_Array MATLAB Commands end

40. Control Structures • While Loop Syntax while (condition) MATLAB Commands end Dummy Example while ((a>3) & (b==5)) Some MATLAB Commands; end

41. You can perform operations in MATLAB in two ways: 1. In the interactive mode, in which all commands are entered directly in the Command window, or 2. By running a MATLAB program stored in script file. This type of file contains MATLAB commands, so running it is equivalent to typing all the commands—one at a time—at the Command window prompt. You can run the file by typing its name at the Command window prompt.

42. Scripts and Functions • Scripts do not accept input arguments, nor do they produce output arguments. Scripts are simply MATLAB commands written into a file. They operate on the existing workspace. • Functions accept input arguments and produce output variables. All internal variables are local to the function and commands operate on the function workspace. • A file containing a script or function is called an m-file • If duplicate functions (names) exist, the first in the search path (from path command) is executed.

43. Use of M-File Click to create a new M-File • Extension “.m” • A text file containing script or function or program to run

44. Save file as Denem430.m Use of M-File If you include “;” at the end of each statement, result will not be shown immediately

45. Writing User Defined Functions • Functions are m-files which can be executed by specifying some inputs and supply some desired outputs. • The code telling the MATLAB that an m-file is actually a function is • You should write this command at the beginning of the m-file and you should save the m-file with a file name same as the function name function out1=functionname(in1) function out1=functionname(in1,in2,in3) function [out1,out2]=functionname(in1,in2)

46. Same Name Writing User Defined Functions • Examples • Write a function : out=squarer (A, ind) • Which takes the square of the input matrix if the input indicator is equal to 1 • And takes the element by element square of the input matrix if the input indicator is equal to 2

47. Writing User Defined Functions • Another function which takes an input array and returns the sum and product of its elements as outputs • The function sumprod(.) can be called from command window or an m-file as

48. Keep in mind when using script files: 1. The name of a script file must begin with a letter, and may include digits and the underscore character, up to 63 characters. 2. Do not give a script file the same name as a variable. 3. Do not give a script file the same name as a MATLAB command or function. You can check to see if a command, function or file name already exists by using the exist command.

49. MATLAB Graphics x = 0:pi/100:2*pi; y = sin(x); plot(x,y) xlabel('x = 0:2\pi') ylabel('Sine of x') title('Plot of the Sine Function')

50. A graphics window showing a plot.