1. WELCOME EF 105 Fall 2006 Week 10

2. Topics: 1. Engineering Problem Solving 2.Programming Logic 3.Intro to MATLAB

3. Engineering Problem Solving Define the problem clearly Work hand examples Develop the Algorithm (Steps to follow) Document the Algorithm with a FLOWCHART Implement the Algorithm (Write computer program) Test the Implementation (Run the Program) Evaluate the Results

4. PROGRAMMING LOGIC: Top-Down Algorithm Development Divide and Conquer Break Problem into smaller tasks. Define the interaction between tasks. Recursively solve the individual tasks. Build up the overall solution from the pieces.

5. Structured Programming Combination of –Sequences –Selections –Loops Sequences Series of operations that are performed in order. Selections Choose one path from two or more possible paths. Loops Execute a block of code repeatedly as long as some condition is met.

6. Basic Flowcharting Elements test? F T start task I/O task stop Selection Block Arrows show the flow - cannot diverge but can converge. Exit Point Execution Block Input/Output Block Entry Point

7. Selection Statements Selectively choose one path of execution. –Based on the evaluation of a test. –Logical Test outcome is either TRUE or FALSE. test? if_codeif()T F test? if_codeelse_code if()...else F T

8. Loop Structures Special case of Selection Statement One branch eventually leads back to the original selection statement. Permits a block of code to be executed repeatedly as long as some test condition is satisfied. loop_cod e test? F T inc_code ini_co de next_cod e

9. Basic Flowchart Symbols Entry Exit TaskI/OQ? T F

10. Practice: Algorithm and Flowchart Compute a sum of all integers from 1 to 100 and displays the result Step 1: Understand the problem: Computes a sum of all integers from 1 to 100 Step 2: What is the input? Step 3: What is the output? Start from 1, stop if reach 100 or (1 and 100) Sum

11. Algorithm Step 4: How do we compute the output? (first solution) Step 4.1: Start with the current integer: 1 Step 4.3: Add the current integer to Sum Step 4.2: Sum starts with 0 Step 4.4: If the current integer is less than 100, keep on adding the current integer to sum and increase It by 1(i.e, go back to 4.3). Step 4.5:Otherwise, print out the sum

12. Flowchart Step 4.3: Add the current integer to Sum Step 4.1: Start with the first integer: 1 Step 4.2: Sum starts with 0 Step 4.4: If the current integer is less than 100, go to next integer and keep on adding the current integer to sum (i.e, go back to 4.3). Step 4.5:Otherwise, print out the sum Stop Current Integer=1 Sum=0 Sum = Sum + Current Integer < 100 Increase Current Integer by 1 Print Sum Start

13. Intro to Matlab Inside Matlab This is what you should see once Matlab has loaded. The three most useful areas in the Matlab window are: 1. Right ‘command’ window is used for inputting commands 2. Top left ‘workspace’ window notes size of matrices used 3. Bottom left ‘command history’ window maintains a sequential list of past commands. Command History Workspace Command Window Command History Command Window Command Window

14. Help in MATLAB The following are three ways to access Matlab’s help files: 1. a. From options at top of Matlab window select Help  Matlab Help b. Select ‘Index’ tab c. Type topic to be searched in box 2. In Matlab window type a command preceded by ‘help’ or 'doc' For example,the following commands would produce a help file for the ‘plot’ command. >> help plot or >>doc plot 3. a. Double click command for which you want help b. Right-click on command c. Select ‘Help on Selection’

15. Creating files in MATLAB A. To create a new ‘M-file’ do one of the following: 1. In top left corner of Matlab window select File  New  M-file 2. Select ‘New M-file’ shortcut button located at the top left corner of Matlab screen B. Typing the following clears the command window: >> clc C. Typing a semicolon at the end of a command suppresses output. Note the difference between typing the following commands: >> x=0:0.5:10 >> x=0:0.5:10;

16. How/Where to write program Go to MATLAB command window File-New-M-File M-file is an Editor window Write your program in M-file Save in temp/ or your Disk. In command window, Run this file.

17. + addition - subtraction * multiplication / right division ^ power Basic Operators

18. Review Arithmetic Operations and Precedence OperationAlgebraicMatlab FormScalar additiona + ba + b subtractiona – ba – b multiplicationa x ba * b divisiona ÷ ba / b exponentiation a b a ^ b PrecedenceOperation 1Parenthesis, innermost first. 2Exponentiation, left to right 3Multiplication & division, left to right 4Addition & subtraction, left to right

19. Use Parentheses to Override Operator Precedence Normal evaluation of expressions –Left-to-Right if same level and no parentheses e.g. 3^3-8/4+7-5*2 = 27-2+7-10 = 25+7-10 = 32-10 = 22 Use parentheses to override e.g. (3^3-8)/4+(7-5)*2 = (9-8)/4+2*2 = 1/4+4 = 4.25

20. Overview of MatLab Variables Variables are names used to hold values that may change throughout the program. MatLab variables are created when they appear on the left of an equal sign. >> variable = expression creates the "variable'' and assigns to it the value of the expression on the right hand side. You do not need to define or declare a variable before it is used. >> x = 2 % creates a scalar The variable is x and % indicates a comment

21. Hands-On DEMO: Expression Evaluation In MatLab, enter the following: >> x = 1.4; >> numerator = x^3 - 2*x^2 + x - 6.3; >> denominator = x^2 + 0.05005*x – 3.14; >> f = numerator / denominator

22. Variable Naming Naming Rules –must begin with a letter, cannot contain blank spaces –can contain any combination of letters, numbers and underscore (_) –must be unique in the first 31 characters MatLab is case sensitive: “name”, “Name” and “NAME” are considered different variables Never use a variable with the same name as a MatLab command (see next slide) Naming convention: –Usually use all_lowercase_letters –-or- camelNotation ("hump" in middle)

23. Reserved Words… MatLab has some special (reserved) words that you may not use as variable names: break case catch continue else elseif end for function global if otherwise persistent return switch try while

24. Commands involving variables –who: lists the names of defined variables –whos: lists the names and sizes of defined variables –what: l ists all your m-files stored in memory. –clear: clears all variables, reset the default values of special variables. –clear name: clears the variable named –clc: clears the command window –clf: clears the current figure and the graph window.

25. Scalars and Vectors and Matrices In MatLab, a scalar is a variable with one row and one column. A vector is a matrix with only one row OR only one column. The distinction between row and column vectors is crucial. When working with MatLab you will need to understand how to properly perform linear algebra using scalars, vectors and matrices. MatLab enforces rules on the use of each of these variables

26. Scalars Scalars are the simple variables that we use and manipulate in simple algebraic equations. To create a scalar you simply introduce it on the left hand side of an equal sign. –>> x = 1; –>> y = 2; –>> z = x + y;

27. Vectors A row vector in MATLAB can be created by an explicit list, starting with a left bracket, entering the values separated by spaces (or commas) and closing the vector with a right bracket. A column vector can be created the same way, and the rows are separated by semicolons. Example: >> x = [ 0 0.25*pi 0.5*pi 0.75*pi pi ] x = 0 0.7854 1.5708 2.3562 3.1416 >> y = [ 0; 0.25*pi; 0.5*pi; 0.75*pi; pi ] y = 0 0.7854 1.5708 2.3562 3.1416 x is a row vector. y is a column vector.

28. Simple Vector Commands x = start:end create row vector x starting with start, counting by one, ending at end x = start:increment:end create row vector x starting with start, counting by increment, ending at or before end linspace(start,end,number) create row vector x starting with start, ending at end, having number elements length(x) returns the length of vector x y = x' transpose of vector x (row to column, or columnn to row)

29. Hands-On DEMO: Creating Vectors >> a = 1:10 % leave off semi-colon to see what you get each time >> b = 0:0.1:1 >> c = [7 8 9] >> d = [10; 11; 12] >> length(b) >> linspace(0,100,21)

30. Hands-On DEMO: linspace function % Plotting a function using vector math x = linspace(0, 20, 100); % define 100 x values (from 0 to 20) y = 5*exp(-0.3*x).*sin(x); % compute y vector plot(x,y), xlabel('X'), ylabel('Y'), title('Vector calc') linspace( ) function can be very effective for creating the x vector…

31. A = [1 2 3; 4 5 6; 7 8 9] OR A = [1 2 3 4 5 6 7 8 9] Must be enclosed in brackets Elements must be separated by commas or spaces Matrix rows must be separated by semicolons or a return Matlab is case sensitive Entering Matrices

32. x = [-1.3 sqrt(3) (1+2+3)*4/5]; –Output -> x = -1.3000 1.7321 4.8000 Matrix Manipulation: –x(5) = abs(x(1)); –Let r = [1 2 3 4 5]; –xx = [x;r]; –z = xx(2,2); –T = xx(2,1:3); %row 2, col. 1-3 Semicolon at the end of a line means don’t print to the command window. Matrix Elements

33. Format short –1.3333 0.0000 Format short e –1.3333E+000 1.2345E-006 Format long –1.333333333333338 0.000001234500000 Format long e –1.33333333333333E+000 1.234500000000003E- 006 Format hex –3FF555555555555 3EB4B6231ABFD271 Defaults to format short. Output Format

34. Transpose: A = [1 2 3; 4 5 6; 7 8 9]; C = A’; D = [-1 0 2]’; Matrix Operations

35. The term array operations refer to element-by- element operations. Preceding an operator (*, /, ^, ‘) by a period indicates an element-by-element operation. The addition and subtraction, matrix and array operations are the same and don’t need a period before these operators. Example: –X = [1 2 3]; Y=[4 5 6]; –W = X.*Y; % to mult. X and Y arrays Array Operations(using the period)

36. Most often used for a time vector. time = 0.0:100.0; Time = 10.0:0.5:100.0; B_time = 100.0:-0.5:50.0; Variable = first:increment:last Generating Vectors

37. Empty Matrix E = []; EE([2 4],:) = []; –Empties rows 2 & 4 and all columns in rows 2 & 4. Zeros –Ze = zeros(2,3); –Creates a 2 x 3 matrix consisting all of zeros. Ones –O = ones(3,3); –Creates a 3 x 3 matrix consisting all of ones. Eye –I = eye(3,3); –Creates a 3 x 3 matrix consisting of an identity matrix. (I’s on diagonal and 0’s elsewhere) Useful Matrices

38. h = [1 2 3]; h' (nothing) ans = 1 2 3 Switches from row to column vector. h * h' h.* h ans = 14 ans = 1 4 9 * is matrix multiplication, and so the dimensions must line up correctly. (more on this later).* is entry-by-entry multiplication. Hands-On DEMO: Matrix Operations - Transposes Transpose – (indicated by `)new matrix created by exchanging rows and columns of original matrix

39. Hands-On DEMO: Functions of Vectors Most Matlab functions will work equally well with both scalars and arrays (of any dimension) >> A=[1 2 3 4 5]; >> sin(A) ans = 0.8415 0.9093 0.1411 -0.7568 -0.9589 >> sqrt(A) ans = 1.0000 1.4142 1.7321 2.0000 2.2361

40. Strings of Characters MatLab variables may also contain strings, which are vectors of individual characters. There is no typographical difference in appearance between numerical variables and string variables. The type of variable (numerical or string) is determined when the variable is created. –>> x = 5.2 % numeric –>> y = 'Chewbacca'% string

41. What are Character Strings? Arrays! Example: » C = 'Hello'; %C is a 1x5 character array. » D = 'Hello there'; %D is a 1x11 character array. » A = 43; %A is a 1x1 double array. » T = 'How about this character string?' » size(T) ans = 1 32 » whos % What do you observe? Name Size Bytes Class A 1x1 8 double array C 1x5 10 char array D 1x11 22 char array T 1x32 64 char array ans 1x2 16 double array Grand total is 51 elements using 120 bytes

42. Hands-On DEMO: Strings of Characters >> h = 'Hello'; >> w = 'World'; >> [h ', ' w] % called concatenation

43. format Examples ( MATLAB performs all computations in double precision) The format command described below switches among different display formats. Command Result Example format short 5 digit scaled fixed point 3.1416 format long 15 digit scaled fixed point 3.14159265358979 format short e 5 digit floating-point 3.1416e+00 format long e 15 digit floating-point 3.141592653589793e+00 format short g general purpose 5 or 1.25 or 3.0e-12 format bank Fixed dollars and cents 7.95 format rat Ratio of small integers 355/113 format compact Suppresses excess line feeds. format loose Add line feeds.

44. Hands-On DEMO: Formatting p=0:20; format short e % exponential [p' pow2(p)' pow2(-p)'] format short g % general purpose [p' pow2(p)' pow2(-p)']

45. In-Class Exercise : MatLab Calculations Do the following in MatLab –Create a matrix with the form: [2 3] [5 1] –Create a row (or "horizontal") vector of 2 elements, 3 and 4 (inclusive). –Create a second column (or 'vertical') vector with the elements 2 and 1 in that order. –Type 'whos' to view your variables. It should read (for example): –>> whos Name Size Elements Bytes Density Complex a 2 by 2 4 32 Full No b 1 by 2 2 16 Full No c 2 by 1 2 16 Full No Grand total is 14 elements using 112 bytes Here, a is the matrix, b is the first vector, and c is the second vector. Now complete the following exercise: –Multiply your matrix by your first vector, above. –Perform element by element division of your resulting vector, divided by your second vector transposed. (The result should be a two element horizontal vector with 13 as each entry. ) –Type 'clear' to clear all variables from the workspace. Add your name as % comment, print Command Window and turn in

46. Saving/Loading Data Values Be sure you have the correct Current Directory set clear, clc –clear workspace and command window to start assign and calc a few values save file_name –saves file_name.mat in current directory –saves all defined variables clear; load file_name –brings workspace back

47. Hands-On DEMO: Saving Workspace First make sure your workspace is clear, and that your Current Directory is set to "My Documents" subfolder with your username (e.g. Djackson) Create a few scalars and vectors check workspace window for variables >> save demo -OR- click corresponding button look at your folder in My Documents subfolder Clear workspace, check Workspace then Reload variables, check Workspace

48. Scripts Scripts allow us to group and save MatLab commands for future use If we make an error, we can edit statements and commands Can modify later to solve other related problems Script is the MatLab terminology for a program NOTE: Scripts may use variables already defined in the workspace. –This can lead to unexpected results. –It is a good idea to clear the workspace (and the command window) at the beginning of all scripts. clear, clc

49. M-files: Scripts A Script is the simplest example of an M-file. When a script-file is invoked, MatLab simply executes the commands found in the file. Any variables created in the script are added to the MatLab Workspace. Scripts are particularly useful for automating long sequences of command.

50. Writing a MATLAB Script (program) File  New  M-File usually start with: clear, clc, format compact comments after % –for in-class exercises include at least: Course, date,section & # (e.g. EF105, Monday 8:00 ) a short title your name semi-colons to suppress variable initialization –omit semi-colons to display results –You can leave off ALL semi-colons to trace a program

51. Matlab Editor (note "Save and Run" button) Color keyed text with auto indents tabbed sheets for other files being edited Access to commands

52. Script Files (filename.m) Always check Current Directory Window –Set to MyDocuments\username Running scripts –from editor window, click "Save and run" button –-or- just type filename: –-or- type run filename

53. Hands-On DEMO: Creating our First Script (factorial) %fact_n – Compute n-factorial, n!=1*2*...*n % by DFJ fact = prod(1:n) % no semi-colon so fact displays %fact_n – Compute n-factorial, n!=1*2*...*n % by DFJ fact = prod(1:n) % no semi-colon so fact displays File  New  M-File File  Save As... fact_n Operates on a variable in "global" workspace –Variable n must exist in workspace –Variable fact is created (or over-written)

54. Hands-On DEMO: Running your Script To Run just type >> n=5; >> fact_n -OR- >> n=10; >> run fact_n

55. Displaying Code and Getting Help To list code, use type command >> type fact_n The help command displays first consecutive comment lines >> help fact_n

56. MATLAB Exercise 1 See the Word document for this exercise and perform at end of class on your own!!