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WELCOME

WELCOME. EF 105 Fall 2006 Week 10. Topics:. E ngineering Problem Solving Programming Logic Intro to MATLAB. Engineering Problem Solving. Define the problem clearly Work hand examples Develop the Algorithm (Steps to follow) Document the Algorithm with a FLOWCHART

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WELCOME

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  1. WELCOME EF 105 Fall 2006 Week 10

  2. Topics: • Engineering Problem Solving • Programming Logic • 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 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. start task test? F T I/O task stop Basic Flowcharting Elements Arrows show the flow - cannot diverge but can converge. Execution Block Entry Point Selection Block Exit Point Input/Output Block

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

  8. ini_code test? F T loop_code inc_code next_code 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.

  9. F Entry Task I/O Q? Exit T Basic Flowchart Symbols

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

  11. Algorithm Step 4: How do we compute the output? (first solution) Step 4.1: Start with the current integer: 1 Step 4.2: Sum starts with 0 Step 4.3: Add the current integer to Sum 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. Start Current Integer=1 Sum=0 Step 4.1: Start with the first integer: 1 Step 4.2: Sum starts with 0 Sum = Sum + Current Integer Increase Current Integer by 1 Current Integer < 100 Print Sum Stop Flowchart Step 4.3: Add the current integer to Sum 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

  13. Intro to Matlab Inside Matlab This is what you should see once Matlab has loaded. The three most usefulareas 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 ofpast commands. Workspace Command Window Command Window Command Window Command History Command History

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

  18. Operation Algebraic Matlab Form Scalar addition a + b a + bsubtraction a – b a – bmultiplication a x b a * bdivision a ÷ b a / bexponentiation ab a ^ b Precedence Operation 1 Parenthesis, innermost first. 2 Exponentiation, left to right 3 Multiplication & division, left to right 4 Addition & subtraction, left to right Review Arithmetic Operations and Precedence

  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:

  24. Commands involving variables • who: lists the names of defined variables • whos: lists the names and sizes of defined variables • what: lists all your m-files stored in memory. • clear: clears all variables, reset the default values of special variables. • clearname: 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

  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. Entering Matrices • 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

  32. Matrix Elements • 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.

  33. Output Format • 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.

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

  35. Array Operations(using the period) • 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

  36. Generating Vectors • 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

  37. Useful Matrices • 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)

  38. Hands-On DEMO: Matrix Operations - TransposesTranspose – (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 • usuallystart 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

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