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Matlab Beginner Training Session Review: Introduction to Matlab for Graduate Research

Matlab Beginner Training Session Review: Introduction to Matlab for Graduate Research. Non-Accredited Matlab Tutorial Sessions for beginner to intermediate level users

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Matlab Beginner Training Session Review: Introduction to Matlab for Graduate Research

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  1. Matlab Beginner Training Session Review:Introduction to Matlab for Graduate Research

  2. Non-Accredited Matlab Tutorial Sessions for beginner to intermediate level users Winter Session Dates:  February 13, 2007 - March 7, 2007Session times: Tuesdays from 8:30am-10:00am, Wednesdays from 8:30pm-10:00amSession Locations: Humphrey Hall - Room 219 Instructors: Robert Marino rmarino@biomed.queensu.ca Course Website: http://www.queensu.ca/neurosci/Matlab Training Sessions.htm

  3. Last Semester Weeks: • Introduction to Matlab and its Interface • Fundamentals (Operators) • Fundamentals (Flow) • Importing Data • Functions and M-Files • Plotting (2D and 3D) • Statistical Tools in Matlab • Analysis and Data Structures

  4. Intermediate Sessions • Intermediate Lectures • Term 1 review • Loading Binary Data • Nonlinear Curve Fitting • Statistical Tools in Matlab II • Creating Graphic User Interfaces (GUIs) • Other possible topics: • Writing ascii text data files • 3D plotting and animating • Debugging Tools • Simulink Toolbox

  5. Why Matlab? Common Uses for Matlab in Research • Data Acquisition • Multi-platform, Multi Format data importing • Analysis Tools (Existing,Custom) • Statistics • Graphing • Modeling

  6. Why Matlab? Multi-platform, Multi Format data importing • Data can be loaded into Matlab from almost any format and platform • Binary data files (eg. REX, PLEXON etc.) • Ascii Text (eg. Eyelink I, II) • Analog/Digital Data files PC 100101010 UNIX Subject 1 143 Subject 2 982 Subject 3 87 …

  7. Why Matlab? Analysis Tools • A Considerable library of analysis tools exist for data analysis • Provides a framework for the design, creation, and implementation of any custom analysis tool imaginable

  8. Why Matlab? Graphing • A Comprehensive array of plotting options available from 2 to 4 dimensions • Full control of formatting, axes, and other visual representational elements

  9. Why Matlab? Modeling • Models of complex dynamic system interactions can be designed to test experimental data

  10. Understanding the Matlab Environment: • Executing Commands • Basic Calculation Operators: • + Addition • - Subtraction • * Multiplication • / Division • ^ Exponentiation

  11. Using Matlab • Solving equations using variables • Matlab is an expression language • Expressions typed by the user are interpreted and evaluated by the Matlab system • Variables are names used to store values • Variable names allow stored values to be retrieved for calculations or permanently saved • Variable = Expression • Or • Expression • **Variable Names are Case Sensitive! >> x * y Ans = 12 >> x / y Ans = 3 >> x ^ y Ans = 36 >> x = 6 x = 6 >> y = 2 y = 2 >> x + y Ans = 8

  12. Using Matlab • Working with Matrices • Matlab works with essentially only one kind of object, a rectangular numerical matrix • A matrix is a collection of numerical values that are organized into a specific configuration of rows and columns. • The number of rows and columns can be any number • Example • 3 rows and 4 columns define a 3 x 4 matrix having 12 elements • A scalar is a single number and is represented by a 1 x 1 matrix in matlab. • A vector is a one dimensional array of numbers and is represented by an n x 1 column vector or a 1 x n row vector of n elements

  13. Exercises Enter the following Matrices in matlab using spaces, commas, and semicolons to separate rows and columns: A = B = D = D = C = E = a 5 x 9 matrix of 1’s

  14. Exercises Change the following elements in each matrix: 76 76 0 A = B = 0 D = 76 0 D = C = 76 E = a 5 x 9 matrix of 1’s 76

  15. Matrix Operations • Indexing Matrices • A = [1 2 4 5 • 6 3 8 2] • The colon operator can can be used to remove entire rows or columns • >> A(:,3) = [ ] • A = [1 2 5 • 6 3 2] • >> A(2,:) = [ ] • A = [1 2 5]

  16. Matrix Operations • Scalar Operations • Scalar (single value) calculations can be can performed on matrices and arrays • Basic Calculation Operators • + Addition • - Subtraction • * Multiplication • / Division • ^ Exponentiation

  17. Matrix Operations • Element by Element Multiplication • Element by element multiplication of matrices is performed with the .* operator • Matrices must have identical dimensions • A = [1 2 B = [1 D = [2 2 E = [2 4 3 6] • 6 3 ] 7 2 2 ] • 3 • 3] • >>A .* D • Ans = [ 2 4 • 12 6]

  18. Matrix Operations • Element by Element Division • Element by element division of matrices is performed with the ./ operator • Matrices must have identical dimensions • A = [1 2 4 5 B = [1 D = [2 2 2 2 E = [2 4 3 6] • 6 3 8 2] 7 2 2 2 2] • 3 • 3] • >>A ./ D • Ans = [ 0.5000 1.0000 2.0000 2.5000 • 3.0000 1.5000 4.0000 1.0000 ]

  19. Matrix Operations • Matrix Exponents • Built in matrix Exponentiation in Matlab is either: • A series of Algebraic dot products • Element by element exponentiation • Examples: • A^2 = A * A (Matrix must be square) • A.^2 = A .* A

  20. Matrix Operations • Shortcut: Transposing Matrices • The transpose of a matrix is the matrix formed by interchanging the rows and columns of a given matrix • A = [1 2 4 5 B = [1 • 6 3 8 2] 7 • 3 • 3] • >> transpose(A) >> B’ • A = [1 6 B = [1 7 3 3] • 2 3 • 4 8 • 5 2]

  21. Relational Operators • Relational operators are used to compare two scaler values or matrices of equal dimensions • Relational Operators • < less than • <= less than or equal to > Greater than >= Greater than or equal to == equal ~= not equal

  22. Relational Operators • Comparison occurs between pairs of corresponding elements • A 1 or 0 is returned for each comparison indicating TRUE or FALSE • Matrix dimensions must be equal! • >> 5 == 5 • Ans 1 • >> 20 >= 15 • Ans 1

  23. Relational Operators A = [1 2 4 5 B = 7 C = [2 2 2 2 6 3 8 2] 2 2 2 2] Try: >>A > B >> A < C

  24. Relational Operators • The Find Function • A = [1 2 4 5 B = 7 C = [2 2 2 2 D = [0 2 0 5 0 2] • 6 3 8 2] 2 2 2 2] • The ‘find’ function can also return the row and column indexes of of matching elements by specifying row and column arguments • >> [x,y] = find(A == 5) • The matching elements will be indexed by (x1,y1), (x2,y2), … • >> A(x,y) = 10 • A = [ 1 2 4 10 • 6 3 8 2 ]

  25. Control and Flow • Control flow capability enables matlab to function beyond the level of a simple desk calculator • With control flow statements, matlab can be used as a complete high-level matrix language • Flow control in matlab is performed with condition statements and loops

  26. Matlab Scripts • Advantages of M-files • Easy editing and saving of work • Undo changes • Readability/Portability - non executable comments can be added using the ‘%’ symbol to make make commands easier to understand • Saving M-files is far more memory efficient than saving a workspace

  27. Condition Statements • It is often necessary to only perform matlab operations when certain conditions are met • Relational and Logical operators are used to define specific conditions • Simple flow control in matlab is performed with the ‘If’, ‘Else’, ‘Elseif’ and ‘Switch’ statements

  28. Condition Statements • If, Else, and Elseif • An if statement evaluates a logical expression and evaluates a group of commands when the logical expression is true • The list of conditional commands are terminated by the end statement • If the logical expression is false, all the conditional commands are skipped • Execution of the script resumes after the end statement • Basic form: • iflogical_expression • commands • end

  29. Condition Statements Example A = 6 B = 0 if A > 3 D = [1 2 6] A = A + 1 elseif A > 2 D = D + 1 A = A + 2 end What is evaluated in the code above?

  30. Condition Statements • Switch • The switch statement can act as many elseif statements • Only the one case statement who’s value satisfies the original expression is evaluated • Basic form: • switchexpression (scalar or string) • casevalue 1 • commands 1 • case value 2 • commands 2 • case value n • commands n • end

  31. Condition Statements • Example • A = 6 B = 0 • switch A • case 4 • D = [ 0 0 0] • A = A - 1 • case 5 • B = 1 • case 6 • D = [1 2 6] • A = A + 1 • end • ** Only case 6 is evaluated

  32. Loops • Loops are an important component of flow control that enables matlab to repeat multiple statements in specific and controllable ways • Simple repetition in matlab is controlled by two types of loops: • For loops • While loops

  33. Loops • For Loops • The for loop executes a statement or group of statements a predetermined number of times • Basic Form: • for index = start:increment:end • statements • end • ** If ‘increment’ is not specified, an increment of 1 is assumed by matlab

  34. Loops • For Loops • Examples: • for i = 1:1:100 • x(i) = 0 • end • Assigns 0 to the first 100 elements of vector x • If x does not exist or has fewer than 100 elements, additional space will be automatically allocated

  35. Loops • For Loops • Loops can be nested in other loops • A = [ ] • for i = 1:m • for j = 1:n • A(i,j) = i + j • end • end • Creates an m by n matrix A whose elements are the sum of their matrix position

  36. Loops • While Loops • The while loop executes a statement or group of statements repeatedly as long as the controlling expression is true • Basic Form: • whileexpression • statements • end

  37. Loops • While Loops • Examples: • A = 6 B = 15 • while A > 0 & B < 10 • A = A + 1 • B = B – 2 • end • Iteratively increase A and decrease B until the two conditions of the while loop are met • ** Be very careful to ensure that your while loop will eventually reach its termination condition to prevent an infinite loop

  38. Loops • Breaking out of loops • The ‘break’ command instantly terminates a for and while loop • When a break is encountered by matlab, execution of the script continues outside and after the loop

  39. Loops • Breaking out of loops • Example: • A = 6 B = 15 • count = 1 • while A > 0 & B < 10 • A = A + 1 • B = B + 2 • count = count + 1 • if count > 100 • break • end • end • Break out of the loop after 100 repetitions if the while condition has not been met

  40. Functions in Matlab • In Matlab, each function is a .m file • It is good protocol to name your .m file the same as your function name, i.e. funcname.m • function outargs=funcname(inargs); Function input output

  41. Importing Data • Basic issue: • How do we get data from other sources into Matlab so that we can play with it? • Other Issues: • Where do we get the data? • What types of data can we import • Easily or Not

  42. Basics • Matlab has a powerful plotting engine that can generate a wide variety of plots.

  43. Generating Data • Matlab does not understand functions, it can only use arrays of numbers. • a=t2 • b=sin(2*pi*t) • c=e-10*t note: matlab command is exp() • d=cos(4*pi*t) • e=2t3-4t2+t • Generate it numerically over specific range • Try and generate a-e over the interval 0:0.01:2 t=0:0.01:10; %make x vector y=t.^2; %now we have the appropriate y % but only over the specified range

  44. Quick Assignment 1 • Plot a as a thick black line • Plot b as a series of red circles. • Label each axis, add a title and a legend

  45. Quick Assignment 1 figure plot(t,a,'k','LineWidth',3); hold on; plot(t,b,'ro') xlabel('Time (ms)'); ylabel('f(t)'); legend('t^2','sin(2*pi*t)'); title('Mini Assignment #1')

  46. Part A: Basics • The Matlab installation contains basic statistical tools. • Including, mean, median, standard deviation, error variance, and correlations • More advanced statistics are available from the statistics toolbox and include parametric and non-parametric comparisons, analysis of variance and curve fitting tools

  47. Mean and Median Mean: Average or mean value of a distribution Median: Middle value of a sorted distribution M = mean(A), M = median(A) M = mean(A,dim), M = median(A,dim) M = mean(A), M = median(A): Returns the mean or median value of vector A. If A is a multidimensional mean/median returns an array of mean values. Example: A = [ 0 2 5 7 20] B = [1 2 3 3 3 6 4 6 8 4 7 7]; mean(A) = 6.8 mean(B) = 3.0000 4.5000 6.0000 (column-wise mean) mean(B,2) = 2.0000 4.0000 6.0000 6.0000 (row-wise mean)

  48. Standard Deviation and Variance • Standard deviation is calculated using the std() function • std(X) : Calcuate the standard deviation of vector x • If x is a matrix, std() will return the standard deviation of each column • Variance (defined as the square of the standard deviation) is calculated using the var() function • var(X) : Calcuate the variance of vector x • If x is a matrix, var() will return the standard deviation of each column

  49. Standard Error of the Mean In Class Exercise 1: • Create a function called se that calculates the standard error of some vector supplied to the function Eg. se(x) should return the standard error of matrix x

  50. Data Correlations • Matlab can calculate statistical correlations using the corrcoef() function • [R,P] = corrcoef(A,B) • Calculates a matrix of R correlation coefficiencts and P significance values (95% confidence intervals) for variables A and B A B R = A AcorA BcorA B AcorB BcorB

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