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

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Matlab Beginner Training Session
ReviewIntroduction to Matlab for Graduate
Research
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• Non-Accredited Matlab Tutorial Sessions for
  beginner to intermediate level users
• Winter Session Dates  February 13, 2007 - March
  7, 2007Session times Tuesdays from
  830am-1000am, Wednesdays from
  830pm-1000amSession Locations Humphrey Hall -
  Room 219
• Instructors
• Robert Marino rmarino_at_biomed.queensu.ca
• Course Website
• http//www.queensu.ca/neurosci/Matlab Training
  Sessions.htm

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• 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

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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

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Why Matlab?

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

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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
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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

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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

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Why Matlab?

• Modeling
• Models of complex dynamic system interactions can
  be designed to test experimental data

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Understanding the Matlab Environment

• Executing Commands
• Basic Calculation Operators
• Addition
• - Subtraction
• Multiplication
• / Division
• Exponentiation

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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!

gtgt x y Ans 12 gtgt x / y Ans 3 gtgt x y
Ans 36
gtgt x 6 x 6 gtgt y 2 y 2 gtgt x y Ans 8
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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

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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 1s
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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 1s
76
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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
• gtgt A(,3)
• A 1 2 5
• 6 3 2
• gtgt A(2,)
• A 1 2 5

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Matrix Operations

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

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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
• gtgtA . D
• Ans 2 4
• 12 6

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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
• gtgtA ./ D
• Ans 0.5000 1.0000 2.0000 2.5000
• 3.0000 1.5000 4.0000 1.0000

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Matrix Operations

• Matrix Exponents
• Built in matrix Exponentiation in Matlab is
  either
• A series of Algebraic dot products
• Element by element exponentiation
• Examples
• A2 A A (Matrix must be square)
• A.2 A . A

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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
• gtgt transpose(A) gtgt
  B
• A 1 6
  B 1 7 3 3
• 2 3
• 4 8
• 5 2

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Relational Operators

• Relational operators are used to compare two
  scaler values or matrices of equal dimensions
• Relational Operators
• lt less than
• lt less than or equal to
• gt Greater than
• gt Greater than or equal to
• equal
• not equal

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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!
• gtgt 5 5
• Ans 1
• gtgt 20 gt 15
• Ans 1

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Relational Operators
A 1 2 4 5 B 7 C 2 2 2 2
6 3 8 2 2 2 2
2 Try gtgtA gt B gtgt A lt C

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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
• gtgt x,y find(A 5)
• The matching elements will be indexed by (x1,y1),
  (x2,y2),
• gtgt A(x,y) 10
• A 1 2 4 10
• 6 3 8 2

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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

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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

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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

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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
• if logical_expression
• commands
• end

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Condition Statements
Example A 6 B 0 if A gt 3
D 1 2 6 A A 1 elseif A gt 2 D
D 1 A A 2 end What is evaluated in
the code above?
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Condition Statements

• Switch
• The switch statement can act as many elseif
  statements
• Only the one case statement whos value satisfies
  the original expression is evaluated
• Basic form
• switch expression (scalar or string)
• case value 1
• commands 1
• case value 2
• commands 2
• case value n
• commands n
• end

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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
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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

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Loops

• For Loops
• The for loop executes a statement or group of
  statements a predetermined number of times
• Basic Form
• for index startincrementend
• statements
• end
• If increment is not specified, an increment
  of 1 is assumed by matlab

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Loops

• For Loops
• Examples
• for i 11100
• 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

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Loops

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

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Loops

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

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Loops

• While Loops
• Examples
• A 6 B 15
• while A gt 0 B lt 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

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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

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Loops

• Breaking out of loops
• Example
• A 6 B 15
• count 1
• while A gt 0 B lt 10
• A A 1
• B B 2
• count count 1
• if count gt 100
• break
• end
• end
• Break out of the loop after 100 repetitions if
  the while condition has not been met

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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 outargsfuncname(inargs)

Function
input
output
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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

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Basics

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

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Generating Data

• Matlab does not understand functions, it can only
  use arrays of numbers.
• at2
• bsin(2pit)
• ce-10t note matlab command is exp()
• dcos(4pit)
• e2t3-4t2t
• Generate it numerically over specific range
• Try and generate a-e over the interval 00.012

t00.0110 make x vector yt.2 now we have
the appropriate y but only over the
specified range
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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

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Quick Assignment 1
figure plot(t,a,'k','LineWidth',3) hold
on plot(t,b,'ro') xlabel('Time
(ms)') ylabel('f(t)') legend('t2','sin(2pit)'
) title('Mini Assignment 1')
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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

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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)
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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

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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

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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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Part B Statistics Toolbox

• The Statistics tool box contains a large array of
  statistical tools.
• This lecture will concentrate on some of the most
  commonly used statistics for research
• Parametric and non-parametric comparisons
• Curve Fitting

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Comparison of Means

• A wide variety of mathametical methods exist for
  determining whether the means of different groups
  are statistically different
• Methods for comparing means can be either
  parametric (assumes data is normally distributed)
  or non-parametric (does not assume normal
  distribution)

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Parametric Tests - TTEST

• H,P ttest2(X,Y)
• Determines whether the means from matrices X and
  Y are statistically different.
• H return a 0 or 1 indicating accept or reject nul
  hypothesis (that the means are the same)
• P will return the significance level

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Parametric Tests - TTEST

• Example
• For the data from exercise 3
• H,P ttest2(var1,var2)
• gtgt H,P ttest2(var1,var2)
• H 1
• P 0.00000000000014877

Variable 1
Variable 2

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Curve Fitting

• A least squares linear fit minimizes the square
  of the distance between every data point and the
  line of best fit
• P robustfit(X,Y) returns the vector B of the y
  intercept and slope, obtained by performing
  robust linear fit

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Curve Fitting

• Plotting a line of best fit in Matlab can be
  performed using either a traditional least
  squares fit or a robust fitting method.

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10
8
6
Least squares

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Robust
2
0
-2
1
2
3
4
5
6
7
8
9
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