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MATrix LABoratory. Matlab is an interpreted language for doing numerical and symbolic computations and scientific visualizations Advantages: Simple and has powerful set of toolboxes Easy manipulating vectors and matrices Programs are platform independent

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matrix laboratory
MATrix LABoratory
  • Matlab is an interpreted language for doing numerical and symbolic computations and scientific visualizations
  • Advantages:
    • Simple and has powerful set of toolboxes
    • Easy manipulating vectors and matrices
    • Programs are platform independent
    • Excellent Graphic/Visualization Tools
    • Easy to debug

MATLAB is EASY

matlab workspace
Matlab Workspace
  • Workspace is area of memory accessible from command line
  • Check Variables in workspace
    • who: short list
    • Whos: long list with storage and size information
  • Clear Variables in workspace
    • clear x y: clears variables x and y from workspace
    • clear : will clear all variables in workspace
  • Save Variables in workspace
    • save sept17: saves workspace variables in file called sept17

Matlab is Case Sensitive

basic commands
Basic Commands
  • cd: current directory
    • cd directory: change working directory
  • Editor
    • Type edit in the matlab workspace to bring up the matlab editor
    • edit myfile.txt : opens file in the matlab editor
  • Exclamation Point
    • Initiates a shell escape function
    • Input line is command to operating system
  • Quit Matlab
    • Type exit in the matlab workspace
  • Interrupt Matlab
    • cntrl-c: interrupts a ongoing calculation
basic structure matrix matrixname row column
Basic Structure: MatrixmatrixName(row,column)
  • Creating a Matrix:
    • Comma or Space for entries on same row
      • Scalar: x=2;
      • Vector or 1-D matrix = x1 = [ 5 3 4]
      • For odd series: x = [1:2:10] = [1 3 5 7 9]
    • Carriage Return or Semicolons to separate rows
      • 2x2 matrix: x2 = [2 3; 3 4]
      • 3x3 matrix: x3 = [1 2 3; 4 5 6; 7 8 9]
      • x4(3,3,3)=0;
  • Parentheses used to index matrices and commas to separate dimensions
    • x3(2,1) = 4
creating a matrix using built in functions
Creating a Matrix(Using Built In Functions)
  • zeros (m,n): creates a mxn matrix of zeros
  • ones (m,n): creates a mxn matrix of ones
  • eye (n) : creates a nxn identity matrix
  • diag (r): creates a nxn diagonal matrix with r in the diagonal
  • rand (m,n): creates a mxn random number matrix from uniform distribution
  • randn (m,n): creates a mxn random matrix from normal distribution
  • magic (n): nxn square matrix
matrix operations
Matrix Operations
  • Multiplication, Addition, Subtraction
    • Add and Subtract require matrices to be of same size
    • X = [1 2; 3 3], Y = [ 4 5 ; 8 9]

Z=X*Y or Z=X+Y or Z=X-Y

    • immultiply (X,Y) or X.*Y : element by element multiplication
  • Power: X^2 or X.^2
  • Transpose: X’
  • Inverse: inv (X)
  • Determinant: det (X)
  • Logarithm: log (X)
  • Exponential: exp(X)
  • Eigen Values: eig (X)
control structures
Control Structures
  • Loops
    • if else end
    • for   end
    • while end 
    • Example
      • for k=1:10
      • y(k) = exp(x);
      • x=x+0.01;
      • end 

Life is too short to waste it on for-loops: try to avoid them!

m files
M-Files
  • Files ending with .m
    • Contains scripts or functions
    • Can be saved anywhere and called in matlab by adding to the search path
    • Executed by typing m-file name in workspace
  • Create Diary of a matlab session
    • diary myfile
    • diary on: starts log
    • diary off: ends log
  • Run Batch Jobs with M-Files
    • nice matlab < myfile.m >& myfile.out &
descriptive statistics
Descriptive Statistics
  • Maximum and Minimum of Sample
    • max (x)
    • min (x)
  • Mean and Median of Sample
    • mean (x)
    • median (x)
  • Percentiles
    • prctile (x, 50)
  • Correlation Coefficients
    • [R,P] = corrcoeff (x,y)
  • Variance of Sample
    • y = var (x)
  • Standard Deviation of Sample
    • y = std (x)
hypothesis testing
Hypothesis Testing
  • BOLD fMRI data was collected when subjects (N=10) looked at three kinds of stimuli: self face, familiar face and unfamiliar face. Mean Percent signal change from baseline was estimated from the Fusiform Gyrus region for the three stimuli
    • self = [ 1.20 1.53 2.33 2.55 2.63 2.88 3.19 2.31 1.51 1.78]
    • fam = [0.92 1.89 2.32 1.67 1.49 3.2 2.3 1.11 0.83 2.1]
    • ufam = [0.56 0.89 1.32 1.0 1.4 0.2 0.3 1.11 0.83 2.1
  • T-test:
    • [test, p, ci] = ttest (self, 1, 0.05)
    • H0: mean = 1
    • Test = 0 then do not reject H0 at alpha=0.05
hypothesis testing contd
Hypothesis Testing (contd.)
  • Anova:
    • H0: All the three means are equal
    • X=[self;fam;ufam]’;
    • [p,table,stat] = anova1(X);
    • Computes Anova table, F statistics and boxplots for all columns in X
    • anova2: 2-way anova
    • anovan: n-way anova
    • manova
regression
Regression
  • Simple Linear Regression:
    • x=[1.0;2.3;3.1;4.8;5.6;6.3]
    • y=[2.6;2.8;3.1;4.7;5.1;5.3]
    • Coefficient = [inv (x’x)]x’y = 0.9379
    • coeff = regress(y,x) = 0.9379 which is also same as x\y = 0.9379
    • regstats : detailed output
multiple regression
Multiple Regression
  • Multiple Regression Using Least Squares:
    • X1 = [1 2 3 4 5 6 7 8 9 10]’;
    • Y = [2 0.3 5.2 7.8 12 12.1 14 15 18 19.9]’;
    • Model-1: Y = b1 + b2 X1
      • Plot (X1,Y,’o’)
      • Create Design Matrix X = [ones(size(X1)) X1];
      • [bhat bint R Rint Stats] = regress (Y,X,0.05) = [-1.1267 2.1376]
      • Least Squares Fit model is: Y = -1.1267 +2.1376 X1
    • Add Autoregressive Component of order one
    • Model-2: Y = b1 + b2X1 + b3 Yx-1 + error, where x=2,3,…10
      • Xar = [ones(9,1) X1(2:10) Y(1:9) ]
      • [b,bint] = regress(Y(2:10), Xar)
plotting
Plotting
  • Boxplots
    • boxplot (x)
  • Histograms
    • hist(x, nb)
    • nb is the number of bins (deault=10)
  • Scatter Plot or Bubble Graph
    • Scatter(x,y)
    • Creates a 2-d scatter plot
  • Multiple Plots
    • Different Plots: Use subplot(2,2,1)
    • Two plots on same plot: Use hold
      • Yfit = 1.1267 + (2.1376 * X1)
      • Hold on
      • Plot(X1,Yfit)
plotting contd
Plotting (contd.)
  • Linear plot
    • plot (x,y): 2-D line plot defined by vectors x and y
    • plot3(x,y,z): 3-D line plot connecting 3 vectors x, y and z
    • Plot functions: y = sin (x) on interval [0,10]
      • x = 0:.3:10; y = sin (x); plot (x,y)
  • Probability Plot
    • normplot (x): normal probability plot of data in vector x
    • probplot(‘distname’,y) : probability plot for the specified distribution
  • Quantile-Quantile Plot
    • qqplot (x,y): x and y are samples from same distribution
i o operations
I/O Operations
  • Read files
    • load filename: loads entire file
    • importdata (‘filename’)
      • A= importdata (‘filename’,’delimiter’)
  • Write files
    • save filename: saves variables in workspace in a file specified
    • file operations: fopen – fprintf – fclose
    • sprintf
    • Example1
      • A=[2 2; 3 3];
      • fid = fopen(‘test.txt’, ‘a+’); fprintf(fid, ‘%d\n’, A(:,1)); fclose(fid);
    • Example2
      • i=2
      • fout = sprintf('myfile%03d.mat',i); save(fout, ‘A’);
slide17
HELP
  • To get help on the syntax for any command, type help
  • Most commands have intuitive names; if you want to know how to find the mean of

a vector

    • try help mean.
  • If you want a command that performs some function but you can’t think of the name of the command, use lookfor
    • try lookfor xls.
  • Some useful commands:
    • find
    • why (answer to everything)
websites
Websites
  • http://www.mathworks.com/
  • Newsgroup: http://www.mathworks.com/matlabcentral/newsreader/
  • File Exchange: http://www.mathworks.com/matlabcentral/fileexchange/
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