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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 <condition> <body> else <body> end

    • for <iterator>  <body> end

    • while <condition> <body> 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’);


HELP

  • To get help on the syntax for any command, type help <command>

  • 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 <keyword>

    • 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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