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Matlab Introduction

Matlab Introduction. Getting Around Matlab Matrix Operations Drawing Graphs Calculating Statistics (How to read data). Interface with Mathlab 2012. Command window Only >> line is active, the other lines only remind which previous commands you used

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Matlab Introduction

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  1. Matlab Introduction • Getting Around Matlab • Matrix Operations • Drawing Graphs • Calculating Statistics • (How to read data)

  2. Interface with Mathlab 2012 • Command window • Only >> line is active, the other lines only remind which previous commands you used • NB Matlab does not manipulate symbols; only numbers • Command history window • Double click on command to repeat previous command • Single click to copy into command window and then modify • Workspace: list of created variables and matrices • Current Folder • Where to up-load files into Matlab (use load command to bring in variables from disk)

  3. Matlab Introduction • Getting Around Matlab • Matrix Operations • Drawing Graphs • Calculating Statistics • (How to read data)

  4. Creating A Matrix A = [1 2 0; 2 5 -1; 4 10 -1] semicolon starts new row B = [3,4,5] create row vector: use “_” (space) or “,” (comma) to separate elements C = [A;B] put column vector B as new row in matrix A D = [A,B’] put new column B in matrix A B is now transposed (single quote) E = eye(5) create 5 x 5 identity matrix F = ones(2,3) create 2 row x 3 col matrix of 1s clear C, D, E erases matrix (can also over-write)

  5. Matrix Operations B = A’ transpose matrix A C = A + 3 * B D = A * B E = A .* B element by element multiplication F = A^2 multiply matrix A by itself G = A.^2 raise each A element to 2nd power X = inv(A) form inverse of matrix format (controls format of numeric values) format short g

  6. Useful Matrix Functions det(A) gives determinant rank(A) gives rank trace(A) gives trace eig(A) gives eigenvalues For complete list, see help -> matlab -> mathematics -> matrices and linear algebra -> function summary

  7. Matlab Introduction • Getting Around Matlab • Matrix Operations • Drawing Graphs • Calculating Statistics • (How to read data)

  8. Drawing graph (traditional method) x = [-10: .1: 10]; create row vector from -10 to +10 in increments of 1/10 To avoid an echo of input, use “;” at end of command y = 3*x.^2 – 5*x + 6; plot(x,y) displays graph of x and y grid on displays reference lines

  9. Graphs in 3 Dimensions [x, y] = meshgrid(-3:.02:3, -5:.02:5); Creates matrix of x between -3 & 3 and y between -5 & 5 in .02 increments to graph z in 3rd dimension z = x.*y.^2 create function of x and y plot3(x,y,z) To change the perspective use the “Rotate 3D” icon on the menu

  10. A graph with a message !! • [x, y] = meshgrid(-3:.02:3, -5:.02:5); • z = max(0.0003, min(.0004, exp(-3.*(((0.5+x).^2)+(y.^2)/2)) + exp((-x.^2-(y.^2)/2)) .* cos(4.*x))); • plot3(x,y,z) To change the perspective use the “Rotate 3D” icon on the menu • http://www.npr.org/blogs/krulwich/2012/01/10/144991340/don-t-make-me-do-this-the-equations-screamed

  11. Other Example Graphs T=R.^2+R.*S+2.*S.^2+3; a bowl plot3(R,S,T) T=-R.^2-S.^2+6.*R+2.*S; a dome plot3(R,S,T) T=R.^3-R.*S+S.^3 a beach towel on a hill

  12. Interactive Finishing Touches • use “plottools” • Add labels, titles, change perspective, etc. • see help -> matlab -> graphics -> plots and plotting tools -> “interactive plot creation with plot tools demo”

  13. Matlab Introduction • Getting Around Matlab • Matrix Operations • Drawing Graphs • Calculating Statistics • (How to read data)

  14. Calculating Statistics – a traditional way Z = beta(1:end,3); mean(Z) median(Z) min(Z) max(Z) std(Z) standard deviation cov(Z) hist(Z,20) draws histogram with 20 categories

  15. Matlab Introduction • Getting Around Matlab • Matrix Operations • Drawing Graphs • Calculating Statistics • (How to read data)

  16. Working with files – a traditional way Cd(‘w:\’) change directory to W disk The file named col2row.prn was saved in excel file using “save as” menu with file delimited by spaces It contains three rows of numbers: 1 2 4 -3 4 1 F = load(‘col2row.prn'); looks for spaces or columns Or G = dlmread(‘col2row.prn’,’\t’); the “\t” looks for tab-delimited

  17. Reading a data file – an interactive mode Choose “import data” from file menu. Select file “beta” to import from Format short g (so data looks non-zero) X = beta(1:end,1) declare X is beta’s 1st column Y = beta(1:end,2) declare Y as beta’s 2nd column Scatter(X,Y) shows X vs. Y Regress(Y,X) best-fit slope (Y ind, X dep)

  18. Regression – Manual Method n = size(X,1); X = [ones(n,1),X]; puts new col of 1s as 1st col in new X matrix slop = inv(X’*X)*X’*Y calculates slope eps = Y – X*slop; calculates error from line sigma = eps’*eps/n; slop_var = sigma*inv(X’*X) covariance matrix

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