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

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 vectors & matrices Current Folder

Where to up-load files into Matlab (use load command to bring in variables from disk)

Matlab Introduction

Getting Around Matlab Matrix Operations Drawing Graphs Calculating Statistics (How to read data)

Creating A Matrix

A = [1 2 0; 2 5 -1; 4 10 -1] semicolon starts new rowB = [3,4,5] create row vector: “ ” (space) or “,”

(comma) separates elements

C = [A;B] put row vector B as new row in AD = [A,B’] put new column B in matrix A

B is now transposed (single quote)E = eye(5) create 5 x 5 identity matrixF = ones(2,3) create 2 row x 3 col matrix of 1s

clear C, D, E erases matrix (or you can over-write it)

Matrix OperationsB = A’ transpose matrix AC = A + 3 * BD = A * BE = A .* B element by element multiplication

F = A^2 multiply matrix A by itselfG = 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

Useful Matrix Functions

det(A) gives determinantrank(A) gives ranktrace(A) gives traceeig(A) gives eigenvalues

For complete list, see help -> matlab -> mathematics -> matrices and linear algebra -> function summary

Matlab Introduction

Getting Around Matlab Matrix Operations Drawing Graphs Calculating Statistics (How to read data)

Drawing graph (traditional method)

x = [-10 : 0.1 : 10]; create row vector from -10 to +10 in increments of 1/10

To avoid an input echo, use “;” at end of command

y = 3*x.^2 – 5*x + 6;

plot(x,y) displays graph of x and ygrid on displays reference lines

Graphs in 3 Dimensions[x, y] = meshgrid(-3:0.02:3, -5:0.02:5);

Creates matrix of x between -3 & 3 and y between -5 & 5 in 0.02 incrementsto graph z in 3rd dimension

z = x.*y.^2 create function of x and yplot3(x,y,z)

To change the perspective use the “Rotate 3D” icon on the menu

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

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 domeplot3(R,S,T)

T=R.^3-R.*S+S.^3 a beach towel on a hill

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”

Matlab Introduction

Getting Around Matlab Matrix Operations Drawing Graphs Calculating Statistics (How to read data)

Calculating Statistics – a traditional way

Z = beta(1:end,3);mean(Z)median(Z)min(Z)max(Z)std(Z) standard deviationcov(Z)hist(Z,20) draws histogram with 20 categories

Matlab Introduction

Getting Around Matlab Matrix Operations Drawing Graphs Calculating Statistics (How to read data)

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 columnsOrG = dlmread(‘col2row.prn’,’\t’); the “\t” looks for tab-delimited

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

columnY = 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)

Regression – Manual Method

n = size(X,1);X = [ones(n,1),X]; puts new col of 1s as 1st

col in new X matrixslop = 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