1. Demo of Basic Matlab Features
Getting Around Matlab
How to do matrix calculation
How to draw graphs
How to read data
How to calculate statistics
A very brief look at optimization in Matlab

2. Matlab’s User Interface
Command window
Only >> line is active, the remainder of the screen is only a reminder of previous commands
NB Matlab does not manipulate symbols; only numbers
Command history window
Double click on command to repeat previous command
Current Directory
Where to up-load files into Matlab (use load command to bring in variables from disk)
Toggle to workspace giving list of vectors, matrices created (this window more useful for our class than the current directory window)

3. Demo of Basic Matlab Features
Getting Around Matlab
how to do matrix calculation
how to draw graphs
how to read data
how to calculate statistics

4. Creating A Matrix
A = [1 2 0; ; ] 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. Operations on Matrices
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. Other 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. Demo of Basic Matlab Features
Getting Around Matlab
how to do matrix calculation
how to draw graphs
how to read data
how to calculate statistics

8. Drawing a graph – a traditional way
x = [-10 : .1 : 10]; create row vector from -10 to +10
in increments of 1/10
If do not want an echo of your 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. 3 Dimension Graphs and y between -5 & 5 in .02 increments
[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

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

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

13. Demo of Basic Matlab Features
Getting around Matlab
how to do matrix calculation
how to draw graphs
how to read data
how to calculate statistics

14. 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

15. 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)

16. 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

17. Demo of Basic Matlab Features
Getting Around Matlab
how to do matrix calculation
how to draw graphs
how to read data
how to calculate statistics

18. 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