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Matlab Introduction
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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 row
B = [3,4,5]
create row vector: “ ” (space) or “,” (comma)
separates elements
C = [A;B]
put row vector B as new row in 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 (or you can over-write it)
Matrix Operations
B = A’
C=A+3*B
D=A*B
E = A .* B
transpose matrix A
F = A^2
G = A.^2
multiply matrix A by itself
raise each A element to 2nd power
X = inv(A)
form inverse of matrix
format
format short g
(controls format of numeric values)
element by element multiplication
Useful Matrix Functions
det(A)
rank(A)
trace(A)
eig(A)
gives
gives
gives
gives
determinant
rank
trace
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)
grid on
displays graph of x and y
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 increments
to graph z in 3rd dimension
z = x.*y.^2
plot3(x,y,z)
create function of x and y
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/2012/01/10/144991
340/don-t-make-me-do-this-the-equations-screamed
Other Example Graphs
T=R.^2+R.*S+2.*S.^2+3;
plot3(R,S,T)
a bowl
T=-R.^2-S.^2+6.*R+2.*S;
plot3(R,S,T)
a dome
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 deviation
cov(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:
12
4 -3
4 1
F = load(‘col2row.prn');
looks for spaces or columns
Or
G = dlmread(‘col2row.prn’,’\t’);
the “\t” looks for tabdelimited
Reading a data file – an interactive mode
Choose “import data” from file menu.
Select file “beta” to import from
Format short g
X = beta(1:end,1)
Y = beta(1:end,2)
(so data looks non-zero)
declare X is beta’s 1st column
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 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