Transcript Document
Intro to Matlab
for Data Analysis
and
Statistical Modeling
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Useful links
http://statlab.stat.yale.edu/help/FAQ/matlab_FAQ.jsp
The help links on this page include:
Mathworks’ Getting Started (the official
online documentation of Matlab)
Kermit Sigmon’s MATLAB Primer (a very good
beginner manual);
University of Utah’s MATLAB Tutorial
Some others.
MATLAB’s online help manual
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What is MATLAB?
MATLAB is a matrix-based tool for
numerical computations. It’s very
powerful and easy to use.
Both programming language and
interactive environment
Very fast native functions; somehow
slow when processing loops
Lots of available toolboxes
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Launching Matlab
Click “MATLAB xx” from the start menu
(on Unix systems: type “matlab” to
enter interactive mode)
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The Interface
Main Window: Input/Output
Workspace: consists of the variables you
create during a MATLAB session;
Current Directory browser: shows you where
you are.
Command History: double click them to
evaluate them;
Editor/Debugger: pops up when you create an
M-file (click on “New” button to launch it.)
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Entering Matrices
Matrices can be
Entered manually
A = [1 2 3 ; 4 5 6 ; 7 8 9]
Generated by built-in functions (e.g.,
eye(3), ones(2,1), zeros(3,3)
Loaded from a file (e.g.,data)
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Matrix operations:
+ addition
- subtraction
* multiplication
^ power
‘ transpose
\ left division, / division
x = A \ b is the solution of A * x = b
x = b / A is the solution of x * A = b
To make ‘*’ , ‘^’, ‘\’ and ‘/’ apply elementby-element, we precede the operators by ‘.’
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Subscripts:
Subscripts: the element in row i and column j of A
is denoted by A(i, j).
i,j can also be vectors of indices or logical
arrays:
A=4*[1 2 3 4 5 6 7 8 9]’
b=A>18; c=(5 6 7 8 9)’
A(b) gives same result as A(5;6;7;8;9)
because b=(0 0 0 0 1 1 1 1 1)’
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The Colon Operator ‘:’
The colon ‘:’ is one of MATLAB ’s most
important operators. It has many formats:
[0:0.2:3] is a row vector containing
numbers from 0 to 3, in increments of 0.2
e.g., A=[0:0.2:3] or A=0:0.2:3
Subscript expressions involving colons refer
to portions of a matrix:
A(1:3 , 2) is the first to the third elements
of the second column of A.
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Working with Matrices:
Four functions that generate basic matrices:
Zeros: all zeros. A = zeros(1,3)
Ones: all ones.
A = ones(2,4)
Rand: elements are U[0,1] random variables
A = rand(3,5)
Randn: elements are standard-normal random
variables
A = randn(2,5)
Be careful: Matlab always sets the same seed.
Get ‘more random’ numbers by typing
rand('state', sum(100*clock))
Sometimes you want the seed to be fixed
in your code, you can set rand(‘state’,r)
where r is the rth simulation
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A=eye(3) gives a 3-by-3 identity matrix
sparse(m,n): same as zeros(m,n), use if
most elements are zeros.
e.g., A=eye(3); B=sparse(A)
Concatenation: join small (compatible)
matrices to make bigger ones:
B = [A A-2; A*2 A/4]
Deleting rows and columns:
B(:,2) = [ ]
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Putting it together
Many operations can take Matrix inputs.
Example:
A = [1 2 3 ; 4 5 6 ; 7 8 9]
B=A>5
Use indices and element-by-element
operations to avoid slow and unwieldy loops:
beta=0.925;
auxil=1:200;
betavec(auxil)=beta.^auxil;
betavec=betavec’
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Suppressing Output:
If you simply type a statement and press
Enter, MATLAB automatically displays the
results on screen. If you end the line with a
semicolon ‘;’, MATLAB performs the
computation but does not display any result.
Example: C = randn(5,1) versus
C = randn(5,1);
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Functions:
MATLAB provides a large number of standard elementary
mathematical functions, including abs, sqrt, exp,
sin.
For a list of the elementary mathematical functions, type:
help elfun
(e.g.,sin, cos, exp, log, log10,log2,abs,real)
For a list of more advanced specificic mathematical
functions and elematary matrix functions, type
help specfun (e.g., factorial,erf)
help elmat (e.g., zeros,ones,eye
For a list of data analysis functions, type
help datafun (e.g., max,min, mean,median,
std, var, sort, hist, corrcoeff skewness,
kurtosis,cumsum)
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Flow Control:
MATLAB has following flow controls:
If statement
For loops
While loops
Continue statement
Break statement
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if … elseif … else … end
If A > B
‘greater’
elseif A < B
‘less’
elseif A = = B
‘equal’
else error(‘Unexpected situation’)
end
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for … end
for i = 1:m
for j = 1:n
H(i,j) = 1/(i+j);
end
end
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Graphics: plot
x = [0 : .01 : 2*pi];
y = sin(x);
plot(x,y)
y2 = sin(x-.25)
y3 = sin(x-.5)
plot(x,y,x,y2,x,y3)
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Programming with MATLAB:
Files that contain code in the MATLAB
language are called M-files. You can
create M-files using the matlab editor,
then use them as you would any other
MATLAB functions or commands. There
are two types of M-files: Scripts and
Functions.
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Scripts
Scripts: a bunch of code grouped together;
doesn’t accept argument or return output.
Example
open m-file editor
type disp(‘Hello, China!’)
save as test.m in c:\temp
add c:\temp to path directory (File/Set Path)
Execute by typing “test”
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Functions:
Functions are M-files that can accept
input arguments and return output
arguments. The name of the M-file and
of the function should be the same.
For example, save this as area.m in
c:\temp:
function ar = area(radius)
ar=pi*radius^2;
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Function functions
Once you have defined a function, you can
use functions that have functions as
arguments – function functions!
E. g. search for minima, zero values.
Example: first we define the function x2-3:
function x=example(input)
x=input.^2-3;
Now, we can easily find minima and zeros:
fminbnd(@example,-2,2),
fzero(@example,2)
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Learn from others
There are lots of Matlab functions already
out there:
Google them!
http://www.mathworks.com/matlabcentral/
James LeSage’s econometrics toolbox:
http://www.spatial-econometrics.com/
Don’t forget to “set paths” so that Matlab
can find your new .m-files.
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