1. StatLab Matlab Workshop
11/15/2018

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Resources
Useful links: 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 and 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; very slow when processing loops
Lots of available toolboxes
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Launching Matlab
Click MATLAB in 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;
Command History: double click lines to evaluate them;
Current Directory browser: shows you where you are.
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 ; ; 7 8 9]
Generated by built-in functions
Loaded from a file
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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 element-by-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*[ ]’ b=A>18; c=[ ]’
A(b) gives same result as A(c)
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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 integers from 0 to 3, in increments of 0.2
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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10. 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))
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11. Working with Matrices (2)
A=eye(3) gives a 3-by-3 identity matrix
sparse(m,n): same as zeros(m,n), use if most elements are zeros.
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 ; ; 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) v.s.
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
For a list of more advanced mathematical and matrix functions, type
help specfun
help elmat
For a list of data analysis functions, type
help datafun
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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
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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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19. 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 World’)
save as test.m in c:\temp
add c:\temp to path (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:
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Learn from others
There are lots of Matlab functions already out there:
Google them!
James LeSage’s econometrics toolbox:
Don’t forget to “set paths” so that Matlab can find your new .m-files.
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24. A Simple Linear Regression Example
v = mvnrnd([0,1], sqrt([10,1;1,5]), 100);
x=v(:,1)
y=v(:,2)
scatter( x', y' )
hold()
x=[x(:,:),diag(eye(100))]
a = (x'*x)^-1*x'*y
plot( x, x*a(1) + a(2) )
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