MATLAB
Programming I
Joy
Outline
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Examples
What is Matlab?
History
Characteristics
Organization of Matlab – Toolboxes
Basic Applications
Programming
Example I
• Obtain the result of matrix multiply
4
9


8
6 
3

15  
7

7 

• Matlab Code
>>A=[4,6; 9,15; 8,7];
>>B=[3,24,5; 7,19,2];
>>C=A*B
C=
54 210 32
132 501 75
73 325 54
24
19
5

2
C Code
#include <cstdlib>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <vector>
using namespace std;
typedef vector<vector<int> > Mat;
void input(istream& in, Mat& a);
Mat matrix_product(const Mat& a, const Mat& b);
void print(const Mat& a);
C Codes
int main(int argc, char *argv[])
{
ifstream in1 ( "Matrix A.txt" );
ifstream in2 ( "Matrix B.txt" );
int row, row1, col, col1;
in1>>row>>col;
in2>>row1>>col1;
Mat a(row, vector<int>(col));
input(in1, a);
Mat b(row1, vector<int>(col1));
input(in2, b);
print(matrix_product(a,b));
system("PAUSE");
return EXIT_SUCCESS;
}
C Code Cond.
void input(istream& in, Mat& a)
{
for(int i = 0; i < a.size(); ++i)
for(int j = 0; j < a[0].size(); ++j)
in>>a[i][j];
}
void print(const Mat& a)
{
for(int i = 0; i < a.size(); ++i)
{ cout<<endl;
for(int j = 0; j < a[0].size(); ++j)
cout<<setw(5)<<a[i][j];
}
cout<<endl;
}
C Code Cond.
Mat matrix_product(const Mat& a, const Mat& b)
{
Mat c(a.size(), vector<int>(b[0].size()));
for(int i = 0; i < c.size(); ++i)
for(int j = 0; j < c[0].size(); ++j)
{
c[i][j] = 0;
for(int k = 0; k < b.size() ; ++k)
c[i][j] = c[i][j] + a[i][k] * b[k][j];
}
return c;
}
Example II
• Calculate the transpose of the matrix:
3 17 2 
5 19 7 


6 4 54 
• Matlab Code
>>A=[3,17,2;5,19,7;6,4,54]
>>A^(-1)
ans =
-0.9327 0.8505 -0.0757
0.2131 -0.1402 0.0103
0.0879 -0.0841 0.0262
What is MATLAB?
• Abbreviation of MATrix LABoratory
• Is a high-performance language for
technical computing
• It integrates computation, visualization,
and programming in an easy-to-use
environment where problems and
solutions are expressed in familiar
mathematical notation.
Usage of MATLAB
•
•
•
•
•
•
•
Math and computation
Algorithm development
Data acquisition
Modeling, simulation, and prototyping
Data analysis, exploration, and visualization
Scientific and engineering graphics
Application development
including graphical user interface building
History
• In 1970s – Dr.Cleve Moler
Based on Fortran on EISPACK and LINPACK
Only solve basic matrix calculation and graphic
• 1984 – MathWorks Company by Cleve Moler and
Jack Little
Matlab 1.0 based on C
Included image manipulations, multimedia etc.
toolboxes
• In 1990 – run on Windows
Simulink, Notebook, Symbol Operation, etc.
• 21 Century
Main Features
• Powerful tool for matrix calculations
Basic data type is double complex matrix with subscript is 1
High efficient/reliable algorithms
• Multi-paradigm
- interactive environment (no compiler)
- programming
• Most input/output parameters in Matlab
functions are variable
• User friendly with extensively help system
MATLAB SYSTEM
MATLAB
Simulink
Applications
Develop Tools
Stateflow
Toolboxes
Module Libraries
DATA
Data-Accessing Tools
Generating-Codes Tools
Third parties modules
C
Buildup of MATLAB
• Development Environment
MATLAB desktop and Command Window, a command history, an editor
and debugger, and browsers for viewing help, the workspace, files, and the
search path.
• The MATLAB Mathematical Function Library
A vast collection of computational algorithms ranging from elementary
functions to more sophisticated functions
• The MATLAB Language
A high-level matrix/array language with control flow statements,
functions, data structures, input/output, and object-oriented
programming features
• Graphics
Display vectors and matrices as graphs
two-dimensional and three-dimensional data visualization
image processing
animation and presentation graphics
• The MATLAB Application Program Interface (API)
Interchange the C/Fortran codes with Matlab codes
Basic Applications I
• Matrices and Arrays
Generating Arrays/Matrices
Elementary Matrices:
sum, transpose, diagonal, subscripts
Variables: does not require any type
declarations or dimension statements
Operators: +,-,*,/, ^, etc.
Examples of Expressions
Generating Matrices
• Directly enter
A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]
• Use Functions
zeros
All 0’s
ones
All 1’s
rand
Uniformly distributed random elements
randn
Normally distributed random elements
Example: B = zeros(1,5) – row vector/array
C = ones(7,1) –column vector/array
D = rand(5,8,3) – multiple dimension matrix
• Load/Import from files
Elementary Matrices
>>D=rand(3,2,3)
D(:,:,1) =
D(:,:,2) =
0.9501 0.4860
0.4565 0.4447
0.2311 0.8913
0.0185 0.6154
0.6068 0.7621
0.8214 0.7919
>> sum(D(:,1,1))
ans =
1.7881
>> E=D(:,:,2)'
E=
0.4565 0.0185 0.8214
0.4447 0.6154 0.7919
>> a=diag(D(:,:,3))
a=
0.9218
0.9355
>> F=[D(1,:,1),D(2,:,3); D(1,:,1)+1, D(2,:,3)-1]
F=
0.9501 0.4860 0.7382 0.9355
1.9501 1.4860 -0.2618 -0.0645
>>F(:,2)=[]
F=
0.9501 0.7382 0.9355
1.9501 -0.2618 -0.0645
>> F(2:1:4)=[]
F=
0.9501 0.9355 -0.0645
D(:,:,3) =
0.9218 0.4057
0.7382 0.9355
0.1763 0.9169
Examples of Expression
>>rho = (1+sqrt(5))/2
rho =
1.6180
>>a = abs(3+4i)
a=
5
>>huge = exp(log(realmax))
huge =
1.7977e+308 =1.8X10308
Basic Application II
• Graphic
Programming
• Flow Control
Selector: if, switch & case
Loop: for, while, continue, break, try & catch
Other: return
• Other Data Structures
Multidimensional arrays, Cell arrays, Structures,
etc.
• Scripts and Functions
Flow Control Examples I
• Selector:
2-way:
if rand < 0.3
flag = 0;
else
flag = 1;
end
Multiple-ways:
%Condition
%then_expression_1
%then_expression_2
%endif
if A > B
'greater‘
elseif A < B
'less‘
elseif A == B
'equal‘
else
error('Unexpected situation')
end
| switch (grade)
| case 0
|
‘Excellent’
| case 1
|
‘Good’
| case 2
|
‘Average’
| otherwise
|
‘Failed’
| end
Flow Control Examples II
• Loop
>>Generate a matrix
for i = 1:2
for j = 1:6
H(i,j) = 1/(i+j);
end
end
>>H
H=
0.5000
0.3333
0.3333
0.2500
0.2500
0.2000
0.2000
0.1667
0.1667
0.1429
0.1429
0.1250
• Loop Cond.
>>%Obtain the result is a root of the polynomial x3 - 2x – 5
a = 0; fa = -Inf;
b = 3; fb = Inf;
while b-a > eps*b
x = (a+b)/2;
fx = x^3-2*x-5;
if sign(fx) == sign(fa)
a = x; fa = fx;
else
b = x; fb = fx;
end
end
>>x
x=
2.09455148154233
Scripts
• MATLAB simply executes the commands found
in the file
• Example
% Investigate the rank of magic squares
r = zeros(1,32); %generation a row array 1X 32
% “;” tell the system does not display
% the result on the screen
for n = 3:32
r(n) = rank(magic(n));
end
r
bar(r) %display r in bar figure
Scripts Cond.
• Note:
No input/output parameters
(Different from functions! )
Write the script in editor, which can be
activated by command “edit” in command
window, save it with its specific name
Next time you want to execute the script just
call the name in the command window
Functions
• Functions are M-files that can accept input
arguments and return output arguments.
The names of the M-file and of the
function should be the same.
Function Example I
• Background of AIC
AIC is used to compare the quality of nested
models
AIC requires a bias-adjustment in small sample
sizes
AIC  2  ln(likelihood )  2  K
AICad  2  ln(likelihood )  2  K 
deltai  AICi  min( AIC )
wi 
exp( 0.5  deltai )
R
 exp(0.5  delta
r 1
r
)
2  K  ( K  1)
n  K 1
Function Head (Comments)
%AICad Function
%Date:Dec.29th, 2008
%Purpose: Calculate the adjusted
%
Akaike’s Information Criteria (AIC)
%InPut: AIC
%
n (the sample size)
%
K (the number of parameters in the model)
%OutPut: AICad
%
delta
%
weight
%Functions Called: None
%Called by: None
IN Command Window
>>AIC=[-123; -241.7; -92.4; -256.9];
>>n=12;
>>K=[4;8;2;6];
>>[AICad, delta, w] = CalAIC(AIC, n, K)
AICad =
delta =
w=
-83.0000
-97.7000
-80.4000
-172.9000
89.9000
75.2000
92.5000
0
0.0000
0.0000
0.0000
1.0000
M file
function[AICad,delta,w]=CalAIC(AIC,n,K)
AICad = AIC+2.*K.*(K+1);
a = min(AICad);
delta = AICad - a;
b = exp(-0.5.*delta);
c = sum(b);
w = b./c;
Function Example II
• Background of PCA
Comparing more than two communities or samples
Sample
1
2
3
4
5
Post Oak
66
48
26
15
11
Red Oak
25
30
55
20
50
Water Oak
24
31
42
49
58
Ycombine  wpost  x post  wred  xred  wwater  xwater
Background of PCA
Cond.
• Principal Components Analysis (PCA)
• It finds weighted sums of samples or
observations (linear combinations) that are
highly correlated with the values of the response
variables (e.g., species’ abundances)
PCA objectively “chooses” these weights in such a way
as to maximize the variance in the weighted sums
Based on correlations between response variables
.
Function Head
%Principle Component Analysis Function
%Date:Dec.29th, 2008
%Purpose: Obtain the axis scores of PCA
%InPut: the abundance of 3 species
%
in 5 different samples
%OutPut: sample scores of PCA axis
%Functions Called: None
%Called by: None
IN Command Window
>>a=[66;48;26;15;11];
>>b=[25;30;55;20;50];
>>c=[24;31;42;49;58];
>>[score1, score2]=PCA(a,b,c)
score1 =
score2 =
-2.2233
-0.1963
-1.1519
-0.0743
0.8734
-1.0888
0.4871
1.5120
2.0147
-0.1526
M file
function[x11,x12,x13,x21,x22,x23]=PCA(a,b,c)
%Calculate the mean and population standard deviation of 3 species
for i=1:5
d(i)=(a(i)-mean(a))^2;
stda=sqrt(sum(d)/5);
e(i)=(b(i)-mean(b))^2;
stdb=sqrt(sum(e)/5);
f(i)=(c(i)-mean(c))^2;
stdc=sqrt(sum(f)/5);
end
%Obtain the z-scores of 3 species
for i=1:5
za(i)=(a(i)-mean(a))/stda;
zb(i)=(b(i)-mean(b))/stdb;
zc(i)=(c(i)-mean(c))/stdc;
end
N=[za',zb',zc'];
M file Cond.
%Obtain the original correlation matrix
M=[1,corr(a,b),corr(a,c);corr(a,b),1,corr(b,c);corr(a,c),corr(b,c),1];
[V1,D1]= eig(M); %Calculate the eigenvector and eigenvalues
weight1=V1(:,3); %Get the maximum eigenvector
score1=N*weight1;
%We use the exact same procedure that we used for axis 1,
%except that we use a partial correlation matrix
%The partial correlation matrix is made up of all pairwise correlations
%among the 3 species, independent of their correlation with the axis 1
%sample scores. Hence, axis 2 sample scores will be uncorrelated
%with (or orthogonal to) axis 1 scores.
M file Cond.
new=[a,b,c,score1];
M2=[1,corr(a,b),corr(a,c),corr(a,score1);…
corr(a,b),1,corr(b,c),corr(b,score1);…
corr(a,c), corr(b, c), 1, corr(c,score1);…
corr(a,score1),corr(b,score1),corr(c,score1),1];
for i=1:3
for j=1:3
corrnew(i,j)=M2(i,j);
end
end
g=[M2(4,1)*M2(4,1),M2(4,1)*M2(4,2),M2(4,1)*M2(4,3);…
M2(4,2)*M2(4,1),M2(4,2)*M2(4,2),M2(4,2)*M2(4,3);…
M2(4,3)*M2(4,1),M2(4,3)*M2(4,2),M2(4,3)*M2(4,3)];
corrmatrix=corrnew-g;
[V2,D2]=eig(corrmatrix);
weight2=V2(:,3); %signs needs to be checked with JMP
score2=N*weight2;
MATLAB in MCSR
• Matlab is available on willow and sweetgum
• www.mcsr.olemiss.edu
• assist@mcsr.olemiss.edu
• Enter matlab can activate Matlab in willow
or sweetgum
• Use ver to obtain the version of Matlab,
which can tell you which toolboxes of
Matlab in that machine
• Price of personal purchase is 500$ include update
releases (only include MATLAB & Simulink)
You need pay separate fee for each toolbox such as
statistical, bioinformatics, etc
Take Home Message