Matlabtalk2

7/28/2019 Matlabtalk2

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MATLAB

Programming I

Joy


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Outline

Examples What is Matlab?

History

Characteristics

Organization of Matlab Toolboxes

Basic Applications Programming


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Example I

Obtain the result of matrix multiply

Matlab Code

>>A=[4,6; 9,15; 8,7];

>>B=[3,24,5; 7,19,2];

>>C=A*BC =

54 210 32

132 501 75

73 325 54

4 63 24 5

9 157 19 2

8 7


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C Code

#include #include #include #include

#include #include

using namespace std;typedef vector Mat;void input(istream& in, Mat& a);Mat matrix_product(const Mat& a, const Mat& b);

void print(const Mat& a);


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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(col));input(in1, a);Mat b(row1, vector(col1));

input(in2, b);

print(matrix_product(a,b));system("PAUSE");return EXIT_SUCCESS;

}


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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


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C Code Cond.

Mat matrix_product(const Mat& a, const Mat& b){

Mat c(a.size(), vector(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;

}


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Example II

Calculate the transpose of the matrix:

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

3 17 2

5 19 7

6 4 54


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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-useenvironment where problems andsolutions are expressed in familiarmathematical notation.


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Usage of MATLAB

Math and computation Algorithm development

Data acquisition

Modeling, simulation, and prototyping Data analysis, exploration, and visualization

Scientific and engineering graphics

Application developmentincluding graphical user interface building


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History

In 1970s Dr.Cleve MolerBased on Fortran on EISPACK and LINPACKOnly solve basic matrix calculation and graphic

1984 MathWorks Company by Cleve Moler and

Jack LittleMatlab 1.0 based on CIncluded image manipulations, multimedia etc.toolboxes

In 1990 run on WindowsSimulink, Notebook, Symbol Operation, etc.

21 Century


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Main Features

Powerful tool for matrix calculationsBasic 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


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MATLAB SYSTEM

Develop Tools

Toolboxes

Data-Accessing Tools

Stateflow

Generating-Codes Tools

Module Libraries

Third parties modules

Applications

DATA

C

Simulink

MATLAB


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Buildup of MATLAB

Development EnvironmentMATLAB desktop and Command Window, a command history, an editorand debugger, and browsers for viewing help, the workspace, files, and thesearch path.

The MATLAB Mathematical Function LibraryA 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-orientedprogramming features

GraphicsDisplay vectors and matrices as graphstwo-dimensional and three-dimensional data visualizationimage processinganimation and presentation graphics

The MATLAB Application Program Interface (API)Interchange the C/Fortran codes with Matlab codes


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Basic Applications I

Matrices and ArraysGenerating Arrays/Matrices

Elementary Matrices:

sum, transpose, diagonal, subscriptsVariables: does not require any typedeclarations or dimension statements

Operators: +,-,*,/, ^, etc.Examples of Expressions


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Generating Matrices

Directly enterA = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

Use Functions

Example: B = zeros(1,5) row vector/arrayC = ones(7,1)column vector/array

D = rand(5,8,3) multiple dimension matrix

Load/Import from files

zeros All 0sones All 1s

rand Uniformly distributed random elements

randn Normally distributed random elements


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Elementary Matrices

>>D=rand(3,2,3)D(:,:,1) = D(:,:,2) = D(:,:,3) =

0.9501 0.4860 0.4565 0.4447 0.9218 0.40570.2311 0.8913 0.0185 0.6154 0.7382 0.93550.6068 0.7621 0.8214 0.7919 0.1763 0.9169

>> sum(D(:,1,1))ans =

1.7881>> E=D(:,:,2)'E =

0.4565 0.0185 0.82140.4447 0.6154 0.7919

>> a=diag(D(:,:,3))a =

0.92180.9355

>> F=[D(1,:,1),D(2,:,3); D(1,:,1)+1, D(2,:,3)-1]F =

0.9501 0.4860 0.7382 0.93551.9501 1.4860 -0.2618 -0.0645

>>F(:,2)=[]F =

0.9501 0.7382 0.93551.9501 -0.2618 -0.0645

>> F(2:1:4)=[]F =

0.9501 0.9355 -0.0645


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Examples of Expression

>>rho = (1+sqrt(5))/2rho =

1.6180

>>a = abs(3+4i)

a =

5

>>huge = exp(log(realmax))

huge =

1.7977e+308 =1.8X10308


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Basic Application II

Graphic


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Programming

Flow ControlSelector: if, switch & case

Loop: for, while, continue, break, try & catch

Other: return Other Data Structures

Multidimensional arrays, Cell arrays, Structures,etc.

Scripts and Functions


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Flow Control Examples II

Loop>>Generate a matrix

fori = 1:2

forj = 1:6

H(i,j) = 1/(i+j);end

end

>>H

H =

0.5000 0.3333 0.2500 0.2000 0.1667 0.1429

0.3333 0.2500 0.2000 0.1667 0.1429 0.1250


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Loop Cond.>>%Obtain the result is a root of the polynomial x3 - 2x 5a = 0; fa = -Inf;b = 3; fb = Inf;while b-a > eps*b

x = (a+b)/2;fx = x^3-2*x-5;ifsign(fx) == sign(fa)

a = x; fa = fx;else

b = x; fb = fx;end

end>>x

x =2.09455148154233


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Scripts

MATLAB simply executes the commands foundin 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

forn = 3:32

r(n) = rank(magic(n));end

r

bar(r) %display r in bar figure


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Scripts Cond.

Note:No input/output parameters

(Different from functions! )

Write the script in editor, which can beactivated by command edit in command

window, save it with its specific name

Next time you want to execute the script justcall the name in the command window


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Functions

Functions are M-files that can accept inputarguments and return output arguments.The names of the M-file and of the

function should be the same.


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Function Example I

Background of AICAIC is used to compare the quality of nestedmodels

AIC requires a bias-adjustment in small samplesizes

1

2 ln( ) 2

2 ( 1)

2 ln( ) 2 1

min( )

exp( 0.5 )

exp( 0.5 )

i i

i

i R

r

r

AIC likelihood K

K K

AICad likelihood K n K

delta AIC AIC

deltaw

delta


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Function Head (Comments)

%AICad Function%Date:Dec.29th, 2008%Purpose: Calculate the adjusted% Akaikes 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


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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 89.9000 0.0000-97.7000 75.2000 0.0000

-80.4000 92.5000 0.0000-172.9000 0 1.0000


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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;


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Function Example II

Background of PCAComparing more than two communities or samples

Sample Post Oak Red Oak Water Oak

1 66 25 24

2 48 30 31

3 26 55 42

4 15 20 495 11 50 58

combine post post red red water water Y w x w x w x


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Background of PCA

Cond.

Principal Components Analysis (PCA) It finds weighted sums of samples or

observations (linear combinations) that arehighly correlated with the values of the responsevariables (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

.


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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


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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 -0.07430.8734 -1.0888

0.4871 1.51202.0147 -0.1526


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M file

function[x11,x12,x13,x21,x22,x23]=PCA(a,b,c)

%Calculate the mean and population standard deviation of 3 speciesfor 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=1:5za(i)=(a(i)-mean(a))/stda;zb(i)=(b(i)-mean(b))/stdb;zc(i)=(c(i)-mean(c))/stdc;

endN=[za',zb',zc'];


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M file Cond.

%Obtain the original correlation matrixM=[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 eigenvaluesweight1=V1(:,3); %Get the maximum eigenvectorscore1=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.


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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=1:3corrnew(i,j)=M2(i,j);

endendg=[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;


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MATLAB in MCSR

Matlab is available on willow and sweetgum www.mcsr.olemiss.edu

[email protected]
http://www.mcsr.olemiss.edu/mailto:[email protected]:[email protected]://www.mcsr.olemiss.edu/


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Enter matlab can activate Matlab in willowor sweetgum

Use ver to obtain the version of Matlab,

which can tell you which toolboxes ofMatlab in that machine

Price of personal purchase is 500$ include updatereleases (only include MATLAB & Simulink)

You need pay separate fee for each toolbox such asstatistical, bioinformatics, etc


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Take Home Message


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