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MATLAB Programming I

MATLAB Programming I. Joy. Outline. Examples What is Matlab? History Characteristics Organization of Matlab – Toolboxes Basic Applications Programming. Example I. Obtain the result of matrix multiply Matlab Code >>A=[4,6; 9,15; 8,7]; >>B=[3,24,5; 7,19,2];

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MATLAB Programming I

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  1. MATLAB Programming I Joy

  2. Outline • Examples • What is Matlab? • History • Characteristics • Organization of Matlab – Toolboxes • Basic Applications • Programming

  3. 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*B C = 54 210 32 132 501 75 73 325 54

  4. 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);

  5. 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; }

  6. 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; }

  7. 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; }

  8. 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

  9. 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.

  10. 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

  11. 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

  12. 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

  13. MATLAB SYSTEM MATLAB Simulink Applications Develop Tools Stateflow Toolboxes Module Libraries Data-Accessing Tools DATA Generating-Codes Tools C Third parties modules

  14. 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

  15. 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

  16. Generating Matrices • Directly enter A = [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/array C = ones(7,1) –column vector/array D = rand(5,8,3) – multiple dimension matrix • Load/Import from files

  17. Elementary Matrices >>D=rand(3,2,3) D(:,:,1) = D(:,:,2) = D(:,:,3) = 0.9501 0.4860 0.4565 0.4447 0.9218 0.4057 0.2311 0.8913 0.0185 0.6154 0.7382 0.9355 0.6068 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 0.8214 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

  18. 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

  19. Basic Application II • Graphic

  20. 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

  21. Flow Control Examples I • Selector: 2-way: if rand < 0.3 %Condition flag = 0; %then_expression_1 else flag = 1; %then_expression_2 end %endif Multiple-ways: if A > B | switch (grade) 'greater‘ | case 0 elseif A < B | ‘Excellent’ 'less‘ | case 1 elseif A == B | ‘Good’ 'equal‘ | case 2 else |‘Average’ error('Unexpected situation') | otherwise end |‘Failed’ | end

  22. 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 0.2500 0.2000 0.1667 0.1429 0.3333 0.2500 0.2000 0.1667 0.1429 0.1250

  23. 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

  24. 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

  25. 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

  26. 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.

  27. 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

  28. 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

  29. 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

  30. 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;

  31. Function Example II • Background of PCA Comparing more than two communities or samples

  32. 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 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 .

  33. 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

  34. 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

  35. 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'];

  36. 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.

  37. 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;

  38. MATLAB in MCSR • Matlab is available on willow and sweetgum • www.mcsr.olemiss.edu • assist@mcsr.olemiss.edu

  39. 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

  40. Take Home Message More Practise, More Confidence!

  41. Thank You!

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