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Introduction to MATLAB Computational Probability and Statistics CIS 2033 Section 003 Djordje Gligorijevic, Temple University, Spring 2015

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About MATLAB MATLAB (MATrix LABoratory) is a high level language made for: Numerical Computation (Technical computing) Visualization Application Development Everything is a matrix – easy to do Linear Algebra and other mathematical fields that use Linear Algebra (Statistics, Fourier Analysis, Optimization, Filtering,…) Useful tool for mathematical analysis and simulation Djordje Gligorijevic, Temple University, Spring 2015

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MATLAB Software Access All Temple University in-campus computers have student-version MATLAB installed Temple University also provides a student license for every student, just go to MATLAB Site Licensed Software page: https://computerservices.temple.edu/matlab-site-licensed- software https://computerservices.temple.edu/matlab-site-licensed- software Djordje Gligorijevic, Temple University, Spring 2015

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Matlab Layouts Layouts of versions MATLAB 1.0 to MATLAB 8.2 Djordje Gligorijevic, Temple University, Spring 2015 Current folder view Editor Workspace Command History Command Window

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Matlab Layouts – new movement Layouts of versions MATLAB 8.3 - Djordje Gligorijevic, Temple University, Spring 2015 Current Window Workspace Editor/Variables View Command Window

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MATLAB competition Due to its cost, MATLAB has a hard time finding a dominance in the industry. Other languages provide a “bigger bang for the buck” thanks to the active communities that maintain widely used libraries. An examples of such languages that have became a “hot topic” recently are: Python (NumPy, SciPy, Matplotlib, SciKit Learn,…) R However, MATLAB is still completely dominating when it comes to performance. Djordje Gligorijevic, Temple University, Spring 2015

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MATLAB Variables There are a few predefined variables in MATLAB: Djordje Gligorijevic, Temple University, Spring 2015 ans Variable which has been assigned a value of most recent expression, which hasn’t had assigned a value of its output to a specific variable pi Number pi = 3.1415926535897932384626433832795 eps Smallest difference between two numbers MATALB can see inf Stands for an infinite value NaN Undefined value (Not-a-Number), Ex. 0/0 i Imaginary one

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Matlab Structures Numeric Types: Matlab provides wide range of numerical and floating point types such are double, int (8,16,32 and 64 bits), uint ( 8,16,32,64 bits). Some functions on numeric types: Djordje Gligorijevic, Temple University, Spring 2015

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Elementary math functions Djordje Gligorijevic, Temple University, Spring 2015 sqrt(x) Square root sin(x) Sinus x (in radians) exp(x) Exponential function - e x cos(x) Cosinus s abs(x) Absolute value tan(x) Tangens x log(x) Natural logarithm - ln(x), log e (x) cot(x) Cotangens x log10(x) Logarithm with basis 10 round(x) Round to an integer factorial(x) Factoriel x – x! ceil(x) Round to higher value fix(x) Round to lower value rem(y,x) Remainder of x/y division sign(x) Signum function

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Matlab Structures, Contd. Matrices and Vectors To enter a matrix: 2 5 3 6 4 1 >> A = [2, 5, 3; 6, 4, 1] >> B = [1:1.5:6; 2 3 4 5] >> for i=1:4 for j=1:3 C(i,j)=i*j; end >> D =[]; D=[D;5]; D=[D;6;7] >> E = zeros(4, 5) Djordje Gligorijevic, Temple University, Spring 2015

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Matlab Structures, Contd. Matrices and Vectors As every variable in MATLAB can be a matrix, we can do basic operations on them: Addition: >> C = A + B Subtraction: >> D = A – B Multiplication: >> E = A * B (Matrix multiplication) >> E = A.* B (Element wise multiplication, A and B same size) Division: Left Division and Right Division >> F = A. / B (Element wise division) >> F = A / B = A*inv(B) (A * inverse of B) >> F = A. \ B (Element wise division) >> F = A \ B=inv(A)*B (inverse of A * B) Djordje Gligorijevic, Temple University, Spring 2015

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Elementary matrix functions Djordje Gligorijevic, Temple University, Spring 2015 max Maximum of elements + Matrix addition min Minimum of elements - Matrix substraction sum Sum of elements * Matrix multiplication prod Product of elements / Matrix division median Median (Middle value) \ Left matrix division mean Mean (Agerage) ^ Power std Standard deviation ' Transpose any Is there any zero invInverse of the matrix Never use it!!!! all Are all elements zero sortSort columns (or rows)

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Generating basic matrices Matrix with ZEROS: >> A = zeros(m, n) Matrix with ONES: >> B = ones(m, n) IDENTITY Matrix: >> I = eye(m, n) RANDOM Matrix: >> I = rand(m, n) MAGIC SQUARE Matrix: >> I = magic(n) m Rows n Columns zeros, ones, eye, rand, magic Matlab functions Djordje Gligorijevic, Temple University, Spring 2015

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Random Number Generators Rand(m,n): matrix with each entry ~ U(0,1) Randn(m,n): standard normal distribution Mvnrnd(Mu, Sigma): Multivariate normal random numbers Djordje Gligorijevic, Temple University, Spring 2015

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Array indexing, obtaining information Size(A): return [m n] Length(A): length of a vector Length(A) = max(size(A)) B = A(2:4,3:5) B is the subset of A from row 2 to row 4, column 3 to column 5 C = A(2) C is a scalar with value of second index in matrix A Matlab matrix indicies go iteratively top-down, column by column D = A(:, [1,15,20]) Select all rows but a few columns A(:, 2)=[] Delete second column Djordje Gligorijevic, Temple University, Spring 2015

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Characters and Strings Djordje Gligorijevic, Temple University, Spring 2015 A sequence of characters enclosed in single quotes assign a string to a variable A = ‘Alice’ use two single quotes within the deﬁnition if the text includes a single quote Concatenaton With square brackets as concatenate numeric arrays A = [‘Alice’, ’followed’, ’the’, ’rabbit.’] Convert numeric values to strings num2str int2str

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Save/Load Data Save fname Save all workspace data into fname.mat Save fname x y z Save(fname): when fname is a variable Save large files save('fname.mat','fname','-v7.3'); Load fname Load fname x y No error in data You can run simulation intermittently Save/load data between runs Djordje Gligorijevic, Temple University, Spring 2015

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Programming in MATLAB - Scripts A file with a.m extension containing Multiple sequential lines of MATLAB commands Function calls To run a script Save a file in the current folder and type its name at the command line Run scripts from the Editor by pressing the Run button Comments To describe the code Add comments whenever you write code For comments add % symbol first Djordje Gligorijevic, Temple University, Spring 2015

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Programming in MATLAB - Functions Equivalent to subroutines or methods in other programming languages To call a function, enclose its input arguments in parentheses If there are multiple input arguments, separate them with commas Return output from a function by assigning it to a variable When there are multiple output arguments, enclose them in square brackets To call a function that does not require any inputs and does not return any outputs, type only the function name Djordje Gligorijevic, Temple University, Spring 2015

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Programming in MATLAB – Control Flow MATLAB allows control flow operations: Conditional statements, loops, branching Djordje Gligorijevic, Temple University, Spring 2015

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Plotting in MATLAB – Basic 2-D Figure Plot Plot(X, Y): Plots vector Y versus vector X Hold: next plot action on the same figure Title(‘title text here’) Xlabel(‘…’), ylabel(‘…’) Axis([XMIN XMAX YMIN YMAX]) Or use xlim or ylim Legend(‘…’) Grid Example demo Djordje Gligorijevic, Temple University, Spring 2015

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Plotting in MATLAB – Basic 3-D Figure Plot x=[0:10]; y=[0:10]; z=x ’ *y; mesh(x,y,z); figure; surf(x,y,z); Djordje Gligorijevic, Temple University, Spring 2015

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MATLAB – Help The most important thing to remmember about MATLAB – it has great Help and Documentation Just press Shift + F1 to search for needed function Or select a function and press F1 Djordje Gligorijevic, Temple University, Spring 2015

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End of MATLAB introduction Any Questions? Djordje Gligorijevic, Temple University, Spring 2015

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