Introduction to MATLAB. Computational Probability and Statistics CIS 2033 Section 003

Transcription

1 Introduction to MATLAB Computational Probability and Statistics CIS 2033 Section 003

2 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

3 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:

4 Matlab Layouts Layouts of versions MATLAB 1.0 to MATLAB 8.2 Editor Workspace Current folder view Command Window Command History

5 Matlab Layouts new movement Layouts of versions MATLAB Editor/Variables View Current Window Workspace Command Window

6 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.

7 MATLAB Variables There are a few predefined variables in MATLAB: 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 = eps inf Smallest difference between two numbers MATALB can see Stands for an infinite value NaN Undefined value (Not-a-Number), Ex. 0/0 i Imaginary one

8 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:

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

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

11 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)

12 Elementary matrix functions 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 inv Inverse of the matrix Never use it!!!! all Are all elements zero sort Sort columns (or rows)

13 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

14 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

15 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

16 Characters and Strings 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

17 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

18 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

19 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

20 Programming in MATLAB Control Flow MATLAB allows control flow operations: Conditional statements, loops, branching

21 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

22 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);

23 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

24 End of MATLAB introduction Any Questions?