introduction to matlab computational probability and statistics cis 2033 section 003 djordje...

Introduction to MATLAB

Computational Probability and Statistics

CIS 2033 Section 003

Djordje Gligorijevic, Temple University, Spring 2015

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


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-soft

ware


https://computerservices.temple.edu/matlab-site-licensed-software

https://computerservices.temple.edu/matlab-site-licensed-software

Matlab Layouts

Layouts of versions MATLAB 1.0 to MATLAB 8.2


Current folder view

Editor

Workspace

Command HistoryCommand Window

Matlab Layouts – new movement

Layouts of versions MATLAB 8.3 -


Current Window

Workspace

Editor/Variables View

Command Window

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.


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 = 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

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:


Elementary math functions


sqrt(x) Square root sin(x) Sinus x (in radians)

exp(x) Exponential function - ex

cos(x) Cosinus s

abs(x) Absolute value tan(x) Tangens x

log(x) Natural logarithm - ln(x), loge(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

Matlab Structures, Contd.

Matrices and Vectors

To enter a matrix:

2 5 36 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 end >> D =[]; D=[D;5]; D=[D;6;7] >> E = zeros(4, 5)


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)


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 matrixNever use it!!!!

all Are all elements zero

sort Sort columns (or rows)

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 Rowsn Columnszeros, ones, eye, rand, magic Matlab functions


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


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 columnDjordje Gligorijevic, Temple University, Spring 2015

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 stringsnum2str int2str

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


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


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


Programming in MATLAB – Control Flow

MATLAB allows control flow operations: Conditional statements, loops, branching


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 demoDjordje Gligorijevic, Temple University, Spring 2015

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);


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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


End of MATLAB introduction

Any Questions?


introduction to matlab computational probability and statistics cis 2033 section 003 djordje...

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