what is matlab? - spsc · programming environment working directory >> dir >> cd...

1Introduction to MATLAB

Computational Intelligence, CI 2015

What is MATLAB?

A software environment for interactive numerical calculations

MATrix LABoratory: Based on matrices computations standard for numerical simulations

Examples:

Linearly Algebra

Solving nonlinear equations

Numerical solution of differential equations

Mathematical optimization

Statistics and data analysis

Signal processing

Modeling of dynamic system

Solving partial differential equations

Simulation of Systems Engineering



Why do we need MATLAB?

MATLAB use:

implementation of simple learning algorithms

evaluate the results / data visualization

Using toolboxes:

Training of neural networks: pattern matching for face detection of hidden

Markov models: for example for speech processing



Alternative/Similar software

• GNU Octave (https://www.gnu.org/software/octave/ )

• Can run most MATLAB scripts but not all!

• Doesn’t have the same “toolboxes”• Python/numpy (http://www.numpy.org/ )

• Different syntax, but easier if you’re already familiar with python syntax

• more flexible because one can use other standard python libraries also

• Julia (http://julialang.org/ )

• Very new, not very popular yet

• Looks promising, has an impressive list of features

https://www.gnu.org/software/octave/

http://www.numpy.org/

http://julialang.org/



Structure

Core functionality: compiled C routines

Most functionality is given by m-files, grouped into toolboxes

m-files contain source code, can be copied and changed

m-files are platform independent (PC, Unix / Linux, MAC)

Interpreted language which makes it well suited for prototyping / debugging! :)

But slow! :(

m-filesC-kernel

Sig. Proc. Neural

Networks

Contr. Syst.



The help system

Search for matching functions

>> lookfor keyword

Quick help with syntax and function definition

>> help function

Advanced hyperlinked help system is started by

>> Helpdesk

Online: http://www.mathworks.com/help/

http://www.mathworks.com/help/



Interactive calculations

MATLAB is interactive. There are no variable declarations required

>> 2 + 3 * 4/2

ans = 8

>> A = 5e-3; b = 1; a + b;

Variables are created automatically and are not bound to any type

Variable names are case-sensitive

Most mathematical functions and constants are already defined

>> Cos (pi)

>> Abs (1 + i)



Variables and memory management

MATLAB uses double precision

>> format long

>> pi

ans = 3.141592653589793

>> format short

>> pi

ans = 3.1416



Variables and memory management

All variables in the "Workspace" are indicated by

>> who

>> whos

Variables can be stored in .mat files

>> save filename a b

>> clear a b % clear all variables for from workspace

>> load filename a b



Vectors and matrices

Vectors (arrays) are defined as:

>> V = [1, 2, 4, 5]

>> W = [1; 2; 4; 5]

Matrices (2D arrays) are defined

>> A = [1,2,3; 4,-5,6; 5,-6,7]

Ascending list of numbers using ":" Operator

>> X = 1: 5

>> X = 1: 2: 5



Matrix Operators

All common operators are overloaded

>> V + 2

Usual operators are available

>> B = A’ % Complex Conjugate Transpose

>> A * B

>> A + B

Note:

Operators that begin with a point (.) always use each item individually in the matrices.

>> A .* B % elementwise multiplication

>> A .^ 2 % elementwise Square



Indexing matrices

Indexing is by brackets

>> A (2,3)

1. Index: line

2. Index: Column

... Or partial matrices byRow and column index.

>> A ([2 3], [1 2])

Order of the indices is important!

>> B = A ([3: 2], [2 1])

>> B = [A (3,2), A (3,1), A (2,2), A (2,1)]

Access to the latest index

>> A (end, 2)



Indexing matrices

Indexing all the rows or

Columns by “:” Operator

>> A (1, :)

equivalent to

>> A (1,1: end)

Indexing of subregions

>> A (1: 2 :)

>> A ([1 2], :)

Indexing using logical expressions

>> x(x > 0) % all elements of x where x>0. This is an array of booleans



Matrices functions

Predefined elementary matrices

>> I = eye (3)

>> A = zeros (5,3)

>> A = ones (6,4)

Elementary functions are often overloaded and applicable to matrices

>> help elmat

>> sin (A)

Important matrix functions:

>> repmat (A, 4, 1);

>> reshape (A, 2, 2);



Numerical linear algebra

Basic numerical linear algebra

>> Z = [1, 2, 3]; x = inv (A) * Z

Many predefined standard functions

>> det (A)

>> rank (A)

>> eig (A)

The number of input / output arguments may vary

>> [V, D] = eig (A)



Visualization in Matlab

Visualization of vector data

>> x = -pi: 0.1: pi; y = sin (x);

>> figure;

>> plot (x, y)

>> hold on;

>> plot (x, y, 'rs')

>> xlabel ('x'); ylabel ('y = sin (x)');

Change of plot properties via "handle"

>> h = plot (x, y); set (h, 'linewidth', 4);

Many other plot functions available (help Graph2D)

>> v = 1: 4; pie (v)



MATLAB Programming

Programming environment and path

M-file scripts and functions

Flow control

Programmer tips and tricks



Programming environment

Working directory

>> dir >> cd catalog >> pwd

The path variable defines the MATLAB search path

>> Path >> addpath >> pathtool

Need access to functions in other directories

MATLAB looks for a name in the following order:

1. variable in the current workspace

2. built-in variable

3. built-in m-file

4. m-file in the current directory

5. m-file in the search path



Script files

Script files containing a sequence of MATLAB commands

Equivalent to the console input

% FACT SCRIPT - Compute factorial n, n = 1 * 2 * ... * n!

y = prod (1: n);

factscript.m

Executed (stored script in factscript.m) by

>> n = 10; fact script; y

Works with variables in the global workspace

Variable n must exist before calling in the workspace

Variable y is created (or overwritten)

Comment lines begin with “%”



Functions

Functions are subroutines

Have local variables (not global workspace)

Parameter passing and return values

Global variables only with extra keyword (globally) Used

function [output_arguments] = function_name (input_arguments)

% comment lines

<function body>

function [z] = factfun (s)

% FACTFUN - Compute factorial

% Z = FACTFUN(N)

z = prod (1: n);

factfun.m

>> y = factfun (10);



Displaying code and Help

List of code with the grade Command

>> type factscript

The help Command displays the first comment lines

>> help factscript



Logical expressions

Relational operators (compare matrices gl. Size)

== (Equal to) ~ = (Not equal)< (Less than) <= (Less than or equal to)> (Greater than) > = (Greater than or equal to)

Logical Operators

& (And)| (Or)~ (Not)

Logical functions:xorisemptyanyall

if (x> = 0) & (x <= 10)

disp ('x is in range [0,10]')

else

disp ('x is out of range')

end



Flow control - Selection

The if-elseif-else construction

if <logical expression>

<Commands>

elseif <logical expression>

<Commands>

else

<Commands>

end

if height> 170

disp ('tall')

elseif height <150

disp ('small')

else

disp ('average')

end



Flow control - Repetitions

Fixed number of repetitions

for index = <vector>

<statements>

end

In each iteration, the variable is index the next value of <vector>

assigned.

for k = 1: 12

kfac = prod (1: k);

fprintf ('%d: factorial %d \ n', k, kfac)

end



Flow control - conditional repetition

while-loops

<statements> is processed, unless <logical expression> is true.

while <logical expression>

<statements>

end

k = 1;

while prod (1: k) ~ = Inf,

k = k + 1;

end

fprintf ('Largest factorial in matlab: %d \ n', k-1);



Programmer tips and tricks

tic;

x = -250: 0.01: 250;

for ii = 1: length (x)

if x(ii )>= 0,

s(ii) = sqrt (x(ii));

else

s(ii) = 0;

end;

end;

toc

Elapsed time is 0.053471 seconds.

tic

x = -250: 0.01: 250;

s = zeros(size(x));

index = x> 0;

s(index) = sqrt(x(index));

toc;

Elapsed time is 0.030688 seconds.

slow.m

fast.m

Loops are slow: Use vector operations.

Dynamic memory allocation requires a lot of time: memory Default

Create empty matrices before the loop, not expand iteratively !!



Advanced MATLAB Programming

Functions

Variable number of inputs and outputs (See: nargin, nargout, varargin, varargout)

Local auxiliary functions

Other types of data:

Strings s = 'string';

Structures a.name = 'Alex';

Cell arrays A {1,1} = s; A {1,2} = a;

Can store any type of data

File handling:

Supports most C commands for file I / O (fprintf, ...)fprintf without fileHandle use for standard output.



Advanced MATLAB Programming

Object-oriented

Object "structure" + methods

Generation, transmission shown in the directory tree

Graphical user interface

Based on the "handle" approach to graphics

Menus, buttons, slides and interactive graphics

Interface to other code

Call of compiled C / C ++ ("mex"), Java and ActiveX



Data Visualization

1-Dimensional Data

Histogram

>> hist (Accelerations, 20);

Box and Whisker Plot

>> boxplot (Horsepower, org);

Box: Displays median and 1 and 3. quantile

Whiskers: Displays outliers



Data Visualization

2-D data: Scatter plots

>> gscatter (Weight, Horsepower, org, '', 'XOS')



Data Visualization

More Dimensional Data

gplotmatrix

Scatterplot for 2 combinations of features

Shows no multidimensional relationships



matlab.tugraz.at

ssh -Y [email protected]

what is matlab? - spsc · programming environment working directory >> dir >> cd...

Documents