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Adaptive Algorithms andParallel Computing

Object-Oriented Programming in MATLAB (Primer)

Academic year 2014-2015

Simone Scardapane

Overview1 FUNDAMENTALS OF OOP

What is OOP?Syntax: defining a basic class

2 MORE OOPStatic and private elementsClass documentationHandle and Value classesEvents and notifications

3 CUSTOM MATLAB BEHAVIOROverloading an operatorOverloading indexingCustom displaying

4 INHERITANCEInheritance and PolymorphismAbstract classes

5 EXAMPLESimple Filtering Application

FUNDAMENTALS OF OOP MORE OOP CUSTOM MATLAB BEHAVIOR INHERITANCE EXAMPLE

What is OOP?

Procedural programming

• Procedural programming languages (e.g. C) focus on definingprocedures that implement the core logic of your problem.

• This is decoupled from identifying suitable data structures.• Object-oriented programming (OOP) is a programming

paradigm where the focus is on representing the domain of yourproblem using objects.

• An object encapsulates an internal state, and exposes somemethods through an interface. In this sense, it combineshandling data and operations.

• Note: a class is the source code, from which multiple objects areinstantiated.


What is OOP?

Benefits of OOP

ModularityOOP forces the developer to design modular software.

Data encapsulationAn object can hide part of its information at run-time.

Logic encapsulationIt is not necessary to understand the internal logic of an objectbefore using it.

MaintainabilityOOP code is easier to maintain/document/debug.

ExtensibilityFeatures such as inheritance makes OOP code easier to extend.


What is OOP?

OOP in MATLAB

• Full support for OOP (with a completely rewritten syntax) wasintroduced in MATLAB R2008a.

• Since then, many basic functionalities have been re-introduced tobe compatible with an OOP standard.

• As an example, the graphic engine from MATLAB R2014b isclass-based (so-called HG2).

• MATLAB R2015a has introduced additional functionalities interm of editing capabilities.


Syntax: defining a basic class

Defining a class

A class is instantiated with the classdef keyword:

c l a s s d e f Rectangle

p r o p e r t i e s% P r o p e r t i e s go here

end

methods% Methods go here

end

end

The source code must go inside a file with the same name (e.g. ‘Rect-angle.m’).



Defining a property

The internal state of the class is saved as properties of the class:

p r o p e r t i e swidth ; % The width of the r e c t a n g l eheight ; % The height of the r e c t a n g l e

end

MATLAB is weakly typed, meaning there is no need of defining the typeof each property. A class without methods is equivalent to a struct.

>> r = Rectangler =

Rectangle with properties:width: []height: []

>> r.width = 5r =Rectangle with properties:width: 5height: []



Defining a constructorAn object is created by invoking a special method known as construc-tor. Let us define a custom constructor for our class:

methodsfunct ion obj = Rectangle (w , h )

obj .width = w ;obj .height = h ;

endend

The constructor has a very specific syntax. By default, MATLAB gen-erates a default constructor with no input arguments. Since each classcan only have a single constructor, our definition overrides the MAT-LAB one:

>> r = Rectangle(3, 2)r =

Rectangle with properties:width: 3height: 2

>> r = RectangleError using Rectangle (line 10)Not enough input arguments.



Defining a methodThe third essential element of a class definition is a set of methods:

methods

% Constructor goes here

funct ion p = get_perimeter (obj )p = 2 * (obj .width + obj .height ) ;

end

funct ion obj = scale (obj , n )obj .width = n*obj .width ;obj .height = n*obj .height ;

endend

>> r = Rectangle(5, 3);>> per = r.get_perimeter()per =

16


Static and private elements

Defining a static methodA static method is associated to a class, but not to any specific instanceof that class. Here is an example of a static method:

c l a s s d e f Rectangle% Previous code goes here

methods (Static )func t ion s = get_description ( )

s = ' Class f o r represent ing r e c t a n g l e s ' ;end

end

Note that a static method does not need an instance of the class as ar-gument. In this way, you can call a static method without first declar-ing an object:

>> Rectangle.get_description()ans =

’Class for representing rectangles’



Defining a constant property

A class in MATLAB can have a constant property (or more than one),i.e. a property whose value is never modified after the first assign-ment:

c l a s s d e f Circlep r o p e r t i e s (Constant )

pi = 3 . 1 4 ;end% Other d e f i n i t i o n s

end

>> Circle.pians =

3.1400

>> r.pi = 2You cannot set the read-only property ’pi’ of Rectangle.



Defining a private propertyFinally, a MATLAB class can have one or more private properties, i.e.properties that should not be visible (nor modifiable) from the outside:

c l a s s d e f Rectanglep r o p e r t i e s (Access = private )

width ;height ;

end% Other d e f i n i t i o n s go here

end

>> r = Rectangle(3,2)

r =Rectangle with no properties.

You can also have private methods (using an equivalent syntax). Simi-larly, you can have properties that are visible but not modifiable: [Spec-ifying Property Attributes].

http://it.mathworks.com/help/matlab/matlab_oop/property-attributes.html

http://it.mathworks.com/help/matlab/matlab_oop/property-attributes.html


Class documentation

Writing the documentationWhen documenting your class, you should be careful in respectingMATLAB conventions:

c l a s s d e f Rectangle% Rectangle − Class f o r def in ing r e c t a n g l e s% This c l a s s can be used to def ine o b j e c t s represent ing r e c t a n g l e s .% I n i t i a l i z e the c l a s s as :% r = Rectangle ( 3 , 2 ) ;% Then , [ . . . ] .% See a l s o : UINT32

p r o p e r t i e swidth ; % Width of the r e c t a n g l eheight ; % Height of the r e c t a n g l e

end

methodsfunct ion p = get_perimeter (obj )

% Compute the perimeter of the r e c t a n g l ep = 2 * (obj .width + obj .height ) ;

endend

end


Class documentation

Accessing the documentation

>> help RectangleRectangle - Class for defining rectanglesThis class can be used to define objects representing rectangles.Initialize the class as:r = Rectangle(3, 2);

Then, [...].See also: uint32

>> help Rectangle.widthwidth - Width of the rectangle

>> help Rectangle.get_perimeterCompute the perimeter of the rectangle

>> % See for yourselfdoc Rectangle


Handle and Value classes

Difference between handle and value classes

• All the classes that we defined up to now are value classes. Whenyou pass a value class’ object to a function, a copy is created(similarly when you assign to another variable).

• You can create handle classes that work in the opposite way.Passing an object of an handle class to a function passes areference to the object itself.

• Value classes are useful when the semantics of your objects issimilar to numerical classes or data structures. Similarly, handleclasses are useful when there is often the need of sharing objects.

• This is especially confusing because the resulting syntax is mixedwith respect to other common programming languages (e.g. Javaor C++).



Defining an handle classAn handle class should derive from the basic handle class (more on thissyntax later on):

c l a s s d e f Rectangle < handle

p r o p e r t i e swidth ; % Width of the r e c t a n g l eheight ; % Height of the r e c t a n g l e

end

methodsfunct ion obj = Rectangle (w , h )

obj .width = w ;obj .height = h ;

end

funct ion scale (obj , n )obj .width = n*obj .width ;obj .height = n*obj .height ;

end

endend



Using an handle class

>> r = Rectangle(3, 2);>> r2 = r;>> r2.scale(2)>> r2

r2 =

Rectangle with properties:

width: 6height: 4

>> r

r =


width: 6height: 4


Events and notifications

What is an event?

• A very interesting aspect of handle classes is their ability ofdefining events.

• Roughly, an event is a specific message which is triggered atcertain points in the code. This is known as notification.

• It is possible to associate one (or more) listeners (also known ascallbacks) to a specific notification.

• In this way, you can define a dynamic behavior that is executedat runtime depending on how the class is used.

• As an example, we will show how to keep track of how manytimes a specific function is called.



Defining an event (1/3)

First of all, you must define any event that can be triggered using asimilar syntax with respect to a property:

c l a s s d e f Rectangle < handle

eventsComputePerimeter

end

% Other d e f i n i t i o n s

end

At this point, it is possible to trigger this event whenever required:

func t ion p = compute_perimeter (obj )p = 2 * (obj .width + obj .height ) ;notify (obj , ' ComputePerimeter ' ) ;

end




We keep track of how many times the function is called by using aninternal private counter:

p r o p e r t i e s (Access = private )nComputedPerimeter ;

end

We add a property to initialize the counter and link the event to itsspecific listener:

func t ion track_perimeter_method (obj )obj .nComputedPerimeter = 0 ;addlistener (obj , ' ComputePerimeter ' , @Rectangle .←↩

update_nComputedPerimeter ) ;end




Finally, we define the listener:

methods (Static )func t ion update_nComputedPerimeter (r , ˜ )

r .nComputedPerimeter = r .nComputedPerimeter + 1 ;end

end

We also need a function to print the result:

func t ion print_tracking_info (obj )f p r i n t f ( ' The ' ' ge t per ime ter ' ' func t ion has been c a l l e d %i times .\n '←↩

, obj .nComputedPerimeter ) ;end



The event in action

>> r = Rectangle(3, 2);>> r.track_perimeter_method>> r.compute_perimeter;>> r.compute_perimeter;>> r.print_tracking_infoThe ’get_perimeter’ function has been called 2 times.>> r.nComputedPerimeterYou cannot get the ’nComputedPerimeter’ property of Rectangle.


Overloading an operator

Overloading the times operator

By using OOP, it is possible to overload several basic MATLAB behav-iors for your custom object. As an example, we can overload the oper-ator ∗ for our rectangle class:

func t ion r = mtimes (obj1 ,obj2 )i f (isa (obj1 , ' Rectangle ' ) && isnumeric (obj2 ) )

r = obj1 .scale (obj2 ) ;e l s e i f (isnumeric (obj1 ) && isa (obj2 , ' Rectangle ' ) )

r = obj2 .scale (obj1 ) ;e l s e

e r r o r ( 'One operator must be a r e c t a n g l e and the other numeric ' ) ;end

end

Note that in our implementation we have to explicitly check for theorder of the operands. There is a large number of overloadable opera-tors: [MATLAB Operators and Associated Functions].

http://it.mathworks.com/help/matlab/matlab_oop/implementing-operators-for-your-class.html


Overloading an operator

Rectangle multiplication

>> r = Rectangle(3, 2);>> r = r*2r =


width: 6height: 4

>> r = 1/2*rr =


width: 3height: 2

>> r = ’a’*rError using Rectangle/mtimes (line 27)One operator must be a rectangle and the other numeric


Overloading indexing

Indexing in MATLAB

Just like operators, every indexing operation in MATLAB has an asso-ciated function:

• subsref: subscripted reference, e.g. A(1:3) or A{1:3} orA.area.

• subsasgn: subscripted assignment, e.g. A(3) = 1.• subsindex: subscripted indexing using an object.

Each of these functions can be overloaded to implement custom be-havior.



Example: a class for damped oscillationsConsider the following class representing the function y = sin(x)

x .

c l a s s d e f DampedSinep r o p e r t i e s

limit ; % x−l i m i t f o r funct ionendmethods

funct ion obj = DampedSine (limit )obj .limit = limit ;

endfunct ion v = get_value (obj , x )

% Get the value of the funct ioni f ( any (x < 0) | | any (x > obj .limit ) )

e r r o r ( ' Argument i s outs ide s p e c i f i e d bounds ' ) ;endv = s in (x ) ./x ;

endfunct ion p l o t (obj )

% P l o t the funct ionx = 0 : 0 . 0 1 : obj .limit ; p l o t (x , obj .get_value (x ) ) ;

endend

end



Overloading indexingWe can implement a custom indexing operation to create a sort of“callable” object:

func t ion B = subsref (A ,S )i f ( strcmp (S ( 1 ) . type , ' ( ) ' ) && length (S ( 1 ) .subs ) == 1)

B = A .get_value (S ( 1 ) .subs{1}) ;i f ( length (S ) > 1)

B = builtin ( ' subsre f ' , B , S ( 2 : end ) ) ;end

e l s eB = builtin ( ' subsre f ' , A , S ) ;

endend

>> ds = DampedSine(20);>> ds.get_value(5)ans =

-0.1918>> ds(5)ans =

-0.1918


Custom displaying

Custom displaying

You can overload how a variable is displayed on the console:

func t ion disp (obj )f p r i n t f ( ' Rectangle with width=%.2 f and height =%.2 f\n ' , obj .width , ←↩

obj .height ) ;end

>> r = Rectangle(3, 2)

r =

Rectangle with width=3.00 and height=2.00

There are many other custom behaviors that you can implement: [Cus-tomize MATLAB Behavior].

http://it.mathworks.com/help/matlab/customize-matlab-behavior.html

http://it.mathworks.com/help/matlab/customize-matlab-behavior.html


Inheritance and Polymorphism

What is inheritance?

• Inheritance is a feature of OOP languages that lets one class to‘inherits’ the behavior from a specific super-class.

• This allows a strong amount of code reuse, and the possibility ofcreating hierarchies of classes for your application (e.g. thehierarchy of data types in MATLAB).

• You can think of class B inheriting from class A as theimplementation of the semantic “B is-a A” (not to be confusedwith the classical “B has-a A”).

• Closely connected is the idea of polymorphism: a single interfaceis declined in multiple forms, and the specific implementation isdecided only at run-time.



An example of inheritance

A square “is-a” rectangle, whose width and height are equivalent:

c l a s s d e f Square < Rectangle

p r o p e r t i e send

methods

funct ion obj = Square (l )obj = obj@Rectangle (l , l ) ;

end

end

end

Note the syntax of the call to a constructor of the super-class.



Method overridingThe class Square inherits all the behavior of its superclass, thus allow-ing a strong amount of code reusing between implementations:

>> s = Square(3);>> s.compute_perimeter

ans =12

You can also override a specific method (in this case, for computationalreasons):

c l a s s d e f Square < Rectangle% . . .methods

% . . .func t ion p = compute_perimeter (obj )

p = 4*obj .height ;end

endend



Adding methods to the subclassYou can define methods that are exclusive of a particular subclass:

c l a s s d e f Square < Rectangle% . . .methods

% . . .func t ion l = get_length (obj )

l = obj .width ;end

endend

>> s = Square(3);>> s.get_lengthans =

3>> r = Rectangle(3, 2);>> r.get_lengthNo appropriate method, property, or field

get_length for class Rectangle.



Sealed and protected attributes

You can specify that a property (or method) is accessible only to classesinheriting the super-class:

c l a s s d e f Ap r o p e r t i e s (Access=protected )

foo ;end

end

Additionally, you can specify that a particular class cannot be inher-ited from:

c l a s s d e f A (Sealed = true )% . . .

endc l a s s d e f B < A

% ERRORend


Abstract classes

Abstract classes

Inheritance allows to define abstract classes. These cannot be instanti-ated, but they can:

• Abstract code from any specific sub-class.• Provide an interface for a set of functions that any sub-class must

implement.

Let us consider the following class hierarchy:

Shape (Abstract)

Rectangle

Square

Circle


Abstract classes

Defining the abstract class

c l a s s d e f Shapep r o p e r t i e s

n_sides ; % Number of s i d e send

methods (Abstract=true )p = compute_perimeter (obj ) ; % Compute the perimeterobj = scale (obj , n ) ; % S c a l e the o b j e c t

end

methodsfunct ion obj = Shape (n )

obj .n_sides = n ;endfunct ion print_info (obj )

f p r i n t f ( ' This i s a geometric shape with %.2 f s i d e s .\n ' , obj←↩.n_sides ) ;

endend

end


Abstract classes

Defining the first sub-class

c l a s s d e f Rectangle < Shapep r o p e r t i e s

width ; % Width of the r e c t a n g l eheight ; % Height of the r e c t a n g l e

endmethods

funct ion obj = Rectangle (w , h )obj = obj@Shape ( 4 ) ;obj .width = w ;obj .height = h ;

end

funct ion obj = scale (obj , n )obj .width = n*obj .width ;obj .height = n*obj .height ;

end

funct ion p = compute_perimeter (obj )p = 2 * (obj .width + obj .height ) ;

endend

end


Abstract classes

Defining a new sub-class

Note: the class for the Square is unchanged with respect to before.

c l a s s d e f Circle < Shapep r o p e r t i e s

radius ; % Radius of the c i r c l eendmethods

funct ion obj = Circle (r )obj = obj@Shape ( I n f ) ;obj .radius = r ;

end

funct ion obj = scale (obj , n )obj .radius = n*obj .radius ;

end

funct ion p = compute_perimeter (obj )p = 2* pi *obj .radius ;

endend

end


Abstract classes

Using the class hierarchy

>> r = Rectangle(3,2);>> r.scale(2)

ans =


width: 6height: 4n_sides: 4

>> s = Shape(3);Error using ShapeAbstract classes cannot be instantiated.

Class ’Shape’ defines abstract methods and/or properties.


Abstract classes

Refactoring

We can see that the code of the scale method is semantically equiva-lent in all cases: it multiplies by n all properties, except the number ofsides. We can, in principle, abstract this into the class Shape to providea default implementation:

c l a s s d e f Shape% . . .func t ion obj = scale (obj , n )

pr = p r o p e r t i e s (class (obj ) ) ;f o r ii = 1 : length (pr )

i f ( ˜ strcmp (pr{ii} , ' n s i d e s ' ) )obj . ( pr{ii}) = n*obj . ( pr{ii}) ;

endend

end% . . .

end

This is known as code refactoring.


Simple Filtering Application

Description of the example

As a final example, we implement a relatively simple (but with lotof possible extensions) filtering application. We have the followingspecifics:

• A class for generating the underlying system to be identified. Forsimplicity, the system is supposed to be linear, and the outputcorrupted with Gaussian noise.

• An abstract class for implementing any linear adaptive filter.One particular implementation of this class implementing thestandard LMS filter with constant step size.

• One class taking care of plotting the results. For simplicity, weimplement only one method for plotting the MSE in logarithmicscale.



Signal generation

c l a s s d e f SignalGenerator% SignalGenerator − Class f o r generat ing input and output s i g n a l s

p r o p e r t i e staps ; % taps of the f i l t e rnoise_var ; % var iance of the noisewo ; % optimal weights of the l i n e a r system

end

methods

funct ion obj = SignalGenerator (taps , noise_var )obj .taps = taps ;i f ( nargin < 2)

obj .noise_var = 0 . 0 1 ;e l s e

obj .noise_var = noise_var ;endobj .wo = rand (taps , 1 ) *2 − 1 ;

end

endend



Signal generation (cntd)

c l a s s d e f SignalGenerator% . . .

func t ion [X , d ] = generate_signal (obj , N )

% Generate s i g n a l of length N% The outputs are :% X : a NxM input matrix , where M i s the number of taps% d : a Nx1 vec tor of output values , corrupted by noise

X = randn (N , obj .taps ) ;d = X*obj .wo + randn (N , 1 ) * s q r t (obj .noise_var ) ;

end

% . . .end



Abstract class for filters

c l a s s d e f AdaptiveFilter% A d a p t i v e F i l t e r − Abstrac t c l a s s f o r adaptive f i l t e r s

p r o p e r t i e sw_estimated ; % Estimated weightserror_history ; % Vector of a−p r i o r i e r r o r s

end

methodsfunct ion obj = AdaptiveFilter (taps )

obj .w_estimated = zeros (taps , 1 ) ;end

% Here we need :% 1) one funct ion f o r process ing the f u l l d a t a s e t one item% at a time .% 2) one ( a b s t r a c t ) func t ion f o r implementing the s i n g l e% adaptat ion step .

end

end



Abstract class for filters (cntd)

c l a s s d e f AdaptiveFilter% . . .methods

% . . .func t ion obj = process (obj , X , d )

% Process the o v e r a l l s i g n a l X/dN = length (d ) ;obj .error_history = zeros (N , 1 ) ;f o r ii = 1 :N

obj .error_history (ii ) = d (ii ) − X (ii , : ) *obj .←↩w_estimated ;

obj = obj .adapt (X (ii , : ) ' , d (ii ) , obj .error_history (ii )←↩) ;

endend

end

methods (Abstract )obj = adapt (obj , x , y , e ) ; % Signa l adaptat ion step

end

end



Least Mean-Square Filter

c l a s s d e f LMSFilter < AdaptiveFilter% LmsFi l ter − Least Mean−Square adaptive f i l t e r with constant s tep ←↩

s i z e

p r o p e r t i e sstep_size ; % Step s i z e

end

methodsfunct ion obj = LMSFilter (taps , step_size )

obj = obj@AdaptiveFilter (taps ) ;obj .step_size = step_size ;

endfunct ion obj = adapt (obj , x , ˜ , e )

obj .w_estimated = obj .w_estimated + obj .step_size*e*x ;end

end

end



Helper function for plotting

c l a s s d e f PlotHelper% PlotHelper − Helper c l a s s f o r p l o t t i n g

p r o p e r t i e s (Constant )font_size = 8 ; % Fonts izefont_size_leg = 6 ; % Font s i z e ( legend )font_name = 'TimesNewRoman ' ; % Font nameline_width = 1 ; % LineWidth

end

methods (Static )

func t ion plot_MSE_db (xlab , ylab , leg , varargin )% Inputs are : x−l a b e l y−l a b e l , c e l l array of s t r i n g s f o r ←↩

the% legend . Each a d d i t i o n a l input i s a time−s e r i e s to be ←↩

p l o t t e d .

% Code goes hereend

end

end



Helper function for plotting (cntd)

func t ion plot_MSE_db (xlab , ylab , leg , varargin )% Each a d d i t i o n a l argument i s a time s e r i e s to be p l o t t e d

% Simple f i l t e r f o r smoothing the r e s u l t s[bb , aa ] = butter ( 2 , 0 . 0 2 ) ;

N_series = length (varargin ) ;

cmap = hsv (N_series ) ;f i g u r e ( ) ; hold on ; box on ; gr id on ;

f o r ii = 1 :N_seriesp l o t ( f i l t e r (bb , aa , 10* log10 (varargin{ii} . ˆ 2 ) ) , ' LineWidth ' , ←↩

PlotHelper .line_width , ' Color ' , cmap (ii , : ) ) ;end

x l a b e l (xlab , ' FontSize ' , PlotHelper .font_size , ' FontName ' , ←↩PlotHelper .font_name ) ;

y l a b e l (ylab , ' FontSize ' , PlotHelper .font_size , ' FontName ' , ←↩PlotHelper .font_name ) ;

legend (leg , ' FontSize ' , PlotHelper .font_size , ' FontName ' , ←↩PlotHelper .font_name ) ;

end



Testing the application

% Repeatable experimentrng ( 1 ) ;

% Generate data f o r s imulat ionsg = SignalGenerator ( 5 , 0 . 1 ) ;[X , y ] = sg .generate_signal ( 5 0 0 0 ) ;

% Create two f i l t e r sf1 = LMSFilter ( 5 , 0 . 0 1 ) ;f2 = LMSFilter ( 5 , 0 . 0 0 1 ) ;

% Adapt the f i l t e rf1 = f1 .process (X , y ) ;f2 = f2 .process (X , y ) ;

% P l o tPlotHelper .plot_MSE_db ( ' Sample ' , 'MSE ' , { ' F i l t e r 1 ' , ' F i l t e r 2 ' } , f1 .←↩

error_history , f2 .error_history ) ;



Result

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000−20

−15

−10

−5

0

5

Sample

MS

E

Filter 1

Filter 2

adaptive algorithms and parallel computing -...

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