ÚvodÚvod

ČO JEČO JE MATLAB MATLAB?

MATLAB® MATLAB® je vysoko-výkonný prostriedok pre vedecko-je vysoko-výkonný prostriedok pre vedecko-technické výpočty a ich aplikáciu v rôznych oblastiach technické výpočty a ich aplikáciu v rôznych oblastiach (technika, zdravotníctvo, astronautika,(technika, zdravotníctvo, astronautika, financie, …financie, …Integruje výpočty, umožňuje vizualizáciu a programovanie v uživateľsky príjemnom prostredí, pričom riešené problémy a výsledky sú vyjadrované v jasne zrozumiteľných numerických a grafických formách.

Typické úlohy riešiteľné v MatlabeTypické úlohy riešiteľné v Matlabe::

• Matematické výpočty, jednoduchá a zložitá numerika Matematické výpočty, jednoduchá a zložitá numerika • Vývoj algoritmov v interpreteri Matlabu Vývoj algoritmov v interpreteri Matlabu

• ModelModelovanie statických a dynamických procesov, simulácia a navrhovanie ovanie statických a dynamických procesov, simulácia a navrhovanie optimálnych štruktúr obvodov, procesov optimálnych štruktúr obvodov, procesov

• Analýza údajovAnalýza údajov,, testovanie, vizualizácia, filtrácia testovanie, vizualizácia, filtrácia• Inžinierska a vedecká grafikaInžinierska a vedecká grafika

• Vývoj nových aplikácií vo vysoko efektívnom numerickom a grafickom Vývoj nových aplikácií vo vysoko efektívnom numerickom a grafickom prostredíprostredí

2001 Štefan Kozák

MATLAB je interaktívny systém spracúvajúci údaje vo forme vektorov, matíc bez deklarácie dimenzovania premenných

1. umožňuje riešiť mnohé technické a vedecké problémy 2.umožňuje spájať algoritmy v rôznych prostrediach (Fortran, C++, Java,….

Názov MatlabNázov Matlab – Matrix Laboratory – pôvodne zameraný na maticové operácie. Pôvodné projekty na tvorbu algoritmov v Matlabe LINPACKLINPACK

EISPACKEISPACKSúčasnosť - software pre Matlab vyvíjaný v projekte

LAPACKLAPACK

ARPACKARPACKVývoj nových algoritmov a nové verzie v MATLAB-e každý rok – veľa riešiteľov (príprava nových toolboxov náročná a nemožná bežnému riešiteľovi

Matlab je predovšetkým vhodný pre :1.Všetky univerzity (aj medicína a farmácia) 2.Moderné prednášky a cvičenia s podporou vysoko efektívnej numeriky a grafiky3.Vedecký výskum, analýza vedeckých výsledkov, vývoj nových materiálov (NASA, MIR – simulácia zostupu – Moskva, vesmír…)

• MATLAB predstavuje dnes rodinu (asi 300 problémovo-orientovaných aplikačných knižníc nazývaných Toolboxy, základných Toolboxov je dnes 31).

• Toolboxy sú súborom všeobecných MATLAB funkcií (M-files)

• Oblasti použitia - Signal Processing, Control Systems, Neuralnetworks, Fuzzy logic, Wavelets, Simulation,…

Čo Matlab 6.1 – 6.5 ponúka• Rýchle výpočtové jadro• Otvorený a rozširíteľný systém• Efektívna 2D a 3D grafika• Konfigurovateľné užívateľské rozhranie Matlab Desktop• Veľké množstvo aplikačných knižníc• Programovací jazyk 4. Generácie• Objektové programovanie• Integrácie s jazykom Java• Podpora viacrozmerných polí a užívateľom definovaných dátových

štruktúr• Interaktívny nástroj pre tvorbu grafických a užívateľských rozhraní

• Podpora zápisu a výpočtu s tzv. riedkymi maticami• Interaktívny sprievodca importu údajov• Zvukový vstup a výstup, animácia• Komunikácia s externým prístrojovým vybavením

(sériova linka, GPIB, VISA)• Výpočtové jadro pre programy písané v iných jazykoch

(Fortran, C,...)• Distribucia nezávislých uživateľských aplikácií, preklad

do jazyka C, runtime modul, WWW technológie• Rozsiahla tlačená a hypertexová on-line dokumentácia

MATLABMATLAB

SIMULINKSIMULINK

Simulink-rozšírenia• Simulink accelerator• Real-Time• PC-Targit Blocksets• DSP•Fixed-Point• Nonlinear Control Design•Communication

Matlab-ExtensionMatlab-Extension

Matlab Compiler Matlab C/C++ Math Libr.Matlab Compiler Matlab C/C++ Math Libr.

Matlab C/C++ Graph. Libr.Matlab C/C++ Graph. Libr.

ToolboxyToolboxyControl Systems Control Systems Partial Dif. equationPartial Dif. equation

CommunicationCommunication Robust ControlRobust Control

Filter DesignFilter Design Signal Processing Signal Processing

Spline StatisticsSpline Statistics

Optimization Optimization System IdentificattionSystem Identificattion

Symbolic Math DatabaseSymbolic Math Database

Fuzzy LogicFuzzy Logic Wavelet Wavelet

Image Processing Data AcquisitionImage Processing Data Acquisition

Instrument Control Filter Design Instrument Control Filter Design

LMI Control FinancialLMI Control Financial

Model Predictive ControlModel Predictive Control

- Analysis and Synthesis- Analysis and Synthesis

Neural NetworkNeural Network

OptimizationOptimization

Vývojové prostredie

Všeobecné príkazy

Špeciálne príkazy (Sound Processing Functions)

File I/O Functions

Matematika

Elementárne matice a operácie s maticami

Špeciálne matice

Elementárne Math funkcie

Špeciálne Math funkcie

Konverzia súradnicových systémov

Maticové funkcie - Numerika Lineárna Algebra

Analýza údajov a Fourierova transformácia

Polynomiálne a Interpolačné funkcie

Funkcie – „funkcií“ – Nelineárne numerické metódy

Riedké maticové operácie a funkcie

Symbolická matematika

syms gp

Gp=1/2/(s^2+2*s+1)

yt=ilaplace(Gp)

yt =1/2*t*exp(-t)

ezplot(yt,t)

Matrices and Linear Algebra - describes matrix creation and matrix operations that are directly supported by MATLAB. Topics covered include matrix arithmetic, linear equations, eigenvalues, singular values, and matrix factorizations.

Polynomials and Interpolation - describes functions for standard polynomial operations such as polynomial roots, evaluation, and differentiation. Additional topics covered include curve fitting and partial fraction expansion.

Data Analysis and Statistics - describes how to organize arrays for data analysis, how to use simple descriptive statistics functions, and how to perform data pre-processing tasks in MATLAB. Additional topics covered include regression, curve fitting, data filtering, and fast Fourier transforms (FFTs).

Function Functions - describes MATLAB functions that work with mathematical functions instead of numeric arrays. These function functions include plotting, optimization, zero finding, and numerical

integration (quadrature).

Differential EquationsDifferential Equations - describes the solution, in MATLAB, of initial value problems for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), and the solution of boundary value problems for ODEs. It also describes the solution of initial-boundary value problems for systems of parabolic and elliptic partial differential equations (PDEs). Topics covered include representing problems in MATLAB, solver syntax, and using integration parameters.

Sparse MatricesSparse Matrices - describes how to create sparse matrices in MATLAB, and how to use them in both specialized and general mathematical operations.

Development EnvironmentDevelopment Environment - the MATLAB desktop for managing your workspace, functions, and files.

Mathematics - mathematical operations, functions, and data analysis.

Programming and Data Types - programming features and techniques.

Graphics - 2-D plotting, graph formatting, printing, and programming with Handle Graphics.

3-D Visualization - visualization techniques for 2-D surface and 3-D volume data sets.

External Interfaces - MEX-files, the MATLAB engine, and interfacing to Java, ActiveX, and the serial port.

Creating Graphical User InterfacesCreating Graphical User Interfaces - GUI-building tools and how to write callback routines.

Programming and Data Types

Operators and Special Characters

Logical Functions

Language Constructs and Debugging

Character String Functions

Bitwise Functions

Structure Functions

MATLAB Object Functions

Cell Array Functions

Multidimensional Array Functions

. Decimal point

... Continuation, Comma; Semicolon% Comment! Exclamation point' Transpose and quote.' Nonconjugated transpose= Assignment== Equality< > Relational operators& Logical AND| Logical OR~ Logical NOTxor Logical EXCLUSIVE OR

+ Plus

- Minus

* Matrix multiplication

.* Array multiplication

^ Matrix power

.^ Array power

kron Kronecker tensor product

\ Backslash or left division

/ Slash or right division

./ and .\ Array division, right and left

: Colon

( ) Parentheses

[ ] Brackets

{} Curly braces

Elementary Math Functions

• abs abs Absolute value and complex magnitudeAbsolute value and complex magnitude• acos, acoshacos, acosh Inverse cosine and inverse hyperbolic cosine Inverse cosine and inverse hyperbolic cosine• acot, acothacot, acoth Inverse cotangent and inverse hyperbolic cotangent Inverse cotangent and inverse hyperbolic cotangent• acsc, acschacsc, acsch Inverse cosecant and inverse hyperbolic cosecantInverse cosecant and inverse hyperbolic cosecant• angle angle Phase anglePhase angle• asec, asechasec, asech Inverse secant and inverse hyperbolic secantInverse secant and inverse hyperbolic secant• asin, asinhasin, asinh Inverse sine and inverse hyperbolic sineInverse sine and inverse hyperbolic sine• atan, atanhatan, atanh Inverse tangent and inverse hyperbolic tangentInverse tangent and inverse hyperbolic tangent• atan2 atan2 Four-quadrant inverse tangentFour-quadrant inverse tangent• ceil ceil Round toward infinityRound toward infinity• complex complex Construct complex data from real and imag. component Construct complex data from real and imag. component • conj conj Complex conjugateComplex conjugate• cos, coshcos, cosh Cosine and hyperbolic cosineCosine and hyperbolic cosine• cot, cothcot, coth Cotangent and hyperbolic cotangentCotangent and hyperbolic cotangent• csc, cschcsc, csch Cosecant and hyperbolic c osecantCosecant and hyperbolic c osecant• exp exp ExponentialExponential

Fix Round towards zero

Floor Round towards minus infinity

Gcd Greatest common divisor

Imag Imaginary part of a complex number

Lcm Least common multiple

Log Natural logarithm

Log2 Base 2 logarithm and dissect floating-point numbers into exponent and mantissa

Log10 Common (base 10) logarithm

Mod Modulus (signed remainder after division)

Nchoosek Binomial coefficient or all combinations

Real Real part of complex number

Rem Remainder after division

Round Round to nearest integer

Real Real part of complex number

Rem Remainder after division

Round Round to nearest integer

sec, sech Secant and hyperbolic secant

Sign Signum function

sin, sinh Sine and hyperbolic sine

Sqrt Square root

tan, tanh Tangent and hyperbolic tangent

Creating GUIs

Graphical User Interface Creation

External Interfaces

MATLAB Interface to Java

Serial Port I/O

Graphics

Plotting and Data Visualization

Variables Managing and the Workspace

Clear Remove items from the workspace

Disp Display text or array

Length Length of vector

Load Retrieve variables from disk

Memory Help for memory limitations

Mlock Prevent M-file clearing

Munlock Allow M-file clearing

Openvar Open workspace variable in Array Editor, for graphical editing

Pack Consolidate workspace memory

Save Save workspace variables on disk

Saveas Save figure or model using specified format

size Array dimensions

who, whosList the variables in the workspace

SIMULINK- blokové schémy a modelovanie dy- namických systémov-dif.rovnicami- simulácia, linearizácia - lineárne a nelineárne modely- spojité a diskrétne modely- ovládanie myšou, vysoká interaktívnosť- práca v prostredí X Windows/Motif, Microsoft Windows a Macintosh

SIGNAL PROCESSING TOOLBOX (Knižnica programov "Spracovanie signálov")- návrh spojitých a číslicových filtrov- spektrálna analýza- konvolučná, korelačná a FFT analýza- spracovanie 1-D a 2-D signálov- spracovanie a filtrácia procesných údajov

SYSTEM IDENTIFICATION TOOLBOX (Knižnica programov "Identifikácia systémov")- generovanie prenosovej funkcie a stavového modelu zo vstupno /výs-tupných údajov- identifikácia parametrické a nepa-rametrické modely: typu MA, AR, ARMA a Box-Jenkinsovho modelu- spektrálna analýza

OPTIMIZATION TOOLBOX (Knižnica programov "Optimalizácia")-lineárne a kvadratické prog. - minim. a maximalizácia funkcií (hľadanie extrému funkcií)- riešenie úloh s obmedzením a bez obmedzenia- nelineárna metóda najm.štvor.

CONTROL SYSTEM TOOLBOX

(Knižnica programov "Riadenie systémov")

- moderné a klasické metódy riadenia- modely v stavovom priestore a v tvare prenosových funkcií- metóda GMK, pole-placement, LQR a LQG- Bodeho, Nyquistove, Nicholsove a SVD (singular value decomposition) frekvenčné charakteristiky- impulzné, prechodové a všeobecné charakteristiky- algebra prenosov- vzájomné transformácie medzi jednotlivými typmi modelov- analýza stability vo frekvenčnej a časovej oblasti- algebra prenosov

CONTROL SYSTEM TOOLBOX

(Knižnica programov "Riadenie systémov")

- moderné a klasické metódy riadenia- modely v stavovom priestore a v tvare prenosových funkcií- metóda GMK, pole-placement, LQR a LQG- Bodeho, Nyquistove, Nicholsove a SVD (singular value decomposition) frekvenčné charakteristiky- impulzné, prechodové a všeobecné charakteristiky- algebra prenosov- vzájomné transformácie medzi jednotlivými typmi modelov- analýza stability vo frekvenčnej a časovej oblasti- algebra prenosov

Inteligentné metódy modelovania a riadenia

• NEURAL NETWORK TOOLBOX

• (Knižnica programov "Neurónové siete")

• modelovanie procesov neuróno-vými sieťami

• model perceptronu,Widrow-Holf pravidlá, Kohonenova siet, ART siete,..

• backpropagation, modelovanie rôznych typov nelin.systémov

• metódy učenia a trénovania

• FUZZY TOOLBOX• (Knižnica programov

"Fuzzy množiny"

• - fuzzy logika, fuzzy pravidla

• - neurčité modely• - metódy fuzifikácie• - metódy defuzifikácie• - fuzzy regulátory• - fuzzy rozhodovanie

Products with Major UpgradesProducts with Major UpgradesRelease 12 includes major version upgrades to many Release 12 includes major version upgrades to many

products, highlighted in the following sections of theseproducts, highlighted in the following sections of these

• Release Notes:Release Notes:• MATLAB 6.0MATLAB 6.0• MATLAB Runtime Server 6.0MATLAB Runtime Server 6.0• MATLAB Compiler 2.1MATLAB Compiler 2.1• Simulink 4.0Simulink 4.0• Stateflow 4.0Stateflow 4.0• Stateflow Coder 4.0Stateflow Coder 4.0• Real-Time Workshop 4.0Real-Time Workshop 4.0• Real-Time Workshop Ada Coder 4.0Real-Time Workshop Ada Coder 4.0• Real-Time Windows Target 2.0Real-Time Windows Target 2.0• Communications Blockset 2.0Communications Blockset 2.0• Communications Toolbox 2.0Communications Toolbox 2.0• Control System Toolbox 5.0Control System Toolbox 5.0

•Data Acquisition Toolbox 2.0Data Acquisition Toolbox 2.0•DSP Blockset 4.0DSP Blockset 4.0•Fixed-Point Blockset 3.0Fixed-Point Blockset 3.0•Neural Network Toolbox 4.0Neural Network Toolbox 4.0•Power System Blockset 2.0Power System Blockset 2.0•Signal Processing Toolbox 5.0Signal Processing Toolbox 5.0•Spline Toolbox 3.0Spline Toolbox 3.0•Statistics Toolbox 3.0Statistics Toolbox 3.0•System Identification Toolbox 5.0System Identification Toolbox 5.0•Wavelet Toolbox 2.0Wavelet Toolbox 2.0

Platform LimitationsPlatform Limitations

For Release 12, all the features described in these Release Notes and in the Release 12 documentation are supported in full for the following platforms:

Microsoft Windows 95, Windows 98, Windows 2000, Windows Microsoft Windows 95, Windows 98, Windows 2000, Windows Millenium, and Windows NT Compaq Alpha Linux SGI Sun Millenium, and Windows NT Compaq Alpha Linux SGI Sun SolarisSolaris

Note As in Release 11, there are some minor differences between Windows and UNIX for specific tools, as documented for those tools.

For details about each of these platforms, see the Support page of the MathWorks Web page, at http://www.mathworks.com.

Differences for the HP and IBM Platforms

Because of problems with the Java VM, there are limitations for MATLAB on the HP and IBM platforms.

Platform

Limitations

HP 11.0 (HP UX)

IBM

Graphical user interfaces that are based on Java, such as the MATLAB desktop, are not available.

HP 10.2 (HP

700)

Java-based tools and applications are not supported.

Starting MATLAB on Windows Platforms

Starting MATLAB on UNIX Platforms

Startup Directory for MATLAB

Startup Options

Reducing Startup Time with Toolbox Path Caching

Quitting MATLAB

Running a Script When Quitting MATLAB

Development EnvironmentDevelopment Environment - the MATLAB desktop for managing your workspace, functions, and files.

Mathematics - mathematical operations, functions, and data analysis.

Programming and Data Types - programming features and techniques.

Graphics - 2-D plotting, graph formatting, printing, and programming with Handle Graphics.

3-D Visualization - visualization techniques for 2-D surface and 3-D volume data sets.

External Interfaces - MEX-files, the MATLAB engine, and interfacing to Java, ActiveX, and the serial port.

Creating Graphical User InterfacesCreating Graphical User Interfaces - GUI-building tools and how to write callback routines.

Matrices and Linear Algebra - describes matrix creation and matrix operations that are directly supportedby MATLAB. Topics covered include matrix arithmetic, linear equations, eigenvalues, singular values, and matrix factorizations.

Polynomials and Interpolation - describes functions for standard polynomial operations such as polynomial roots, evaluation, and differentiation. Additional topics covered include curve fitting and partial fraction expansion.

Data Analysis and Statistics - describes how to organize arrays for data analysis, how to use simple descriptive statistics functions, and how to perform data pre-processing tasks in MATLAB. Additional topics covered include regression, curve fitting, data filtering, and fast Fourier transforms (FFTs).

Function Functions - describes MATLAB functions that work with mathematical functions instead of numeric arrays. These function functions include plotting, optimization, zero finding, and numerical

integration (quadrature).

Differential EquationsDifferential Equations - describes the solution, in MATLAB, of initial value problems for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), and the solution of boundary value problems for ODEs. It also describes the solution of initial-boundary value problems for systems of parabolic and elliptic partial differential equations (PDEs). Topics covered include representing problems in MATLAB, solver syntax, and using integration parameters.

Sparse MatricesSparse Matrices - describes how to create sparse matrices in MATLAB, and how to use them in both specialized and general mathematical operations.

New Products (Since Release 11.0)

The following products are being introduced with Release 12:

•Communications Blockset 2.0Communications Blockset 2.0

•Filter Design Toolbox 2.0Filter Design Toolbox 2.0

•Instrument Control Toolbox 1.0Instrument Control Toolbox 1.0

•Simulink Performance Tools 4.0Simulink Performance Tools 4.0

•Real-Time Workshop Embedded CoderReal-Time Workshop Embedded Coder

In addition, Release 12 includes a number of products that have In addition, Release 12 includes a number of products that have been introduced since Release 11.0 (released in Web-been introduced since Release 11.0 (released in Web-downloadable form and/or on the Release 11.1 CD):downloadable form and/or on the Release 11.1 CD):

•CDMA Reference Blockset 1.0.2CDMA Reference Blockset 1.0.2

•Datafeed Toolbox 1.2Datafeed Toolbox 1.2

•Dials & Gauges Blockset 1.1Dials & Gauges Blockset 1.1

•Financial Time Series Toolbox 1.0Financial Time Series Toolbox 1.0

•Financial Derivatives Toolbox 1.0Financial Derivatives Toolbox 1.0

•Motorola DSP Developer's Kit 1.1Motorola DSP Developer's Kit 1.1

•GARCH Toolbox 1.0GARCH Toolbox 1.0

•Requirements Management Interface 1.0.1Requirements Management Interface 1.0.1

•xPC Target and xPC Target Embedded Option 1.1xPC Target and xPC Target Embedded Option 1.1

MATLAB®MATLAB® provides many graphics functionsgraphics functions that allow you to create 2-D plots of your data. This collection includes the following topics.

•Overview of MATLAB Graphics - describes plot editing mode and the Overview of MATLAB Graphics - describes plot editing mode and the Property Editor.Property Editor.

Basic Plotting - describes how to plot vector and matrix data in 2-D Basic Plotting - describes how to plot vector and matrix data in 2-D representations.representations.

Formatting Graphs - describes how to customize the format of a plot to help Formatting Graphs - describes how to customize the format of a plot to help explain your data. This section includes information about adding labels, titles, explain your data. This section includes information about adding labels, titles, and annotations to a plot.and annotations to a plot.

Creating Specialized Plots - describes how to create bar graphs, histograms, Creating Specialized Plots - describes how to create bar graphs, histograms, and contour plots.and contour plots.

Basic Printing and Exporting - describes frequently used ways to print or Basic Printing and Exporting - describes frequently used ways to print or export a MATLAB figure, and explains the basic printing and exporting export a MATLAB figure, and explains the basic printing and exporting interfaces.interfaces.

Handle Graphics® Objects - introduces MATLAB's graphics objects and Handle Graphics® Objects - introduces MATLAB's graphics objects and properties.properties.

•Figure Properties - discusses the features that are implemented with figure Figure Properties - discusses the features that are implemented with figure properties.properties.

•Axes Properties - discusses the features that are implemented with axes Axes Properties - discusses the features that are implemented with axes properties.properties.

•Related InformationRelated Information

•These other collections provide additional information about plotting.These other collections provide additional information about plotting.

•3-D Visualization describes how to use views and lighting to achieve more 3-D Visualization describes how to use views and lighting to achieve more complex graphic effects than can be achieved using the basic plotting functions.complex graphic effects than can be achieved using the basic plotting functions.

•Creating GUIs describes how to include menus, push buttons, text boxes, and Creating GUIs describes how to include menus, push buttons, text boxes, and other user interface objects in MATLAB applications.other user interface objects in MATLAB applications.