Úvod ČO JE MATLAB ?

1. Úvod • ČO JE MATLAB? • MATLAB® je vysoko-výkonný prostriedok pre vedecko-technické výpočty a ich aplikáciu v rôznych oblastiach (technika, zdravotníctvo, astronautika,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 Matlabe: • Matematické výpočty, jednoduchá a zložitá numerika • Vývoj algoritmov v interpreteri Matlabu • Modelovanie statických a dynamických procesov, simulácia a navrhovanie optimálnych štruktúr obvodov, procesov • Analýza údajov, testovanie, vizualizácia, filtrácia • Inžinierska a vedecká grafika • Vývoj nových aplikácií vo vysoko efektívnom numerickom a grafickom prostredí 2001 Štefan Kozák

2. MATLAB je interaktívny systém spracúvajúci údaje vo forme vektorov, matíc bez deklarácie dimenzovania premenných • umožňuje riešiť mnohé technické a vedecké problémy • umožňuje spájať algoritmy v rôznych prostrediach (Fortran, C++, Java,…. • Názov Matlab – Matrix Laboratory – pôvodne zameraný na maticové operácie. • Pôvodné projekty na tvorbu algoritmov v Matlabe LINPACK • EISPACK • Súčasnosť - software pre Matlab vyvíjaný v projekte • LAPACK • ARPACK • Vývoj 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 : • Všetky univerzity (aj medicína a farmácia) • Moderné prednášky a cvičenia s podporou vysoko efektívnej numeriky a grafiky • Vedecký výskum, analýza vedeckých výsledkov, vývoj nových materiálov (NASA, MIR – simulácia zostupu – Moskva, vesmír…)

3. 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, Neural • networks, Fuzzy logic, Wavelets, Simulation,…

4. 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

5. 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

6. MATLAB SIMULINK Matlab-Extension Matlab Compiler Matlab C/C++ Math Libr. Matlab C/C++ Graph. Libr. Toolboxy Control Systems Partial Dif. equation Communication Robust Control Filter Design Signal Processing Spline Statistics Optimization System Identificattion Symbolic Math Database Fuzzy Logic Wavelet Image Processing Data Acquisition Instrument Control Filter Design LMI Control Financial Model Predictive Control - Analysis and Synthesis Neural Network Optimization • Simulink-rozšírenia • Simulink accelerator • Real-Time • PC-Targit • Blocksets • DSP • Fixed-Point • Nonlinear Control • Design • Communication

8. 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

9. Symbolická matematika syms gp Gp=1/2/(s^2+2*s+1) yt=ilaplace(Gp) yt =1/2*t*exp(-t) ezplot(yt,t)

10. 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).

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

12. Development 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 Interfaces - GUI-building tools and how to write callback routines.

13. 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

14. . Decimal point ... Continuation , Comma ; Semicolon % Comment ! Exclamation point ' Transpose and quote .' Nonconjugated transpose = Assignment == Equality < > Relational operators & Logical AND | Logical OR ~ Logical NOT xor Logical EXCLUSIVE OR

15. + 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

16. Elementary Math Functions • abs Absolute value and complex magnitude • acos, acosh Inverse cosine and inverse hyperbolic cosine • acot, acoth Inverse cotangent and inverse hyperbolic cotangent • acsc, acsch Inverse cosecant and inverse hyperbolic cosecant • angle Phase angle • asec, asech Inverse secant and inverse hyperbolic secant • asin, asinh Inverse sine and inverse hyperbolic sine • atan, atanh Inverse tangent and inverse hyperbolic tangent • atan2 Four-quadrant inverse tangent • ceil Round toward infinity • complex Construct complex data from real and imag. component • conj Complex conjugate • cos, cosh Cosine and hyperbolic cosine • cot, coth Cotangent and hyperbolic cotangent • csc, csch Cosecant and hyperbolic c osecant • exp Exponential

17. FixRound towards zero FloorRound towards minus infinity GcdGreatest common divisor ImagImaginary part of a complex number LcmLeast common multiple LogNatural logarithm Log2Base 2 logarithm and dissect floating-point numbersinto exponent and mantissa Log10Common (base 10) logarithm ModModulus (signed remainder after division) NchoosekBinomial coefficient or all combinations RealReal part of complex number RemRemainder after division RoundRound to nearest integer

18. RealReal part of complex number RemRemainder after division RoundRound to nearest integer sec, sechSecant and hyperbolic secant SignSignum function sin, sinhSine and hyperbolic sine SqrtSquare root tan, tanhTangent and hyperbolic tangent

19. Creating GUIs Graphical User Interface Creation External Interfaces MATLAB Interface to Java Serial Port I/O Graphics Plotting and Data Visualization

20. Variables Managing and the Workspace ClearRemove items from the workspace DispDisplay text or array LengthLength of vector LoadRetrieve variables from disk MemoryHelp for memory limitations MlockPrevent M-file clearing MunlockAllow M-file clearing OpenvarOpen workspace variable in Array Editor, for graphical editing PackConsolidate workspace memory SaveSave workspace variables on disk SaveasSave figure or model using specified format sizeArray dimensions who, whosList the variables in the workspace

22. 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.

23. 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

24. Inteligentné metódy modelovania a riadenia • FUZZY TOOLBOX • (Knižnica programov "Fuzzy množiny" • - fuzzy logika, fuzzy pravidla • - neurčité modely • - metódy fuzifikácie • - metódy defuzifikácie • - fuzzy regulátory • - fuzzy rozhodovanie • 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

25. Products with Major UpgradesRelease 12 includes major version upgrades to many products, highlighted in the following sections of these • Release Notes: • MATLAB 6.0 • MATLAB Runtime Server 6.0 • MATLAB Compiler 2.1 • Simulink 4.0 • Stateflow 4.0 • Stateflow Coder 4.0 • Real-Time Workshop 4.0 • Real-Time Workshop Ada Coder 4.0 • Real-Time Windows Target 2.0 • Communications Blockset 2.0 • Communications Toolbox 2.0 • Control System Toolbox 5.0

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

27. Platform 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 Millenium, and Windows NT Compaq Alpha Linux SGI Sun Solaris 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.

28. 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.

29. 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

30. Development 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 Interfaces - GUI-building tools and how to write callback routines.

31. 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).

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

33. New Products (Since Release 11.0) • The following products are being introduced with Release 12: • Communications Blockset 2.0 • Filter Design Toolbox 2.0 • Instrument Control Toolbox 1.0 • Simulink Performance Tools 4.0 • Real-Time Workshop Embedded Coder

34. In addition, Release 12 includes a number of products that have been introduced since Release 11.0 (released in Web-downloadable form and/or on the Release 11.1 CD): • CDMA Reference Blockset 1.0.2 • Datafeed Toolbox 1.2 • Dials & Gauges Blockset 1.1 • Financial Time Series Toolbox 1.0 • Financial Derivatives Toolbox 1.0 • Motorola DSP Developer's Kit 1.1 • GARCH Toolbox 1.0 • Requirements Management Interface 1.0.1 • xPC Target and xPC Target Embedded Option 1.1

35. MATLAB® provides many graphics 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 Property Editor. • Basic Plotting - describes how to plot vector and matrix data in 2-D representations. • Formatting Graphs - describes how to customize the format of a plot to help explain your data. This section includes information about adding labels, titles, and annotations to a plot. • Creating Specialized Plots - describes how to create bar graphs, histograms, and contour plots. • Basic Printing and Exporting - describes frequently used ways to print or export a MATLAB figure, and explains the basic printing and exporting interfaces. • Handle Graphics® Objects - introduces MATLAB's graphics objects and properties.

36. Figure Properties - discusses the features that are implemented with figure properties. • Axes Properties - discusses the features that are implemented with axes properties. • Related Information • These other collections provide additional information about plotting. • 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. • Creating GUIs describes how to include menus, push buttons, text boxes, and other user interface objects in MATLAB applications.