Freemat V3.6 Documentation

Total Page:16

File Type:pdf, Size:1020Kb

Freemat V3.6 Documentation FreeMat v3.6 Documentation Samit Basu November 16, 2008 2 Contents 1 Introduction and Getting Started 5 1.1 INSTALL Installing FreeMat . 5 1.1.1 General Instructions . 5 1.1.2 Linux . 5 1.1.3 Windows . 6 1.1.4 Mac OS X . 6 1.1.5 Source Code . 6 2 Variables and Arrays 7 2.1 CELL Cell Array Definitions . 7 2.1.1 Usage . 7 2.1.2 Examples . 7 2.2 Function Handles . 8 2.2.1 Usage . 8 2.3 GLOBAL Global Variables . 8 2.3.1 Usage . 8 2.3.2 Example . 9 2.4 INDEXING Indexing Expressions . 9 2.4.1 Usage . 9 2.4.2 Array Indexing . 9 2.4.3 Cell Indexing . 13 2.4.4 Structure Indexing . 14 2.4.5 Complex Indexing . 16 2.5 MATRIX Matrix Definitions . 17 2.5.1 Usage . 17 2.5.2 Examples . 17 2.6 PERSISTENT Persistent Variables . 19 2.6.1 Usage . 19 2.6.2 Example . 19 2.7 STRING String Arrays . 20 2.7.1 Usage . 20 2.8 STRUCT Structure Array Constructor . 22 2.8.1 Usage . 22 2.8.2 Example . 22 3 4 CONTENTS 3 Functions and Scripts 25 3.1 ANONYMOUS Anonymous Functions . 25 3.1.1 Usage . 25 3.1.2 Examples . 25 3.2 FUNCTION Function Declarations . 26 3.2.1 Usage . 26 3.2.2 Examples . 28 3.3 KEYWORDS Function Keywords . 30 3.3.1 Usage . 30 3.3.2 Example . 31 3.4 NARGIN Number of Input Arguments . 32 3.4.1 Usage . 32 3.4.2 Example . 32 3.5 NARGOUT Number of Output Arguments . 33 3.5.1 Usage . 33 3.5.2 Example . 33 3.6 SCRIPT Script Files . 34 3.6.1 Usage . 34 3.6.2 Example . 35 3.7 SPECIAL Special Calling Syntax . 35 3.7.1 Usage . 35 3.7.2 Example . 36 3.8 VARARGIN Variable Input Arguments . 36 3.8.1 Usage . 36 3.8.2 Example . 36 3.9 VARARGOUT Variable Output Arguments . 37 3.9.1 Usage . 37 3.9.2 Example . 37 4 Mathematical Operators 39 4.1 COLON Index Generation Operator . 39 4.1.1 Usage . 39 4.1.2 Function Internals . 39 4.1.3 Examples . 41 4.2 COMPARISONOPS Array Comparison Operators . 42 4.2.1 Usage . 42 4.2.2 Examples . 42 4.3 DOTLEFTDIVIDE Element-wise Left-Division Operator . 43 4.3.1 Usage . 43 4.3.2 Function Internals . 44 4.3.3 Examples . 44 4.4 DOTPOWER Element-wise Power Operator . 46 4.4.1 Usage . 46 4.4.2 Function Internals . 46 4.4.3 Examples . 47 4.5 DOTRIGHTDIVIDE Element-wise Right-Division Operator . 48 CONTENTS 5 4.5.1 Usage . 48 4.5.2 Function Internals . 48 4.5.3 Examples . 49 4.6 DOTTIMES Element-wise Multiplication Operator . 51 4.6.1 Usage . 51 4.6.2 Function Internals . 51 4.6.3 Examples . 51 4.7 HERMITIAN Matrix Hermitian (Conjugate Transpose) Operator . 54 4.7.1 Usage . 54 4.7.2 Function Internals . 54 4.7.3 Examples . 54 4.8 LEFTDIVIDE Matrix Equation Solver/Divide Operator . 55 4.8.1 Usage . 55 4.8.2 Function Internals . 56 4.8.3 Examples . 56 4.9 LOGICALOPS Logical Array Operators . 58 4.9.1 Usage . 58 4.9.2 Examples . 59 4.10 MINUS Subtraction Operator . ..
Recommended publications
  • A Comparative Evaluation of Matlab, Octave, R, and Julia on Maya 1 Introduction
    A Comparative Evaluation of Matlab, Octave, R, and Julia on Maya Sai K. Popuri and Matthias K. Gobbert* Department of Mathematics and Statistics, University of Maryland, Baltimore County *Corresponding author: [email protected], www.umbc.edu/~gobbert Technical Report HPCF{2017{3, hpcf.umbc.edu > Publications Abstract Matlab is the most popular commercial package for numerical computations in mathematics, statistics, the sciences, engineering, and other fields. Octave is a freely available software used for numerical computing. R is a popular open source freely available software often used for statistical analysis and computing. Julia is a recent open source freely available high-level programming language with a sophisticated com- piler for high-performance numerical and statistical computing. They are all available to download on the Linux, Windows, and Mac OS X operating systems. We investigate whether the three freely available software are viable alternatives to Matlab for uses in research and teaching. We compare the results on part of the equipment of the cluster maya in the UMBC High Performance Computing Facility. The equipment has 72 nodes, each with two Intel E5-2650v2 Ivy Bridge (2.6 GHz, 20 MB cache) proces- sors with 8 cores per CPU, for a total of 16 cores per node. All nodes have 64 GB of main memory and are connected by a quad-data rate InfiniBand interconnect. The tests focused on usability lead us to conclude that Octave is the most compatible with Matlab, since it uses the same syntax and has the native capability of running m-files. R was hampered by somewhat different syntax or function names and some missing functions.
    [Show full text]
  • Ordinary Differential Equations (ODE) Using Euler's Technique And
    Mathematical Models and Methods in Modern Science Ordinary Differential Equations (ODE) using Euler’s Technique and SCILAB Programming ZULZAMRI SALLEH Applied Sciences and Advance Technology Universiti Kuala Lumpur Malaysian Institute of Marine Engineering Technology Bandar Teknologi Maritim Jalan Pantai Remis 32200 Lumut, Perak MALAYSIA [email protected] http://www.mimet.edu.my Abstract: - Mathematics is very important for the engineering and scientist but to make understand the mathematics is very difficult if without proper tools and suitable measurement. A numerical method is one of the algorithms which involved with computer programming. In this paper, Scilab is used to carter the problems related the mathematical models such as Matrices, operation with ODE’s and solving the Integration. It remains true that solutions of the vast majority of first order initial value problems cannot be found by analytical means. Therefore, it is important to be able to approach the problem in other ways. Today there are numerous methods that produce numerical approximations to solutions of differential equations. Here, we introduce the oldest and simplest such method, originated by Euler about 1768. It is called the tangent line method or the Euler method. It uses a fixed step size h and generates the approximate solution. The purpose of this paper is to show the details of implementing of Euler’s method and made comparison between modify Euler’s and exact value by integration solution, as well as solve the ODE’s use built-in functions available in Scilab programming. Key-Words: - Numerical Methods, Scilab programming, Euler methods, Ordinary Differential Equation. 1 Introduction availability of digital computers has led to a Numerical methods are techniques by which veritable explosion in the use and development of mathematical problems are formulated so that they numerical methods [1].
    [Show full text]
  • Numerical Methods for Ordinary Differential Equations
    CHAPTER 1 Numerical Methods for Ordinary Differential Equations In this chapter we discuss numerical method for ODE . We will discuss the two basic methods, Euler’s Method and Runge-Kutta Method. 1. Numerical Algorithm and Programming in Mathcad 1.1. Numerical Algorithm. If you look at dictionary, you will the following definition for algorithm, 1. a set of rules for solving a problem in a finite number of steps; 2. a sequence of steps designed for programming a computer to solve a specific problem. A numerical algorithm is a set of rules for solving a problem in finite number of steps that can be easily implemented in computer using any programming language. The following is an algorithm for compute the root of f(x) = 0; Input f, a, N and tol . Output: the approximate solution to f(x) = 0 with initial guess a or failure message. ² Step One: Set x = a ² Step Two: For i=0 to N do Step Three - Four f(x) Step Three: Compute x = x ¡ f 0(x) Step Four: If f(x) · tol return x ² Step Five return ”failure”. In analogy, a numerical algorithm is like a cook recipe that specify the input — cooking material, the output—the cooking product, and steps of carrying computation — cooking steps. In an algorithm, you will see loops (for, while), decision making statements(if, then, else(otherwise)) and return statements. ² for loop: Typically used when specific number of steps need to be carried out. You can break a for loop with return or break statement. 1 2 1. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS ² while loop: Typically used when unknown number of steps need to be carried out.
    [Show full text]
  • Getting Started with Euler
    Getting started with Euler Samuel Fux High Performance Computing Group, Scientific IT Services, ETH Zurich ETH Zürich | Scientific IT Services | HPC Group Samuel Fux | 19.02.2020 | 1 Outlook . Introduction . Accessing the cluster . Data management . Environment/LMOD modules . Using the batch system . Applications . Getting help ETH Zürich | Scientific IT Services | HPC Group Samuel Fux | 19.02.2020 | 2 Outlook . Introduction . Accessing the cluster . Data management . Environment/LMOD modules . Using the batch system . Applications . Getting help ETH Zürich | Scientific IT Services | HPC Group Samuel Fux | 19.02.2020 | 3 Intro > What is EULER? . EULER stands for . Erweiterbarer, Umweltfreundlicher, Leistungsfähiger ETH Rechner . It is the 5th central (shared) cluster of ETH . 1999–2007 Asgard ➔ decommissioned . 2004–2008 Hreidar ➔ integrated into Brutus . 2005–2008 Gonzales ➔ integrated into Brutus . 2007–2016 Brutus . 2014–2020+ Euler . It benefits from the 15 years of experience gained with those previous large clusters ETH Zürich | Scientific IT Services | HPC Group Samuel Fux | 19.02.2020 | 4 Intro > Shareholder model . Like its predecessors, Euler has been financed (for the most part) by its users . So far, over 100 (!) research groups from almost all departments of ETH have invested in Euler . These so-called “shareholders” receive a share of the cluster’s resources (processors, memory, storage) proportional to their investment . The small share of Euler financed by IT Services is open to all members of ETH . The only requirement
    [Show full text]
  • Towards a Fully Automated Extraction and Interpretation of Tabular Data Using Machine Learning
    UPTEC F 19050 Examensarbete 30 hp August 2019 Towards a fully automated extraction and interpretation of tabular data using machine learning Per Hedbrant Per Hedbrant Master Thesis in Engineering Physics Department of Engineering Sciences Uppsala University Sweden Abstract Towards a fully automated extraction and interpretation of tabular data using machine learning Per Hedbrant Teknisk- naturvetenskaplig fakultet UTH-enheten Motivation A challenge for researchers at CBCS is the ability to efficiently manage the Besöksadress: different data formats that frequently are changed. Significant amount of time is Ångströmlaboratoriet Lägerhyddsvägen 1 spent on manual pre-processing, converting from one format to another. There are Hus 4, Plan 0 currently no solutions that uses pattern recognition to locate and automatically recognise data structures in a spreadsheet. Postadress: Box 536 751 21 Uppsala Problem Definition The desired solution is to build a self-learning Software as-a-Service (SaaS) for Telefon: automated recognition and loading of data stored in arbitrary formats. The aim of 018 – 471 30 03 this study is three-folded: A) Investigate if unsupervised machine learning Telefax: methods can be used to label different types of cells in spreadsheets. B) 018 – 471 30 00 Investigate if a hypothesis-generating algorithm can be used to label different types of cells in spreadsheets. C) Advise on choices of architecture and Hemsida: technologies for the SaaS solution. http://www.teknat.uu.se/student Method A pre-processing framework is built that can read and pre-process any type of spreadsheet into a feature matrix. Different datasets are read and clustered. An investigation on the usefulness of reducing the dimensionality is also done.
    [Show full text]
  • A Case Study in Fitting Area-Proportional Euler Diagrams with Ellipses Using Eulerr
    A Case Study in Fitting Area-Proportional Euler Diagrams with Ellipses using eulerr Johan Larsson and Peter Gustafsson Department of Statistics, School of Economics and Management, Lund University, Lund, Sweden [email protected] [email protected] Abstract. Euler diagrams are common and user-friendly visualizations for set relationships. Most Euler diagrams use circles, but circles do not always yield accurate diagrams. A promising alternative is ellipses, which, in theory, enable accurate diagrams for a wider range of input. Elliptical diagrams, however, have not yet been implemented for more than three sets or three-set diagrams where there are disjoint or subset relationships. The aim of this paper is to present eulerr: a software package for elliptical Euler diagrams for, in theory, any number of sets. It fits Euler diagrams using numerical optimization and exact-area algorithms through a two-step procedure, first generating an initial layout using pairwise relationships and then finalizing this layout using all set relationships. 1 Background The Euler diagram, first described by Leonard Euler in 1802 [1], is a generalization of the popular Venn diagram. Venn and Euler diagrams both visualize set relationships by mapping areas in the diagram to relationships in the data. They differ, however, in that Venn diagrams require all intersections to be present| even if they are empty|whilst Euler diagrams do not, which means that Euler diagrams lend themselves well to be area-proportional. Euler diagrams may be fashioned out of any closed shape, and have been implemented for triangles [2], rectangles [2], ellipses [3], smooth curves [4], poly- gons [2], and circles [5, 2].
    [Show full text]
  • The Python Interpreter
    The Python interpreter Remi Lehe Lawrence Berkeley National Laboratory (LBNL) US Particle Accelerator School (USPAS) Summer Session Self-Consistent Simulations of Beam and Plasma Systems S. M. Lund, J.-L. Vay, R. Lehe & D. Winklehner Colorado State U, Ft. Collins, CO, 13-17 June, 2016 Python interpreter: Outline 1 Overview of the Python language 2 Python, numpy and matplotlib 3 Reusing code: functions, modules, classes 4 Faster computation: Forthon Overview Scientific Python Reusing code Forthon Overview of the Python programming language Interpreted language (i.e. not compiled) ! Interactive, but not optimal for computational speed Readable and non-verbose No need to declare variables Indentation is enforced Free and open-source + Large community of open-souce packages Well adapted for scientific and data analysis applications Many excellent packages, esp. numerical computation (numpy), scientific applications (scipy), plotting (matplotlib), data analysis (pandas, scikit-learn) 3 Overview Scientific Python Reusing code Forthon Interfaces to the Python language Scripting Interactive shell Code written in a file, with a Obtained by typing python or text editor (gedit, vi, emacs) (better) ipython Execution via command line Commands are typed in and (python + filename) executed one by one Convenient for exploratory work, Convenient for long-term code debugging, rapid feedback, etc... 4 Overview Scientific Python Reusing code Forthon Interfaces to the Python language IPython (a.k.a Jupyter) notebook Notebook interface, similar to Mathematica. Intermediate between scripting and interactive shell, through reusable cells Obtained by typing jupyter notebook, opens in your web browser Convenient for exploratory work, scientific analysis and reports 5 Overview Scientific Python Reusing code Forthon Overview of the Python language This lecture Reminder of the main points of the Scipy lecture notes through an example problem.
    [Show full text]
  • The Freemat Primer Page 1 of 218 Table of Contents About the Authors
    The Freemat 4.0 Primer By Gary Schafer Timothy Cyders First Edition August 2011 The Freemat Primer Page 1 of 218 Table of Contents About the Authors......................................................................................................................................5 Acknowledgements...............................................................................................................................5 User Assumptions..................................................................................................................................5 How This Book Was Put Together........................................................................................................5 Licensing...............................................................................................................................................6 Using with Freemat v4.0 Documentation .............................................................................................6 Topic 1: Working with Freemat.................................................................................................................7 Topic 1.1: The Main Screen - Ver 4.0..................................................................................................7 Topic 1.1.1: The File Browser Section...........................................................................................10 Topic 1.1.2: The History Section....................................................................................................10 Topic 1.1.3: The
    [Show full text]
  • Freemat V4.0 Documentation
    FreeMat v4.0 Documentation Samit Basu October 4, 2009 2 Contents 1 Introduction and Getting Started 39 1.1 INSTALL Installing FreeMat . 39 1.1.1 General Instructions . 39 1.1.2 Linux . 39 1.1.3 Windows . 40 1.1.4 Mac OS X . 40 1.1.5 Source Code . 40 2 Variables and Arrays 41 2.1 CELL Cell Array Definitions . 41 2.1.1 Usage . 41 2.1.2 Examples . 41 2.2 Function Handles . 42 2.2.1 Usage . 42 2.3 GLOBAL Global Variables . 42 2.3.1 Usage . 42 2.3.2 Example . 42 2.4 INDEXING Indexing Expressions . 43 2.4.1 Usage . 43 2.4.2 Array Indexing . 43 2.4.3 Cell Indexing . 46 2.4.4 Structure Indexing . 47 2.4.5 Complex Indexing . 49 2.5 MATRIX Matrix Definitions . 49 2.5.1 Usage . 49 2.5.2 Examples . 49 2.6 PERSISTENT Persistent Variables . 51 2.6.1 Usage . 51 2.6.2 Example . 51 2.7 STRUCT Structure Array Constructor . 51 2.7.1 Usage . 51 2.7.2 Example . 52 3 4 CONTENTS 3 Functions and Scripts 55 3.1 ANONYMOUS Anonymous Functions . 55 3.1.1 Usage . 55 3.1.2 Examples . 55 3.2 FUNCTION Function Declarations . 56 3.2.1 Usage . 56 3.2.2 Examples . 57 3.3 KEYWORDS Function Keywords . 60 3.3.1 Usage . 60 3.3.2 Example . 60 3.4 NARGIN Number of Input Arguments . 61 3.4.1 Usage . 61 3.4.2 Example . 61 3.5 NARGOUT Number of Output Arguments .
    [Show full text]
  • MATHCAD's PROGRAM FUNCTION and APPLICATION in TEACHING of MATH
    MATHCAD'S PROGRAM FUNCTION and APPLICATION IN TEACHING OF MATH DE TING WU Depart of Math Morehouse College Atlanta, GA.30314, USA [email protected] 1. Introduction 1.1 About Mathcad Mathcad is one of popular computer algebra system (math software) in the world. Like other CAS's, it has the capabilities to perform algebraic operations, calculus operations and draw graph of 2 or 3 dimensions. We can use it to get numerical, symbolic and graphic solution of math problem. Besides above common capabilities, it has some feature: its words processor function is better than other CAS. This feature makes it look like a scientifical words processor and it easy to create a woksheet. Following current trend to add program function to math software, it added program function to itself , started in Mathcad V7. This improvement makes its function more complete and more powerful. 1.2 Role of program function in teac hing of Math. Without doubt, math softwares and technology are helpful aide in teaching of Math. They are effecting the teaching of Math profoundly and it can be expected the emerging newer technologies will penetrate and reconfigure the teaching of Math. The program function is a new function of math software. It is natural we want to know whether or not it is useful in teaching of Math? I think: although for most problems we meet in teaching of Math it is enough to use computation ability, in certain cases the program function becomes necessary and very helpful. For example, for Numerical Analysis the program function is very useful but for Abstract Algebra it is less necessary.
    [Show full text]
  • Programming for Computations – Python
    15 Svein Linge · Hans Petter Langtangen Programming for Computations – Python Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick Texts in Computational 15 Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick More information about this series at http://www.springer.com/series/5151 Svein Linge Hans Petter Langtangen Programming for Computations – Python A Gentle Introduction to Numerical Simulations with Python Svein Linge Hans Petter Langtangen Department of Process, Energy and Simula Research Laboratory Environmental Technology Lysaker, Norway University College of Southeast Norway Porsgrunn, Norway On leave from: Department of Informatics University of Oslo Oslo, Norway ISSN 1611-0994 Texts in Computational Science and Engineering ISBN 978-3-319-32427-2 ISBN 978-3-319-32428-9 (eBook) DOI 10.1007/978-3-319-32428-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2016945368 Mathematic Subject Classification (2010): 26-01, 34A05, 34A30, 34A34, 39-01, 40-01, 65D15, 65D25, 65D30, 68-01, 68N01, 68N19, 68N30, 70-01, 92D25, 97-04, 97U50 © The Editor(s) (if applicable) and the Author(s) 2016 This book is published open access. Open Access This book is distributed under the terms of the Creative Commons Attribution-Non- Commercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, a link is provided to the Creative Commons license and any changes made are indicated.
    [Show full text]
  • Sageko Matlabin Korvaaja?
    Mikko Moilanen Sageko Matlabin korvaaja? Opinnäytetyö Tietotekniikan koulutusohjelma Elokuu 2012 KUVAILULEHTI Opinnäytetyön päivämäärä 4.9.2012 Tekijä(t) Koulutusohjelma ja suuntautuminen Mikko Moilanen Tietotekniikan koulutusohjelma Nimeke Sageko Matlabin korvaaja? Tiivistelmä Tässä insinöörityössä tutkitaan voiko Sagella korvata Matlabin korkeakouluopinnoissa matemaattisen analyysin opiskelutyövälineenä. Tutkimuksen perusteella arvioidaan, että onko Sagella tulevaisuutta ohjelmistona, varmistetaan Sagen toimivuus matemaattisessa analyysissa ja selvitetään, että miten helppoa yksittäisen käyttäjän on ottaa Sage käyttöön ja miten oppilaitos saa Sagen käyttöönsä. Matlab on kiistaton standardiohjelmisto matemaattisessa mallinnuksessa ja analyysissa. Sen peruslisenssimaksut ja Toolboxien lisenssimaksut ovat kuitenkin kohonneet ehkä juuri tästä syystä korkeiksi ja mikään ei estä lisenssimaksujen jatkuvaa kohoamista. Näin ollen halvemman vaihtoehdon löytäminen Matlabille korkeakouluopintojen työvälineenä on mielenkiintoinen ja hyödyllinen tutkimuskohde. Eräs mielenkiintoinen vaihtoehto Matlabille on Sage, koska se kokoaa lähes 100 matemaattista laskentaohjelmistoa yhden ja saman käyttöliittymän alle. Sage on myös suunniteltu toimimaan palvelin/asiakas -mallilla WWW-selaimella, mistä voi olla erityistä hyötyä laajoissa asennuksissa ylläpidon ja luokkahuoneidan varaamisen kannalta . Tutkimuksen tuloksena havaittiin Sagen olevan niin erilainen ja epäyhteensopiva Matlabin kanssa, että Matlab ei ole suoraan korvattavissa Sagella. Sen sijaan todettiin,
    [Show full text]