Introduction to the GNU Octave
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Introduction to IDL®
Introduction to IDL® Revised for Print March, 2016 ©2016 Exelis Visual Information Solutions, Inc., a subsidiary of Harris Corporation. All rights reserved. ENVI and IDL are registered trademarks of Harris Corporation. All other marks are the property of their respective owners. This document is not subject to the controls of the International Traffic in Arms Regulations (ITAR) or the Export Administration Regulations (EAR). Contents 1 Introduction To IDL 5 1.1 Introduction . .5 1.1.1 What is ENVI? . .5 1.1.2 ENVI + IDL, ENVI, and IDL . .6 1.1.3 ENVI Resources . .6 1.1.4 Contacting Harris Geospatial Solutions . .6 1.1.5 Tutorials . .6 1.1.6 Training . .7 1.1.7 ENVI Support . .7 1.1.8 Contacting Technical Support . .7 1.1.9 Website . .7 1.1.10 IDL Newsgroup . .7 2 About This Course 9 2.1 Manual Organization . .9 2.1.1 Programming Style . .9 2.2 The Course Files . 11 2.2.1 Installing the Course Files . 11 2.3 Starting IDL . 11 2.3.1 Windows . 11 2.3.2 Max OS X . 11 2.3.3 Linux . 12 3 A Tour of IDL 13 3.1 Overview . 13 3.2 Scalars and Arrays . 13 3.3 Reading Data from Files . 15 3.4 Line Plots . 15 3.5 Surface Plots . 17 3.6 Contour Plots . 18 3.7 Displaying Images . 19 3.8 Exercises . 21 3.9 References . 21 4 IDL Basics 23 4.1 IDL Directory Structure . 23 4.2 The IDL Workbench . 24 4.3 Exploring the IDL Workbench . -
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. -
Sage 9.4 Reference Manual: Finite Rings Release 9.4
Sage 9.4 Reference Manual: Finite Rings Release 9.4 The Sage Development Team Aug 24, 2021 CONTENTS 1 Finite Rings 1 1.1 Ring Z=nZ of integers modulo n ....................................1 1.2 Elements of Z=nZ ............................................ 15 2 Finite Fields 39 2.1 Finite Fields............................................... 39 2.2 Base Classes for Finite Fields...................................... 47 2.3 Base class for finite field elements.................................... 61 2.4 Homset for Finite Fields......................................... 69 2.5 Finite field morphisms.......................................... 71 3 Prime Fields 77 3.1 Finite Prime Fields............................................ 77 3.2 Finite field morphisms for prime fields................................. 79 4 Finite Fields Using Pari 81 4.1 Finite fields implemented via PARI’s FFELT type............................ 81 4.2 Finite field elements implemented via PARI’s FFELT type....................... 83 5 Finite Fields Using Givaro 89 5.1 Givaro Finite Field............................................ 89 5.2 Givaro Field Elements.......................................... 94 5.3 Finite field morphisms using Givaro................................... 102 6 Finite Fields of Characteristic 2 Using NTL 105 6.1 Finite Fields of Characteristic 2..................................... 105 6.2 Finite Fields of characteristic 2...................................... 107 7 Miscellaneous 113 7.1 Finite residue fields........................................... -
A Fast Dynamic Language for Technical Computing
Julia A Fast Dynamic Language for Technical Computing Created by: Jeff Bezanson, Stefan Karpinski, Viral B. Shah & Alan Edelman A Fractured Community Technical work gets done in many different languages ‣ C, C++, R, Matlab, Python, Java, Perl, Fortran, ... Different optimal choices for different tasks ‣ statistics ➞ R ‣ linear algebra ➞ Matlab ‣ string processing ➞ Perl ‣ general programming ➞ Python, Java ‣ performance, control ➞ C, C++, Fortran Larger projects commonly use a mixture of 2, 3, 4, ... One Language We are not trying to replace any of these ‣ C, C++, R, Matlab, Python, Java, Perl, Fortran, ... What we are trying to do: ‣ allow developing complete technical projects in a single language without sacrificing productivity or performance This does not mean not using components in other languages! ‣ Julia uses C, C++ and Fortran libraries extensively “Because We Are Greedy.” “We want a language that’s open source, with a liberal license. We want the speed of C with the dynamism of Ruby. We want a language that’s homoiconic, with true macros like Lisp, but with obvious, familiar mathematical notation like Matlab. We want something as usable for general programming as Python, as easy for statistics as R, as natural for string processing as Perl, as powerful for linear algebra as Matlab, as good at gluing programs together as the shell. Something that is dirt simple to learn, yet keeps the most serious hackers happy.” Collapsing Dichotomies Many of these are just a matter of design and focus ‣ stats vs. linear algebra vs. strings vs. -
Introduction to Ggplot2
Introduction to ggplot2 Dawn Koffman Office of Population Research Princeton University January 2014 1 Part 1: Concepts and Terminology 2 R Package: ggplot2 Used to produce statistical graphics, author = Hadley Wickham "attempt to take the good things about base and lattice graphics and improve on them with a strong, underlying model " based on The Grammar of Graphics by Leland Wilkinson, 2005 "... describes the meaning of what we do when we construct statistical graphics ... More than a taxonomy ... Computational system based on the underlying mathematics of representing statistical functions of data." - does not limit developer to a set of pre-specified graphics adds some concepts to grammar which allow it to work well with R 3 qplot() ggplot2 provides two ways to produce plot objects: qplot() # quick plot – not covered in this workshop uses some concepts of The Grammar of Graphics, but doesn’t provide full capability and designed to be very similar to plot() and simple to use may make it easy to produce basic graphs but may delay understanding philosophy of ggplot2 ggplot() # grammar of graphics plot – focus of this workshop provides fuller implementation of The Grammar of Graphics may have steeper learning curve but allows much more flexibility when building graphs 4 Grammar Defines Components of Graphics data: in ggplot2, data must be stored as an R data frame coordinate system: describes 2-D space that data is projected onto - for example, Cartesian coordinates, polar coordinates, map projections, ... geoms: describe type of geometric objects that represent data - for example, points, lines, polygons, ... aesthetics: describe visual characteristics that represent data - for example, position, size, color, shape, transparency, fill scales: for each aesthetic, describe how visual characteristic is converted to display values - for example, log scales, color scales, size scales, shape scales, .. -
Introduction to GNU Octave
Introduction to GNU Octave Hubert Selhofer, revised by Marcel Oliver updated to current Octave version by Thomas L. Scofield 2008/08/16 line 1 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 8 6 4 2 -8 -6 0 -4 -2 -2 0 -4 2 4 -6 6 8 -8 Contents 1 Basics 2 1.1 What is Octave? ........................... 2 1.2 Help! . 2 1.3 Input conventions . 3 1.4 Variables and standard operations . 3 2 Vector and matrix operations 4 2.1 Vectors . 4 2.2 Matrices . 4 1 2.3 Basic matrix arithmetic . 5 2.4 Element-wise operations . 5 2.5 Indexing and slicing . 6 2.6 Solving linear systems of equations . 7 2.7 Inverses, decompositions, eigenvalues . 7 2.8 Testing for zero elements . 8 3 Control structures 8 3.1 Functions . 8 3.2 Global variables . 9 3.3 Loops . 9 3.4 Branching . 9 3.5 Functions of functions . 10 3.6 Efficiency considerations . 10 3.7 Input and output . 11 4 Graphics 11 4.1 2D graphics . 11 4.2 3D graphics: . 12 4.3 Commands for 2D and 3D graphics . 13 5 Exercises 13 5.1 Linear algebra . 13 5.2 Timing . 14 5.3 Stability functions of BDF-integrators . 14 5.4 3D plot . 15 5.5 Hilbert matrix . 15 5.6 Least square fit of a straight line . 16 5.7 Trapezoidal rule . 16 1 Basics 1.1 What is Octave? Octave is an interactive programming language specifically suited for vectoriz- able numerical calculations. -
A Tutorial on Reliable Numerical Computation
A tutorial on reliable numerical computation Paul Zimmermann Dagstuhl seminar 17481, Schloß Dagstuhl, November 2017 The IEEE 754 standard First version in 1985, first revision in 2008, another revision for 2018. Standard formats: binary32, binary64, binary128, decimal64, decimal128 Standard rounding modes (attributes): roundTowardPositive, roundTowardNegative, roundTowardZero, roundTiesToEven p Correct rounding: required for +; −; ×; ÷; ·, recommended for other mathematical functions (sin; exp; log; :::) 2 Different kinds of arithmetic in various languages fixed precision arbitrary precision real double (C) GNU MPFR (C) numbers RDF (Sage) RealField(p) (Sage) MPFI (C) Boost Interval (C++) RealIntervalField(p) (Sage) real INTLAB (Matlab, Octave) RealBallField(p) (Sage) intervals RIF (Sage) libieeep1788 (C++) RBF (Sage) Octave Interval (Octave) libieeep1788 is developed by Marco Nehmeier GNU Octave Interval is developed by Oliver Heimlich 3 An example from Siegfried Rump Reference: S.M. Rump. Gleitkommaarithmetik auf dem Prüfstand [Wie werden verifiziert(e) numerische Lösungen berechnet?]. Jahresbericht der Deutschen Mathematiker-Vereinigung, 118(3):179–226, 2016. a p(a; b) = 21b2 − 2a2 + 55b4 − 10a2b2 + 2b Evaluate p at a = 77617, b = 33096. 4 Rump’s polynomial in the C language #include <stdio.h> TYPE p (TYPE a, TYPE b) { TYPE a2 = a * a; TYPE b2 = b * b; return 21.0*b2 - 2.0*a2 + 55*b2*b2 - 10*a2*b2 + a/(2.0*b); } int main() { printf ("%.16Le\n", (long double) p (77617.0, 33096.0)); } 5 Rump’s polynomial in the C language: results $ gcc -DTYPE=float rump.c && ./a.out -4.3870930862080000e+12 $ gcc -DTYPE=double rump.c && ./a.out 1.1726039400531787e+00 $ gcc -DTYPE="long double" rump.c && ./a.out 1.1726039400531786e+00 $ gcc -DTYPE=__float128 rump.c && ./a.out -8.2739605994682137e-01 6 The MPFR library A reference implementation of IEEE 754 in (binary) arbitrary precision in the C language. -
01 Introduction Lab.Pdf
AN INTRODUCTION TO R DEEPAYAN SARKAR Introduction and examples What is R?. R provides an environment in which you can perform statistical analysis and produce graphics. It is actually a complete programming language, although that is only marginally described in this book. |Peter Dalgaard, \Introductory Statistics with R", 2002 R can be viewed as a programming language that happens to come with a large library of pre-defined functions that can be used to perform various tasks. A major focus of these pre-defined functions is statistical data analysis, and these allow R to be used purely as a toolbox for standard statistical techniques. However, some knowledge of R programming is essential to use it well at any level. For advanced users in particular, the main appeal of R (as opposed to other data analysis software) is as a programming environment suited to data analysis. Our goal will be to learn R as a statistics toolbox, but with a fairly strong emphasis on its programming language aspects. In this tutorial, we will do some elementary statistics, learn to use the documentation system, and learn about common data structures and programming features in R. Some follow-up tutorials are available for self-study at http://www.isid.ac.in/~deepayan/R-tutorials/. For more resources, see the R Project homepage http://www.r-project.org, which links to various manuals and other user-contributed documentation. A list of books related to R is available at http://www.r-project.org/doc/bib/R-jabref.html. An excellent introductory book is Peter Dalgaard, \Introductory Statistics with R", Springer (2002). -
Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology Polina Lemenkova
Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology Polina Lemenkova To cite this version: Polina Lemenkova. Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology. International Journal of Environmental Trends (IJENT), 2019, 3 (1), pp.39 - 59. hal-02163671 HAL Id: hal-02163671 https://hal.archives-ouvertes.fr/hal-02163671 Submitted on 3 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License International Journal of Environmental Trends (IJENT) 2019: 3 (1),39-59 ISSN: 2602-4160 Research Article REGRESSION MODELS BY GRETL AND R STATISTICAL PACKAGES FOR DATA ANALYSIS IN MARINE GEOLOGY Polina Lemenkova 1* 1 ORCID ID number: 0000-0002-5759-1089. Ocean University of China, College of Marine Geo-sciences. 238 Songling Rd., 266100, Qingdao, Shandong, P. R. C. Tel.: +86-1768-554-1605. Abstract Received 3 May 2018 Gretl and R statistical libraries enables to perform data analysis using various algorithms, modules and functions. The case study of this research consists in geospatial analysis of Accepted the Mariana Trench, a hadal trench located in the Pacific Ocean. -
Gretl User's Guide
Gretl User’s Guide Gnu Regression, Econometrics and Time-series Allin Cottrell Department of Economics Wake Forest university Riccardo “Jack” Lucchetti Dipartimento di Economia Università di Ancona November, 2005 Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation (see http://www.gnu.org/licenses/fdl.html). Contents 1 Introduction 1 1.1 Features at a glance ......................................... 1 1.2 Acknowledgements ......................................... 1 1.3 Installing the programs ....................................... 2 2 Getting started 4 2.1 Let’s run a regression ........................................ 4 2.2 Estimation output .......................................... 6 2.3 The main window menus ...................................... 7 2.4 The gretl toolbar ........................................... 10 3 Modes of working 12 3.1 Command scripts ........................................... 12 3.2 Saving script objects ......................................... 13 3.3 The gretl console ........................................... 14 3.4 The Session concept ......................................... 14 4 Data files 17 4.1 Native format ............................................. 17 4.2 Other data file formats ....................................... 17 4.3 Binary databases ........................................... 17 4.4 Creating a data file from scratch ................................ -
A Quick Guide to Gnuplot
A Quick Guide to Gnuplot Andrea Mignone Physics Department, University of Torino AA 2020-2021 What is Gnuplot ? • Gnuplot is a free, command-driven, interactive, function and data plotting program, providing a relatively simple environment to make simple 2D plots (e.g. f(x) or f(x,y)); • It is available for all platforms, including Linux, Mac and Windows (http://www.gnuplot.info) • To start gnuplot from the terminal, simply type > gnuplot • To produce a simple plot, e.g. f(x) = sin(x) and f(x) = cos(x)^2 gnuplot> plot sin(x) gnuplot> replot (cos(x))**2 # Add another plot • By default, gnuplot assumes that the independent, or "dummy", variable for the plot command is "x” (or “t” in parametric mode). Mathematical Functions • In general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC may be plotted. The precedence of operators is determined by the specifications of the C programming language. • Gnuplot supports the same operators of the C programming language, except that most operators accept integer, real, and complex arguments. • Exponentiation is done through the ** operator (as in FORTRAN) Using set/unset • The set/unset commands can be used to controls many features, including axis range and type, title, fonts, etc… • Here are some examples: Command Description set xrange[0:2*pi] Limit the x-axis range from 0 to 2*pi, set ylabel “f(x)” Sets the label on the y-axis (same as “set xlabel”) set title “My Plot” Sets the plot title set log y Set logarithmic scale on the y-axis (same as “set log x”) unset log y Disable log scale on the y-axis set key bottom left Position the legend in the bottom left part of the plot set xlabel font ",18" Change font size for the x-axis label (same as “set ylabel”) set tic font ",18" Change the major (labelled) tics font size on all axes. -
Python Data Plotting and Visualisation Extravaganza 1 Introduction
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by The Python Papers Anthology The Python Papers Monograph, Vol. 1 (2009) 1 Available online at http://ojs.pythonpapers.org/index.php/tppm Python Data Plotting and Visualisation Extravaganza Guy K. Kloss Computer Science Institute of Information & Mathematical Sciences Massey University at Albany, Auckland, New Zealand [email protected] This paper tries to dive into certain aspects of graphical visualisation of data. Specically it focuses on the plotting of (multi-dimensional) data us- ing 2D and 3D tools, which can update plots at run-time of an application producing or acquiring new or updated data during its run time. Other visual- isation tools for example for graph visualisation, post computation rendering and interactive visual data exploration are intentionally left out. Keywords: Linear regression; vector eld; ane transformation; NumPy. 1 Introduction Many applications produce data. Data by itself is often not too helpful. To generate knowledge out of data, a user usually has to digest the information contained within the data. Many people have the tendency to extract patterns from information much more easily when the data is visualised. So data that can be visualised in some way can be much more accessible for the purpose of understanding. This paper focuses on the aspect of data plotting for these purposes. Data stored in some more or less structured form can be analysed in multiple ways. One aspect of this is post-analysis, which can often be organised in an interactive exploration fashion. One may for example import the data into a spreadsheet or otherwise suitable software tool which allows to present the data in various ways.