Interdisciplinary Qualifying Project Visualization for Finite Element Method Education
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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. -
Alternatives to Python: Julia
Crossing Language Barriers with , SciPy, and thon Steven G. Johnson MIT Applied Mathemacs Where I’m coming from… [ google “Steven Johnson MIT” ] Computaonal soPware you may know… … mainly C/C++ libraries & soPware … Nanophotonics … oPen with Python interfaces … (& Matlab & Scheme & …) jdj.mit.edu/nlopt www.w.org jdj.mit.edu/meep erf(z) (and erfc, erfi, …) in SciPy 0.12+ & other EM simulators… jdj.mit.edu/book Confession: I’ve used Python’s internal C API more than I’ve coded in Python… A new programming language? Viral Shah Jeff Bezanson Alan Edelman julialang.org Stefan Karpinski [begun 2009, “0.1” in 2013, ~20k commits] [ 17+ developers with 100+ commits ] [ usual fate of all First reacBon: You’re doomed. new languages ] … subsequently: … probably doomed … sll might be doomed but, in the meanBme, I’m having fun with it… … and it solves a real problem with technical compuBng in high-level languages. The “Two-Language” Problem Want a high-level language that you can work with interacBvely = easy development, prototyping, exploraon ⇒ dynamically typed language Plenty to choose from: Python, Matlab / Octave, R, Scilab, … (& some of us even like Scheme / Guile) Historically, can’t write performance-criBcal code (“inner loops”) in these languages… have to switch to C/Fortran/… (stac). [ e.g. SciPy git master is ~70% C/C++/Fortran] Workable, but Python → Python+C = a huge jump in complexity. Just vectorize your code? = rely on mature external libraries, operang on large blocks of data, for performance-criBcal code Good advice! But… • Someone has to write those libraries. • Eventually that person may be you. -
Data Visualization in Python
Data visualization in python Day 2 A variety of packages and philosophies • (today) matplotlib: http://matplotlib.org/ – Gallery: http://matplotlib.org/gallery.html – Frequently used commands: http://matplotlib.org/api/pyplot_summary.html • Seaborn: http://stanford.edu/~mwaskom/software/seaborn/ • ggplot: – R version: http://docs.ggplot2.org/current/ – Python port: http://ggplot.yhathq.com/ • Bokeh (live plots in your browser) – http://bokeh.pydata.org/en/latest/ Biocomputing Bootcamp 2017 Matplotlib • Gallery: http://matplotlib.org/gallery.html • Top commands: http://matplotlib.org/api/pyplot_summary.html • Provides "pylab" API, a mimic of matlab • Many different graph types and options, some obscure Biocomputing Bootcamp 2017 Matplotlib • Resulting plots represented by python objects, from entire figure down to individual points/lines. • Large API allows any aspect to be tweaked • Lengthy coding sometimes required to make a plot "just so" Biocomputing Bootcamp 2017 Seaborn • https://stanford.edu/~mwaskom/software/seaborn/ • Implements more complex plot types – Joint points, clustergrams, fitted linear models • Uses matplotlib "under the hood" Biocomputing Bootcamp 2017 Others • ggplot: – (Original) R version: http://docs.ggplot2.org/current/ – A recent python port: http://ggplot.yhathq.com/ – Elegant syntax for compactly specifying plots – but, they can be hard to tweak – We'll discuss this on the R side tomorrow, both the basics of both work similarly. • Bokeh – Live, clickable plots in your browser! – http://bokeh.pydata.org/en/latest/ -
Ipython: a System for Interactive Scientific
P YTHON: B ATTERIES I NCLUDED IPython: A System for Interactive Scientific Computing Python offers basic facilities for interactive work and a comprehensive library on top of which more sophisticated systems can be built. The IPython project provides an enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation. he backbone of scientific computing is All these systems offer an interactive command mostly a collection of high-perfor- line in which code can be run immediately, without mance code written in Fortran, C, and having to go through the traditional edit/com- C++ that typically runs in batch mode pile/execute cycle. This flexible style matches well onT large systems, clusters, and supercomputers. the spirit of computing in a scientific context, in However, over the past decade, high-level environ- which determining what computations must be ments that integrate easy-to-use interpreted lan- performed next often requires significant work. An guages, comprehensive numerical libraries, and interactive environment lets scientists look at data, visualization facilities have become extremely popu- test new ideas, combine algorithmic approaches, lar in this field. As hardware becomes faster, the crit- and evaluate their outcome directly. This process ical bottleneck in scientific computing isn’t always the might lead to a final result, or it might clarify how computer’s processing time; the scientist’s time is also they need to build a more static, large-scale pro- a consideration. For this reason, systems that allow duction code. rapid algorithmic exploration, data analysis, and vi- As this article shows, Python (www.python.org) sualization have become a staple of daily scientific is an excellent tool for such a workflow.1 The work. -
Writing Mathematical Expressions with Latex
APPENDIX A Writing Mathematical Expressions with LaTeX LaTeX is extensively used in Python. In this appendix there are many examples that can be useful to represent LaTeX expressions inside Python implementations. This same information can be found at the link http://matplotlib.org/users/mathtext.html. With matplotlib You can enter the LaTeX expression directly as an argument of various functions that can accept it. For example, the title() function that draws a chart title. import matplotlib.pyplot as plt %matplotlib inline plt.title(r'$\alpha > \beta$') With IPython Notebook in a Markdown Cell You can enter the LaTeX expression between two '$$'. $$c = \sqrt{a^2 + b^2}$$ c= a+22b 537 © Fabio Nelli 2018 F. Nelli, Python Data Analytics, https://doi.org/10.1007/978-1-4842-3913-1 APPENDIX A WRITING MaTHEmaTICaL EXPRESSIONS wITH LaTEX With IPython Notebook in a Python 2 Cell You can enter the LaTeX expression within the Math() function. from IPython.display import display, Math, Latex display(Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx')) Subscripts and Superscripts To make subscripts and superscripts, use the ‘_’ and ‘^’ symbols: r'$\alpha_i > \beta_i$' abii> This could be very useful when you have to write summations: r'$\sum_{i=0}^\infty x_i$' ¥ åxi i=0 Fractions, Binomials, and Stacked Numbers Fractions, binomials, and stacked numbers can be created with the \frac{}{}, \binom{}{}, and \stackrel{}{} commands, respectively: r'$\frac{3}{4} \binom{3}{4} \stackrel{3}{4}$' 3 3 æ3 ö4 ç ÷ 4 è 4ø Fractions can be arbitrarily nested: 1 5 - x 4 538 APPENDIX A WRITING MaTHEmaTICaL EXPRESSIONS wITH LaTEX Note that special care needs to be taken to place parentheses and brackets around fractions. -
Ipython Documentation Release 0.10.2
IPython Documentation Release 0.10.2 The IPython Development Team April 09, 2011 CONTENTS 1 Introduction 1 1.1 Overview............................................1 1.2 Enhanced interactive Python shell...............................1 1.3 Interactive parallel computing.................................3 2 Installation 5 2.1 Overview............................................5 2.2 Quickstart...........................................5 2.3 Installing IPython itself....................................6 2.4 Basic optional dependencies..................................7 2.5 Dependencies for IPython.kernel (parallel computing)....................8 2.6 Dependencies for IPython.frontend (the IPython GUI).................... 10 3 Using IPython for interactive work 11 3.1 Quick IPython tutorial..................................... 11 3.2 IPython reference........................................ 17 3.3 IPython as a system shell.................................... 42 3.4 IPython extension API..................................... 47 4 Using IPython for parallel computing 53 4.1 Overview and getting started.................................. 53 4.2 Starting the IPython controller and engines.......................... 57 4.3 IPython’s multiengine interface................................ 64 4.4 The IPython task interface................................... 78 4.5 Using MPI with IPython.................................... 80 4.6 Security details of IPython................................... 83 4.7 IPython/Vision Beam Pattern Demo............................. -
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. -
Easybuild Documentation Release 20210907.0
EasyBuild Documentation Release 20210907.0 Ghent University Tue, 07 Sep 2021 08:55:41 Contents 1 What is EasyBuild? 3 2 Concepts and terminology 5 2.1 EasyBuild framework..........................................5 2.2 Easyblocks................................................6 2.3 Toolchains................................................7 2.3.1 system toolchain.......................................7 2.3.2 dummy toolchain (DEPRECATED) ..............................7 2.3.3 Common toolchains.......................................7 2.4 Easyconfig files..............................................7 2.5 Extensions................................................8 3 Typical workflow example: building and installing WRF9 3.1 Searching for available easyconfigs files.................................9 3.2 Getting an overview of planned installations.............................. 10 3.3 Installing a software stack........................................ 11 4 Getting started 13 4.1 Installing EasyBuild........................................... 13 4.1.1 Requirements.......................................... 14 4.1.2 Using pip to Install EasyBuild................................. 14 4.1.3 Installing EasyBuild with EasyBuild.............................. 17 4.1.4 Dependencies.......................................... 19 4.1.5 Sources............................................. 21 4.1.6 In case of installation issues. .................................. 22 4.2 Configuring EasyBuild.......................................... 22 4.2.1 Supported configuration -
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. -
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 ................................