Programming in Matlab/Octave Or Python Getting Started with Matlab
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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. -
Using Mathematica As a Teaching Tool in the Undergraduate Economics Curriculum
USING MATHEMATICA AS A TEACHING TOOL IN THE UNDERGRADUATE ECONOMICS CURRICULUM Gary Hodgin* Abstract In recent years, the quantitative skills required of economics students have increased significantly. Students often experience difficulty in making the transition from their mathematics courses to the use of mathematics in their economics courses. Symbolic computation programs are mathematical tools that can potentially smooth this transition. This paper illustrates a few ways in which one symbolic computation program, Mathematica, has been used in the undergraduate economics curriculum. I. Introduction The undergraduate curriculum in economics has become increasingly quantitative. An economics major typically includes college algebra, statistics, and some form of calculus in its degree requirements.1 In addition, mathematical economics and econometrics are now standard courses in many undergraduate programs. Moreover, this quantitative emphasis generally extends to other courses across the economics curriculum, particularly the intermediate theory and managerial economics courses. For example, approximately 90 percent of the intermediate microeconomics instructors included in von Allmen and Brower's survey (1998, 279) use calculus in their courses. Although one might question whether too much emphasis is placed on quantitative skills, there appears to be consensus among economics professors that mathematics is an important ingredient in undergraduate economic education. Over the past three years, I have used a symbolic computation program entitled Mathematica in two of my intermediate microeconomics and three of my managerial economics courses. My observations in these courses suggests that some students experience difficulty in making the transition from their courses in mathematics to their use of mathematics in economics. By smoothing this transition, symbolic computation programs can assist students in learning economics. -
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............................. -
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 -
Intro to Jupyter Notebook
Evan Williamson University of Idaho Library 20160302 Introducing Jupyter Notebook for Python and R Three questions: http://goo.gl/forms/uYRvebcJkD Try Jupyter https://try.jupyter.org/ Install Jupyter ● Get Python (suggested: Anaconda, Py3, 64bit, https://www.continuum.io/downloads ) ● Manually install (if necessary), http://jupyter.readthedocs.org/en/latest/install.html pip3 install jupyter Install R for Jupyter ● Get R, https://cran.cnr.berkeley.edu/ (suggested: RStudio, https://www.rstudio.com/products/RStudio/#Desktop ) ● Open R console and follow: http://irkernel.github.io/installation/ Start a Notebook ● Open terminal/command prompt jupyter notebook ● Notebook will open at http://127.0.0.1:8888 ● Exit by closing the browser, then typing Ctrl+C in the terminal window Create Slides ● Open terminal/command prompt jupyter nbconvert slideshow.ipynb --to slides --post serve ● Note: “post serve” locally serves the file so you can give a presentation in your browser. If you only want to convert, leave this option off. The resulting HTML file must be served to render correctly. Slides use Reveal.js, http://lab.hakim.se/revealjs/ Reference ● Jupyter docs, http://jupyter.readthedocs.org/en/latest/index.html ● IPython docs, http://ipython.readthedocs.org/en/stable/index.html ● List of kernels, https://github.com/ipython/ipython/wiki/IPythonkernelsforotherlanguages ● A gallery of interesting IPython Notebooks, https://github.com/ipython/ipython/wiki/AgalleryofinterestingIPythonNotebooks ● Markdown basics, -
Principal Components Analysis Tutorial 4 Yang
Principal Components Analysis Tutorial 4 Yang 1 Objectives Understand the principles of principal components analysis (PCA) Know the principal components analysis method Study the PCA function of sickit-learn.decomposition Process the data set by the PCA of sickit-learn Learn to apply PCA in a reality example 2 Principal Components Analysis Method: ̶ Subtract the mean ̶ Calculate the covariance matrix ̶ Calculate the eigenvectors and eigenvalues of the covariance matrix ̶ Choosing components and forming a feature vector ̶ Deriving the new data set 3 Example 1 x y 퐷푎푡푎 = 2.5 2.4 0.5 0.7 2.2 2.9 1.9 2.2 3.1 3.0 2.3 2.7 2 1.6 1 1.1 1.5 1.6 1.1 0.9 4 sklearn.decomposition.PCA It uses the LAPACK implementation of the full SVD or a randomized truncated SVD by the method of Halko et al. 2009, depending on the shape of the input data and the number of components to extract. It can also use the scipy.sparse.linalg ARPACK implementation of the truncated SVD. Notice that this class does not upport sparse input. 5 Parameters of PCA n_components: Number of components to keep. svd_solver: if n_components is not set: n_components == auto: default, if the input data is larger than 500x500 min (n_samples, n_features), default=None and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient ‘randomized’ method is enabled. if n_components == ‘mle’ and svd_solver == ‘full’, Otherwise the exact full SVD is computed and Minka’s MLE is used to guess the dimension optionally truncated afterwards. -
Sage Tutorial (Pdf)
Sage Tutorial Release 9.4 The Sage Development Team Aug 24, 2021 CONTENTS 1 Introduction 3 1.1 Installation................................................4 1.2 Ways to Use Sage.............................................4 1.3 Longterm Goals for Sage.........................................5 2 A Guided Tour 7 2.1 Assignment, Equality, and Arithmetic..................................7 2.2 Getting Help...............................................9 2.3 Functions, Indentation, and Counting.................................. 10 2.4 Basic Algebra and Calculus....................................... 14 2.5 Plotting.................................................. 20 2.6 Some Common Issues with Functions.................................. 23 2.7 Basic Rings................................................ 26 2.8 Linear Algebra.............................................. 28 2.9 Polynomials............................................... 32 2.10 Parents, Conversion and Coercion.................................... 36 2.11 Finite Groups, Abelian Groups...................................... 42 2.12 Number Theory............................................. 43 2.13 Some More Advanced Mathematics................................... 46 3 The Interactive Shell 55 3.1 Your Sage Session............................................ 55 3.2 Logging Input and Output........................................ 57 3.3 Paste Ignores Prompts.......................................... 58 3.4 Timing Commands............................................ 58 3.5 Other IPython -
Pandas: Powerful Python Data Analysis Toolkit Release 0.25.3
pandas: powerful Python data analysis toolkit Release 0.25.3 Wes McKinney& PyData Development Team Nov 02, 2019 CONTENTS i ii pandas: powerful Python data analysis toolkit, Release 0.25.3 Date: Nov 02, 2019 Version: 0.25.3 Download documentation: PDF Version | Zipped HTML Useful links: Binary Installers | Source Repository | Issues & Ideas | Q&A Support | Mailing List pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language. See the overview for more detail about whats in the library. CONTENTS 1 pandas: powerful Python data analysis toolkit, Release 0.25.3 2 CONTENTS CHAPTER ONE WHATS NEW IN 0.25.2 (OCTOBER 15, 2019) These are the changes in pandas 0.25.2. See release for a full changelog including other versions of pandas. Note: Pandas 0.25.2 adds compatibility for Python 3.8 (GH28147). 1.1 Bug fixes 1.1.1 Indexing • Fix regression in DataFrame.reindex() not following the limit argument (GH28631). • Fix regression in RangeIndex.get_indexer() for decreasing RangeIndex where target values may be improperly identified as missing/present (GH28678) 1.1.2 I/O • Fix regression in notebook display where <th> tags were missing for DataFrame.index values (GH28204). • Regression in to_csv() where writing a Series or DataFrame indexed by an IntervalIndex would incorrectly raise a TypeError (GH28210) • Fix to_csv() with ExtensionArray with list-like values (GH28840). 1.1.3 Groupby/resample/rolling • Bug incorrectly raising an IndexError when passing a list of quantiles to pandas.core.groupby. DataFrameGroupBy.quantile() (GH28113).