An Introduction to Python Programming with Numpy, Scipy and Matplotlib/Pylab
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Sagemath and Sagemathcloud
Viviane Pons Ma^ıtrede conf´erence,Universit´eParis-Sud Orsay [email protected] { @PyViv SageMath and SageMathCloud Introduction SageMath SageMath is a free open source mathematics software I Created in 2005 by William Stein. I http://www.sagemath.org/ I Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 2 / 7 SageMath Source and language I the main language of Sage is python (but there are many other source languages: cython, C, C++, fortran) I the source is distributed under the GPL licence. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 3 / 7 SageMath Sage and libraries One of the original purpose of Sage was to put together the many existent open source mathematics software programs: Atlas, GAP, GMP, Linbox, Maxima, MPFR, PARI/GP, NetworkX, NTL, Numpy/Scipy, Singular, Symmetrica,... Sage is all-inclusive: it installs all those libraries and gives you a common python-based interface to work on them. On top of it is the python / cython Sage library it-self. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 4 / 7 SageMath Sage and libraries I You can use a library explicitly: sage: n = gap(20062006) sage: type(n) <c l a s s 'sage. interfaces .gap.GapElement'> sage: n.Factors() [ 2, 17, 59, 73, 137 ] I But also, many of Sage computation are done through those libraries without necessarily telling you: sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]]) sage : G . g a p () Group( [ (3,4), (1,2,3)(4,5) ] ) Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 5 / 7 SageMath Development model Development model I Sage is developed by researchers for researchers: the original philosophy is to develop what you need for your research and share it with the community. -
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. -
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. -
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/ -
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. -
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. -
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 Politecnica delle Marche December, 2008 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 I Running the program 4 2 Getting started 5 2.1 Let’s run a regression ........................................ 5 2.2 Estimation output .......................................... 7 2.3 The main window menus ...................................... 8 2.4 Keyboard shortcuts ......................................... 11 2.5 The gretl toolbar ........................................... 11 3 Modes of working 13 3.1 Command scripts ........................................... 13 3.2 Saving script objects ......................................... 15 3.3 The gretl console ........................................... 15 3.4 The Session concept ......................................... 16 4 Data files 19 4.1 Native format ............................................. 19 4.2 Other data file formats ....................................... 19 4.3 Binary databases .......................................... -
Automated Likelihood Based Inference for Stochastic Volatility Models H
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Knowledge at Singapore Management University Singapore Management University Institutional Knowledge at Singapore Management University Research Collection School Of Economics School of Economics 11-2009 Automated Likelihood Based Inference for Stochastic Volatility Models H. Skaug Jun YU Singapore Management University, [email protected] Follow this and additional works at: https://ink.library.smu.edu.sg/soe_research Part of the Econometrics Commons Citation Skaug, H. and YU, Jun. Automated Likelihood Based Inference for Stochastic Volatility Models. (2009). 1-28. Research Collection School Of Economics. Available at: https://ink.library.smu.edu.sg/soe_research/1151 This Working Paper is brought to you for free and open access by the School of Economics at Institutional Knowledge at Singapore Management University. It has been accepted for inclusion in Research Collection School Of Economics by an authorized administrator of Institutional Knowledge at Singapore Management University. For more information, please email [email protected]. Automated Likelihood Based Inference for Stochastic Volatility Models Hans J. SKAUG , Jun YU November 2009 Paper No. 15-2009 ANY OPINIONS EXPRESSED ARE THOSE OF THE AUTHOR(S) AND NOT NECESSARILY THOSE OF THE SCHOOL OF ECONOMICS, SMU Automated Likelihood Based Inference for Stochastic Volatility Models¤ Hans J. Skaug,y Jun Yuz October 7, 2008 Abstract: In this paper the Laplace approximation is used to perform classical and Bayesian analyses of univariate and multivariate stochastic volatility (SV) models. We show that imple- mentation of the Laplace approximation is greatly simpli¯ed by the use of a numerical technique known as automatic di®erentiation (AD). -
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 -
How Maple Compares to Mathematica
How Maple™ Compares to Mathematica® A Cybernet Group Company How Maple™ Compares to Mathematica® Choosing between Maple™ and Mathematica® ? On the surface, they appear to be very similar products. However, in the pages that follow you’ll see numerous technical comparisons that show that Maple is much easier to use, has superior symbolic technology, and gives you better performance. These product differences are very important, but perhaps just as important are the differences between companies. At Maplesoft™, we believe that given great tools, people can do great things. We see it as our job to give you the best tools possible, by maintaining relationships with the research community, hiring talented people, leveraging the best available technology even if we didn’t write it ourselves, and listening to our customers. Here are some key differences to keep in mind: • Maplesoft has a philosophy of openness and community which permeates everything we do. Unlike Mathematica, Maple’s mathematical engine has always been developed by both talented company employees and by experts in research labs around the world. This collaborative approach allows Maplesoft to offer cutting-edge mathematical algorithms solidly integrated into the most natural user interface available. This openness is also apparent in many other ways, such as an eagerness to form partnerships with other organizations, an adherence to international standards, connectivity to other software tools, and the visibility of the vast majority of Maple’s source code. • Maplesoft offers a solution for all your academic needs, including advanced tools for mathematics, engineering modeling, distance learning, and testing and assessment. By contrast, Wolfram Research has nothing to offer for automated testing and assessment, an area of vital importance to academic life. -
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). -
Using MATLAB
MATLAB® The Language of Technical Computing Computation Visualization Programming Using MATLAB Version 6 How to Contact The MathWorks: www.mathworks.com Web comp.soft-sys.matlab Newsgroup [email protected] Technical support [email protected] Product enhancement suggestions [email protected] Bug reports [email protected] Documentation error reports [email protected] Order status, license renewals, passcodes [email protected] Sales, pricing, and general information 508-647-7000 Phone 508-647-7001 Fax The MathWorks, Inc. Mail 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Using MATLAB COPYRIGHT 1984 - 2001 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro- duced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by or for the federal government of the United States. By accepting delivery of the Program, the government hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part 252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain to the government’s use and disclosure of the Program and Documentation, and shall supersede any conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to MathWorks.