DOCSLIB.ORG

Intermediate Python: Using Numpy, Scipy and Matplotlib

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Intermediate Python: Using Numpy, Scipy and Matplotlib Intermediate Python: Using NumPy, SciPy and Matplotlib Lesson 19 – Odds and Ends 1 Lambda Operator • Python also has a simple way of defining a one-line function. • These are created using the Lambda operator. • The code must be a single, valid Python statement. • Looping, if-then constructs, and other control statements cannot be use in Lambdas. >>> bar = lambda x,y: x + y >>> bar(2,3) 5 >>> cube_volume = lambda l, w, h: l*w*h >>> cube_volume(2, 4.5, 7) 63.0 2 Physical Constants • The scipy.constants module contains many physical constants! 3 Physical Constants R molar gas constant c speed of light in vacuum alpha fine-structure constant mu_0 the magnetic constant N_A Avogadro constant the electric constant (vacuum epsilon_0 k Boltzmann constant permittivity), sigma Stefan-Boltzmann constant h the Planck constant hbar the Planck constant divided by 2. Wien Wien displacement law constant Rydberg Rydberg constant G Newtonian constant of gravitation m_e electron mass g standard acceleration of gravity m_p proton mass m_n neutron mass e elementary charge Always verify that they are in the correct units!!! 4 Examples >>> import scipy.constants as sc >>> sc.R >>> sc.c 8.3144621 299792458.0 >>> sc.N_A >>> sc.h 6.02214129e+23 6.62606957e-34 >>> sc.k >>> sc.G 1.3806488e-23 6.67384e-11 >>> sc.sigma >>> sc.g 9.80665 5.670373e-08 >>> sc.e >>> sc.m_e 1.602176565e-19 9.10938291e-31 5 Constants Database • There are more constants in the constants database. • These are accecces using dictionary keys. • The methods available are: – value() # the value of the constant – unit() # the units of the contant – precision() # the precision of the constant • To see a list of available constants, go to: http://docs.scipy.org/doc/scipy/reference/constants.html# module-scipy.constants 6 Constants Database Example >>> sc.value('Rydberg constant') 10973731.568539 >>> sc.unit('Rydberg constant') 'm^-1' >>> sc.precision('Rydberg constant') 5.011968778030033e-12 7 Metric Prefixes >>> sc.yotta 1e+24 >>> sc.mega 1000000.0 >>> sc.nano 1e-09 8 Conversions • There are conversion factors to MKS units. >>> sc.gram 0.001 >>> sc.gallon >>> sc.lb 0.0037854117839999997 0.45359236999999997 >>> sc.mph >>> sc.mile 0.44703999999999994 1609.3439999999998 >>> sc.knot >>> sc.foot 0.5144444444444445 0.30479999999999996 >>> sc.atm >>> sc.erg 101325.0 1e-07 >>> sc.psi >>> sc.Btu 6894.757293168361 1055.05585262 9 Temperature Conversions zero_Celsius zero of Celsius scale in Kelvin degree_Fahrenheit one degree Fahrenheit difference in Kelvin C2K(C) Convert Celsius to Kelvin K2C(K) Convert Kelvin to Celsius F2C(F) Convert Fahrenheit to Celsius C2F(C) Convert Celsius to Fahrenheit F2K(F) Convert Fahrenheit to Kelvin K2F(K) Convert Kelvin to Fahrenheit 10 Special Functions • The scipy.special module contains many special functions, such as Bessel functions, Legendre Polynomials, etc. 11 Interpolation • The scipy.interpolate module contains functions for interpolating 1D and 2D data. 12 scipy.interpolate.interp1d() • This function takes an array of x values and an array of y values, and then returns a function. By passing an x value to the function the function returns the interpolated y value. • It uses linear interpolation as the default, but also can use other forms of interpolation including cubic splines or higher-order splines. 13 interp1d() Example from scipy.interpolate import interp1d import numpy as np import matplotlib.pyplot as plt x = np.arange(0, 10) y = np.array([3.0, -4.0, -2.0, -1.0, 3.0, 6.0, 10.0, 8.0, 12.0, 20.0]) f = interp1d(x, y, kind = 'cubic') Cubic Spline xint = 3.5 yint = f(xint) Interpolated Point plt.plot(x, y, 'o', c = 'b') plt.plot(xint, yint, 's', c = 'r') plt.show() 14 Results Interpolated Point 15 interp1d() Example from scipy.interpolate import interp1d import numpy as np import matplotlib.pyplot as plt x = np.arange(0, 10) y = np.array([3.0, -4.0, -2.0, -1.0, 3.0, 6.0, 10.0, 8.0, 12.0, 20.0]) f = interp1d(x, y, kind = 'cubic') Cubic Spline xint = np.arange(0, 9.01, 0.01) yint = f(xint) Interpolated Points plt.plot(x, y, 'o', c = 'b') plt.plot(xint, yint, '-r') plt.show() 16 Results Interpolated Curve 17 scipy.interpolate.interp2d() • This function works similarly to interp1d(), but can interpolate values on a 2D grid. • The input values can be either regularly spaced, or irregularly spaced. 18 Numerical Differentiation • scipy.misc.derivative(f, x, dx=dx, n = n) is a function to find the nth derivative of a function f. • The function can either be a lambda or a user defined function. 19 Derivatives Example from scipy.misc import derivative import numpy as np f = lambda x : np.exp(-x)*np.sin(x) import matplotlib.pyplot as plt …… x = np.arange(0,10, 0.1) fig, ax = plt.subplots(3,1,sharex = True) first = derivative(f,x,dx=1,n=1) ax[0].plot(x,f(x)) second = derivative(f,x,dx=1,n=2) ax[0].set_ylabel(r'$f(x)$') ax[1].plot(x,first) ax[1].set_ylabel(r'$f\/\prime(x)$') ax[2].plot(x,second) ax[2].set_ylabel(r'$f\/\prime\prime(x)$') ax[2].set_xlabel(r'$x$') plt.show() 20 Derivatives Results 21 Numerical Integration • scipy.integrate is a module that contains functions for integration. • Integration can be performed on a function defined by a lambda. • Integration can also be performed given an array of y values. 22 Numerical Integration • scipy.integrate is a module that contains functions for integration. • Integration can be performed on a function defined by a lambda. • Integration can also be performed given an array of y values. 23 Integration Example • Suppose we want to evaluate the integral. 2 ex sin xdx 0 24 Integration Example >>> import scipy.integrate as integrate >>> import numpy as np >>> f = lambda x : np.exp(-x)*np.sin(x) >>> I = integrate.quad(f, 0, 2*np.pi) >>> print(I) (0.49906627863414593, 6.023731631928322e-15) Value of integral. Estimate of absolute error. 25 Can Even Do Infinite Bounds • Suppose we want to evaluate the integral. ex sin xdx 0 26 Infinite Integration Example >>> I = integrate.quad(f, 0, float('inf')) >>> print(I) (0.5000000000000002, 1.4875911858955308e-08) Note: The exact value of the integral is 0.5. 27 Double and Triple Integrals • There are also functions for doing double and triple integrals. 28 Integration of Array Data • If you only have an array of y values, without knowing the functional dependence of x and y, you can still integrate. • For this, use the scipy.integrate.simps() function, which uses Simpson’s rule. • You can either specify the x values, or just give the x increment, dx. 29 Example of Cumulative Integration import scipy.integrate as integrate import numpy as np x = np.arange(0, 20, 2) y = np.array([0, 3, 5, 2, 8, 9, 0, -3, 4, 9], dtype = float) I = integrate.simps(y,x) print(I) • Note that I is an array with one less element than y. 30 .
Load more

Recommended publications
  • 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.
    [Show full text]
  • How to Access Python for Doing Scientific Computing
    How to access Python for doing scientific computing1 Hans Petter Langtangen1,2 1Center for Biomedical Computing, Simula Research Laboratory 2Department of Informatics, University of Oslo Mar 23, 2015 A comprehensive eco system for scientific computing with Python used to be quite a challenge to install on a computer, especially for newcomers. This problem is more or less solved today. There are several options for getting easy access to Python and the most important packages for scientific computations, so the biggest issue for a newcomer is to make a proper choice. An overview of the possibilities together with my own recommendations appears next. Contents 1 Required software2 2 Installing software on your laptop: Mac OS X and Windows3 3 Anaconda and Spyder4 3.1 Spyder on Mac............................4 3.2 Installation of additional packages.................5 3.3 Installing SciTools on Mac......................5 3.4 Installing SciTools on Windows...................5 4 VMWare Fusion virtual machine5 4.1 Installing Ubuntu...........................6 4.2 Installing software on Ubuntu....................7 4.3 File sharing..............................7 5 Dual boot on Windows8 6 Vagrant virtual machine9 1The material in this document is taken from a chapter in the book A Primer on Scientific Programming with Python, 4th edition, by the same author, published by Springer, 2014. 7 How to write and run a Python program9 7.1 The need for a text editor......................9 7.2 Spyder................................. 10 7.3 Text editors.............................. 10 7.4 Terminal windows.......................... 11 7.5 Using a plain text editor and a terminal window......... 12 8 The SageMathCloud and Wakari web services 12 8.1 Basic intro to SageMathCloud...................
    [Show full text]
  • An Introduction to Numpy and Scipy
    An introduction to Numpy and Scipy Table of contents Table of contents ............................................................................................................................ 1 Overview ......................................................................................................................................... 2 Installation ...................................................................................................................................... 2 Other resources .............................................................................................................................. 2 Importing the NumPy module ........................................................................................................ 2 Arrays .............................................................................................................................................. 3 Other ways to create arrays............................................................................................................ 7 Array mathematics .......................................................................................................................... 8 Array iteration ............................................................................................................................... 10 Basic array operations .................................................................................................................. 11 Comparison operators and value testing ....................................................................................
    [Show full text]
  • Homework 2 an Introduction to Convolutional Neural Networks
    Homework 2 An Introduction to Convolutional Neural Networks 11-785: Introduction to Deep Learning (Spring 2019) OUT: February 17, 2019 DUE: March 10, 2019, 11:59 PM Start Here • Collaboration policy: { You are expected to comply with the University Policy on Academic Integrity and Plagiarism. { You are allowed to talk with / work with other students on homework assignments { You can share ideas but not code, you must submit your own code. All submitted code will be compared against all code submitted this semester and in previous semesters using MOSS. • Overview: { Part 1: All of the problems in Part 1 will be graded on Autolab. You can download the starter code from Autolab as well. This assignment has 100 points total. { Part 2: This section of the homework is an open ended competition hosted on Kaggle.com, a popular service for hosting predictive modeling and data analytic competitions. All of the details for completing Part 2 can be found on the competition page. • Submission: { Part 1: The compressed handout folder hosted on Autolab contains four python files, layers.py, cnn.py, mlp.py and local grader.py, and some folders data, autograde and weights. File layers.py contains common layers in convolutional neural networks. File cnn.py contains outline class of two convolutional neural networks. File mlp.py contains a basic MLP network. File local grader.py is foryou to evaluate your own code before submitting online. Folders contain some data to be used for section 1.3 and 1.4 of this homework. Make sure that all class and function definitions originally specified (as well as class attributes and methods) in the two files layers.py and cnn.py are fully implemented to the specification provided in this write-up.
    [Show full text]
  • User Guide Release 1.18.4
    NumPy User Guide Release 1.18.4 Written by the NumPy community May 24, 2020 CONTENTS 1 Setting up 3 2 Quickstart tutorial 9 3 NumPy basics 33 4 Miscellaneous 97 5 NumPy for Matlab users 103 6 Building from source 111 7 Using NumPy C-API 115 Python Module Index 163 Index 165 i ii NumPy User Guide, Release 1.18.4 This guide is intended as an introductory overview of NumPy and explains how to install and make use of the most important features of NumPy. For detailed reference documentation of the functions and classes contained in the package, see the reference. CONTENTS 1 NumPy User Guide, Release 1.18.4 2 CONTENTS CHAPTER ONE SETTING UP 1.1 What is NumPy? NumPy is the fundamental package for scientific computing in Python. It is a Python library that provides a multidi- mensional array object, various derived objects (such as masked arrays and matrices), and an assortment of routines for fast operations on arrays, including mathematical, logical, shape manipulation, sorting, selecting, I/O, discrete Fourier transforms, basic linear algebra, basic statistical operations, random simulation and much more. At the core of the NumPy package, is the ndarray object. This encapsulates n-dimensional arrays of homogeneous data types, with many operations being performed in compiled code for performance. There are several important differences between NumPy arrays and the standard Python sequences: • NumPy arrays have a fixed size at creation, unlike Python lists (which can grow dynamically). Changing the size of an ndarray will create a new array and delete the original.
    [Show full text]
  • Introduction to Python in HPC
    Introduction to Python in HPC Omar Padron National Center for Supercomputing Applications University of Illinois at Urbana Champaign [email protected] Outline • What is Python? • Why Python for HPC? • Python on Blue Waters • How to load it • Available Modules • Known Limitations • Where to Get More information 2 What is Python? • Modern programming language with a succinct and intuitive syntax • Has grown over the years to offer an extensive software ecosystem • Interprets JIT-compiled byte-code, but can take full advantage of AOT-compiled code • using python libraries with AOT code (numpy, scipy) • interfacing seamlessly with AOT code (CPython API) • generating native modules with/from AOT code (cython) 3 Why Python for HPC? • When you want to maximize productivity (not necessarily performance) • Mature language with large user base • Huge collection of freely available software libraries • High Performance Computing • Engineering, Optimization, Differential Equations • Scientific Datasets, Analysis, Visualization • General-purpose computing • web apps, GUIs, databases, and tons more • Python combines the best of both JIT and AOT code. • Write performance critical loops and kernels in C/FORTRAN • Write high level logic and “boiler plate” in Python 4 Python on Blue Waters • Blue Waters Python Software Stack (bw-python) • Over 60 python modules supporting HPC applications • Implements the Scipy Stack Specification (http://www.scipy.org/stackspec.html) • Provides extensions for parallel programming (mpi4py, pycuda) and scientific data IO (h5py, pycuda) • Numerical routines linked from ACML • Built specifically for running jobs on the compute nodes module swap PrgEnv-cray PrgEnv-gnu module load bw-python python ! Python 2.7.5 (default, Jun 2 2014, 02:41:21) [GCC 4.8.2 20131016 (Cray Inc.)] on Blue Waters Type "help", "copyright", "credits" or "license" for more information.
    [Show full text]
  • Sage 9.4 Reference Manual: Coercion Release 9.4
    Sage 9.4 Reference Manual: Coercion Release 9.4 The Sage Development Team Aug 24, 2021 CONTENTS 1 Preliminaries 1 1.1 What is coercion all about?.......................................1 1.2 Parents and Elements...........................................2 1.3 Maps between Parents..........................................3 2 Basic Arithmetic Rules 5 3 How to Implement 9 3.1 Methods to implement..........................................9 3.2 Example................................................. 10 3.3 Provided Methods............................................ 13 4 Discovering new parents 15 5 Modules 17 5.1 The coercion model........................................... 17 5.2 Coerce actions.............................................. 36 5.3 Coerce maps............................................... 39 5.4 Coercion via construction functors.................................... 40 5.5 Group, ring, etc. actions on objects................................... 68 5.6 Containers for storing coercion data................................... 71 5.7 Exceptions raised by the coercion model................................ 78 6 Indices and Tables 79 Python Module Index 81 Index 83 i ii CHAPTER ONE PRELIMINARIES 1.1 What is coercion all about? The primary goal of coercion is to be able to transparently do arithmetic, comparisons, etc. between elements of distinct sets. As a concrete example, when one writes 1 + 1=2 one wants to perform arithmetic on the operands as rational numbers, despite the left being an integer. This makes sense given the obvious
    [Show full text]
  • 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).
    [Show full text]
  • MATLAB Commands in Numerical Python (Numpy) 1 Vidar Bronken Gundersen /Mathesaurus.Sf.Net
    MATLAB commands in numerical Python (NumPy) 1 Vidar Bronken Gundersen /mathesaurus.sf.net MATLAB commands in numerical Python (NumPy) Copyright c Vidar Bronken Gundersen Permission is granted to copy, distribute and/or modify this document as long as the above attribution is kept and the resulting work is distributed under a license identical to this one. The idea of this document (and the corresponding xml instance) is to provide a quick reference for switching from matlab to an open-source environment, such as Python, Scilab, Octave and Gnuplot, or R for numeric processing and data visualisation. Where Octave and Scilab commands are omitted, expect Matlab compatibility, and similarly where non given use the generic command. Time-stamp: --T:: vidar 1 Help Desc. matlab/Octave Python R Browse help interactively doc help() help.start() Octave: help -i % browse with Info Help on using help help help or doc doc help help() Help for a function help plot help(plot) or ?plot help(plot) or ?plot Help for a toolbox/library package help splines or doc splines help(pylab) help(package=’splines’) Demonstration examples demo demo() Example using a function example(plot) 1.1 Searching available documentation Desc. matlab/Octave Python R Search help files lookfor plot help.search(’plot’) Find objects by partial name apropos(’plot’) List available packages help help(); modules [Numeric] library() Locate functions which plot help(plot) find(plot) List available methods for a function methods(plot) 1.2 Using interactively Desc. matlab/Octave Python R Start session Octave: octave -q ipython -pylab Rgui Auto completion Octave: TAB or M-? TAB Run code from file foo(.m) execfile(’foo.py’) or run foo.py source(’foo.R’) Command history Octave: history hist -n history() Save command history diary on [..] diary off savehistory(file=".Rhistory") End session exit or quit CTRL-D q(save=’no’) CTRL-Z # windows sys.exit() 2 Operators Desc.
    [Show full text]
  • Scipy and Numpy
    www.it-ebooks.info SciPy and NumPy Eli Bressert Beijing • Cambridge • Farnham • Koln¨ • Sebastopol • Tokyo www.it-ebooks.info 9781449305468_text.pdf 1 10/31/12 2:35 PM SciPy and NumPy by Eli Bressert Copyright © 2013 Eli Bressert. All rights reserved. Printed in the United States of America. Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472. O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are also available for most titles (http://my.safaribooksonline.com). For more information, contact our corporate/institutional sales department: (800) 998-9938 or [email protected]. Interior Designer: David Futato Project Manager: Paul C. Anagnostopoulos Cover Designer: Randy Comer Copyeditor: MaryEllen N. Oliver Editors: Rachel Roumeliotis, Proofreader: Richard Camp Meghan Blanchette Illustrators: EliBressert,LaurelMuller Production Editor: Holly Bauer November 2012: First edition Revision History for the First Edition: 2012-10-31 First release See http://oreilly.com/catalog/errata.csp?isbn=0636920020219 for release details. Nutshell Handbook, the Nutshell Handbook logo, and the O’Reilly logo are registered trademarks of O’Reilly Media, Inc. SciPy and NumPy, the image of a three-spined stickleback, and related trade dress are trademarks of O’Reilly Media, Inc. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and O’Reilly Media, Inc., was aware of a trademark claim, the designations have been printed in caps or initial caps. While every precaution has been taken in the preparation of this book, the publisher and authors assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.
    [Show full text]
  • Scikit-Learn
    Scikit-Learn i Scikit-Learn About the Tutorial Scikit-learn (Sklearn) is the most useful and robust library for machine learning in Python. It provides a selection of efficient tools for machine learning and statistical modeling including classification, regression, clustering and dimensionality reduction via a consistence interface in Python. This library, which is largely written in Python, is built upon NumPy, SciPy and Matplotlib. Audience This tutorial will be useful for graduates, postgraduates, and research students who either have an interest in this Machine Learning subject or have this subject as a part of their curriculum. The reader can be a beginner or an advanced learner. Prerequisites The reader must have basic knowledge about Machine Learning. He/she should also be aware about Python, NumPy, Scipy, Matplotlib. If you are new to any of these concepts, we recommend you take up tutorials concerning these topics, before you dig further into this tutorial. Copyright & Disclaimer Copyright 2019 by Tutorials Point (I) Pvt. Ltd. All the content and graphics published in this e-book are the property of Tutorials Point (I) Pvt. Ltd. The user of this e-book is prohibited to reuse, retain, copy, distribute or republish any contents or a part of contents of this e-book in any manner without written consent of the publisher. We strive to update the contents of our website and tutorials as timely and as precisely as possible, however, the contents may contain inaccuracies or errors. Tutorials Point (I) Pvt. Ltd. provides no guarantee regarding the accuracy, timeliness or completeness of our website or its contents including this tutorial.
    [Show full text]
  • Python: Computing with Cython
    Lab 20 Python: Computing with Cython Lab Objective: Use Cython to avoid the overhead of some parts of the Python language. For small computations, Python is reasonably fast for computing the solutions to problems. However, for large computations, Python quickly becomes unable to solve anything in a reasonable amount of time. You might ask, why use Python at all if it's so slow? The answer lies in the amount of time to write the code. Low- level languages like C are renowned for their speed. These languages are compiled to machine code that can run directly on a computer's processor. When a C program adds two numbers together, we have to be very specific about what two numbers are added together. The computer can understand basic data types such as integers, floats, and arrays. Python represents each of these data types using its own objects. These are objects are generally fast and we don't notice much the incurred overhead. Over large calculations, the overhead of these objects is compounded and can slow things down tremendously. In these cases, we need to be able to access the machine- level data types for integers, floats, and strings for maximum efficiency. A common way of doing this is to write slower portions of the code in a lower-level, compiled language. This is usually accomplished by writing a C-extension for Python. A C-extension is a module that can be used like a Python module, but is written in C. This enables performance critical code to be executed as fast as possible in a Python environment.
    [Show full text]