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IPython Interactive Computing and Visualization Cookbook

Name: IPython Interactive Computing and Visualization Cookbook
Author: Cyrille Rossant
ISBN: 9781783284818

by Cyrille Rossant

September 2014

Intermediate to advanced

512 pages

12h 39m

English

Packt Publishing

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IPython Interactive Computing and Visualization Cookbook
Table of Contents
IPython Interactive Computing and Visualization Cookbook
Credits
About the Author
About the Reviewers
www.PacktPub.com
Support files, eBooks, discount offers, and moreWhy Subscribe?Free Access for Packt account holders
Preface
What this book is
What this book covers
Part 1 – Advanced High-Performance Interactive ComputingPart 2 – Standard Methods in Data Science and Applied Mathematics
What you need for this book
Installing PythonGitHub repositories

Who this book is for
Conventions
Reader feedback
Customer support
Downloading the example codeDownloading the color imagesErrataPiracyQuestions
1. A Tour of Interactive Computing with IPython
IntroductionWhat is IPython?A brief historical retrospective on Python as a scientific environmentWhat's new in IPython 2.0?Roadmap for IPython 3.0 and 4.0References
Introducing the IPython notebook
Getting readyHow to do it...There's more...See also
Getting started with exploratory data analysis in IPython
How to do it...There's more...See also
Introducing the multidimensional array in NumPy for fast array computations
How to do it...How it works...There's more...See also
Creating an IPython extension with custom magic commands
How to do it...How it works...The InteractiveShell classLoading an extensionThere's more...See also
Mastering IPython's configuration system
How to do it...How it works...ConfigurablesMagicsThere's more...See also
Creating a simple kernel for IPython
Getting readyHow to do it...How it works...There's more...
2. Best Practices in Interactive Computing
Introduction
Choosing (or not) between Python 2 and Python 3
How to do it...Main differences in Python 3 compared to Python 2Python 2 or Python 3?Supporting both Python 2 and Python 3Using 2to3Writing code that works in Python 2 and Python 3There's more...See also
Efficient interactive computing workflows with IPython
How to do it...The IPython terminalIPython and text editorThe IPython notebookIntegrated Development EnvironmentsThere's more...See also
Learning the basics of the distributed version control system Git
Getting readyHow to do it…Creating a local repositoryCloning a remote repositoryHow it works…There's more…See also
A typical workflow with Git branching
Getting readyHow to do it…StashingHow it works…There's more…See also
Ten tips for conducting reproducible interactive computing experiments
How to do it…How it works…There's more...See also
Writing high-quality Python code
How to do it...How it works...There's more...See also
Writing unit tests with nose
Getting readyHow to do it...How it works...There's more...Test coverageWorkflows with unit testingUnit testing and continuous integration
Debugging your code with IPython
How to do it...The post-mortem modeStep-by-step debuggingThere's more...GUI debuggers
3. Mastering the Notebook
IntroductionWhat is the notebook?The notebook ecosystemArchitecture of the IPython notebookConnecting multiple clients to one kernelSecurity in notebooksReferences
Teaching programming in the notebook with IPython blocks
Getting readyHow to do it...There's more...
Converting an IPython notebook to other formats with nbconvert
Getting readyHow to do it...How it works...There's more...
Adding custom controls in the notebook toolbar
How to do it...There's more...See also
Customizing the CSS style in the notebook
Getting readyHow to do it...There's more...See also
Using interactive widgets – a piano in the notebook
Getting readyHow to do it...How it works...There's more...See also
Creating a custom JavaScript widget in the notebook – a spreadsheet editor for pandas
Getting readyHow to do it...How it works...There's more...See also
Processing webcam images in real time from the notebook
Getting readyHow to do it...How it works...There's more...See also
4. Profiling and Optimization
Introduction
Evaluating the time taken by a statement in IPython
How to do it...How it works...There's more...See also
Profiling your code easily with cProfile and IPython
How to do it...How it works..."Premature optimization is the root of all evil"There's more...See also
Profiling your code line-by-line with line_profiler
Getting readyHow do to it...How it works...There's more...Tracing the step-by-step execution of a Python programSee also
Profiling the memory usage of your code with memory_profiler
Getting readyHow to do it...How it works...There's more...Using memory_profiler for standalone Python programsUsing the %memit magic command in IPythonOther toolsSee also
Understanding the internals of NumPy to avoid unnecessary array copying
Getting readyHow to do it...How it works...Why are NumPy arrays efficient?What is the difference between in-place and implicit-copy operations?Why can't some arrays be reshaped without a copy?What are NumPy broadcasting rules?There's more...See also
Using stride tricks with NumPy
Getting readyHow to do it...How it works...See also
Implementing an efficient rolling average algorithm with stride tricks
Getting readyHow to do it...See also
Making efficient array selections in NumPy
Getting readyHow to do it...How it works...There's more...
Processing huge NumPy arrays with memory mapping
How to do it...How it works...There's more...See also
Manipulating large arrays with HDF5 and PyTables
Getting readyHow to do it...How it works...There's more...See also
Manipulating large heterogeneous tables with HDF5 and PyTables
Getting readyHow to do it...How it works...There's more...See also
5. High-performance Computing
IntroductionCPython and concurrent programmingCompiler-related installation instructionsLinuxMac OS XWindowsPython 32-bitPython 64-bitDLL hellReferences
Accelerating pure Python code with Numba and just-in-time compilation
Getting readyHow to do it…How it works…There's more…See also
Accelerating array computations with Numexpr
Getting readyHow to do it…How it works...See also
Wrapping a C library in Python with ctypes
Getting readyHow to do it…How it works…There's more…
Accelerating Python code with Cython
Getting readyHow to do it…How it works…There's more…See also
Optimizing Cython code by writing less Python and more C
How to do it…How it works…There's more…See also
Releasing the GIL to take advantage of multicore processors with Cython and OpenMP
Getting readyHow to do it…How it works…See also
Writing massively parallel code for NVIDIA graphics cards (GPUs) with CUDA
Getting readyHow to do it...How it works…There's more…See also
Writing massively parallel code for heterogeneous platforms with OpenCL
Getting readyHow to do it…How it works…There's more…See also
Distributing Python code across multiple cores with IPython
How to do it…How it works…There's more…Dependent parallel tasksAlternative parallel computing solutionsReferencesSee also
Interacting with asynchronous parallel tasks in IPython
Getting readyHow to do it…How it works…There's more…See also
Parallelizing code with MPI in IPython
Getting readyHow to do it…How it works…See also
Trying the Julia language in the notebook
Getting readyHow to do it…How it works…There's more…
6. Advanced Visualization
Introduction
Making nicer matplotlib figures with prettyplotlib
Getting readyHow to do it…How it works…There's more…See also
Creating beautiful statistical plots with seaborn
Getting readyHow to do it…There's more…See also
Creating interactive web visualizations with Bokeh
Getting readyHow to do it…There's more…See also
Visualizing a NetworkX graph in the IPython notebook with D3.js
Getting readyHow to do it…There's more…See also
Converting matplotlib figures to D3.js visualizations with mpld3
Getting readyHow to do it…How it works…There's more…See also
Getting started with Vispy for high-performance interactive data visualizations
Getting readyHow to do it…How it works…There's more…Vispy for scientific visualization
7. Statistical Data Analysis
IntroductionWhat is statistical data analysis?A bit of vocabularyExploration, inference, decision, and predictionUnivariate and multivariate methodsFrequentist and Bayesian methodsParametric and nonparametric inference methods
Exploring a dataset with pandas and matplotlib
Getting readyHow to do it...There's more...
Getting started with statistical hypothesis testing – a simple z-test
Getting readyHow to do it...How it works...There's more...See also
Getting started with Bayesian methods
Getting readyHow to do it...How it works...Bayes' theoremComputation of the posterior distributionMaximum a posteriori estimationThere's more...Credible intervalConjugate distributionsNon-informative (objective) prior distributionsSee also
Estimating the correlation between two variables with a contingency table and a chi-squared test
Getting readyHow to do it...How it works...Pearson's correlation coefficientContingency table and chi-squared testThere's more...See also
Fitting a probability distribution to data with the maximum likelihood method
Getting readyHow to do it...How it works...There's more...See also
Estimating a probability distribution nonparametrically with a kernel density estimation
Getting readyHow to do it...How it works...See also
Fitting a Bayesian model by sampling from a posterior distribution with a Markov chain Monte Carlo method
Getting readyHow to do it...How it works...There's more...See also
Analyzing data with the R programming language in the IPython notebook
Getting readyHow to do it...How it works...There's more...See also
8. Machine Learning
IntroductionA bit of vocabularyLearning from dataSupervised learningUnsupervised learningFeature selection and feature extractionOverfitting, underfitting, and the bias-variance tradeoffModel selectionMachine learning references
Getting started with scikit-learn
Getting readyHow to do it...How it works...The scikit-learn APIOrdinary least squares regressionPolynomial interpolation with linear regressionRidge regressionCross-validation and grid searchThere's more…See also
Predicting who will survive on the Titanic with logistic regression
Getting readyHow to do it...How it works...There's more...See also
Learning to recognize handwritten digits with a K-nearest neighbors classifier
How to do it...How it works...There's more…See also
Learning from text – Naive Bayes for Natural Language Processing
Getting readyHow to do it...How it works...There's more…See also
Using support vector machines for classification tasks
How to do it...How it works...There's more…See also
Using a random forest to select important features for regression
How to do it...How it works...There's more...See also
Reducing the dimensionality of a dataset with a principal component analysis
How to do it...How it works...There's more…See also
Detecting hidden structures in a dataset with clustering
How to do it...How it works...There's more...See also
9. Numerical Optimization
IntroductionThe objective functionLocal and global minimaConstrained and unconstrained optimizationDeterministic and stochastic algorithmsReferences
Finding the root of a mathematical function
How to do it…How it works…There's more…See also
Minimizing a mathematical function
How to do it…How it works…There's more…See also
Fitting a function to data with nonlinear least squares
How to do it…How it works…There's more…See also
Finding the equilibrium state of a physical system by minimizing its potential energy
How to do it…How it works…There's more…See also
10. Signal Processing
IntroductionAnalog and digital signalsThe Nyquist–Shannon sampling theoremCompressed sensingReferences
Analyzing the frequency components of a signal with a Fast Fourier Transform
Getting readyHow to do it...How it works...The Discrete Fourier TransformInverse Fourier TransformThere's more...See also
Applying a linear filter to a digital signal
Getting readyHow to do it...How it works...What are linear filters?Linear filters and convolutionsThe FIR and IIR filtersFilters in the frequency domainThe low-, high-, and band-pass filtersThere's more...See also
Computing the autocorrelation of a time series
Getting readyHow to do it...How it works...There's more...See also
11. Image and Audio Processing
IntroductionImagesSoundsReferences
Manipulating the exposure of an image
Getting readyHow to do it...How it works...There's more...See also
Applying filters on an image
How it works...How it works...There's more...See also
Segmenting an image
How to do it...How it works...There's more...See also
Finding points of interest in an image
Getting readyHow to do it...How it works...There's more...
Detecting faces in an image with OpenCV
Getting readyHow to do it...How it works...There's more...
Applying digital filters to speech sounds
Getting readyHow to do it…How it works...There's more...See also
Creating a sound synthesizer in the notebook
How to do it...How it works...There's more...See also
12. Deterministic Dynamical Systems
IntroductionTypes of dynamical systemsDifferential equationsReferences
Plotting the bifurcation diagram of a chaotic dynamical system
How to do it...There's more...See also
Simulating an elementary cellular automaton
How to do it...How it works...There's more...
Simulating an ordinary differential equation with SciPy
How to do it...How it works...There's more...See also
Simulating a partial differential equation – reaction-diffusion systems and Turing patterns
How to do it...How it works...There's more...See also
13. Stochastic Dynamical Systems
IntroductionReferences
Simulating a discrete-time Markov chain
How to do it...How it works...There's more...See also
Simulating a Poisson process
How to do it...How it works...There's more...See also
Simulating a Brownian motion
How to do it...How it works...There's more...See also
Simulating a stochastic differential equation
How to do it...How it works...There's more...See also
14. Graphs, Geometry, and Geographic Information Systems
IntroductionGraphsProblems in graph theoryRandom graphsGraphs in PythonGeometry in PythonGeographical Information Systems in PythonReferences
Manipulating and visualizing graphs with NetworkX
Getting readyHow to do it…There's more…See also
Analyzing a social network with NetworkX
Getting readyHow to do it…There's more…See also
Resolving dependencies in a directed acyclic graph with a topological sort
Getting readyHow to do it…There's more…
Computing connected components in an image
How to do it…How it works…There's more…
Computing the Voronoi diagram of a set of points
Getting readyHow to do it…How it works…There's more…See also
Manipulating geospatial data with Shapely and basemap
Getting readyHow to do it…See also
Creating a route planner for a road network
Getting readyHow to do it…How it works…There's more…
15. Symbolic and Numerical Mathematics
IntroductionLaTeX
Diving into symbolic computing with SymPy
Getting readyHow to do it...How it works...See also
Solving equations and inequalities
Getting readyHow to do it...There's more...
Analyzing real-valued functions
Getting readyHow to do it...There's more...
Computing exact probabilities and manipulating random variables
How to do it...How it works...
A bit of number theory with SymPy
Getting readyHow to do it...How it works...There's more...
Finding a Boolean propositional formula from a truth table
How to do it...How it works...There's more...
Analyzing a nonlinear differential system – Lotka-Volterra (predator-prey) equations
Getting readyHow to do it...How it works...There's more...
Getting started with Sage
Getting readyHow to do it...There's more...See also
Index

Content preview from IPython Interactive Computing and Visualization Cookbook

Solving equations and inequalities

SymPy offers several ways to solve linear and nonlinear equations and systems of equations. Of course, these functions do not always succeed in finding closed-form exact solutions. In this case, we can fall back to numerical solvers and obtain approximate solutions.

Getting ready

We first need to import SymPy. We also initialize pretty printing in the notebook (see the first recipe of this chapter).

How to do it...

Let's define a few symbols:

In [2]: var('x y z a')
Out[2]: (x, y, z, a)

We use the solve() function to solve equations (the right-hand side is 0 by default):
```
In [3]: solve(x**2 - a, x)
Out[3]: [-sqrt(a), sqrt(a)]
```
We can also solve inequalities. Here, we need to use the solve_univariate_inequality() function ...

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