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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

By : Cyrille Rossant
4.5 (13)
Buy this Book
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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

4.5 (13)
By: Cyrille Rossant
Buy this Book

Overview of this book

Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.
Table of Contents (22 chapters)
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IPython Interactive Computing and Visualization Cookbook
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IPython Interactive Computing and Visualization Cookbook
Credits
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Credits
About the Author
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About the Author
About the Reviewers
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About the Reviewers
www.PacktPub.com
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www.PacktPub.com
Preface
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Preface
Free Chapter
1
A Tour of Interactive Computing with IPython
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A Tour of Interactive Computing with IPython
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Introduction
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Introducing the IPython notebook
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Getting started with exploratory data analysis in IPython
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Introducing the multidimensional array in NumPy for fast array computations
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Creating an IPython extension with custom magic commands
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Mastering IPython's configuration system
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Creating a simple kernel for IPython
2
Best Practices in Interactive Computing
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Best Practices in Interactive Computing
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Introduction
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Choosing (or not) between Python 2 and Python 3
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Efficient interactive computing workflows with IPython
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Learning the basics of the distributed version control system Git
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A typical workflow with Git branching
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Ten tips for conducting reproducible interactive computing experiments
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Writing high-quality Python code
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Writing unit tests with nose
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Debugging your code with IPython
3
Mastering the Notebook
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Mastering the Notebook
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Introduction
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Teaching programming in the notebook with IPython blocks
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Converting an IPython notebook to other formats with nbconvert
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Adding custom controls in the notebook toolbar
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Customizing the CSS style in the notebook
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Using interactive widgets – a piano in the notebook
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Creating a custom JavaScript widget in the notebook – a spreadsheet editor for pandas
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Processing webcam images in real time from the notebook
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Profiling and Optimization
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Profiling and Optimization
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Introduction
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Evaluating the time taken by a statement in IPython
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Profiling your code easily with cProfile and IPython
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Profiling your code line-by-line with line_profiler
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Profiling the memory usage of your code with memory_profiler
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Understanding the internals of NumPy to avoid unnecessary array copying
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Using stride tricks with NumPy
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Implementing an efficient rolling average algorithm with stride tricks
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Making efficient array selections in NumPy
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Processing huge NumPy arrays with memory mapping
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Manipulating large arrays with HDF5 and PyTables
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Manipulating large heterogeneous tables with HDF5 and PyTables
5
High-performance Computing
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High-performance Computing
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Introduction
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Accelerating pure Python code with Numba and just-in-time compilation
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Accelerating array computations with Numexpr
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Wrapping a C library in Python with ctypes
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Accelerating Python code with Cython
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Optimizing Cython code by writing less Python and more C
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Releasing the GIL to take advantage of multicore processors with Cython and OpenMP
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Writing massively parallel code for NVIDIA graphics cards (GPUs) with CUDA
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Writing massively parallel code for heterogeneous platforms with OpenCL
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Distributing Python code across multiple cores with IPython
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Interacting with asynchronous parallel tasks in IPython
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Parallelizing code with MPI in IPython
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Trying the Julia language in the notebook
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Advanced Visualization
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Advanced Visualization
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Introduction
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Making nicer matplotlib figures with prettyplotlib
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Creating beautiful statistical plots with seaborn
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Creating interactive web visualizations with Bokeh
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Visualizing a NetworkX graph in the IPython notebook with D3.js
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Converting matplotlib figures to D3.js visualizations with mpld3
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Getting started with Vispy for high-performance interactive data visualizations
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Statistical Data Analysis
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Statistical Data Analysis
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Introduction
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Exploring a dataset with pandas and matplotlib
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Getting started with statistical hypothesis testing – a simple z-test
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Getting started with Bayesian methods
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Estimating the correlation between two variables with a contingency table and a chi-squared test
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Fitting a probability distribution to data with the maximum likelihood method
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Estimating a probability distribution nonparametrically with a kernel density estimation
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Fitting a Bayesian model by sampling from a posterior distribution with a Markov chain Monte Carlo method
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Analyzing data with the R programming language in the IPython notebook
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Machine Learning
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Machine Learning
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Introduction
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Getting started with scikit-learn
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Predicting who will survive on the Titanic with logistic regression
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Learning to recognize handwritten digits with a K-nearest neighbors classifier
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Learning from text – Naive Bayes for Natural Language Processing
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Using support vector machines for classification tasks
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Using a random forest to select important features for regression
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Reducing the dimensionality of a dataset with a principal component analysis
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Detecting hidden structures in a dataset with clustering
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Numerical Optimization
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Numerical Optimization
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Introduction
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Finding the root of a mathematical function
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Minimizing a mathematical function
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Fitting a function to data with nonlinear least squares
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Finding the equilibrium state of a physical system by minimizing its potential energy
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Signal Processing
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Signal Processing
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Introduction
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Analyzing the frequency components of a signal with a Fast Fourier Transform
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Applying a linear filter to a digital signal
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Computing the autocorrelation of a time series
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Image and Audio Processing
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Image and Audio Processing
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Introduction
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Manipulating the exposure of an image
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Applying filters on an image
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Segmenting an image
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Finding points of interest in an image
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Detecting faces in an image with OpenCV
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Applying digital filters to speech sounds
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Creating a sound synthesizer in the notebook
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Deterministic Dynamical Systems
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Deterministic Dynamical Systems
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Introduction
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Plotting the bifurcation diagram of a chaotic dynamical system
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Simulating an elementary cellular automaton
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Simulating an ordinary differential equation with SciPy
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Simulating a partial differential equation – reaction-diffusion systems and Turing patterns
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Stochastic Dynamical Systems
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Stochastic Dynamical Systems
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Introduction
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Simulating a discrete-time Markov chain
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Simulating a Poisson process
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Simulating a Brownian motion
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Simulating a stochastic differential equation
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Graphs, Geometry, and Geographic Information Systems
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Graphs, Geometry, and Geographic Information Systems
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Introduction
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Manipulating and visualizing graphs with NetworkX
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Analyzing a social network with NetworkX
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Resolving dependencies in a directed acyclic graph with a topological sort
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Computing connected components in an image
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Computing the Voronoi diagram of a set of points
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Manipulating geospatial data with Shapely and basemap
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Creating a route planner for a road network
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Symbolic and Numerical Mathematics
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Symbolic and Numerical Mathematics
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Introduction
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Diving into symbolic computing with SymPy
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Solving equations and inequalities
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Analyzing real-valued functions
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Computing exact probabilities and manipulating random variables
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A bit of number theory with SymPy
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Finding a Boolean propositional formula from a truth table
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Analyzing a nonlinear differential system – Lotka-Volterra (predator-prey) equations
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Getting started with Sage
Index
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Index

Analyzing real-valued functions

SymPy contains a rich calculus toolbox to analyze real-valued functions: limits, power series, derivatives, integrals, Fourier transforms, and so on. In this recipe, we will show the very basics of these capabilities.

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...

  1. Let's define a few symbols and a function (which is just an expression depending on x):

    In [1]: var('x z')
Out[1]: (x, z) 
In [2]: f = 1/(1+x**2)

  2. Let's evaluate this function at 1:

    In [3]: f.subs(x, 1)
Out[3]: 1/2

  3. We can compute the derivative of this function:

    In [4]: diff(f, x)
Out[4]: -2*x/(x**2 + 1)**2

  4. What is f's limit to infinity? (Note the double o (oo) for the infinity symbol):

    In [5]: limit(f, x, oo)
Out[5]: 0

  5. Here's how to compute a Taylor series (here, around 0, of order 9). The Big O can be removed with the removeO() method.

    In [6]: series(f, x0=0, n=9)
Out[6]: 1 - x**2 + x**4 - x**6 + x**8 + O...

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