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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
12
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

Computing exact probabilities and manipulating random variables

SymPy includes a module named stats that lets us create and manipulate random variables. This is useful when we work with probabilistic or statistical models; we can compute symbolic expectancies, variances probabilities, and densities of random variables.

How to do it...

  1. Let's import SymPy and the stats module:

    In [1]: from sympy import *
        from sympy.stats import *
        init_printing()

  2. Let's roll two dice, X and Y, with six faces each:

    In [2]: X, Y = Die('X', 6), Die('Y', 6)

  3. We can compute probabilities defined by equalities (with the Eq operator) or inequalities:

    In [3]: P(Eq(X, 3))
Out[3]: 1/6
In [4]: P(X>3)
Out[4]: 1/2

  4. Conditions can also involve multiple random variables:

    In [5]: P(X>Y)
Out[5]: 5/12

  5. We can compute conditional probabilities:

    In [6]: P(X+Y>6, X<5)
Out[6]: 5/12

  6. We can also work with arbitrary discrete or continuous random variables:

    In [7]: Z = Normal('Z', 0, 1)  # Gaussian variable
In [8]: P(Z&gt...

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