Book Image

NumPy Cookbook

Book Image

NumPy Cookbook

Overview of this book

Today's world of science and technology is all about speed and flexibility. When it comes to scientific computing, NumPy is on the top of the list. NumPy will give you both speed and high productivity. "NumPy Cookbook" will teach you all about NumPy, a leading scientific computing library. NumPy replaces a lot of the functionality of Matlab and Mathematica, but in contrast to those products, it is free and open source. "Numpy Cookbook" will teach you to write readable, efficient, and fast code that is as close to the language of Mathematics as much as possible with the cutting edge open source NumPy software library. You will learn about installing and using NumPy and related concepts. At the end of the book, we will explore related scientific computing projects. This book will give you a solid foundation in NumPy arrays and universal functions. You will also learn about plotting with Matplotlib and the related SciPy project through examples. "NumPy Cookbook" will help you to be productive with NumPy and write clean and fast code.

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NumPy Cookbook
Oct, 2012 | 226 pages
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Table of Contents (17 chapters)
NumPy Cookbook
NumPy Cookbook
Credits
Credits
About the Author
About the Author
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Winding Along with IPython
Winding Along with IPython
Introduction
Installing IPython
Using IPython as a shell
Reading manual pages
Installing Matplotlib
Running a web notebook
Exporting a web notebook
Importing a web notebook
Configuring a notebook server
Exploring the SymPy profile
2
Advanced Indexing and Array Concepts
Advanced Indexing and Array Concepts
Introduction
Installing SciPy
Installing PIL
Resizing images
Creating views and copies
Flipping Lena
Fancy indexing
Indexing with a list of locations
Indexing with booleans
Stride tricks for Sudoku
Broadcasting arrays
3
Get to Grips with Commonly Used Functions
Get to Grips with Commonly Used Functions
Introduction
Summing Fibonacci numbers
Finding prime factors
Finding palindromic numbers
The steady state vector determination
Discovering a power law
Trading periodically on dips
Simulating trading at random
Sieving integers with the Sieve of Erasthothenes
4
Connecting NumPy with the Rest of the World
Connecting NumPy with the Rest of the World
Introduction
Using the buffer protocol
Using the array interface
Exchanging data with MATLAB and Octave
Installing RPy2
Interfacing with R
Installing JPype
Sending a NumPy array to JPype
Installing Google App Engine
Deploying NumPy code in the Google cloud
Running NumPy code in a Python Anywhere web console
Setting up PiCloud
5
Audio and Image Processing
Audio and Image Processing
Introduction
Loading images into memory map
Combining images
Blurring images
Repeating audio fragments
Generating sounds
Designing an audio filter
Edge detection with the Sobel filter
6
Special Arrays and Universal Functions
Special Arrays and Universal Functions
Introduction
Creating a universal function
Finding Pythagorean triples
Performing string operations with chararray
Creating a masked array
Ignoring negative and extreme values
Creating a scores table with recarray
7
Profiling and Debugging
Profiling and Debugging
Introduction
Profiling with timeit
Profiling with IPython
Installing line_profiler
Profiling code with line_profiler
Profiling code with the cProfile extension
Debugging with IPython
Debugging with pudb
8
Quality Assurance
Quality Assurance
Introduction
Installing Pyflakes
Performing static analysis with Pyflakes
Analyzing code with Pylint
9
Speed Up Code with Cython
Speed Up Code with Cython
Introduction
Installing Cython
Building a Hello World program
Using Cython with NumPy
Calling C functions
Profiling Cython code
Approximating factorials with Cython
10
Fun with Scikits
Fun with Scikits
Introduction
Installing scikits-learn
Loading an example dataset
Clustering Dow Jones stocks with scikits-learn
Installing scikits-statsmodels
Performing a normality test with scikits-statsmodels
Installing scikits-image
Detecting corners
Detecting edges
Installing Pandas
Estimating stock returns correlation with Pandas
Loading data as pandas objects from statsmodels
Resampling time series data
Index
Index

Finding Pythagorean triples

For this tutorial you may need to read the Wikipedia page about Pythagorean triple (for more information on Pythagorean triple visit http://en.wikipedia.org/wiki/Pythagorean_triple). Pythagorean triples are closely related to the Pythagorean Theorem, which you probably have learned about in high school geometry.

Pythagorean triples represent the three sides of a right triangle, and therefore, obey the Pythagorean Theorem. Let's find the Pythagorean triple that has a components sum of 1000. We will do this using Euclid's formula:

In this example we will see some universal functions in action.

How to do it...

The Euclid's formula defines indices m and n.

  1. Create m and n arrays.

    We will create arrays to hold these indices:

    m = numpy.arange(33)
n = numpy.arange(33)

  2. Calculate a, b, and c of the Pythagorean triple.

    The second step is to calculate a, b, and c of the Pythagorean triple using Euclid's formula. Use the outer function to get the Cartesian products, difference, and...

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