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NumPy Beginner's Guide

NumPy Beginner's Guide

By : Ivan Idris
4.2 (14)
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NumPy Beginner's Guide

NumPy Beginner's Guide

4.2 (14)
By: Ivan Idris

Overview of this book

NumPy is an extension to, and the fundamental package for scientific computing with Python. In today's world of science and technology, it is all about speed and flexibility. When it comes to scientific computing, NumPy is on the top of the list. NumPy Beginner's Guide will teach you about NumPy, a leading scientific computing library. NumPy replaces a lot of the functionality of Matlab and Mathematica, but in contrast to those products, is free and open source. Write readable, efficient, and fast code, which is as close to the language of mathematics as is currently possible with the cutting edge open source NumPy software library. Learn all the ins and outs of NumPy that requires you to know basic Python only. Save thousands of dollars on expensive software, while keeping all the flexibility and power of your favourite programming language.You will learn about installing and using NumPy and related concepts. At the end of the book we will explore some related scientific computing projects. This book will give you a solid foundation in NumPy arrays and universal functions. Through examples, you will also learn about plotting with Matplotlib and the related SciPy project. NumPy Beginner's Guide will help you be productive with NumPy and have you writing clean and fast code in no time at all.
Table of Contents (19 chapters)
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Numpy Beginner's Guide Second Edition
Numpy Beginner's Guide Second Edition
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
NumPy Quick Start
NumPy Quick Start
Python
Time for action – installing Python on different operating systems
Windows
Time for action – installing NumPy, Matplotlib, SciPy, and IPython on Windows
Linux
Time for action – installing NumPy, Matplotlib, SciPy, and IPython on Linux
Mac OS X
Time for action – installing NumPy, Matplotlib, and SciPy on Mac OS X
Time for action – installing NumPy, SciPy, Matplotlib, and IPython with MacPorts or Fink
Building from source
Arrays
Time for action – adding vectors
IPython—an interactive shell
Online resources and help
Summary
2
Beginning with NumPy Fundamentals
Beginning with NumPy Fundamentals
NumPy array object
Time for action – creating a multidimensional array
Time for action – creating a record data type
One-dimensional slicing and indexing
Time for action – slicing and indexing multidimensional arrays
Time for action – manipulating array shapes
Time for action – stacking arrays
Time for action – splitting arrays
Time for action – converting arrays
Summary
3
Get in Terms with Commonly Used Functions
Get in Terms with Commonly Used Functions
File I/O
Time for action – reading and writing files
CSV files
Time for action – loading from CSV files
Volume-weighted average price
Time for action – calculating volume-weighted average price
Value range
Time for action – finding highest and lowest values
Statistics
Time for action – doing simple statistics
Stock returns
Time for action – analyzing stock returns
Dates
Time for action – dealing with dates
Weekly summary
Time for action – summarizing data
Average true range
Time for action – calculating the average true range
Simple moving average
Time for action – computing the simple moving average
Exponential moving average
Time for action – calculating the exponential moving average
Bollinger bands
Time for action – enveloping with Bollinger bands
Linear model
Time for action – predicting price with a linear model
Trend lines
Time for action – drawing trend lines
Methods of ndarray
Time for action – clipping and compressing arrays
Factorial
Time for action – calculating the factorial
Summary
4
Convenience Functions for Your Convenience
Convenience Functions for Your Convenience
Correlation
Time for action – trading correlated pairs
Polynomials
Time for action – fitting to polynomials
On-balance volume
Time for action – balancing volume
Simulation
Time for action – avoiding loops with vectorize
Smoothing
Time for action – smoothing with the hanning function
Summary
5
Working with Matrices and ufuncs
Working with Matrices and ufuncs
Matrices
Time for action – creating matrices
Creating a matrix from other matrices
Time for action – creating a matrix from other matrices
Universal functions
Time for action – creating universal function
Universal function methods
Time for action – applying the ufunc methods on add
Arithmetic functions
Time for action – dividing arrays
Time for action – computing the modulo
Fibonacci numbers
Time for action – computing Fibonacci numbers
Lissajous curves
Time for action – drawing Lissajous curves
Square waves
Time for action – drawing a square wave
Sawtooth and triangle waves
Time for action – drawing sawtooth and triangle waves
Bitwise and comparison functions
Time for action – twiddling bits
Summary
6
Move Further with NumPy Modules
chevron up
Move Further with NumPy Modules
Linear algebra
Time for action – inverting matrices
Solving linear systems
Time for action – solving a linear system
Finding eigenvalues and eigenvectors
Time for action – determining eigenvalues and eigenvectors
Singular value decomposition
Time for action – decomposing a matrix
Pseudoinverse
Time for action – computing the pseudo inverse of a matrix
Determinants
Time for action – calculating the determinant of a matrix
Fast Fourier transform
Time for action – calculating the Fourier transform
Shifting
Time for action – shifting frequencies
Random numbers
Time for action – gambling with the binomial
Hypergeometric distribution
Time for action – simulating a game show
Continuous distributions
Time for action – drawing a normal distribution
Lognormal distribution
Time for action – drawing the lognormal distribution
Summary
7
Peeking into Special Routines
Peeking into Special Routines
Sorting
Time for action – sorting lexically
Complex numbers
Time for action – sorting complex numbers
Searching
Time for action – using searchsorted
Array elements' extraction
Time for action – extracting elements from an array
Financial functions
Time for action – determining future value
Present value
Time for action – getting the present value
Net present value
Time for action – calculating the net present value
Internal rate of return
Time for action – determining the internal rate of return
Periodic payments
Time for action – calculating the periodic payments
Number of payments
Time for action – determining the number of periodic payments
Interest rate
Time for action – figuring out the rate
Window functions
Time for action – plotting the Bartlett window
Blackman window
Time for action – smoothing stock prices with the Blackman window
Hamming window
Time for action – plotting the Hamming window
Kaiser window
Time for action – plotting the Kaiser window
Special mathematical functions
Time for action – plotting the modified Bessel function
sinc
Time for action – plotting the sinc function
Summary
8
Assure Quality with Testing
Assure Quality with Testing
Assert functions
Time for action – asserting almost equal
Approximately equal arrays
Time for action – asserting approximately equal
Almost equal arrays
Time for action – asserting arrays almost equal
Equal arrays
Time for action – comparing arrays
Ordering arrays
Time for action – checking the array order
Objects comparison
Time for action – comparing objects
String comparison
Time for action – comparing strings
Floating point comparisons
Time for action – comparing with assert_array_almost_equal_nulp
Comparison of floats with more ULPs
Time for action – comparing using maxulp of 2
Unit tests
Time for action – writing a unit test
Nose tests decorators
Time for action – decorating tests
Docstrings
Time for action – executing doctests
Summary
9
Plotting with Matplotlib
Plotting with Matplotlib
Simple plots
Time for action – plotting a polynomial function
Plot format string
Time for action – plotting a polynomial and its derivative
Subplots
Time for action – plotting a polynomial and its derivatives
Finance
Time for action – plotting a year’s worth of stock quotes
Histograms
Time for action – charting stock price distributions
Logarithmic plots
Time for action – plotting stock volume
Scatter plots
Time for action – plotting price and volume returns with scatter plot
Fill between
Time for action – shading plot regions based on a condition
Legend and annotations
Time for action – using legend and annotations
Three dimensional plots
Time for action – plotting in three dimensions
Contour plots
Time for action – drawing a filled contour plot
Animation
Time for action – animating plots
Summary
10
When NumPy is Not Enough – SciPy and Beyond
When NumPy is Not Enough – SciPy and Beyond
MATLAB and Octave
Time for action – saving and loading a .mat file
Statistics
Time for action – analyzing random values
Samples’ comparison and SciKits
Time for action – comparing stock log returns
Signal processing
Time for action – detecting a trend in QQQ
Fourier analysis
Time for action – filtering a detrended signal
Mathematical optimization
Time for action – fitting to a sine
Numerical integration
Time for action – calculating the Gaussian integral
Interpolation
Time for action – interpolating in one dimension
Image processing
Time for action – manipulating Lena
Audio processing
Time for action – replaying audio clips
Summary
11
Playing with Pygame
Playing with Pygame
Pygame
Time for action – installing Pygame
Hello World
Time for action – creating a simple game
Animation
Time for action – animating objects with NumPy and Pygame
Matplotlib
Time for action – using Matplotlib in Pygame
Surface pixels
Time for action – accessing surface pixel data with NumPy
Artificial intelligence
Time for action – clustering points
OpenGL and Pygame
Time for action – drawing the Sierpinski gasket
Simulation game with PyGame
Time for action – simulating life
Summary
Pop Quiz Answers
Pop Quiz Answers
Chapter 1, NumPy Quick Start
Chapter 2, Beginning with NumPy Fundamentals
Chapter 3, Get into Terms with Commonly Used Functions
Chapter 4, Convenience functions for your convenience
Chapter 5, Working with Matrices and ufuncs
Chapter 6, Move further with NumPy modules
Chapter 7, Peeking into special routines
Chapter 8, Assure Quality with Testing
Chapter 9, Plotting with Matplotlib
Chapter 10, When NumPy is not enough Scipy and beyond
Index
Index

Time for action – inverting matrices

The inverse of a matrix A in linear algebra is the matrix A -1, which when multiplied with the original matrix, is equal to the identity matrix I. This can be written, as A* A -1 = I.

The inv function in the numpy.linalg package can do this for us. Let's invert an example matrix. To invert matrices, perform the following steps:

  1. We will create the example matrix with the mat function that we used in the previous chapters.

    A = np.mat("0 1 2;1 0 3;4 -3 8")
print "A\n", A

    The A matrix is printed as follows:

    A
[[ 0  1  2]
 [ 1  0  3]
 [ 4 -3  8]]

  2. Now, we can see the inv function in action, using which we will invert the matrix.

    inverse = np.linalg.inv(A)
print "inverse of A\n", inverse

    The inverse matrix is shown as follows:

    inverse of A
[[-4.5  7.  -1.5]
 [-2.   4.  -1. ]
 [ 1.5 -2.   0.5]]

    Tip

    If the matrix is singular or not square, a LinAlgError exception is raised. If you want, you can check the result manually. This is left as an exercise for the reader.

  3. Let...

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