NumPy Beginner's Guide

NumPy

Beginner's

Guide

Second

Edition

An action

_{packed guide}

_using

real world

_examples

of the

easy

to use,

high performance,

free

open

source

_NumPy

mathematical

_library

Ivan Idris

[

PUBLISHING BIRMINGHAM-MUMBAI

1 open

source

Table

of

Contents

Preface

1

Chapter

1:

_NumPy

Quick Start 9

Python

9

Time for action

-installing Python

on different

operating

systems 10

Windows 10

Time foraction-

installing NumPy, Matplotlib, SciPy,

and

IPython

on Windows 11

Linux 13

Time foraction-

installing

NumPy, Matplotlib, SciPy,

and

_IPython

on Linux 13

Mac OS X 14

Timeforaction

-installing

NumPy,

Matplotlib,

and

_SciPy

onMac OS X 14

Time for action-

installing

NumPy, SciPy,

Matplotlib,

and

_IPython

with MacPorts orFink 17

Building

fromsource 17

Arrays

17

Time for action-

adding

vectors 18

IPython—an

interactive shell 21

Online resources and

help

25

Summary

26

Chapter

2:

_Beginning

with

_NumPy

Fundamentals

27

NumPy

array

object

28

Time foraction

-creating

a multidimensional array 29

Selecting

elements 30

NumPy

numerical

_types

30

Data

_type

_objects

32

Character codes 32

dtype

constructors 33

TableofContents

Time for action-

creating

_a record data type 34

One-dimensional

slicing

and

_indexing

35

Time for action-

slicing

and

indexing

multidimensional arrays 35

Time for action

-manipulating

array

shapes

38

Stacking

39

Time foraction

-stacking

arrays 40

Splitting

43

Time for action-

splitting

arrays 43

Array

attributes 45

Time for action-

converting

arrays 48

Summary

49

Chapter

3: Get

in

Terms

with

_Commonly

Used Functions

51

File

_I/O

51

Time for action-

reading

and

writing

files 52

CSVfiles 52

Time for action-

loading

fromCSV files 53

Volume-weighted

average

price

53

Time for action-

calculating volume-weighted

_average

price

54

Themeanfunction 54

Time-weighted

average

price

54

Value range 55

Time for action

-finding highest

and lowest values 55

Statistics 56

Time for action-

doing simple

statistics 57

Stock returns 59

Time for action-

analyzing

stockreturns 59

Dates 61

Time for action-

dealing

with dates 61

Weekly

summary 65

Time for action

-summarizing

data 65

Average

truerange 69

Time foraction-

calculating

the averagetrue_range 69

Simple

moving

average 72

Time for action-

computing

the

simple moving

_average 72

Exponential moving

average 74

Time for action-

calculating

the

exponential moving

_average 74

Bollinger

bands 76

Time for action-

enveloping

with

Bollinger

bands 76

of

Time

for

action-

predicting price

witha linear model 80

Trend lines 82

Time for action-

drawing

trend lines 82

Methods of

ndarray

86

Time for action

-clipping

and

_compressing

_arrays 87

Factorial 87

Time for action

-calculating

the factorial 88

Summary

89

Chapter

4: Convenience Functions for Your

Convenience

91

Correlation 92

Time

for

action-

trading

correlated

pairs

92

Polynomials

96

Time for action-

fitting

to

polynomials

96

On-balance volume 99

Time for action-

balancing

volume 100

Simulation 102

Time for action-

avoiding loops

with vectorize 102

Smoothing

105

Timeforaction-

smoothing

with the

banning

function 105

Summary

109

Chapter

5:

_Working

with Matrices

and ufuncs 111

Matrices 111

Time for action-

creating

matrices 112

Creating

amatrix from other matrices 113

Time for action

-creating

a matrix from other matrices 113

Universal functions 114

Time for action

-creating

universal function 115

Universal function methods 116

Timeforaction-

applying

the ufunc methodsonadd 116

Arithmetic functions 118

Timefor

_{action-dividing}

_arrays 119

Timeforaction-

computing

the modulo 121

Fibonaccinumbers 122

Timefor action-

computing

Fibonaccinumbers 122

Lissajous

curves 123

Time for action

-drawing

Lissajous

curves 124

Square

waves 125

Time for action

-drawing

asquarewave 125

Table_ofContents

Time for action-

drawing

sawtooth and

triangle

waves 127

Bitwise and

_comparison

functions 129

Timefor

_{action-twiddling}

bits 129

Summary

131

Chapter

6: Move Further with

_{NumPy Modules}

133

Linear

_algebra

133

Timefor action-

inverting

matrices 133

Solving

linear systems 135

Time for action

-solving

a linear

_system

136

Finding eigenvalues

and

_eigenvectors

137

Time foraction

-determining eigenvalues

and

_eigenvectors

137

Singular

value

_{decomposition}

139

Time for action-

decomposing

_amatrix 139

Pseudoinverse 141

Timefor action-

computing

the

pseudo

inverse ofamatrix 141

Determinants 142

Time for action-

calculating

the determinant ofa matrix 142

Fast Fourier transform 143

Time for action-

calculating

the Fouriertransform 143

Shifting

145

Time foraction-

shifting frequencies

145

Randomnumbers 147

Time for action-

gambling

with the binomial 147

Hypergeometric

distribution 149

Timefor action

-simulating

a_{game show} 149

Continuous distributions 151

Time for action

-drawing

anormal distribution 151

Lognormal

distribution 153

Time for action

-drawing

the

_lognormal

distribution 153

Summary

154

Chapter

7:

_Peeking

into

_Special

Routines

155

Sorting

155

Time for

_{action-sorting lexically}

156

Complex

numbers 157

Time for action-

sorting complex

numbers 157

Searching

158

Time for action-

using

searchsorted 159

Time for action

-extracting

elements froman_array 160

Financial functions 161

Time for action

-determining

futurevalue 161

Presentvalue ₁₆₃

Time for action-

getting

thepresent value 163

Net_presentvalue ₁₆₃

Timeforaction-

calculating

thenetpresent value 163

Internal rate ofreturn ₁₆₄

Time for action-

determining

the internal rate of

return 164

Periodic payments 165

Time for action-

calculating

the

periodic

payments 165

Number of payments 165

Time for action-

determining

the number of

periodic payments

165

Interest rate 166

Time foraction-

figuring

outtherate 166

Window functions 166

Time foraction-

plotting

the Bartlett window 167

Blackmanwindow 167

Time for action-

smoothing

stock

prices

with the Blackmanwindow

168

Hamming

window 170

Timefor action

-plotting

the

_Hamming

window 170

Kaiser window 171

Timefor action

-plotting

theKaiser window 171

Special

mathematical functions 172

Time for action

-plotting

the modified Bessel function 172

sine 173

Time for action-

plotting

thesine function 173

Summary

175

Chapter

8:Assure

_Quality

with

_Testing

177

Assert functions ₁₇₈

Time foraction-

asserting

almost

equal

178

Approximately equal

arrays 179

Time foraction-

asserting approximately equal

180

Almost

equal

arrays 180

Time for action

-asserting

arraysalmost

equal

181

Equal

arrays 182

Time for action-

comparing

arrays 182

TableofContents

Time for action

-checking

the_{array order 183}

Objects

comparison

184

Time for action-

comparing

objects

184

String

comparison

184

Time foraction-

comparing strings

185

Floating

point comparisons

185

Timefor action-

comparing

with

assert_array_almost_equal_nulp

186

Comparison

of floats withmore ULPs 187

Timefor action

-comparing using maxulp

of2 187

Unittests ₁₈₇

Time for action-

writing

_a unittest ₁₈₈

Nosetests decorators ₁₉₀

Time foraction-

decorating

tests ₁₉₁

Docstrings

193

Timefor action

-executing

doctests ₁₉₄

Summary

195

Chapter

9:

_Plotting

with

_Matplotlib

₁₉₇

Simple

plots

198

Time for action-

plotting

_a

polynomial

function

198

Plot format

_string

₂₀₀

Timeforaction-

plotting

_a

polynomial

and itsderivative

200

Subplots

201

Timefor action-

plotting

a

polynomial

and its derivatives ₂₀₁

Finance ₂₀₄

Time for action-

plotting

_a

year's

worth of stock

quotes

204

Histograms

207

Time for action-

charting

stock

price

distributions ₂₀₇

Logarithmic

plots

209

Time foraction-

plotting

stock volume

209

Scatter

_plots

₂₁₁

Timefor action

-plotting price

and volume returnswith scatter

_plot

211

Fill between ₂₁₃

Time for action

-shading plot

regions

basedon acondition 213

Legend

and annotations ₂₁₅

Time for action-

using legend

and annotations

215

Three dimensional

_plots

₂₁₈

Time foraction-

plotting

in three dimensions

219

Contour

_plots

₂₂₀

Time foraction-

drawing

_afilled _contour

plot

220

Animation 222

Time for action-

animating plots

222

Summary

223

Chapter

10:

When

_NumPy

is Not

_Enough

-

SciPy

and

Beyond

225

MATLABand Octave 225

Timeforaction

-saving

and

_loading

a .mat file 226

Statistics 227

Time for action-

analyzing

random values 227

Samples' comparison

and SciKits 230

Time for action-

comparing

stock

log

returns 230

Signal processing

232

Time for action-

detecting

atrend in

QQQ

233

Fourier

_analysis

235

Time for action

-filtering

adetrended

_signal

236

Mathematical

_optimization

238

Time for action

-fitting

toa sine 239

Numerical

_integration

242

Timeforaction-

calculating

the Gaussian

integral

242

Interpolation

243

Time for action-

interpolating

inone dimension 243

Image

processing

245

Timefor action-

manipulating

Lena 245

Audio

processing

247

Time for action-

replaying

audio

clips

247

Summary

249

Chapter

11:

_Playing

with

_Pygame

251

Pygame

251

Time foraction-

installing Pygame

252

Hello World 252

Time foraction-

creating

_a

simple

_game 252

Animation 255

Time for action-

animating objects

with

NumPy

and

Pygame

255

Matplotlib

258

Time for action

-using

Matplotlib

in

_Pygame

258

Surface

_pixels

261

Time for action

-accessing

surface

pixel

data with

NumPy

262

Artificial

_intelligence

263

Time for action

-clustering points

264

Table_ofContents

Time foraction-

drawing

the

Sierpinski

gasket

267

Simulation gamewith

PyGame

270

Time foraction-

simulating

life

270

Summary

274

Pop

Quiz

Answers 275

Index

277