Index

As this ebook edition doesn't have fixed pagination, the page numbers below are hyperlinked for reference only, based on the printed edition of this book.

A

Accelerated Linear Algebra (XLA) 96

acceptance probabilities 128

accuracy 216

acos function 6

adjacency matrix

generating, for network 146-148

agg method 174

Akaike information criterion (AIC) 225

Amazon Web Services (AWS) S3 storage 318

Analysis of Variance (ANOVA) 164, 191, 192

hypotheses, testing 191, 192

Anti-Grain Geometry (AGG) library 32

arange routine 11

ARIMA class 238, 239

ARMA 225

time series data, modeling 218-225

array creation routines, NumPy 11

arange 11

linspace 11

art gallery problem 264

asin function 6

atan function 6

autocorrelation function (ACF) 219

autocorrelation property 217

Autograd 96

automatic differentiation

with JAX 96-99

autoregressive (AR) component 201

autoregressive integrated moving average (ARIMA) 201, 225, 226

seasonal data, forecasting 232-238

used, for forecasting from time series data 226-231

average clustering 156

Azimuthal angle 51

Azure data storage 318

B

Basic Linear Algebra Subprograms (BLAS) package 8

basic linear regression

using 203-207

basic mathematical functions 5-8

Bayesian information criterion (BIC) 225

Bayesian probability 123

Bayesian techniques 126-128

used, for analyzing conversion rates 124-127

Bayes’ theorem 126, 127

beta distribution 118, 123

Bezier curves 267, 272, 273

constructing 268-272

bias 180

BitGenerator class 115

Bokeh

interactive plots, creating 196-198

C

caching 338

calculations

uncertainty of variables, accounting 309, 310

calculus 58, 63

differentiation 58, 59

integration 58, 59

with JAX 96-99

working with 59-62

canny routine 260

ceil function 7

central limit theorem 118, 164, 183

Central Processing Unit (CPU) 134

Cerberus

data, validating 319-321

characteristic polynomial 22

choice method 109

clique 157

clustering

quantifying, in network 154-156

cmath module 5, 6

code

accelerating, with Cython 323-329

colormap 51

color mapping 51

comb function 7

complete network 137

complex conjugate 5

complex number 4

reference link 5

compressed sparse column (CSC) 24

compressed sparse row (CSR) 24, 88

conditional probability 127

confidence interval 181

constant of integration 59

constrained linear minimization problem

solving, with SciPy 277-281

continuous probability density functions 118

continuous probability distribution 118

contour plots 43

plotting 45-48

controlled differential equation (CDE) 102

conversion rates

analyzing, with Bayesian techniques 124-127

convex 265

convex hulls 265

computing 265-267

correlation 207

cos function 6

critical values 182

curve_fit routine 297

Cython 322, 329

code, accelerating 323-329

D

Dask 330

computations, performing on DataFrame 330-332

dask_ml 332

data 319

validating, with Cerberus 319-321

DataFrame 165, 167, 173, 174

columns, accessing 167

creating 165-167

data, loading from 168-170

data, manipulating 170-173

data, plotting from 175-177

data, storing from 168-170

descriptive statistics, obtaining from 177-181

operations, performing on grouped data 184-188

data science

reproducible code, writing for 332-338

data science pipeline

steps 337

Decimal type 3, 4

Delaunay triangulation 263

derivative 58

descend routine 291

descriptive statistics 164, 177

deterministic selection 106

differencing 226

differential equations 72

partial differential equations, solving numerically 83-89

solving numerically 72-77

solving, with JAX 100-102

systems, solving 78-82

differentiation 58

differentiating symbolically, SymPy used 63-66

diffrax library 102

reference link 102

DiGraph class 150

directed networks 137, 151

creating 149, 150

discrete Fourier transform (DFT) 90

used, for signal processing 90-95

discrete probability 109

discretization 261

distribution function 115

dominating set 161

Dots per Inch (DPI) 42

draw routine 142, 143, 151

dropna method 173

E

edge coloring 159

edges 137

finding, in image 258-260

eigenvalues 20-22

eigenvectors 20-22

elevation angle 51

Encapsulated PostScript (EPS) 43

equations

solving 66-69

erf function 6

error bars

plotting with 38-42

Euclidean norm 21

Eulerian 154

Eulerian circuit 154

event 107

expected signature 242

exponential distribution 118

F

factorial function 7

FEniCS

URL 89

figure routine 198

figures, Matplotlib

saving, to file 42, 43

fillna method 173

finite element method 62

floor function 7

format string 32

forward time cen (FTCS) scheme 87

four-color theorem 159

Fourier transform (FT) 89

Fraction type 4

free tensor algebra 246

F statistic p-value 207

fsum function 7

G

Gambit project

reference link 301

game theory 275, 298

gamma distribution 118

gamma function 6

General Decimal Arithmetic, operations

reference link 3

geographical data

working with 314-316

geometric figure 252

geometric problems 251

geometry 251

GeoPandas package 316

Geoplot package 316

getitem protocol 9

global clustering 156

gradient 58

gradient descent methods 286, 294

using, in optimization 287-292

gradient-free minimization algorithm 286

Graphics Processing Unit (GPU) 96, 134

graphs 137

H

Hannan-Quinn Information Criterion (HQIC) 225

hypotheses

testing, for non-parametric data 193-196

testing, with ANOVA 191, 192

testing, with t-tests 188-190

hypothesis testing 164

I

identity matrix 13

image

edges, finding in 258-260

imaginary unit 4

incidence matrix 148

Independent and Identically Distributed (IID) random variables 118

inference 164

info routine 146

integration 58

integrating symbolically, SymPy used 63-66

numerical integration, SciPy used 70-72

interactive plots

creating, with Bokeh 196-198

interior points

finding 255-258

interpolate method 173

ipynb extension 317

isclose function 7

items

selecting, at random 106-109

J

JavaScript Object Notation (JSON) 317

JAX

reference link 100

used, for automatic differentiation 96-99

used, for calculus 96-99

used, for solving differential equations 100-102

Jupyter notebook 317, 338

executing, as script 317, 318

K

kernel density estimation plot 195

Königsberg bridge problem 154

Kruskal-Wallis test 193-196

L

Laplacian matrix 148

learning rate 291

least squares 294

using, to fit curve to data 294-298

Lemke-Howson algorithm 303

linalg module 16-21

linalg.svd function 23

linear algebra 16

Linear Algebra PACKage (LAPACK) 17

linear functions 275

linear programming 275

linear regression 203

linprog routine 279-282

linspace routine 11

list coloring problem 159

logarithmic regression 212

log function 6

logistic function 213

logistic regression

used, for solving simple classification problem 213-217

log-odds 212, 216

M

Markov chain 122, 123

Markov Chain Monte Carlo (MCMC) 128

Markov property 122

math module 5-8

Matplotlib 28

figures, saving 42, 43

functions, plotting with 29-35

patch types 255

reference link, for gallery 55

matrix 13

basic methods 14

determinant 16

inverse 17

properties 14

trace 14

matrix arithmetic 13

matrix multiplication 13, 15, 16

maxima 275

merge method 174

minima 275

minimal spanning tree

finding 159-161

minimize routine 284, 285, 292

minimize_scalar routine 286

minimum spanning tree 161

Monte Carlo methods 128, 134

Monte Carlo simulations

parameters, estimating 129-133

moving average (MA) component 201

MT19937 generator 114

multilinear regression

using 208-212

N

Nash equilibria

computing, for rock-paper-scissors game 301, 302

Nash equilibrium 301

natural logarithm 6

ndarray type 8

Nelder-Mead simplex method 282, 286

minimum, finding of general non-linear objective function 283-285

NetCDF files

data, loading from 311-314

data, storing in 311-314

Network Common Data Form (NetCDF) 305, 310

networks 137

adjacency matrix, generating for 146-148

basic characteristics 143-146

chromatic number 159

clustering, quantifying 154-156

coloring 157-159

connected components 146

creating 138-140

density 145, 146

planar 146

shortest paths, finding in 151-153

visualizing 141-143

NetworkX package 140, 141

New Bit Generators, NumPy

reference link 115

Newton-Raphson method 66-68

node coloring problem 159

nodes 137

non-linear function 275

minimizing 282-286

non-parametric data

hypotheses, testing for 193-196

non-parametric tests 164

normal distribution 115, 118

normally distributed random numbers

generating 116, 117

Not a Number (NaN) value 171

No U-turn Sampler (NUTS) 133

Numba package

reference link 330

numerical reasoning 196

numerical types, Python 2

complex type 4

Decimal type 3, 4

Fraction type 4

NumPy 8, 9

array creation routines 11

element access 9

higher-dimensional arrays 11-13

NumPy arrays

arithmetic operations 10

O

objective function 275

object-oriented interface (OOI) 28

one-way ANOVA test 192

optimization 275

gradient descent methods, using in 287-292

optimize module 292

ordinary least squares 206

over-differencing 231

P

paired t-test 190

papermill package 317-319

parameters

estimating, with Monte Carlo simulations 129-133

partial autocorrelation function (PACF) 219

partial differential equations (PDEs) 24, 83

solving numerically 83-89

patch types, Matplotlib 255

PCG64 generator 114

Philox generator 114

pi constant 6

Pint 308

used, for keeping track of units 307, 308

planar figures

triangulating 261-264

Plotly

URL 48

plotting 28

with error bars 38-42

with Matplotlib 28-35

plt.show function 32

pointplot routine 316

Poisson process 118, 122

arrival of buses, modeling 119-121

polynomials 59

working with 60-62

polyplot routine 316

population 164

with sampling 181-184

Portable Document Format (PDF) 43

Portable Network Graphics (PNG) format 43

posterior distribution 123

PostScript (PS) 43

power spectral density (PSD) 90

precision 216

predictor variable 203

principal component analysis (PCA) 22

prior distribution 123

prisoner’s dilemma 299

probability 106, 107

Prophet 239, 242

used, for modeling time series data 239-241

Pseudorandom Number Generator (PRNG) instance 108

pyjion package

reference link 330

pyplot interface 28

Python

numerical types 2

Q

quadratic Bezier curves 272

quiver plot

used, for plotting vector fields 52-54

R

random data

generating 110-112

random module 106, 113

randomness 106

random number generator

modifying 113-115

random numbers 109

random processes

types 122

working with 119-122

ray crossing counting 258

real numbers 4-6

recall 216

Receiver Operating Characteristic (ROC) curve 338

renewal process 122

replace method 173

reproducibility

concerns 338, 339

reproducible code

writing, for data science 332-338

response variable 203

route inspection problem 153

Runge-Kutta-Fehlberg (RKF45) method 76

S

sample space 107

sampling 109

SARIMA model 231, 238

SARIMAX class 238, 239

savefig method 43

Scalable Vector Graphics (SVG) 43

scalar multiplication 13

schema 319

scikit-image package 260

scikit-learn package 208, 217

SciPy

constrained linear minimization problem, solving 277-281

numerical integration, performing with 70-72

Seaborn libraries

reference link 55

seasonal data

forecasting, with ARIMA 232-238

seasonality 231, 238

secant method 66

second-order ODE 100

seed 108

SeedSequence object 114

Series object 165

creating 165-167

rows, accessing 167

SFC64 generator 114

Shapely package 267

Shapely Polygon class 258

shell layout 142

shortest paths

finding, in network 151-153

signal processing

discrete Fourier transform (DFT), using for 90-95

signatures 242

time series data, summarizing 242-248

usage 249

simple classification problem

solving, with logistic regression 213-217

simple linear function

minimizing 276-281

simple linear regression 207, 208

simple networks 137, 140, 148

simple two-player games

analyzing 299-301

simplex method 280

sin function 6

singular matrices 17

singular value decomposition (SVD) 22

singular values 22

slack variables 280

solve_ivp routine 77

spanning tree 161

sparse matrices 23-25

Spearman’s rank correlation coefficient 207

spectral methods 148

sqrt function 6

standard deviation 180

standard error 182

stationary 219

statistics 164

confidence 190

significance 190

statsmodels package

linear regression, performing on two sets of data 203-207

stochastic differential equations (SDEs) 102

stochastic gradient descent 294

subplots 35

adding 35-38

summarizing data 164

summary statistics 177

surface plots 43

plotting 43-48

Swiss cheese 254, 255

SymPy library 63

differentiating symbolically, with 63-66

integrating symbolically, with 63-66

systems, of differential equations

solving 78-82

systems of equations 18-20

T

tan function 6

task graph 332

tensordot routine 281

Tensor Processing Units (TPUs) 96

tensors 11

test statistics 196

three-dimensional plots

customizing 49-52

plotting 43

time series 217

time series data

ARIMA, used for forecasting from 226-231

modeling, with ARMA 218-225

modeling, with Prophet 239-241

summarizing, with signatures 242-248

train_test_split routine 338

transition matrix 123

transpose method 14

traveling salesperson problem 153

tree 137

triangulation 261, 264

t-tests 164, 188

hypotheses, testing 188-190

two-dimensional geometric shapes

visualizing 252-255

two-sample t-test 190

two-way ANOVA test 192

U

uncertainties package 310

uniform algebras 255

uniform distribution 118

uniform probability 109

UnitRegistry object 308

units 309

universal functions (ufuncs) 10

V

variance 180

vector field 52

plotting, with quiver plots 52-54

vertex enumeration algorithm 303

vertices 137

W

weighted networks 137, 151

creating 149, 150

Wilcoxon rank-sum test 193-195

winding number 258

wraps functionality 308

X

xarray 314

reference link 168