Mastering Scipy (Python)

Cover
Copyright
Credits
About the Author
About the Reviewers
www.PacktPub.com
Table of Contents
Preface
Chapter 1: Numerical Linear Algebra
Motivation
Creation of matrices and linear operators
Constructing matrices in the ndarray class
Constructing matrices in the matrix class
Constructing sparse matrices
Linear operators
Basic matrix manipulation
Scalar multiplication, matrix addition, and matrix multiplication
Traces and determinants
Transposes and inverses
Norms and condition numbers
Matrix functions
Matrix factorizations related to solving matrix equations
Relevant factorizations
Pivoted LU decomposition
Cholesky decomposition
QR decomposition
Singular value decomposition
Matrix equations
Back and forward substitution
Basic systems: banded matrices
Basic systems: generic square matrices
Least squares
Regularized least squares
Other matrix equation solvers
Matrix factorizations based on eigenvalues
Spectral decomposition
Schur decomposition
Summary
Chapter 2: Interpolation and Approximation
Motivation
Interpolation
Implementation details
Univariate interpolation
Nearest-neighbors interpolation
Lagrange interpolation
Hermite interpolation
Piecewise polynomial interpolation
Spline interpolation
Multivariate interpolation
Least squares approximation
Linear least squares approximation
Nonlinear least squares approximation
Summary
Chapter 3: Differentiation and Integration
Motivation
Differentiation
Numerical differentiation
Symbolic differentiation
Automatic differentiation
Integration
Symbolic integration
Numerical integration
Functions without singularities on finite intervals
Functions with singularities on bounded domains
Integration on unbounded domains
Numerical multivariate integration
Summary
Chapter 4: Nonlinear Equations
and Optimization
Motivation
Non-linear equations and systems
Iterative methods for univariate functions
Bracketing methods
Secant methods
Brent method
Systems of nonlinear equations
Simple iterative solvers
The Broyden method
Powell's hybrid solver
Large-scale solvers
Optimization
Unconstrained optimization for univariate functions
Constrained optimization for univariate functions
Unconstrained optimization for multivariate functions
The stochastic methods
Deterministic algorithms that exclusively employ function evaluations
The Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method
The conjugate gradient method
Constrained optimization for multivariate functions
Summary
Chapter 5: Initial Value Problems for Ordinary Differential Equations
Symbolic solution of differential equations
Analytic approximation methods
Discrete-variable methods
One-step methods
Two-step methods
Summary
Chapter 6: Computational Geometry
Plane geometry
Combinatorial computational geometry
Static problems
Convex hulls
Voronoi diagrams
Triangulations
Shortest paths
Geometric query problems
Point location
Nearest neighbors
Range searching
Dynamic problems
Numerical computational geometry
Bézier curves
Summary
Chapter 7: Descriptive Statistics
Motivation
Probability
Symbolic setting
Numerical setting
Data exploration
Picturing distributions with graphs
Bar plots and pie charts
Histograms
Time plots
Describing distributions with numbers and boxplots
Relationship between quantitative variables
Scatterplots and correlation
Regression
Analysis of the time series
Summary
Chapter 8: Inference and Data Analysis
Statistical inference
Estimation of parameters
Frequentist approach
Bayesian approach
Likelihood approach
Interval estimation
Frequentist approach
Bayesian approach
Likelihood approach
Data mining and machine learning
Classification
Support vector classification
Trees
Naive Bayes
Nearest neighbors
Dimensionality reduction
Principal component analysis
Isometric mappings
Spectral embedding
Locally linear embedding
Clustering
MeanShift
Gaussian mixture models
Kmeans
Spectral clustering
Summary
Chapter 9: Mathematical Imaging
Digital images
Binary
Gray-scale
Color
Alpha channels
High-level operations on digital images
Object measurements
Mathematical morphology
Smoothing filters
Multivariate calculus
Statistical filters
Fourier analysis
Wavelet decompositions
Image compression
Lossless compression
Lossy compression
Image editing
Transformations of the domain
Rescale and resize
Swirl
Geometric transformations
Intensity adjustment
Histogram equalization
Intensity clipping/resizing
Contrast enhancement
Image restoration
Noise reduction
Sharpening and blurring
Inpainting
Image analysis
Image structure
Object recognition
Edge detection
Line, circle, and ellipse detection
Blob detection
Corner detection
Beyond geometric entities
Summary
Index