Book Image

SciPy Recipes

By : V Kishore Ayyadevara, Ruben Oliva Ramos

Book Image

SciPy Recipes

By: V Kishore Ayyadevara, Ruben Oliva Ramos

Overview of this book

With the SciPy Stack, you get the power to effectively process, manipulate, and visualize your data using the popular Python language. Utilizing SciPy correctly can sometimes be a very tricky proposition. This book provides the right techniques so you can use SciPy to perform different data science tasks with ease. This book includes hands-on recipes for using the different components of the SciPy Stack such as NumPy, SciPy, matplotlib, and pandas, among others. You will use these libraries to solve real-world problems in linear algebra, numerical analysis, data visualization, and much more. The recipes included in the book will ensure you get a practical understanding not only of how a particular feature in SciPy Stack works, but also of its application to real-world problems. The independent nature of the recipes also ensure that you can pick up any one and learn about a particular feature of SciPy without reading through the other recipes, thus making the book a very handy and useful guide.

Preface

What this book covers

What you need for this book

Who this book is for

Reader feedback

Customer support

Free Chapter

Getting to Know the Tools

Getting to Know the Tools

Installing Anaconda on Windows

Installing Anaconda on macOS

Installing Anaconda on Linux

Checking the Anaconda installation

Installing SciPy from a binary distribution on Windows

Installing SciPy from a binary distribution on macOS

Installing SciPy from source on Linux

Installing optional packages with conda

Installing packages with pip

Setting up a virtual environment with conda

Creating a virtual environment for development with conda

Creating a conda environment with a different version of a package

Using conda environments to run different versions of Python

Creating virtual environments with venv

Running SciPy in a script

Running SciPy in Jupyter

Running SciPy in Spyder

Running SciPy in PyCharm

Getting Started with NumPy

Getting Started with NumPy

Creating NumPy arrays

Querying and changing the shape of an array

Storing and retrieving NumPy arrays

Operations on arrays

Using masked arrays to represent invalid data

Using object arrays to store heterogeneous data

Defining, symbolically, a function operating on arrays

Using Matplotlib to Create Graphs

Using Matplotlib to Create Graphs

Creating two-dimensional plots of functions and data

Generating multiple plots in a single figure

Setting line styles and markers

Using different backends to display graphs

Saving plots to disk

Annotating graphs

Generating histograms and box plots

Creating three-dimensional plots

Generating interactive displays in the Jupyter Notebook

Object-oriented graph creation using Artist objects

Creating a map with cartopy

Data Wrangling with pandas

Data Wrangling with pandas

Creating Series objects

Creating DataFrame objects

Inserting and deleting columns to a DataFrame

Inserting and deleting rows to a DataFrame

Selecting items by row indexes and column labels

Selecting items by integer location

Selecting items using mixed indexing

Accessing, selecting, and modifying data

Selecting rows using Boolean selection

Reading and storing data in different formats

Data displays employing different kinds of visual representation

How to apply numerical functions and operations to Series and DataFrame objects

Computing statistical functions on Series and DataFrame objects

How to sort data in Series and DataFrame objects

Performing merging, joins, concatenation, and grouping

Matrices and Linear Algebra

Matrices and Linear Algebra

Matrix operations and functions on two-dimensional arrays

Solving linear systems using matrices

Calculating the null space of a matrix

Calculating the LU decompositions of a matrix

Calculating the QR decomposition of a matrix

Calculating the eigenvalue and eigenvector of a matrix

Diagonalizing a matrix

Calculating the Jordan form of a matrix

Calculating the singular value decomposition of a matrix

Creating a sparse matrix

Computations on top of a sparse matrix

Solving Equations and Optimization

Solving Equations and Optimization

Non-linear equations and systems

System of equations and how to solve it

Choosing the solver used to find the solution of equations

Solving constrained non-linear optimization problems in several variables

Solving one-dimensional optimization problems

Solving multidimensional non-linear equations using the Newton-Krylov method

Solving multidimensional non-linear equations using the Anderson method

Finding the best linear fit for a set of data

Doing non-linear regression for a set of data

Constants and Special Functions

Constants and Special Functions

Physical and mathematical constants available in SciPy

Using constants in the CODATA database

Bessel functions

Error functions

Orthogonal polynomials functions

The Riemann zeta function

Airy and Bairy functions

The Bessel and Struve functions

Calculus, Interpolation, and Differential Equations

Calculus, Interpolation, and Differential Equations

Computing integrals using a Gaussian quadrature

Computing integrals with weighting functions

Computing multiple integrals

Computing a polynomial interpolation for a set of data points

Univariate interpolation

Finding a cubic spline that interpolates a set of data

Defining a B-spline for a given set of control points

Differentiation

Solving a one-dimensional ordinary differential equation

Solving a system of ordinary differential equations

Solving differential equations and systems with parameters

Using ode and the objected-oriented interface to solve differential equations

Statistics and Probability

Statistics and Probability

Computing the probability mass function of a discrete random variable

Computing the probability density function of a continuous random variable

Computing the cumulative distribution function for a random variable

Computing the values of inverse probabilities associated with a random variable

Computing the average, standard deviation, and higher moments of a distribution

Computing probabilities associated with the multivariate Gaussian distribution

Computing the summary statistics of a dataset

Advanced Computations with SciPy

Advanced Computations with SciPy

Discrete Fourier transforms

Computing the discrete Fourier transform (DFT) of a data series using the FFT algorithm

Computing the inverse DFT of a data series

Computing signal construction

Getting started with filters

Computing the DFT for two-dimensional data

How to find the DFT of the derivative of a function

Computing the convolution of two functions

Mathematical imaging

Computing pairwise distances from a dataset, using different distance metrics

How to identify neighborhoods and nearest neighbors for a dataset and a given metric

Nearest neighbors regression

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Differentiation

In the following section, we will look at how to solve differentiation and some of its applications.

Getting ready

There are three ways to approach the computation of derivatives:

Numerical differentiation refers to the process of approximation of the derivative of a given function at a point. In SciPy, we have the following procedures, which will be covered in detail:
- For generic univariate functions, there is the central difference formula with fixed spacing.
- It is always possible to perform numerical differentiation via Cauchy's theorem, which transforms the derivative into a definite integral. This integral is then treated with the techniques of numerical integration explained before.
Symbolic...