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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Creating a conda environment with a different version of a package

We often need to run code that is not compatible with a particular version of a package. In this situation, it is useful to use conda to find out what version of a package is currently installed. For instance, to get information about which version of the numpy package is being used at the moment, we can execute the command shown as follows at the system prompt:

conda info numpy

On my computer, this outputs the following information:

numpy 1.12.1 py36_nomkl_0
file name   : numpy-1.12.1-py36_nomkl_0.tar.bz2
 name        : numpy
version     : 1.12.1

Getting ready

This recipe assumes that you have a working installation of Anaconda. If you don't, follow the recipe for installing Anaconda on your operating system presented previously in this chapter.

How to do it...

Let's now suppose that we have a legacy package that depends on an earlier version of NumPy. For example, let's assume we need version 1.7 of NumPy. We can check what versions of NumPy are available in the Anaconda repository with the following command:

conda search numpy

Running this command will produce a long list, in which we find the following information:

...  
1.7.1                    py33_0  defaults
...
1.7.1                    py33_2  defaults
...

conda shows several available packages of NumPy, some of them compatible with Python 3. Let's now create an environment that has the older version of NumPy installed. Start by creating the new environment with the following command:

conda create --name numpy17 python=3 numpy=1.7

Notice that we specify the required versions for both Python and NumPy. conda will then display the following information about the environment to be created:

The following NEW packages will be INSTALLED:
numpy:      1.7.1-py33_2 
openssl:    1.0.1k-1
pip:        8.0.3-py33_0 
python:     3.3.5-3
readline:   6.2-2
 ...

Notice that conda will downgrade the version of Python in the new environment. conda packages are carefully designed to prevent incompatibilities. Go ahead and accept the changes to start the installation.

When the installation is complete, activate the new package. On Linux and macOS, we do this with with the following command:

source activate numpy17

On Windows, use the following command to activate the environment:

activate numpy17

After the environment is activated, we can install any packages that require version 1.7 of NumPy.

When we have finished working on the project, we need to deactivate the environment. On Linux and macOS, we use the following command:

source deactivate numpy17

On Windows, the command to deactivate an environment is as follows:

deactivate numpy17