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- Herausgeber: Packt Publishing
- Kategorie: Lebensstil
- Sprache: Englisch
NumPy is one of the most important scientific computing libraries available for Python. Mastering Numerical Computing with NumPy teaches you how to achieve expert level competency to perform complex operations, with in-depth coverage of advanced concepts.
Beginning with NumPy's arrays and functions, you will familiarize yourself with linear algebra concepts to perform vector and matrix math operations. You will thoroughly understand and practice data processing, exploratory data analysis (EDA), and predictive modeling. You will then move on to working on practical examples which will teach you how to use NumPy statistics in order to explore US housing data and develop a predictive model using simple and multiple linear regression techniques. Once you have got to grips with the basics, you will explore unsupervised learning and clustering algorithms, followed by understanding how to write better NumPy code while keeping advanced considerations in mind. The book also demonstrates the use of different high-performance numerical computing libraries and their relationship with NumPy. You will study how to benchmark the performance of different configurations and choose the best for your system.
By the end of this book, you will have become an expert in handling and performing complex data manipulations.
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Seitenzahl: 214
Veröffentlichungsjahr: 2018
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Mastering Numerical Computing with NumPy
Copyright © 2018 Packt Publishing
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First published: June 2018
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ISBN 978-1-78899-335-7
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Contributors
About the authors
Umit Mert Cakmak is a data scientist at IBM, where he excels at helping clients solve complex data science problems, from inception to delivery of deployable assets. His research spans multiple disciplines beyond his industry and he likes sharing his insights at conferences, universities, and meet-ups.
Mert Cuhadaroglu is a BI Developer in EPAM, developing E2E analytics solutions for complex business problems in various industries, mostly investment banking, FMCG, media, communication, and pharma. He consistently uses advanced statistical models and ML algorithms to provide actionable insights. Throughout his career, he has worked in several other industries, such as banking and asset management. He continues his academic research in AI for trading algorithms.
About the reviewer
Tiago Antao is a computer scientist turned computational biologist with a PhD from Liverpool School of Tropical Medicine in UK. He is a co-author of Biopython, a major bioinformatics package written in Python.
In his career he has worked at University of Cambridge (UK) and University of Oxford (UK), and is currently a research scientist at University of Montana (USA). He is the author of Bioinformatics with Python Cookbook.
Packt is searching for authors like you
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Table of Contents
Title Page
Copyright and Credits
Mastering Numerical Computing with NumPy
Packt Upsell
Why subscribe?
PacktPub.com
Contributors
About the authors
About the reviewer
Packt is searching for authors like you
Preface
Who this book is for
What this book covers
To get the most out of this book
Download the example code files
Download the color images
Conventions used
Get in touch
Reviews
Working with NumPy Arrays
Technical requirements
Why do we need NumPy?
Who uses NumPy?
Introduction to vectors and matrices
Basics of NumPy array objects
NumPy array operations
Working with multidimensional arrays
Indexing, slicing, reshaping, resizing, and broadcasting
Summary
Linear Algebra with NumPy
Vector and matrix mathematics
What's an eigenvalue and how do we compute it?
Computing the norm and determinant
Solving linear equations
Computing gradient
Summary
Exploratory Data Analysis of Boston Housing Data with NumPy Statistics
Loading and saving files
Exploring our dataset
Looking at basic statistics
Computing histograms
Explaining skewness and kurtosis
Trimmed statistics
Box plots
Computing correlations
Summary
Predicting Housing Prices Using Linear Regression
Supervised learning and linear regression
Independent and dependent variables
Hyperparameters
Loss and error functions
Univariate linear regression with gradient descent
Using linear regression to model housing prices
Summary
Clustering Clients of a Wholesale Distributor Using NumPy
Unsupervised learning and clustering
Hyperparameters
The loss function
Implementing our algorithm for a single variable
Modifying our algorithm
Summary
NumPy, SciPy, Pandas, and Scikit-Learn
NumPy and SciPy
Linear regression with SciPy and NumPy
NumPy and pandas
Quantitative modeling with stock prices using pandas
SciPy and scikit-learn
K-means clustering in housing data with scikit-learn
Summary
Advanced Numpy
NumPy internals
How does NumPy manage memory?
Profiling NumPy code to understand the performance
Summary
Overview of High-Performance Numerical Computing Libraries
BLAS and LAPACK
ATLAS
Intel Math Kernel Library
OpenBLAS
Configuring NumPy with low-level libraries using AWS EC2
Installing BLAS and LAPACK
Installing OpenBLAS
Installing Intel MKL
Installing ATLAS
Compute-intensive tasks for benchmarking
Matrix decomposition
Singular-value decomposition
Cholesky decomposition
Lower-upper decomposition
Eigenvalue decomposition
QR decomposition
Working with sparse linear systems
Summary
Performance Benchmarks
Why do we need a benchmark?
Preparing for a performance benchmark
Performance with BLAS and LAPACK
Performance with OpenBLAS
Performance with ATLAS
Performance with Intel MKL
Results
Summary
Other Books You May Enjoy
Leave a review - let other readers know what you think
Preface
If you are trying to hone your skills in the field of data science, there are many books and courses out there with varying levels of difficulty. What usually happens is that you start to study introductory resources and then continue with more in-depth, technical ones to get a taste of a new field or technology. If you were following this kind of learning path for sometime, you must have realized that it becomes very time consuming journey. We, as lifelong learners, need books with more compact representation of knowledge and experience which requires the right balance between theory and practice. This book aims to bring beginner, intermediate, and advanced concepts together and it is our humble effort to build up your knowledge from scratch.
This book assumes no previous background of scientific computing and will introduce various subjects using practical examples. It may sometimes feel like separate topics pulled together randomly and the book's flow doesn't stick to one consistent path. This was a deliberate decision we made to give you a little taste of several different topics and applications.
We hope that you will read this book to have a broader overview of scientific computing as well as to master the nitty-gritty of NumPy and other supporting scientific libraries of Python such as SciPy and Scikit-Learn.
Who this book is for
This book is for everyone who would like to gain additional knowledge in the data science field. Mastering Numerical Computing with NumPy is for you if you are a Python programmer, data analyst, data engineer, or data science enthusiast who wants to master the intricacies of NumPy and build solutions for your numeric and scientific computational problems. You are expected to have familiarity with mathematics to get the most out of this book.
What this book covers
Chapter 1, Working with Numpy Arrays, explains the basics of numerical computing with NumPy, which is a Python library for working with multi-dimensional arrays and matrices used by scientific computing applications.
Chapter 2, Linear Algebra with Numpy, covers the basics of linear algebra and provides practical NumPy examples.
Chapter 3, Exploratory Data Analysis of Boston Housing Data with NumPy Statistics, explains exploratory data analysis and provides examples using Boston Housing Dataset.
Chapter 4, Predicting Housing Prices Using Linear Regression, covers supervised learning and provides a practical example for predicting housing prices using linear regression.
Chapter 5, Clustering Clients of a Wholesale Distributor Using NumPy, explains unsupervised learning and provides a practical example of a clustering algorithm to model a wholesale distributor sales dataset, which contains information on annual spending in monetary units for diverse product categories.
Chapter 6, NumPy, SciPy, Pandas, and Scikit-Learn, shows the relationship between NumPy and other libraries and provides examples of how they are used together.
Chapter 7, Advanced Numpy, explains the advanced considerations of NumPy library usage.
Chapter 8, Overview of High-Performance Numerical Computing Libraries, introduces several low-level, high-performance numerical computing libraries and their relationship with NumPy.
Chapter 9, Performance Benchmarks, takes a deep dive into the performance of NumPy algorithms depending on the underlying high-performance numerical computing libraries.
To get the most out of this book
Basic Python programming knowledge will definitely help, though it is not strictly necessary
Anaconda distribution for Python 3 will be enough to cover most of the examples used in this book
Download the example code files
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We also have other code bundles from our rich catalog of books and videos available athttps://github.com/PacktPublishing/. Check them out!
Download the color images
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Conventions used
There are a number of text conventions used throughout this book.
CodeInText: Indicates code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input, and Twitter handles. Here is an example: "Another important parameter in this function is learning_rate."
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$ sudo apt-get upgrade
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Working with NumPy Arrays
Scientific computing is a multidisciplinary field, with its applications spanning across disciplines such as numerical analysis, computational finance, and bioinformatics.
Let's consider a case for financial markets. When you think about financial markets, there is a huge interconnected web of interactions. Governments, banks, investment funds, insurance companies, pensions, individual investors, and others are involved in this exchange of financial instruments. You can't simply model all the interactions between market participants because everyone who is involved in financial transactions has different motives and different risk/return objectives. There are also other factors which affect the prices of financial assets. Even modeling one asset price requires you to do a tremendous amount of work, and your success is not guaranteed. In mathematical terms, this doesn't have a closed-form solution and this makes a great case for utilizing scientific computing where you can use advanced computing techniques to attack such problems.
By writing computer programs, you will have the power to better understand the system you are working on. Usually, the computer program you will be writing will be some sort of simulation, such as the Monte Carlo simulation. By using a simulation such as Monte Carlo, you can model the price of option contracts. Pricing financial assets is a good material for simulations, simply because of the complexity of financial markets. All of these mathematical computations need a powerful, scalable and convenient structure for your data (which is mostly in matrix form) when you do your computation. In other words, you need a more compact structure than a list in order to simplify your task. NumPy is a perfect candidate for performant vector/matrix operations and its extensive library of mathematical operations makes numeric computing easy and efficient.
In this chapter, wewill cover the following topics:
The importance of NumPy
Theoretical and practical information about vectors and matrices
NumPy array operations and their usage in multidimensional arrays
The question is, where should we start practicing coding skills? In this book, you will be using Python because of its huge adoption in the scientific community, and you will mainly work with a specific library called NumPy, which stands for numerical Python.
Technical requirements
In this book, we will use Jupyter Notebooks. We will edit and run Python code via a web browser. It's an open source platform which you can install by following the instructions in this link: http://jupyter.org/install.
This book will be using Python 3.x, so when you open a new notebook, you should pick Python 3 kernel. Alternatively, you can install Jupyter Notebook using Anaconda (Python version 3.6), which is highly recommended. You can install it by following the instructions in this link: https://www.anaconda.com/download/.
Why do we need NumPy?
Python has become a rockstar programming language recently, not only because it has friendly syntax and readability, but because it can be used for a variety of purposes. Python's ecosystem of various libraries makes various computations relatively easy for programmers. Stack Overflow is one the most popular websites for programmers. Users can ask questions by tagging which programming language they relate to. The following figure shows the growth of major programming languages by calculating these tags and plot the popularity of major programming languages over the years. The research conducted by Stack Overflow can be further analyzed via this link to their official blog: https://stackoverflow.blog/2017/09/06/incredible-growth-python/:
NumPy is the most fundamental package for scientific computing in Python and is the base for many other packages. Since Python was not initially designed for numerical computing, this need has arised in the late 90's when Python started to become popular among engineers and programmers who needed faster vector operations. As you can see from the following figure, many popular machine learning and computational packages use some of NumPy's features, and the most important thing is that they use NumPy arrays heavily in their methods, which makes NumPy an essential library for scientific projects.
The figure shows some well-known libraries which use NumPy features:
For numerical computing, you mainly work with vectors and matrices. You can manipulate them in different ways by using a range of mathematical functions. NumPy is a perfect fit for these kinds of situations since it allows users to have their computations completed efficiently. Even though Python lists are very easy to create and manipulate, they don't support vectorized operations. Python doesn't have fixed type elements in lists and for example, for loop is not very efficient because, at every iteration, data type needs to be checked. In NumPy arrays, however, the data type is fixed and also supports vectorized operations. NumPy is not just more efficient in multidimensional array operations comparing to Python lists; it also provides many mathematical methods that you can apply as soon as it's imported. NumPy is a core library for the scientific Python data science stack.
SciPy has strong relationship with NumPy as it's using NumPy multidimensional arrays as a base data structure for its scientific functions for linear algebra, optimization. interpolation, integration, FFT, signal and image processing and others. SciPy was built on top of the NumPy array framework and uplifted scientific programming with its advanced mathematical functions. Therefore some parts of the NumPy API have been moved to SciPy. This relationship with NumPy makes SciPy more convenient for advanced scientific computing in many cases.
To sum this up, we can summarize NumPy's advantages as follows:
It's open source and zero-cost
It's a high-level programming language with user-friendly syntax
It's more efficient than Python lists
It has more advanced built-in functions and is well-integrated with other libraries
Who uses NumPy?
In both academic and business circles, you will hear people talking about the tools and technologies they use in their work. Depending on the environment and conditions, you might need to work with specific technologies. For example, if your company has already invested in SAS, you will need to carry out your project in the SAS development environment suited to your problem.
However, one of the advantages of NumPy is that it's open source, and it costs nothing for you to utilize it in your project. If you have already coded in Python, it's super easy to learn. If performance is your concern, you can easily embed C or Fortran code. Moreover, it will introduce you to a whole other set of libraries such as SciPy and Scikit-learn, which you can use to solve almost any problem.
Since data mining and predictive analytics became really important recently, roles like Data Scientist and Data Analyst are mentioned as the hottest jobs of the 21st century in many business journals such as Forbes, Bloomberg, and so on. People who need to work with data and do analysis, modeling, or forecasting should become familiar with NumPy's usage and its capabilities, as it will help you quickly prototype and test your ideas. If you are a working professional, your firm most probably wants to use data analysis methods in order to move one step ahead of its competitors. If they can better understand the data they have, they can understand the business better, and this will lead them to make better decisions. NumPy plays a critical role here as it is capable of performing wide range of operations and making your projects timewise efficient.
Basics of NumPy array objects
As mentioned in the preceding section, what makes NumPy special is the usage of multidimensional arrays called ndarrays. All ndarray items are homogeneous and use the same size in memory. Let's start by importing NumPy and analyzing the structure of a NumPy array object by creating the array. You can easily import this library by typing the following statement into your console. You can use any naming convention instead of np, but in this book, np
