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Python Data Analysis, Second Edition
Python Data Analysis, Second Edition

Python Data Analysis, Second Edition: Data manipulation and complex data analysis with Python , Second Edition

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Python Data Analysis, Second Edition

Chapter 2. NumPy Arrays

Now that we have worked on a real example utilizing the foundational data analysis libraries from SciPy stack, it's time to learn about NumPy arrays. This chapter acquaints you with the fundamentals of NumPy arrays. At the end of this chapter, you will have a basic understanding of NumPy arrays and related functions.

The topics we will address in this chapter are as follows:

  • The NumPy array object
  • Creating a multidimensional array
  • Selecting NumPy array elements
  • NumPy numerical types
  • One-dimensional slicing and indexing
  • Manipulating array shapes
  • Creating array views and copies
  • Fancy indexing
  • Indexing with a list of locations
  • Indexing NumPy arrays with Booleans
  • Broadcasting NumPy arrays

You may want to open the ch-02.ipynb file in Jupyter Notebook to follow along the examples in this chapter or type them in a new notebook of your own.

The NumPy array object

NumPy provides a multidimensional array object called ndarray. NumPy arrays are typed arrays of a fixed size. Python lists are heterogeneous and thus elements of a list may contain any object type, while NumPy arrays are homogenous and can contain objects of only one type. An ndarray consists of two parts, which are as follows:

  • The actual data that is stored in a contiguous block of memory
  • The metadata describing the actual data

Since the actual data is stored in a contiguous block of memory, hence loading of the large dataset as ndarray, it is affected by the availability of a large enough contiguous block of memory. Most of the array methods and functions in NumPy leave the actual data unaffected and only modify the metadata.

We have already discovered in the preceding chapter how to produce an array by applying the arange() function. Actually, we made a one-dimensional array that held a set of numbers. The ndarray can have more than a single dimension.

Advantages of...

Creating a multidimensional array

Now that we know how to create a vector, we are set to create a multidimensional NumPy array. After we produce the matrix we will again need to show it, as demonstrated in the following code snippets:

  1. Create a multidimensional array as follows:
            In: m = np.array([np.arange(2), np.arange(2)]) 
        In: m 
        Out: 
        array([[0, 1], 
               [0, 1]])
  2. We can show the array shape as follows:
            In: m.shape 
        Out: (2, 2)

We made a 2x2 array with the arange() subroutine. The array() function creates an array from an object that you pass to it. The object has to be an array, for example, a Python list. In the previous example, we passed a list of arrays. The object is the only required parameter of the array() function. NumPy functions tend to have a heap of optional arguments with predefined default options.

Selecting NumPy array elements

From time to time, we will wish to select a specific constituent of an array. We will take a look at how to do this, but to kick off, let's make a 2x2 matrix again:

In: a = np.array([[1,2],[3,4]]) 
In: a 
Out: 
array([[1, 2], 
       [3, 4]])

The matrix was made this time by giving the array() function a list of lists. We will now choose each item of the matrix one at a time, as shown in the following code snippet. Recall that the index numbers begin from 0:

In: a[0,0] 
Out: 1 
In: a[0,1] 
Out: 2 
In: a[1,0] 
Out: 3 
In: a[1,1] 
Out: 4

As you can see, choosing elements of an array is fairly simple. For the array a, we just employ the notation a[m,n], where m and n are the indices of the item in the array. Have a look at the following figure for your reference:

Selecting NumPy array elements

NumPy numerical types

Python has an integer type, a float type, and complex type; nonetheless, this is not sufficient for scientific calculations. In practice, we still demand more data types with varying precisions and, consequently, different storage sizes of the type. For this reason, NumPy has many more data types. The bulk of the NumPy mathematical types end with a number. This number designates the count of bits related to the type. The following table (adapted from the NumPy user guide) presents an overview of NumPy numerical types:

Type

Description

bool

Boolean (True or False) stored as a bit

inti

Platform integer (normally either int32 or int64)

int8

Byte (-128 to 127)

int16

Integer (-32768 to 32767)

int32

Integer (-2 ** 31 to 2 ** 31 -1)

int64

Integer (-2 ** 63 to 2 ** 63 -1)

uint8

Unsigned integer (0 to 255)

uint16

Unsigned integer (0 to 65535)

uint32

Unsigned integer (0 to 2 ** 32 - 1)

uint64

Unsigned integer (0 to 2 ** 64 - 1)

...

One-dimensional slicing and indexing

Slicing of one-dimensional NumPy arrays works just like the slicing of standard Python lists. Let's define an array containing the numbers 0, 1, 2, and so on up to and including 8. We can select a part of the array from indexes 3 to 7, which extracts the elements of the arrays 3 through 6:

In: a = np.arange(9) 
In: a[3:7] 
Out: array([3, 4, 5, 6])

We can choose elements from an index of 0 to 7 with an increment of 2:

In: a[:7:2] 
Out: array([0, 2, 4, 6])

Just as in Python, we can use negative indices and reverse the array:

In: a[::-1] 
Out: array([8, 7, 6, 5, 4, 3, 2, 1, 0])

The NumPy array object

NumPy provides a multidimensional array object called ndarray. NumPy arrays are typed arrays of a fixed size. Python lists are heterogeneous and thus elements of a list may contain any object type, while NumPy arrays are homogenous and can contain objects of only one type. An ndarray consists of two parts, which are as follows:

  • The actual data that is stored in a contiguous block of memory

  • The metadata describing the actual data

Since the actual data is stored in a contiguous block of memory, hence loading of the large dataset as ndarray, it is affected by the availability of a large enough contiguous block of memory. Most of the array methods and functions in NumPy leave the actual data unaffected and only modify the metadata.

We have already discovered in the preceding chapter how to produce an array by applying the arange() function. Actually, we made a one-dimensional array that held a set of numbers. The ndarray can have more than a single dimension.

Advantages of...

Creating a multidimensional array

Now that we know how to create a vector, we are set to create a multidimensional NumPy array. After we produce the matrix we will again need to show it, as demonstrated in the following code snippets:

  1. Create a multidimensional array as follows:

            In: m = np.array([np.arange(2), np.arange(2)]) 
        In: m 
        Out: 
        array([[0, 1], 
               [0, 1]])

  2. We can show the array shape as follows:

            In: m.shape 
        Out: (2, 2)

We made a 2x2 array with the arange() subroutine. The array() function creates an array from an object that you pass to it. The object has to be an array, for example, a Python list. In the previous example, we passed a list of arrays. The object is the only required parameter of the array() function. NumPy functions tend to have a heap of optional arguments with predefined default options.

Selecting NumPy array elements

From time to time, we will wish to select a specific constituent of an array. We will take a look at how to do this, but to kick off, let's make a 2x2 matrix again:

In: a = np.array([[1,2],[3,4]]) 
In: a 
Out: 
array([[1, 2], 
       [3, 4]])

The matrix was made this time by giving the array() function a list of lists. We will now choose each item of the matrix one at a time, as shown in the following code snippet. Recall that the index numbers begin from 0:

In: a[0,0] 
Out: 1 
In: a[0,1] 
Out: 2 
In: a[1,0] 
Out: 3 
In: a[1,1] 
Out: 4

As you can see, choosing elements of an array is fairly simple. For the array a, we just employ the notation a[m,n], where m and n are the indices of the item in the array. Have a look at the following figure for your reference:

NumPy numerical types

Python has an integer type, a float type, and complex type; nonetheless, this is not sufficient for scientific calculations. In practice, we still demand more data types with varying precisions and, consequently, different storage sizes of the type. For this reason, NumPy has many more data types. The bulk of the NumPy mathematical types end with a number. This number designates the count of bits related to the type. The following table (adapted from the NumPy user guide) presents an overview of NumPy numerical types:

Type

Description

bool

Boolean (True or False) stored as a bit

inti

Platform integer (normally either int32 or int64)

int8

Byte (-128 to 127)

int16

Integer (-32768 to 32767)

int32

Integer (-2 ** 31 to 2 ** 31 -1)

int64

Integer (-2 ** 63 to 2 ** 63 -1)

uint8

Unsigned integer (0 to 255)

uint16

Unsigned integer (0 to 65535)

uint32

Unsigned integer (0 to 2 ** 32 - 1)

uint64

Unsigned integer (0 to 2 ** 64 - 1)

float16...

One-dimensional slicing and indexing

Slicing of one-dimensional NumPy arrays works just like the slicing of standard Python lists. Let's define an array containing the numbers 0, 1, 2, and so on up to and including 8. We can select a part of the array from indexes 3 to 7, which extracts the elements of the arrays 3 through 6:

In: a = np.arange(9) 
In: a[3:7] 
Out: array([3, 4, 5, 6])

We can choose elements from an index of 0 to 7 with an increment of 2:

In: a[:7:2] 
Out: array([0, 2, 4, 6])

Just as in Python, we can use negative indices and reverse the array:

In: a[::-1] 
Out: array([8, 7, 6, 5, 4, 3, 2, 1, 0])

Manipulating array shapes

We have already learned about the reshape() function. Another repeating chore is the flattening of arrays. Flattening in this setting entails transforming a multidimensional array into a one-dimensional array. Let us create an array b that we shall use for practicing the further examples:

In: b = np.arange(24).reshape(2,3,4) 
 
In: print(b) 
 
Out: [[[ 0,  1,  2,  3], 
        [ 4,  5,  6,  7], 
        [ 8,  9, 10, 11]], 
 
       [[12, 13, 14, 15], 
        [16, 17, 18, 19], 
        [20, 21, 22, 23]]])

We can manipulate array shapes using the following functions:

  • Ravel: We can accomplish this with the ravel() function as follows:

            In: b 
        Out: 
        array([[[ 0,  1,  2,  3], 
                [ 4,  5,  6,  7], 
                [ 8,  9, 10, 11]], 
               [[12, 13, 14, 15], 
                [16, 17, 18, 19], 
                [20, 21, 22, 23]]]) 
...

Creating array views and copies

In the example about ravel(), views were brought up. Views should not be confused with the construct of database views. Views in the NumPy universe are not read-only and you don't have the possibility to protect the underlying information. It is crucial to know when we are handling a shared array view and when we have a replica of the array data. A slice of an array, for example, will produce a view. This entails that if you assign the slice to a variable and then alter the underlying array, the value of this variable will change. We will create an array from the face picture in the SciPy package, and then create a view and alter it at the final stage:

  1. Get the face image:

            face = scipy.misc.face()

  2. Create a copy of the face array:

            acopy = face.copy()

  3. Create a view of the array:

            aview = face.view()

  4. Set all the values in the view to 0 with a flat iterator:

            aview.flat = 0

The final outcome is that only one of the...

Fancy indexing

Fancy indexing is indexing that does not involve integers or slices, which is conventional indexing. In this tutorial, we will practice fancy indexing to set the diagonal values of the Lena photo to 0. This will draw black lines along the diagonals, crossing through them.

The following is the code for this example:

import scipy.misc 
import matplotlib.pyplot as plt 
 
face = scipy.misc.face() 
xmax = face.shape[0] 
ymax = face.shape[1] 
face=face[:min(xmax,ymax),:min(xmax,ymax)] 
xmax = face.shape[0] 
ymax = face.shape[1] 
face[range(xmax), range(ymax)] = 0 
face[range(xmax-1,-1,-1), range(ymax)] = 0 
plt.imshow(face) 
plt.show()

The following is a brief explanation of the preceding code:

  1. Set the values of the first diagonal to 0.

    To set the diagonal values to 0, we need to specify two different ranges for the x and y values (coordinates in a Cartesian coordinate system):

            face[range(xmax), range(ymax)] =...
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Key benefits

  • Find, manipulate, and analyze your data using the Python 3.5 libraries
  • Perform advanced, high-performance linear algebra and mathematical calculations with clean and efficient Python code
  • An easy-to-follow guide with realistic examples that are frequently used in real-world data analysis projects.

Description

Data analysis techniques generate useful insights from small and large volumes of data. Python, with its strong set of libraries, has become a popular platform to conduct various data analysis and predictive modeling tasks. With this book, you will learn how to process and manipulate data with Python for complex analysis and modeling. We learn data manipulations such as aggregating, concatenating, appending, cleaning, and handling missing values, with NumPy and Pandas. The book covers how to store and retrieve data from various data sources such as SQL and NoSQL, CSV fies, and HDF5. We learn how to visualize data using visualization libraries, along with advanced topics such as signal processing, time series, textual data analysis, machine learning, and social media analysis. The book covers a plethora of Python modules, such as matplotlib, statsmodels, scikit-learn, and NLTK. It also covers using Python with external environments such as R, Fortran, C/C++, and Boost libraries.

Who is this book for?

This book is for programmers, scientists, and engineers who have the knowledge of Python and know the basics of data science. It is for those who wish to learn different data analysis methods using Python 3.5 and its libraries. This book contains all the basic ingredients you need to become an expert data analyst.

What you will learn

  • Install open source Python modules such NumPy, SciPy, Pandas, stasmodels, scikit-learn,theano, keras, and tensorflow on various platforms
  • Prepare and clean your data, and use it for exploratory analysis
  • Manipulate your data with Pandas
  • Retrieve and store your data from RDBMS, NoSQL, and distributed filesystems such as HDFS and HDF5
  • Visualize your data with open source libraries such as matplotlib, bokeh, and plotly
  • Learn about various machine learning methods such as supervised, unsupervised, probabilistic, and Bayesian
  • Understand signal processing and time series data analysis
  • Get to grips with graph processing and social network analysis
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Publication date : Mar 27, 2017
Length: 330 pages
Edition : 2nd
Language : English
ISBN-13 : 9781787127487
Category :
Data
Languages :
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Concepts :
Data Analysis
Tools :
Scikit-learn

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Length: 330 pages
Edition : 2nd
Language : English
ISBN-13 : 9781787127487
Category :
Data
Languages :
Python
Concepts :
Data Analysis
Tools :
Scikit-learn

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Table of Contents

15 Chapters
1. Getting Started with Python Libraries Chevron down icon Chevron up icon
1. Getting Started with Python Libraries
Installing Python 3
Using IPython as a shell
Reading manual pages
Jupyter Notebook
NumPy arrays
A simple application
Where to find help and references
Listing modules inside the Python libraries
Visualizing data using Matplotlib
Summary
2. NumPy Arrays Chevron down icon Chevron up icon
2. NumPy Arrays
The NumPy array object
Creating a multidimensional array
Selecting NumPy array elements
NumPy numerical types
One-dimensional slicing and indexing
Manipulating array shapes
Creating array views and copies
Fancy indexing
Indexing with a list of locations
Indexing NumPy arrays with Booleans
Broadcasting NumPy arrays
Summary
References
3. The Pandas Primer Chevron down icon Chevron up icon
3. The Pandas Primer
Installing and exploring Pandas
The Pandas DataFrames
The Pandas Series
Querying data in Pandas
Statistics with Pandas DataFrames
Data aggregation with Pandas DataFrames
Concatenating and appending DataFrames
Joining DataFrames
Handling missing values
Dealing with dates
Pivot tables
Summary
References
4. Statistics and Linear Algebra Chevron down icon Chevron up icon
4. Statistics and Linear Algebra
Basic descriptive statistics with NumPy
Linear algebra with NumPy
Finding eigenvalues and eigenvectors with NumPy
NumPy random numbers
Creating a NumPy masked array
Summary
5. Retrieving, Processing, and Storing Data Chevron down icon Chevron up icon
5. Retrieving, Processing, and Storing Data
Writing CSV files with NumPy and Pandas
The binary .npy and pickle formats
Storing data with PyTables
Reading and writing Pandas DataFrames to HDF5 stores
Reading and writing to Excel with Pandas
Using REST web services and JSON
Reading and writing JSON with Pandas
Parsing RSS and Atom feeds
Parsing HTML with Beautiful Soup
Summary
Reference
6. Data Visualization Chevron down icon Chevron up icon
6. Data Visualization
The matplotlib subpackages
Basic matplotlib plots
Logarithmic plots
Scatter plots
Legends and annotations
Three-dimensional plots
Plotting in Pandas
Lag plots
Autocorrelation plots
Plot.ly
Summary
7. Signal Processing and Time Series Chevron down icon Chevron up icon
7. Signal Processing and Time Series
The statsmodels modules
Moving averages
Window functions
Defining cointegration
Autocorrelation
Autoregressive models
ARMA models
Generating periodic signals
Fourier analysis
Spectral analysis
Filtering
Summary
8. Working with Databases Chevron down icon Chevron up icon
8. Working with Databases
Lightweight access with sqlite3
Accessing databases from Pandas
SQLAlchemy
Pony ORM
Dataset - databases for lazy people
PyMongo and MongoDB
Storing data in Redis
Storing data in memcache
Apache Cassandra
Summary
9. Analyzing Textual Data and Social Media Chevron down icon Chevron up icon
9. Analyzing Textual Data and Social Media
Installing NLTK
About NLTK
Filtering out stopwords, names, and numbers
The bag-of-words model
Analyzing word frequencies
Naive Bayes classification
Sentiment analysis
Creating word clouds
Social network analysis
Summary
10. Predictive Analytics and Machine Learning Chevron down icon Chevron up icon
10. Predictive Analytics and Machine Learning
Preprocessing
Classification with logistic regression
Classification with support vector machines
Regression with ElasticNetCV
Support vector regression
Clustering with affinity propagation
Mean shift
Genetic algorithms
Neural networks
Decision trees
Summary
11. Environments Outside the Python Ecosystem and Cloud Computing Chevron down icon Chevron up icon
11. Environments Outside the Python Ecosystem and Cloud Computing
Exchanging information with Matlab/Octave
Installing rpy2 package
Interfacing with R
Sending NumPy arrays to Java
Integrating SWIG and NumPy
Integrating Boost and Python
Using Fortran code through f2py
PythonAnywhere Cloud
Summary
12. Performance Tuning, Profiling, and Concurrency Chevron down icon Chevron up icon
12. Performance Tuning, Profiling, and Concurrency
Profiling the code
Installing Cython
Calling C code
Creating a process pool with multiprocessing
Speeding up embarrassingly parallel for loops with Joblib
Comparing Bottleneck to NumPy functions
Performing MapReduce with Jug
Installing MPI for Python
IPython Parallel
Summary
A. Key Concepts Chevron down icon Chevron up icon
A. Key Concepts
B. Useful Functions Chevron down icon Chevron up icon
B. Useful Functions
Matplotlib
NumPy
Pandas
Scikit-learn
SciPy
C. Online Resources Chevron down icon Chevron up icon
C. Online Resources

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RAG-Driven Generative AI
RAG-Driven Generative AI
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Hands-On Reinforcement Learning with Python
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LLM Engineer's Handbook
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Customer reviews

Rating distribution
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
(4 Ratings)
5 star 50%
4 star 25%
3 star 0%
2 star 25%
1 star 0%
sutha May 06, 2017
Full star icon Full star icon Full star icon Full star icon Full star icon 5
If you are into data analysis then you have to know python and this book helps to understand various libraries available to use. Also the libraries are well classified by their usage area!Recommended to read...
Amazon Verified review Amazon
AJ Apr 27, 2018
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Bought this book to lay the foundations for Data Analysis and apply to Geospatial datasets- its worth it!
Amazon Verified review Amazon
boots with the fur Apr 05, 2017
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
I was one of the technical reviewers for this book, it provides a strong foundation to begin analysing and visualizing large datasets in python. If you have wanted to analyze baseball stats and salaries, ala moneyball, or view patterns in anual solar flare events. It also explores learning algorithms for sentiment analysis and predictive patterns. While several chapters could really use a whole book all of their own, this will provide you with the tools that you need in order to begin exploring large data in python, and it even has a chapter to help you tune your performance once your data gets even bigger.
Amazon Verified review Amazon
Anand Nov 25, 2017
Full star icon Full star icon Empty star icon Empty star icon Empty star icon 2
Good but the author jumps from one topic to another without covering by leaving the user in confusion.
Amazon Verified review Amazon

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About the author

Profile icon Idris
Idris
Ivan Idris has an MSc in experimental physics. His graduation thesis had a strong emphasis on applied computer science. After graduating, he worked for several companies as a Java developer, data warehouse developer, and QA analyst. His main professional interests are business intelligence, big data, and cloud computing. Ivan Idris enjoys writing clean, testable code and interesting technical articles. Ivan Idris is the author of NumPy 1.5. Beginner's Guide and NumPy Cookbook by Packt Publishing.
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Disclaimer:
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