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Home > Data > Data Analysis > Numpy Beginner's Guide (Update)
Numpy Beginner's Guide (Update)
Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update): Build efficient, high-speed programs using the high-performance NumPy mathematical library

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Numpy Beginner's Guide (Update)

Chapter 2. Beginning with NumPy Fundamentals

After installing NumPy and getting some code to work, it's time to cover NumPy basics.

The topics we shall cover in this chapter are as follows:

  • Data types
  • Array types
  • Type conversions
  • Array creation
  • Indexing
  • Slicing
  • Shape manipulation

Before we start, let me make a few remarks about the code examples in this chapter. The code snippets in this chapter show input and output from several IPython sessions. Recall that IPython was introduced in Chapter 1, NumPy Quick Start, as the interactive Python shell of choice for scientific computing. The advantages of IPython are the --pylab switch that imports many scientific computing Python packages, including NumPy, and the fact that it is not necessary to explicitly call the print() function to display variable values. Other features include easy parallel computation and the notebook interface in the form of a persistent worksheet in a web browser.

However, the source code delivered alongside the...

NumPy array object

NumPy has a multidimensional array object called ndarray. It consists of two parts:

  • The actual data
  • Some metadata describing the data

The majority of array operations leave the raw data untouched. The only aspect that changes is the metadata.

In the previous chapter, we have already learned how to create an array using the arange() function. Actually, we created a one-dimensional array that contained a set of numbers. The ndarray object can have more than one dimension.

The NumPy array is in general homogeneous (there is a special array type that is heterogeneous as described in the Time for action – creating a record data type section)—the items in the array have to be of the same type. The advantage is that, if we know that the items in the array are of the same type, it is easy to determine the storage size required for the array.

NumPy arrays are indexed starting from 0, just like in Python. Data types are represented by special objects. We will discuss these...

Time for action – creating a multidimensional array

Now that we know how to create a vector, we are ready to create a multidimensional NumPy array. After we create the array, we will again want to display its shape:

  1. Create a two-by-two array:
    In: m = array([arange(2), arange(2)])
In: m
Out:
array([[0, 1],
      [0, 1]])
  2. Show the array shape:
    In: m.shape
Out: (2, 2)

What just happened?

We created a two-by-two array with the arange() and array() functions we have come to trust and love. Without any warning, the array() function appeared on the stage.

The array() function creates an array from an object that you give to it. The object needs to be array-like, for instance, a Python list. In the preceding example, we passed in a list of arrays. The object is the only required argument of the array() function. NumPy functions tend to have a lot of optional arguments with predefined defaults. View the documentation for this function from the IPython shell with the help() function given here...

Time for action – creating a record data type

The record data type is a heterogeneous data type—think of it as representing a row in a spreadsheet or a database. To give an example of a record data type, we will create a record for a shop inventory. The record contains the name of the item, a 40-character string, the number of items in the store represented by a 32-bit integer, and, finally, a price represented by a 32-bit float. These consecutive steps show how to create a record data type:

  1. Create the record:
    In: t = dtype([('name', str_, 40), ('numitems', int32), ('price', float32)])
In: t
Out: dtype([('name', '|S40'), ('numitems', '<i4'), ('price', '<f4')])
  2. View the type (we can view the type of a field as well):
    In: t['name']
Out: dtype('|S40')

If you don't give the array() function a data type, it will assume that it is dealing with floating point numbers...

One-dimensional slicing and indexing

Slicing of one-dimensional NumPy arrays works just like slicing of Python lists. Select a piece of an array from index 3 to 7 that extracts the elements 3 through 6:

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

Select elements from index 0 to 7 with step 2 as follows:

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

Similarly, as in Python, use negative indices and reverse the array with this code snippet:

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

Time for action – slicing and indexing multidimensional arrays

The ndarray class supports slicing over multiple dimensions. For convenience, we refer to many dimensions at once, with an ellipsis.

  1. To illustrate, create an array with the arange() function and reshape it:
    In: b = arange(24).reshape(2,3,4)
In: b.shape
Out: (2, 3, 4)
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]]])

    The array b has 24 elements with values 0 to 23 and we reshaped it to be a two-by-three-by-four, three-dimensional array. We can visualize this as a two-story building with 12 rooms on each floor, 3 rows and 4 columns (alternatively we can think of it as a spreadsheet with sheets, rows, and columns). As you have probably guessed, the reshape() function changes the shape of an array. We give it a tuple of integers, corresponding to the new shape. If the dimensions are not compatible with the...

Time for action – manipulating array shapes

We already learned about the reshape() function. Another recurring task is flattening of arrays. When we flatten multidimensional NumPy arrays, the result is a one-dimensional array with the same data.

  1. Ravel: Accomplish this with the ravel() function:
    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]]])
In: b.ravel()
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])
  2. Flatten: The appropriately named function, flatten() does the same as ravel(), but flatten() always allocates new memory whereas ravel() might return a view of the array. A view is a way to share an array, but you need to be careful with views because modifying the view affects the underlying array, and therefore this impacts other views. An array copy is safer; however, it uses more memory:
    In: b...

Time for action – stacking arrays

First, set up some arrays:

In: a = arange(9).reshape(3,3)
In: a
Out:
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
In: b = 2 * a
In: b
Out:
array([[ 0,  2,  4],
       [ 6,  8, 10],
       [12, 14, 16]])
  1. Horizontal stacking: Starting with horizontal stacking, form a tuple of the ndarray objects and give it to the hstack() function as follows:
    In: hstack((a, b))
Out:
array([[ 0,  1,  2,  0,  2,  4],
       [ 3,  4,  5,  6,  8, 10],
       [ 6,  7,  8, 12, 14, 16]])

    Achieve the same with the concatenate() function as follows (the axis argument here is equivalent to axes in a Cartesian coordinate system and corresponds to the array dimensions):

    In: concatenate((a, b), axis=1)
Out:
array([[ 0,  1,  2,  0,  2,  4],
       [ 3,  4,  5,  6,  8, 10],
       [ 6,  7,  8, 12, 14, 16]])

    This image shows horizontal stacking with the concatenate() function:

    Time for action – stacking arrays
  2. Vertical stacking: With vertical stacking, again, a tuple is formed. This time, it is given to the...

Time for action – splitting arrays

The following steps demonstrate arrays splitting:

  1. Horizontal splitting: The ensuing code splits an array along its horizontal axis into three pieces of the same size and shape:
    In: a
Out:
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
In: hsplit(a, 3)
Out:
[array([[0],
       [3],
       [6]]),
 array([[1],
       [4],
       [7]]),
 array([[2],
       [5],
       [8]])]

    Compare it with a call of the split() function, with extra parameter axis=1:

    In: split(a, 3, axis=1)
Out:
[array([[0],
       [3],
       [6]]),
 array([[1],
       [4],
       [7]]),
 array([[2],
       [5],
       [8]])]
  2. Vertical splitting: vsplit() splits along the vertical axis:
    In: vsplit(a, 3)
Out: [array([[0, 1, 2]]), array([[3, 4, 5]]), array([[6, 7, 8]])]

    The split() function, with axis=0, also splits along the vertical axis:

    In: split(a, 3, axis=0)
Out: [array([[0, 1, 2]]), array([[3, 4, 5]]), array([[6, 7, 8]])]
  3. Depth-wise splitting: The dsplit() function, unsurprisingly...

Time for action – converting arrays

Convert a NumPy array to a Python list with the tolist() function:

  1. Convert to a list:
    In: b
Out: array([ 1.+1.j,  3.+2.j])
In: b.tolist()
Out: [(1+1j), (3+2j)]
  2. The astype() function converts the array to an array of the specified type:
    In: b
Out: array([ 1.+1.j,  3.+2.j])
In: b.astype(int)
/usr/local/bin/ipython:1: ComplexWarning: Casting complex values to real discards the imaginary part
  #!/usr/bin/python
Out: array([1, 3])

    Note

    We are losing the imaginary part when casting from the NumPy complex type (not the plain vanilla Python one) to int. The astype() function also accepts the name of a type as a string.

    In: b.astype('complex')
Out: array([ 1.+1.j,  3.+2.j])

It won't show any warning this time because we used the proper data type.

What just happened?

We converted NumPy arrays to a list and to arrays of different data types. The code for this example is in the arrayconversion.py file in this book's code bundle.

Summary

In this chapter, you learned a lot about NumPy fundamentals: data types and arrays. Arrays have several attributes describing them. You learned that one of these attributes is the data type, which, in NumPy, is represented by a fully-fledged object.

NumPy arrays can be sliced and indexed in an efficient manner, just like Python lists. NumPy arrays have the added ability of working with multiple dimensions.

The shape of an array can be manipulated in many ways—stacking, resizing, reshaping, and splitting. A great number of convenience functions for shape manipulation were demonstrated in this chapter.

Having learned about the basics, it's time to move on to the study of commonly used functions in Chapter 3, Getting Familiar with Commonly Used Functions, which includes basic statistical and mathematical functions.

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Description

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.

Who is this book for?

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.

What you will learn

  • Install NumPy, matplotlib, SciPy, and IPython on various operating systems
  • Use NumPy array objects to perform array operations
  • Familiarize yourself with commonly used NumPy functions
  • Use NumPy matrices for matrix algebra
  • Work with the NumPy modules to perform various algebraic operations
  • Test NumPy code with the numpy.testing module
  • Plot simple plots, subplots, histograms, and more with matplotlib

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Table of Contents

15 Chapters
1. NumPy Quick Start Chevron down icon Chevron up icon
1. NumPy Quick Start
Python
Time for action – installing Python on different operating systems
The Python help system
Time for action – using the Python help system
Basic arithmetic and variable assignment
Time for action – using Python as a calculator
Time for action – assigning values to variables
The print() function
Time for action – printing with the print() function
Code comments
Time for action – commenting code
The if statement
Time for action – deciding with the if statement
The for loop
Time for action – repeating instructions with loops
Python functions
Time for action – defining functions
Python modules
Time for action – importing modules
NumPy on Windows
Time for action – installing NumPy, matplotlib, SciPy, and IPython on Windows
NumPy on Linux
Time for action – installing NumPy, matplotlib, SciPy, and IPython on Linux
NumPy on Mac OS X
Time for action – installing NumPy, SciPy, matplotlib, and IPython with MacPorts or Fink
Building from source
Arrays
Time for action – adding vectors
IPython – an interactive shell
Online resources and help
Summary
2. Beginning with NumPy Fundamentals Chevron down icon Chevron up icon
2. Beginning with NumPy Fundamentals
NumPy array object
Time for action – creating a multidimensional array
Time for action – creating a record data type
One-dimensional slicing and indexing
Time for action – slicing and indexing multidimensional arrays
Time for action – manipulating array shapes
Time for action – stacking arrays
Time for action – splitting arrays
Time for action – converting arrays
Summary
3. Getting Familiar with Commonly Used Functions Chevron down icon Chevron up icon
3. Getting Familiar with Commonly Used Functions
File I/O
Time for action – reading and writing files
Comma-seperated value files
Time for action – loading from CSV files
Volume Weighted Average Price
Time for action – calculating Volume Weighted Average Price
Value range
Time for action – finding highest and lowest values
Statistics
Time for action – performing simple statistics
Stock returns
Time for action – analyzing stock returns
Dates
Time for action – dealing with dates
Time for action – using the datetime64 data type
Weekly summary
Time for action – summarizing data
Average True Range
Time for action – calculating the Average True Range
Simple Moving Average
Time for action – computing the Simple Moving Average
Exponential Moving Average
Time for action – calculating the Exponential Moving Average
Bollinger Bands
Time for action – enveloping with Bollinger Bands
Linear model
Time for action – predicting price with a linear model
Trend lines
Time for action – drawing trend lines
Methods of ndarray
Time for action – clipping and compressing arrays
Factorial
Time for action – calculating the factorial
Missing values and Jackknife resampling
Time for action – handling NaNs with the nanmean(), nanvar(), and nanstd() functions
Summary
4. Convenience Functions for Your Convenience Chevron down icon Chevron up icon
4. Convenience Functions for Your Convenience
Correlation
Time for action – trading correlated pairs
Polynomials
Time for action – fitting to polynomials
On-balance volume
Time for action – balancing volume
Simulation
Time for action – avoiding loops with vectorize()
Smoothing
Time for action – smoothing with the hanning() function
Initialization
Time for action – creating value initialized arrays with the full() and full_like() functions
Summary
5. Working with Matrices and ufuncs Chevron down icon Chevron up icon
5. Working with Matrices and ufuncs
Matrices
Time for action – creating matrices
Creating a matrix from other matrices
Time for action – creating a matrix from other matrices
Universal functions
Time for action – creating universal functions
Universal function methods
Time for action – applying the ufunc methods to the add function
Arithmetic functions
Time for action – dividing arrays
Modulo operation
Time for action – computing the modulo
Fibonacci numbers
Time for action – computing Fibonacci numbers
Lissajous curves
Time for action – drawing Lissajous curves
Square waves
Time for action – drawing a square wave
Sawtooth and triangle waves
Time for action – drawing sawtooth and triangle waves
Bitwise and comparison functions
Time for action – twiddling bits
Fancy indexing
Time for action – fancy indexing in-place for ufuncs with the at() method
Summary
6. Moving Further with NumPy Modules Chevron down icon Chevron up icon
6. Moving Further with NumPy Modules
Linear algebra
Time for action – inverting matrices
Solving linear systems
Time for action – solving a linear system
Finding eigenvalues and eigenvectors
Time for action – determining eigenvalues and eigenvectors
Singular value decomposition
Time for action – decomposing a matrix
Pseudo inverse
Time for action – computing the pseudo inverse of a matrix
Determinants
Time for action – calculating the determinant of a matrix
Fast Fourier transform
Time for action – calculating the Fourier transform
Shifting
Time for action – shifting frequencies
Random numbers
Time for action – gambling with the binomial
Hypergeometric distribution
Time for action – simulating a game show
Continuous distributions
Time for action – drawing a normal distribution
Lognormal distribution
Time for action – drawing the lognormal distribution
Bootstrapping in statistics
Time for action – sampling with numpy.random.choice()
Summary
7. Peeking into Special Routines Chevron down icon Chevron up icon
7. Peeking into Special Routines
Sorting
Time for action – sorting lexically
Time for action – partial sorting via selection for a fast median with the partition() function
Complex numbers
Time for action – sorting complex numbers
Searching
Time for action – using searchsorted
Array elements extraction
Time for action – extracting elements from an array
Financial functions
Time for action – determining the future value
Present value
Time for action – getting the present value
Net present value
Time for action – calculating the net present value
Internal rate of return
Time for action – determining the internal rate of return
Periodic payments
Time for action – calculating the periodic payments
Number of payments
Time for action – determining the number of periodic payments
Interest rate
Time for action – figuring out the rate
Window functions
Time for action – plotting the Bartlett window
Blackman window
Time for action – smoothing stock prices with the Blackman window
Hamming window
Time for action – plotting the Hamming window
Kaiser window
Time for action – plotting the Kaiser window
Special mathematical functions
Time for action – plotting the modified Bessel function
sinc
Time for action – plotting the sinc function
Summary
8. Assuring Quality with Testing Chevron down icon Chevron up icon
8. Assuring Quality with Testing
Assert functions
Time for action – asserting almost equal
Approximately equal arrays
Time for action – asserting approximately equal
Almost equal arrays
Time for action – asserting arrays almost equal
Equal arrays
Time for action – comparing arrays
Ordering arrays
Time for action – checking the array order
Object comparison
Time for action – comparing objects
String comparison
Time for action – comparing strings
Floating-point comparisons
Time for action – comparing with assert_array_almost_equal_nulp
Comparison of floats with more ULPs
Time for action – comparing using maxulp of 2
Unit tests
Time for action – writing a unit test
Nose test decorators
Time for action – decorating tests
Docstrings
Time for action – executing doctests
Summary
9. Plotting with matplotlib Chevron down icon Chevron up icon
9. Plotting with matplotlib
Simple plots
Time for action – plotting a polynomial function
Plot format string
Time for action – plotting a polynomial and its derivatives
Subplots
Time for action – plotting a polynomial and its derivatives
Finance
Time for action – plotting a year's worth of stock quotes
Histograms
Time for action – charting stock price distributions
Logarithmic plots
Time for action – plotting stock volume
Scatter plots
Time for action – plotting price and volume returns with a scatter plot
Fill between
Time for action – shading plot regions based on a condition
Legend and annotations
Time for action – using a legend and annotations
Three-dimensional plots
Time for action – plotting in three dimensions
Contour plots
Time for action – drawing a filled contour plot
Animation
Time for action – animating plots
Summary
10. When NumPy Is Not Enough – SciPy and Beyond Chevron down icon Chevron up icon
10. When NumPy Is Not Enough – SciPy and Beyond
MATLAB and Octave
Time for action – saving and loading a .mat file
Statistics
Time for action – analyzing random values
Sample comparison and SciKits
Time for action – comparing stock log returns
Signal processing
Time for action – detecting a trend in QQQ
Fourier analysis
Time for action – filtering a detrended signal
Mathematical optimization
Time for action – fitting to a sine
Numerical integration
Time for action – calculating the Gaussian integral
Interpolation
Time for action – interpolating in one dimension
Image processing
Time for action – manipulating Lena
Audio processing
Time for action – replaying audio clips
Summary
11. Playing with Pygame Chevron down icon Chevron up icon
11. Playing with Pygame
Pygame
Time for action – installing Pygame
Hello World
Time for action – creating a simple game
Animation
Time for action – animating objects with NumPy and Pygame
matplotlib
Time for Action – using matplotlib in Pygame
Surface pixels
Time for Action – accessing surface pixel data with NumPy
Artificial Intelligence
Time for Action – clustering points
OpenGL and Pygame
Time for Action – drawing the Sierpinski gasket
Simulation game with Pygame
Time for Action – simulating life
Summary
A. Pop Quiz Answers Chevron down icon Chevron up icon
Chapter 1, NumPy Quick Start
Chapter 2, Beginning with NumPy Fundamentals
Chapter 3, Getting Familiar with Commonly Used Functions
Chapter 4, Convenience Functions for Your Convenience
Chapter 5, Working with Matrices and ufuncs
Chapter 6, Move Further with NumPy Modules
Chapter 7, Peeking into Special Routines
Chapter 8, Assuring Quality with Testing
Chapter 9, Plotting with matplotlib
Chapter 10, When NumPy Is Not Enough –Scipy and Beyond
B. Additional Online Resources Chevron down icon Chevron up icon
B. Additional Online Resources
Python
Mathematics and statistics
C. NumPy Functions' References Chevron down icon Chevron up icon
C. NumPy Functions' References
Index Chevron down icon Chevron up icon
Index

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Customer reviews

Rating distribution
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(1 Ratings)
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Alexander Sagel Jan 10, 2017
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it's a helpful guide. however, the code examples are inconsistent in style and overflowing with mistakes. requires a thorough revision
Amazon Verified review Amazon

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About the author

Profile icon Ivan Idris
Ivan 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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