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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
2. Beginning with NumPy Fundamentals Chevron down icon Chevron up icon
3. Getting Familiar with Commonly Used Functions Chevron down icon Chevron up icon
4. Convenience Functions for Your Convenience Chevron down icon Chevron up icon
5. Working with Matrices and ufuncs Chevron down icon Chevron up icon
6. Moving Further with NumPy Modules Chevron down icon Chevron up icon
7. Peeking into Special Routines Chevron down icon Chevron up icon
8. Assuring Quality with Testing Chevron down icon Chevron up icon
9. Plotting with matplotlib Chevron down icon Chevron up icon
10. When NumPy Is Not Enough – SciPy and Beyond Chevron down icon Chevron up icon
11. Playing with Pygame Chevron down icon Chevron up icon
A. Pop Quiz Answers Chevron down icon Chevron up icon
B. Additional Online Resources Chevron down icon Chevron up icon
C. NumPy Functions' References Chevron down icon Chevron up icon
Index Chevron down icon Chevron up icon

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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
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