Effective data-driven science and computation requires understanding how data is stored and manipulated. This section outlines and contrasts how arrays of data are handled in the Python language itself, and how NumPy improves on this. Understanding this difference is fundamental to understanding much of the material throughout the rest of the book.
Users of Python are often drawn-in by its ease of use, one piece of which is dynamic typing. While a statically-typed language like C or Java requires each variable to be explicitly declared, a dynamically-typed language like Python skips this specification. For example, in C you might specify a particular operation as follows:
While in Python the equivalent operation could be written this way:
Notice the main difference: in C, the data types of each variable are explicitly declared, while in Python the types are dynamically inferred. This means, for example, that we can assign any kind of data to any variable:
Here we've switched the contents of
x from an integer to a string. The same thing in C would lead (depending on compiler settings) to a compilation error or other unintented consequences:
This sort of flexibility is one piece that makes Python and other dynamically-typed languages convenient and easy to use. Understanding how this works is an important piece of learning to analyze data efficiently and effectively with Python. But what this type-flexibility also points to is the fact that Python variables are more than just their value; they also contain extra information about the type of the value. We'll explore this more in the sections that follow.
The standard Python implementation is written in C.
This means that every Python object is simply a cleverly-disguised C structure, which contains not only its value, but other information as well. For example, when we define an integer in Python, such as
x = 10000,
x is not just a "raw" integer. It's actually a pointer to a compound C structure, which contains several values.
Looking through the Python 3.4 source code, we find that the integer (long) type definition effectively looks like this (once the C macros are expanded):
A single integer in Python 3.4 actually contains four pieces:
ob_refcnt, a reference count that helps Python silently handle memory allocation and deallocation
ob_type, which encodes the type of the variable
ob_size, which specifies the size of the following data members
ob_digit, which contains the actual integer value that we expect the Python variable to represent.
This means that there is some overhead in storing an integer in Python as compared to an integer in a compiled language like C, as illustrated in the following figure:
PyObject_HEAD is the part of the structure containing the reference count, type code, and other pieces mentioned before.
Notice the difference here: a C integer is essentially a label for a position in memory whose bytes encode an integer value. A Python integer is a pointer to a position in memory containing all the Python object information, including the bytes that contain the integer value. This extra information in the Python integer structure is what allows Python to be coded so freely and dynamically. All this additional information in Python types comes at a cost, however, which becomes especially apparent in structures that combine many of these objects.
Let's consider now what happens when we use a Python data structure that holds many Python objects. The standard mutable multi-element container in Python is the list. We can create a list of integers as follows:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Or, similarly, a list of strings:
['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
Because of Python's dynamic typing, we can even create heterogeneous lists:
[bool, str, float, int]
But this flexibility comes at a cost: to allow these flexible types, each item in the list must contain its own type info, reference count, and other information–that is, each item is a complete Python object. In the special case that all variables are of the same type, much of this information is redundant: it can be much more efficient to store data in a fixed-type array. The difference between a dynamic-type list and a fixed-type (NumPy-style) array is illustrated in the following figure:
At the implementation level, the array essentially contains a single pointer to one contiguous block of data. The Python list, on the other hand, contains a pointer to a block of pointers, each of which in turn points to a full Python object like the Python integer we saw earlier. Again, the advantage of the list is flexibility: because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type. Fixed-type NumPy-style arrays lack this flexibility, but are much more efficient for storing and manipulating data.
Python offers several different options for storing data in efficient, fixed-type data buffers.
array module (available since Python 3.3) can be used to create dense arrays of a uniform type:
array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
'i' is a type code indicating the contents are integers.
Much more useful, however, is the
ndarray object of the NumPy package.
array object provides efficient storage of array-based data, NumPy adds to this efficient operations on that data.
We will explore these operations in later sections; here we'll demonstrate several ways of creating a NumPy array.
We'll start with the standard NumPy import, under the alias
First, we can use
np.array to create arrays from Python lists:
array([1, 4, 2, 5, 3])
Remember that unlike Python lists, NumPy is constrained to arrays that all contain the same type. If types do not match, NumPy will upcast if possible (here, integers are up-cast to floating point):
array([ 3.14, 4. , 2. , 3. ])
If we want to explicitly set the data type of the resulting array, we can use the
array([ 1., 2., 3., 4.], dtype=float32)
Finally, unlike Python lists, NumPy arrays can explicitly be multi-dimensional; here's one way of initializing a multidimensional array using a list of lists:
array([[2, 3, 4], [4, 5, 6], [6, 7, 8]])
The inner lists are treated as rows of the resulting two-dimensional array.
Especially for larger arrays, it is more efficient to create arrays from scratch using routines built into NumPy. Here are several examples:
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
array([[ 1., 1., 1., 1., 1.], [ 1., 1., 1., 1., 1.], [ 1., 1., 1., 1., 1.]])
array([[ 3.14, 3.14, 3.14, 3.14, 3.14], [ 3.14, 3.14, 3.14, 3.14, 3.14], [ 3.14, 3.14, 3.14, 3.14, 3.14]])
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])
array([ 0. , 0.25, 0.5 , 0.75, 1. ])
array([[ 0.99844933, 0.52183819, 0.22421193], [ 0.08007488, 0.45429293, 0.20941444], [ 0.14360941, 0.96910973, 0.946117 ]])
array([[ 1.51772646, 0.39614948, -0.10634696], [ 0.25671348, 0.00732722, 0.37783601], [ 0.68446945, 0.15926039, -0.70744073]])
array([[2, 3, 4], [5, 7, 8], [0, 5, 0]])
array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])
array([ 1., 1., 1.])
NumPy arrays contain values of a single type, so it is important to have detailed knowledge of those types and their limitations. Because NumPy is built in C, the types will be familiar to users of C, Fortran, and other related languages.
The standard NumPy data types are listed in the following table. Note that when constructing an array, they can be specified using a string:
Or using the associated NumPy object: