This notebook contains an excerpt from the Python Data Science Handbook by Jake VanderPlas; the content is available on GitHub.

The text is released under the CC-BY-NC-ND license, and code is released under the MIT license. If you find this content useful, please consider supporting the work by buying the book!

No changes were made to the contents of this notebook from the original.

# Data Indexing and Selection¶

In Chapter 2, we looked in detail at methods and tools to access, set, and modify values in NumPy arrays. These included indexing (e.g., arr[2, 1]), slicing (e.g., arr[:, 1:5]), masking (e.g., arr[arr > 0]), fancy indexing (e.g., arr[0, [1, 5]]), and combinations thereof (e.g., arr[:, [1, 5]]). Here we'll look at similar means of accessing and modifying values in Pandas Series and DataFrame objects. If you have used the NumPy patterns, the corresponding patterns in Pandas will feel very familiar, though there are a few quirks to be aware of.

We'll start with the simple case of the one-dimensional Series object, and then move on to the more complicated two-dimesnional DataFrame object.

## Data Selection in Series¶

As we saw in the previous section, a Series object acts in many ways like a one-dimensional NumPy array, and in many ways like a standard Python dictionary. If we keep these two overlapping analogies in mind, it will help us to understand the patterns of data indexing and selection in these arrays.

### Series as dictionary¶

Like a dictionary, the Series object provides a mapping from a collection of keys to a collection of values:

In [1]:
import pandas as pd
data = pd.Series([0.25, 0.5, 0.75, 1.0],
index=['a', 'b', 'c', 'd'])
data

Out[1]:
a    0.25
b    0.50
c    0.75
d    1.00
dtype: float64
In [2]:
data['b']

Out[2]:
0.5

We can also use dictionary-like Python expressions and methods to examine the keys/indices and values:

In [3]:
'a' in data

Out[3]:
True
In [4]:
data.keys()

Out[4]:
Index(['a', 'b', 'c', 'd'], dtype='object')
In [5]:
list(data.items())

Out[5]:
[('a', 0.25), ('b', 0.5), ('c', 0.75), ('d', 1.0)]

Series objects can even be modified with a dictionary-like syntax. Just as you can extend a dictionary by assigning to a new key, you can extend a Series by assigning to a new index value:

In [6]:
data['e'] = 1.25
data

Out[6]:
a    0.25
b    0.50
c    0.75
d    1.00
e    1.25
dtype: float64

This easy mutability of the objects is a convenient feature: under the hood, Pandas is making decisions about memory layout and data copying that might need to take place; the user generally does not need to worry about these issues.

### Series as one-dimensional array¶

A Series builds on this dictionary-like interface and provides array-style item selection via the same basic mechanisms as NumPy arrays – that is, slices, masking, and fancy indexing. Examples of these are as follows:

In [7]:
# slicing by explicit index
data['a':'c']

Out[7]:
a    0.25
b    0.50
c    0.75
dtype: float64
In [8]:
# slicing by implicit integer index
data[0:2]

Out[8]:
a    0.25
b    0.50
dtype: float64
In [9]:
# masking
data[(data > 0.3) & (data < 0.8)]

Out[9]:
b    0.50
c    0.75
dtype: float64
In [10]:
# fancy indexing
data[['a', 'e']]

Out[10]:
a    0.25
e    1.25
dtype: float64

Among these, slicing may be the source of the most confusion. Notice that when slicing with an explicit index (i.e., data['a':'c']), the final index is included in the slice, while when slicing with an implicit index (i.e., data[0:2]), the final index is excluded from the slice.

### Indexers: loc, iloc, and ix¶

These slicing and indexing conventions can be a source of confusion. For example, if your Series has an explicit integer index, an indexing operation such as data[1] will use the explicit indices, while a slicing operation like data[1:3] will use the implicit Python-style index.

In [11]:
data = pd.Series(['a', 'b', 'c'], index=[1, 3, 5])
data

Out[11]:
1    a
3    b
5    c
dtype: object
In [12]:
# explicit index when indexing
data[1]

Out[12]:
'a'
In [13]:
# implicit index when slicing
data[1:3]

Out[13]:
3    b
5    c
dtype: object

Because of this potential confusion in the case of integer indexes, Pandas provides some special indexer attributes that explicitly expose certain indexing schemes. These are not functional methods, but attributes that expose a particular slicing interface to the data in the Series.

First, the loc attribute allows indexing and slicing that always references the explicit index:

In [14]:
data.loc[1]

Out[14]:
'a'
In [15]:
data.loc[1:3]

Out[15]:
1    a
3    b
dtype: object

The iloc attribute allows indexing and slicing that always references the implicit Python-style index:

In [16]:
data.iloc[1]

Out[16]:
'b'
In [17]:
data.iloc[1:3]

Out[17]:
3    b
5    c
dtype: object

A third indexing attribute, ix, is a hybrid of the two, and for Series objects is equivalent to standard []-based indexing. The purpose of the ix indexer will become more apparent in the context of DataFrame objects, which we will discuss in a moment.

One guiding principle of Python code is that "explicit is better than implicit." The explicit nature of loc and iloc make them very useful in maintaining clean and readable code; especially in the case of integer indexes, I recommend using these both to make code easier to read and understand, and to prevent subtle bugs due to the mixed indexing/slicing convention.

## Data Selection in DataFrame¶

Recall that a DataFrame acts in many ways like a two-dimensional or structured array, and in other ways like a dictionary of Series structures sharing the same index. These analogies can be helpful to keep in mind as we explore data selection within this structure.

### DataFrame as a dictionary¶

The first analogy we will consider is the DataFrame as a dictionary of related Series objects. Let's return to our example of areas and populations of states:

In [18]:
area = pd.Series({'California': 423967, 'Texas': 695662,
'New York': 141297, 'Florida': 170312,
'Illinois': 149995})
pop = pd.Series({'California': 38332521, 'Texas': 26448193,
'New York': 19651127, 'Florida': 19552860,
'Illinois': 12882135})
data = pd.DataFrame({'area':area, 'pop':pop})
data

Out[18]:
area pop
California 423967 38332521
Florida 170312 19552860
Illinois 149995 12882135
New York 141297 19651127
Texas 695662 26448193

The individual Series that make up the columns of the DataFrame can be accessed via dictionary-style indexing of the column name:

In [19]:
data['area']

Out[19]:
California    423967
Florida       170312
Illinois      149995
New York      141297
Texas         695662
Name: area, dtype: int64

Equivalently, we can use attribute-style access with column names that are strings:

In [20]:
data.area

Out[20]:
California    423967
Florida       170312
Illinois      149995
New York      141297
Texas         695662
Name: area, dtype: int64

This attribute-style column access actually accesses the exact same object as the dictionary-style access:

In [21]:
data.area is data['area']

Out[21]:
True

Though this is a useful shorthand, keep in mind that it does not work for all cases! For example, if the column names are not strings, or if the column names conflict with methods of the DataFrame, this attribute-style access is not possible. For example, the DataFrame has a pop() method, so data.pop will point to this rather than the "pop" column:

In [22]:
data.pop is data['pop']

Out[22]:
False

In particular, you should avoid the temptation to try column assignment via attribute (i.e., use data['pop'] = z rather than data.pop = z).

Like with the Series objects discussed earlier, this dictionary-style syntax can also be used to modify the object, in this case adding a new column:

In [23]:
data['density'] = data['pop'] / data['area']
data

Out[23]:
area pop density
California 423967 38332521 90.413926
Florida 170312 19552860 114.806121
Illinois 149995 12882135 85.883763
New York 141297 19651127 139.076746
Texas 695662 26448193 38.018740

This shows a preview of the straightforward syntax of element-by-element arithmetic between Series objects; we'll dig into this further in Operating on Data in Pandas.

### DataFrame as two-dimensional array¶

As mentioned previously, we can also view the DataFrame as an enhanced two-dimensional array. We can examine the raw underlying data array using the values attribute:

In [24]:
data.values

Out[24]:
array([[  4.23967000e+05,   3.83325210e+07,   9.04139261e+01],
[  1.70312000e+05,   1.95528600e+07,   1.14806121e+02],
[  1.49995000e+05,   1.28821350e+07,   8.58837628e+01],
[  1.41297000e+05,   1.96511270e+07,   1.39076746e+02],
[  6.95662000e+05,   2.64481930e+07,   3.80187404e+01]])

With this picture in mind, many familiar array-like observations can be done on the DataFrame itself. For example, we can transpose the full DataFrame to swap rows and columns:

In [25]:
data.T

Out[25]:
California Florida Illinois New York Texas
area 4.239670e+05 1.703120e+05 1.499950e+05 1.412970e+05 6.956620e+05
pop 3.833252e+07 1.955286e+07 1.288214e+07 1.965113e+07 2.644819e+07
density 9.041393e+01 1.148061e+02 8.588376e+01 1.390767e+02 3.801874e+01

When it comes to indexing of DataFrame objects, however, it is clear that the dictionary-style indexing of columns precludes our ability to simply treat it as a NumPy array. In particular, passing a single index to an array accesses a row:

In [26]:
data.values[0]

Out[26]:
array([  4.23967000e+05,   3.83325210e+07,   9.04139261e+01])

and passing a single "index" to a DataFrame accesses a column:

In [27]:
data['area']

Out[27]:
California    423967
Florida       170312
Illinois      149995
New York      141297
Texas         695662
Name: area, dtype: int64

Thus for array-style indexing, we need another convention. Here Pandas again uses the loc, iloc, and ix indexers mentioned earlier. Using the iloc indexer, we can index the underlying array as if it is a simple NumPy array (using the implicit Python-style index), but the DataFrame index and column labels are maintained in the result:

In [28]:
data.iloc[:3, :2]

Out[28]:
area pop
California 423967 38332521
Florida 170312 19552860
Illinois 149995 12882135

Similarly, using the loc indexer we can index the underlying data in an array-like style but using the explicit index and column names:

In [29]:
data.loc[:'Illinois', :'pop']

Out[29]:
area pop
California 423967 38332521
Florida 170312 19552860
Illinois 149995 12882135

The ix indexer allows a hybrid of these two approaches:

In [30]:
data.ix[:3, :'pop']

Out[30]:
area pop
California 423967 38332521
Florida 170312 19552860
Illinois 149995 12882135

Keep in mind that for integer indices, the ix indexer is subject to the same potential sources of confusion as discussed for integer-indexed Series objects.

Any of the familiar NumPy-style data access patterns can be used within these indexers. For example, in the loc indexer we can combine masking and fancy indexing as in the following:

In [31]:
data.loc[data.density > 100, ['pop', 'density']]

Out[31]:
pop density
Florida 19552860 114.806121
New York 19651127 139.076746

Any of these indexing conventions may also be used to set or modify values; this is done in the standard way that you might be accustomed to from working with NumPy:

In [32]:
data.iloc[0, 2] = 90
data

Out[32]:
area pop density
California 423967 38332521 90.000000
Florida 170312 19552860 114.806121
Illinois 149995 12882135 85.883763
New York 141297 19651127 139.076746
Texas 695662 26448193 38.018740

To build up your fluency in Pandas data manipulation, I suggest spending some time with a simple DataFrame and exploring the types of indexing, slicing, masking, and fancy indexing that are allowed by these various indexing approaches.

There are a couple extra indexing conventions that might seem at odds with the preceding discussion, but nevertheless can be very useful in practice. First, while indexing refers to columns, slicing refers to rows:

In [33]:
data['Florida':'Illinois']

Out[33]:
area pop density
Florida 170312 19552860 114.806121
Illinois 149995 12882135 85.883763

Such slices can also refer to rows by number rather than by index:

In [34]:
data[1:3]

Out[34]:
area pop density
Florida 170312 19552860 114.806121
Illinois 149995 12882135 85.883763

Similarly, direct masking operations are also interpreted row-wise rather than column-wise:

In [35]:
data[data.density > 100]

Out[35]:
area pop density
Florida 170312 19552860 114.806121
New York 141297 19651127 139.076746

These two conventions are syntactically similar to those on a NumPy array, and while these may not precisely fit the mold of the Pandas conventions, they are nevertheless quite useful in practice.