Table Of Contents

Search

Enter search terms or a module, class or function name.

MultiIndex / Advanced Indexing

This section covers indexing with a MultiIndex and more advanced indexing features.

See the Indexing and Selecting Data for general indexing documentation.

Warning

Whether a copy or a reference is returned for a setting operation, may depend on the context. This is sometimes called chained assignment and should be avoided. See Returning a View versus Copy

Warning

In 0.15.0 Index has internally been refactored to no longer sub-class ndarray but instead subclass PandasObject, similarly to the rest of the pandas objects. This should be a transparent change with only very limited API implications (See the Internal Refactoring)

See the cookbook for some advanced strategies

Hierarchical indexing (MultiIndex)

Hierarchical / Multi-level indexing is very exciting as it opens the door to some quite sophisticated data analysis and manipulation, especially for working with higher dimensional data. In essence, it enables you to store and manipulate data with an arbitrary number of dimensions in lower dimensional data structures like Series (1d) and DataFrame (2d).

In this section, we will show what exactly we mean by “hierarchical” indexing and how it integrates with all of the pandas indexing functionality described above and in prior sections. Later, when discussing group by and pivoting and reshaping data, we’ll show non-trivial applications to illustrate how it aids in structuring data for analysis.

See the cookbook for some advanced strategies

Creating a MultiIndex (hierarchical index) object

The MultiIndex object is the hierarchical analogue of the standard Index object which typically stores the axis labels in pandas objects. You can think of MultiIndex as an array of tuples where each tuple is unique. A MultiIndex can be created from a list of arrays (using MultiIndex.from_arrays), an array of tuples (using MultiIndex.from_tuples), or a crossed set of iterables (using MultiIndex.from_product). The Index constructor will attempt to return a MultiIndex when it is passed a list of tuples. The following examples demo different ways to initialize MultiIndexes.

In [1]: arrays = [['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux'],
   ...:           ['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two']]
   ...: 

In [2]: tuples = list(zip(*arrays))

In [3]: tuples
Out[3]: 
[('bar', 'one'),
 ('bar', 'two'),
 ('baz', 'one'),
 ('baz', 'two'),
 ('foo', 'one'),
 ('foo', 'two'),
 ('qux', 'one'),
 ('qux', 'two')]

In [4]: index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])

In [5]: index
Out[5]: 
MultiIndex(levels=[['bar', 'baz', 'foo', 'qux'], ['one', 'two']],
           labels=[[0, 0, 1, 1, 2, 2, 3, 3], [0, 1, 0, 1, 0, 1, 0, 1]],
           names=['first', 'second'])

In [6]: s = pd.Series(np.random.randn(8), index=index)

In [7]: s
Out[7]: 
first  second
bar    one       0.469112
       two      -0.282863
baz    one      -1.509059
       two      -1.135632
foo    one       1.212112
       two      -0.173215
qux    one       0.119209
       two      -1.044236
dtype: float64

When you want every pairing of the elements in two iterables, it can be easier to use the MultiIndex.from_product function:

In [8]: iterables = [['bar', 'baz', 'foo', 'qux'], ['one', 'two']]

In [9]: pd.MultiIndex.from_product(iterables, names=['first', 'second'])
Out[9]: 
MultiIndex(levels=[['bar', 'baz', 'foo', 'qux'], ['one', 'two']],
           labels=[[0, 0, 1, 1, 2, 2, 3, 3], [0, 1, 0, 1, 0, 1, 0, 1]],
           names=['first', 'second'])

As a convenience, you can pass a list of arrays directly into Series or DataFrame to construct a MultiIndex automatically:

In [10]: arrays = [np.array(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux']),
   ....:           np.array(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'])]
   ....: 

In [11]: s = pd.Series(np.random.randn(8), index=arrays)

In [12]: s
Out[12]: 
bar  one   -0.861849
     two   -2.104569
baz  one   -0.494929
     two    1.071804
foo  one    0.721555
     two   -0.706771
qux  one   -1.039575
     two    0.271860
dtype: float64

In [13]: df = pd.DataFrame(np.random.randn(8, 4), index=arrays)

In [14]: df
Out[14]: 
                0         1         2         3
bar one -0.424972  0.567020  0.276232 -1.087401
    two -0.673690  0.113648 -1.478427  0.524988
baz one  0.404705  0.577046 -1.715002 -1.039268
    two -0.370647 -1.157892 -1.344312  0.844885
foo one  1.075770 -0.109050  1.643563 -1.469388
    two  0.357021 -0.674600 -1.776904 -0.968914
qux one -1.294524  0.413738  0.276662 -0.472035
    two -0.013960 -0.362543 -0.006154 -0.923061

All of the MultiIndex constructors accept a names argument which stores string names for the levels themselves. If no names are provided, None will be assigned:

In [15]: df.index.names
Out[15]: FrozenList([None, None])

This index can back any axis of a pandas object, and the number of levels of the index is up to you:

In [16]: df = pd.DataFrame(np.random.randn(3, 8), index=['A', 'B', 'C'], columns=index)

In [17]: df
Out[17]: 
first        bar                 baz                 foo                 qux  \
second       one       two       one       two       one       two       one   
A       0.895717  0.805244 -1.206412  2.565646  1.431256  1.340309 -1.170299   
B       0.410835  0.813850  0.132003 -0.827317 -0.076467 -1.187678  1.130127   
C      -1.413681  1.607920  1.024180  0.569605  0.875906 -2.211372  0.974466   

first             
second       two  
A      -0.226169  
B      -1.436737  
C      -2.006747  

In [18]: pd.DataFrame(np.random.randn(6, 6), index=index[:6], columns=index[:6])
Out[18]: 
first              bar                 baz                 foo          
second             one       two       one       two       one       two
first second                                                            
bar   one    -0.410001 -0.078638  0.545952 -1.219217 -1.226825  0.769804
      two    -1.281247 -0.727707 -0.121306 -0.097883  0.695775  0.341734
baz   one     0.959726 -1.110336 -0.619976  0.149748 -0.732339  0.687738
      two     0.176444  0.403310 -0.154951  0.301624 -2.179861 -1.369849
foo   one    -0.954208  1.462696 -1.743161 -0.826591 -0.345352  1.314232
      two     0.690579  0.995761  2.396780  0.014871  3.357427 -0.317441

We’ve “sparsified” the higher levels of the indexes to make the console output a bit easier on the eyes.

It’s worth keeping in mind that there’s nothing preventing you from using tuples as atomic labels on an axis:

In [19]: pd.Series(np.random.randn(8), index=tuples)
Out[19]: 
(bar, one)   -1.236269
(bar, two)    0.896171
(baz, one)   -0.487602
(baz, two)   -0.082240
(foo, one)   -2.182937
(foo, two)    0.380396
(qux, one)    0.084844
(qux, two)    0.432390
dtype: float64

The reason that the MultiIndex matters is that it can allow you to do grouping, selection, and reshaping operations as we will describe below and in subsequent areas of the documentation. As you will see in later sections, you can find yourself working with hierarchically-indexed data without creating a MultiIndex explicitly yourself. However, when loading data from a file, you may wish to generate your own MultiIndex when preparing the data set.

Note that how the index is displayed by be controlled using the multi_sparse option in pandas.set_options():

In [20]: pd.set_option('display.multi_sparse', False)

In [21]: df
Out[21]: 
first        bar       bar       baz       baz       foo       foo       qux  \
second       one       two       one       two       one       two       one   
A       0.895717  0.805244 -1.206412  2.565646  1.431256  1.340309 -1.170299   
B       0.410835  0.813850  0.132003 -0.827317 -0.076467 -1.187678  1.130127   
C      -1.413681  1.607920  1.024180  0.569605  0.875906 -2.211372  0.974466   

first        qux  
second       two  
A      -0.226169  
B      -1.436737  
C      -2.006747  

In [22]: pd.set_option('display.multi_sparse', True)

Reconstructing the level labels

The method get_level_values will return a vector of the labels for each location at a particular level:

In [23]: index.get_level_values(0)
Out[23]: Index(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux'], dtype='object', name='first')

In [24]: index.get_level_values('second')
Out[24]: Index(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'], dtype='object', name='second')

Basic indexing on axis with MultiIndex

One of the important features of hierarchical indexing is that you can select data by a “partial” label identifying a subgroup in the data. Partial selection “drops” levels of the hierarchical index in the result in a completely analogous way to selecting a column in a regular DataFrame:

In [25]: df['bar']
Out[25]: 
second       one       two
A       0.895717  0.805244
B       0.410835  0.813850
C      -1.413681  1.607920

In [26]: df['bar', 'one']
Out[26]: 
A    0.895717
B    0.410835
C   -1.413681
Name: (bar, one), dtype: float64

In [27]: df['bar']['one']
Out[27]: 
A    0.895717
B    0.410835
C   -1.413681
Name: one, dtype: float64

In [28]: s['qux']
Out[28]: 
one   -1.039575
two    0.271860
dtype: float64

See Cross-section with hierarchical index for how to select on a deeper level.

Defined Levels

The repr of a MultiIndex shows ALL the defined levels of an index, even if the they are not actually used. When slicing an index, you may notice this. For example:

# original multi-index
In [29]: df.columns
Out[29]: 
MultiIndex(levels=[['bar', 'baz', 'foo', 'qux'], ['one', 'two']],
           labels=[[0, 0, 1, 1, 2, 2, 3, 3], [0, 1, 0, 1, 0, 1, 0, 1]],
           names=['first', 'second'])

# sliced
In [30]: df[['foo','qux']].columns
Out[30]: 
MultiIndex(levels=[['bar', 'baz', 'foo', 'qux'], ['one', 'two']],
           labels=[[2, 2, 3, 3], [0, 1, 0, 1]],
           names=['first', 'second'])

This is done to avoid a recomputation of the levels in order to make slicing highly performant. If you want to see the actual used levels.

In [31]: df[['foo','qux']].columns.values
Out[31]: array([('foo', 'one'), ('foo', 'two'), ('qux', 'one'), ('qux', 'two')], dtype=object)

# for a specific level
In [32]: df[['foo','qux']].columns.get_level_values(0)
Out[32]: Index(['foo', 'foo', 'qux', 'qux'], dtype='object', name='first')

To reconstruct the multiindex with only the used levels

New in version 0.20.0.

In [33]: df[['foo','qux']].columns.remove_unused_levels()
Out[33]: 
MultiIndex(levels=[['foo', 'qux'], ['one', 'two']],
           labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
           names=['first', 'second'])

Data alignment and using reindex

Operations between differently-indexed objects having MultiIndex on the axes will work as you expect; data alignment will work the same as an Index of tuples:

In [34]: s + s[:-2]
Out[34]: 
bar  one   -1.723698
     two   -4.209138
baz  one   -0.989859
     two    2.143608
foo  one    1.443110
     two   -1.413542
qux  one         NaN
     two         NaN
dtype: float64

In [35]: s + s[::2]
Out[35]: 
bar  one   -1.723698
     two         NaN
baz  one   -0.989859
     two         NaN
foo  one    1.443110
     two         NaN
qux  one   -2.079150
     two         NaN
dtype: float64

reindex can be called with another MultiIndex or even a list or array of tuples:

In [36]: s.reindex(index[:3])
Out[36]: 
first  second
bar    one      -0.861849
       two      -2.104569
baz    one      -0.494929
dtype: float64

In [37]: s.reindex([('foo', 'two'), ('bar', 'one'), ('qux', 'one'), ('baz', 'one')])
Out[37]: 
foo  two   -0.706771
bar  one   -0.861849
qux  one   -1.039575
baz  one   -0.494929
dtype: float64

Advanced indexing with hierarchical index

Syntactically integrating MultiIndex in advanced indexing with .loc is a bit challenging, but we’ve made every effort to do so. for example the following works as you would expect:

In [38]: df = df.T

In [39]: df
Out[39]: 
                     A         B         C
first second                              
bar   one     0.895717  0.410835 -1.413681
      two     0.805244  0.813850  1.607920
baz   one    -1.206412  0.132003  1.024180
      two     2.565646 -0.827317  0.569605
foo   one     1.431256 -0.076467  0.875906
      two     1.340309 -1.187678 -2.211372
qux   one    -1.170299  1.130127  0.974466
      two    -0.226169 -1.436737 -2.006747

In [40]: df.loc['bar']
Out[40]: 
               A         B         C
second                              
one     0.895717  0.410835 -1.413681
two     0.805244  0.813850  1.607920

In [41]: df.loc['bar', 'two']
Out[41]: 
A    0.805244
B    0.813850
C    1.607920
Name: (bar, two), dtype: float64

“Partial” slicing also works quite nicely.

In [42]: df.loc['baz':'foo']
Out[42]: 
                     A         B         C
first second                              
baz   one    -1.206412  0.132003  1.024180
      two     2.565646 -0.827317  0.569605
foo   one     1.431256 -0.076467  0.875906
      two     1.340309 -1.187678 -2.211372

You can slice with a ‘range’ of values, by providing a slice of tuples.

In [43]: df.loc[('baz', 'two'):('qux', 'one')]
Out[43]: 
                     A         B         C
first second                              
baz   two     2.565646 -0.827317  0.569605
foo   one     1.431256 -0.076467  0.875906
      two     1.340309 -1.187678 -2.211372
qux   one    -1.170299  1.130127  0.974466

In [44]: df.loc[('baz', 'two'):'foo']
Out[44]: 
                     A         B         C
first second                              
baz   two     2.565646 -0.827317  0.569605
foo   one     1.431256 -0.076467  0.875906
      two     1.340309 -1.187678 -2.211372

Passing a list of labels or tuples works similar to reindexing:

In [45]: df.loc[[('bar', 'two'), ('qux', 'one')]]
Out[45]: 
                     A         B         C
first second                              
bar   two     0.805244  0.813850  1.607920
qux   one    -1.170299  1.130127  0.974466

Using slicers

New in version 0.14.0.

In 0.14.0 we added a new way to slice multi-indexed objects. You can slice a multi-index by providing multiple indexers.

You can provide any of the selectors as if you are indexing by label, see Selection by Label, including slices, lists of labels, labels, and boolean indexers.

You can use slice(None) to select all the contents of that level. You do not need to specify all the deeper levels, they will be implied as slice(None).

As usual, both sides of the slicers are included as this is label indexing.

Warning

You should specify all axes in the .loc specifier, meaning the indexer for the index and for the columns. There are some ambiguous cases where the passed indexer could be mis-interpreted as indexing both axes, rather than into say the MuliIndex for the rows.

You should do this:

df.loc[(slice('A1','A3'),.....), :]

rather than this:

df.loc[(slice('A1','A3'),.....)]
In [46]: def mklbl(prefix,n):
   ....:     return ["%s%s" % (prefix,i)  for i in range(n)]
   ....: 

In [47]: miindex = pd.MultiIndex.from_product([mklbl('A',4),
   ....:                                       mklbl('B',2),
   ....:                                       mklbl('C',4),
   ....:                                       mklbl('D',2)])
   ....: 

In [48]: micolumns = pd.MultiIndex.from_tuples([('a','foo'),('a','bar'),
   ....:                                        ('b','foo'),('b','bah')],
   ....:                                       names=['lvl0', 'lvl1'])
   ....: 

In [49]: dfmi = pd.DataFrame(np.arange(len(miindex)*len(micolumns)).reshape((len(miindex),len(micolumns))),
   ....:                     index=miindex,
   ....:                     columns=micolumns).sort_index().sort_index(axis=1)
   ....: 

In [50]: dfmi
Out[50]: 
lvl0           a         b     
lvl1         bar  foo  bah  foo
A0 B0 C0 D0    1    0    3    2
         D1    5    4    7    6
      C1 D0    9    8   11   10
         D1   13   12   15   14
      C2 D0   17   16   19   18
         D1   21   20   23   22
      C3 D0   25   24   27   26
...          ...  ...  ...  ...
A3 B1 C0 D1  229  228  231  230
      C1 D0  233  232  235  234
         D1  237  236  239  238
      C2 D0  241  240  243  242
         D1  245  244  247  246
      C3 D0  249  248  251  250
         D1  253  252  255  254

[64 rows x 4 columns]

Basic multi-index slicing using slices, lists, and labels.

In [51]: dfmi.loc[(slice('A1','A3'), slice(None), ['C1', 'C3']), :]
Out[51]: 
lvl0           a         b     
lvl1         bar  foo  bah  foo
A1 B0 C1 D0   73   72   75   74
         D1   77   76   79   78
      C3 D0   89   88   91   90
         D1   93   92   95   94
   B1 C1 D0  105  104  107  106
         D1  109  108  111  110
      C3 D0  121  120  123  122
...          ...  ...  ...  ...
A3 B0 C1 D1  205  204  207  206
      C3 D0  217  216  219  218
         D1  221  220  223  222
   B1 C1 D0  233  232  235  234
         D1  237  236  239  238
      C3 D0  249  248  251  250
         D1  253  252  255  254

[24 rows x 4 columns]

You can use a pd.IndexSlice to have a more natural syntax using : rather than using slice(None)

In [52]: idx = pd.IndexSlice

In [53]: dfmi.loc[idx[:, :, ['C1', 'C3']], idx[:, 'foo']]
Out[53]: 
lvl0           a    b
lvl1         foo  foo
A0 B0 C1 D0    8   10
         D1   12   14
      C3 D0   24   26
         D1   28   30
   B1 C1 D0   40   42
         D1   44   46
      C3 D0   56   58
...          ...  ...
A3 B0 C1 D1  204  206
      C3 D0  216  218
         D1  220  222
   B1 C1 D0  232  234
         D1  236  238
      C3 D0  248  250
         D1  252  254

[32 rows x 2 columns]

It is possible to perform quite complicated selections using this method on multiple axes at the same time.

In [54]: dfmi.loc['A1', (slice(None), 'foo')]
Out[54]: 
lvl0        a    b
lvl1      foo  foo
B0 C0 D0   64   66
      D1   68   70
   C1 D0   72   74
      D1   76   78
   C2 D0   80   82
      D1   84   86
   C3 D0   88   90
...       ...  ...
B1 C0 D1  100  102
   C1 D0  104  106
      D1  108  110
   C2 D0  112  114
      D1  116  118
   C3 D0  120  122
      D1  124  126

[16 rows x 2 columns]

In [55]: dfmi.loc[idx[:, :, ['C1', 'C3']], idx[:, 'foo']]
Out[55]: 
lvl0           a    b
lvl1         foo  foo
A0 B0 C1 D0    8   10
         D1   12   14
      C3 D0   24   26
         D1   28   30
   B1 C1 D0   40   42
         D1   44   46
      C3 D0   56   58
...          ...  ...
A3 B0 C1 D1  204  206
      C3 D0  216  218
         D1  220  222
   B1 C1 D0  232  234
         D1  236  238
      C3 D0  248  250
         D1  252  254

[32 rows x 2 columns]

Using a boolean indexer you can provide selection related to the values.

In [56]: mask = dfmi[('a', 'foo')] > 200

In [57]: dfmi.loc[idx[mask, :, ['C1', 'C3']], idx[:, 'foo']]
Out[57]: 
lvl0           a    b
lvl1         foo  foo
A3 B0 C1 D1  204  206
      C3 D0  216  218
         D1  220  222
   B1 C1 D0  232  234
         D1  236  238
      C3 D0  248  250
         D1  252  254

You can also specify the axis argument to .loc to interpret the passed slicers on a single axis.

In [58]: dfmi.loc(axis=0)[:, :, ['C1', 'C3']]
Out[58]: 
lvl0           a         b     
lvl1         bar  foo  bah  foo
A0 B0 C1 D0    9    8   11   10
         D1   13   12   15   14
      C3 D0   25   24   27   26
         D1   29   28   31   30
   B1 C1 D0   41   40   43   42
         D1   45   44   47   46
      C3 D0   57   56   59   58
...          ...  ...  ...  ...
A3 B0 C1 D1  205  204  207  206
      C3 D0  217  216  219  218
         D1  221  220  223  222
   B1 C1 D0  233  232  235  234
         D1  237  236  239  238
      C3 D0  249  248  251  250
         D1  253  252  255  254

[32 rows x 4 columns]

Furthermore you can set the values using these methods

In [59]: df2 = dfmi.copy()

In [60]: df2.loc(axis=0)[:, :, ['C1', 'C3']] = -10

In [61]: df2
Out[61]: 
lvl0           a         b     
lvl1         bar  foo  bah  foo
A0 B0 C0 D0    1    0    3    2
         D1    5    4    7    6
      C1 D0  -10  -10  -10  -10
         D1  -10  -10  -10  -10
      C2 D0   17   16   19   18
         D1   21   20   23   22
      C3 D0  -10  -10  -10  -10
...          ...  ...  ...  ...
A3 B1 C0 D1  229  228  231  230
      C1 D0  -10  -10  -10  -10
         D1  -10  -10  -10  -10
      C2 D0  241  240  243  242
         D1  245  244  247  246
      C3 D0  -10  -10  -10  -10
         D1  -10  -10  -10  -10

[64 rows x 4 columns]

You can use a right-hand-side of an alignable object as well.

In [62]: df2 = dfmi.copy()

In [63]: df2.loc[idx[:, :, ['C1', 'C3']], :] = df2 * 1000

In [64]: df2
Out[64]: 
lvl0              a               b        
lvl1            bar     foo     bah     foo
A0 B0 C0 D0       1       0       3       2
         D1       5       4       7       6
      C1 D0    9000    8000   11000   10000
         D1   13000   12000   15000   14000
      C2 D0      17      16      19      18
         D1      21      20      23      22
      C3 D0   25000   24000   27000   26000
...             ...     ...     ...     ...
A3 B1 C0 D1     229     228     231     230
      C1 D0  233000  232000  235000  234000
         D1  237000  236000  239000  238000
      C2 D0     241     240     243     242
         D1     245     244     247     246
      C3 D0  249000  248000  251000  250000
         D1  253000  252000  255000  254000

[64 rows x 4 columns]

Cross-section

The xs method of DataFrame additionally takes a level argument to make selecting data at a particular level of a MultiIndex easier.

In [65]: df
Out[65]: 
                     A         B         C
first second                              
bar   one     0.895717  0.410835 -1.413681
      two     0.805244  0.813850  1.607920
baz   one    -1.206412  0.132003  1.024180
      two     2.565646 -0.827317  0.569605
foo   one     1.431256 -0.076467  0.875906
      two     1.340309 -1.187678 -2.211372
qux   one    -1.170299  1.130127  0.974466
      two    -0.226169 -1.436737 -2.006747

In [66]: df.xs('one', level='second')
Out[66]: 
              A         B         C
first                              
bar    0.895717  0.410835 -1.413681
baz   -1.206412  0.132003  1.024180
foo    1.431256 -0.076467  0.875906
qux   -1.170299  1.130127  0.974466
# using the slicers (new in 0.14.0)
In [67]: df.loc[(slice(None),'one'),:]
Out[67]: 
                     A         B         C
first second                              
bar   one     0.895717  0.410835 -1.413681
baz   one    -1.206412  0.132003  1.024180
foo   one     1.431256 -0.076467  0.875906
qux   one    -1.170299  1.130127  0.974466

You can also select on the columns with xs(), by providing the axis argument

In [68]: df = df.T

In [69]: df.xs('one', level='second', axis=1)
Out[69]: 
first       bar       baz       foo       qux
A      0.895717 -1.206412  1.431256 -1.170299
B      0.410835  0.132003 -0.076467  1.130127
C     -1.413681  1.024180  0.875906  0.974466
# using the slicers (new in 0.14.0)
In [70]: df.loc[:,(slice(None),'one')]
Out[70]: 
first        bar       baz       foo       qux
second       one       one       one       one
A       0.895717 -1.206412  1.431256 -1.170299
B       0.410835  0.132003 -0.076467  1.130127
C      -1.413681  1.024180  0.875906  0.974466

xs() also allows selection with multiple keys

In [71]: df.xs(('one', 'bar'), level=('second', 'first'), axis=1)
Out[71]: 
first        bar
second       one
A       0.895717
B       0.410835
C      -1.413681
# using the slicers (new in 0.14.0)
In [72]: df.loc[:,('bar','one')]
Out[72]: 
A    0.895717
B    0.410835
C   -1.413681
Name: (bar, one), dtype: float64

New in version 0.13.0.

You can pass drop_level=False to xs() to retain the level that was selected

In [73]: df.xs('one', level='second', axis=1, drop_level=False)
Out[73]: 
first        bar       baz       foo       qux
second       one       one       one       one
A       0.895717 -1.206412  1.431256 -1.170299
B       0.410835  0.132003 -0.076467  1.130127
C      -1.413681  1.024180  0.875906  0.974466

versus the result with drop_level=True (the default value)

In [74]: df.xs('one', level='second', axis=1, drop_level=True)
Out[74]: 
first       bar       baz       foo       qux
A      0.895717 -1.206412  1.431256 -1.170299
B      0.410835  0.132003 -0.076467  1.130127
C     -1.413681  1.024180  0.875906  0.974466

Advanced reindexing and alignment

The parameter level has been added to the reindex and align methods of pandas objects. This is useful to broadcast values across a level. For instance:

In [75]: midx = pd.MultiIndex(levels=[['zero', 'one'], ['x','y']],
   ....:                      labels=[[1,1,0,0],[1,0,1,0]])
   ....: 

In [76]: df = pd.DataFrame(np.random.randn(4,2), index=midx)

In [77]: df
Out[77]: 
               0         1
one  y  1.519970 -0.493662
     x  0.600178  0.274230
zero y  0.132885 -0.023688
     x  2.410179  1.450520

In [78]: df2 = df.mean(level=0)

In [79]: df2
Out[79]: 
             0         1
zero  1.271532  0.713416
one   1.060074 -0.109716

In [80]: df2.reindex(df.index, level=0)
Out[80]: 
               0         1
one  y  1.060074 -0.109716
     x  1.060074 -0.109716
zero y  1.271532  0.713416
     x  1.271532  0.713416

# aligning
In [81]: df_aligned, df2_aligned = df.align(df2, level=0)

In [82]: df_aligned
Out[82]: 
               0         1
one  y  1.519970 -0.493662
     x  0.600178  0.274230
zero y  0.132885 -0.023688
     x  2.410179  1.450520

In [83]: df2_aligned
Out[83]: 
               0         1
one  y  1.060074 -0.109716
     x  1.060074 -0.109716
zero y  1.271532  0.713416
     x  1.271532  0.713416

Swapping levels with swaplevel()

The swaplevel function can switch the order of two levels:

In [84]: df[:5]
Out[84]: 
               0         1
one  y  1.519970 -0.493662
     x  0.600178  0.274230
zero y  0.132885 -0.023688
     x  2.410179  1.450520

In [85]: df[:5].swaplevel(0, 1, axis=0)
Out[85]: 
               0         1
y one   1.519970 -0.493662
x one   0.600178  0.274230
y zero  0.132885 -0.023688
x zero  2.410179  1.450520

Reordering levels with reorder_levels()

The reorder_levels function generalizes the swaplevel function, allowing you to permute the hierarchical index levels in one step:

In [86]: df[:5].reorder_levels([1,0], axis=0)
Out[86]: 
               0         1
y one   1.519970 -0.493662
x one   0.600178  0.274230
y zero  0.132885 -0.023688
x zero  2.410179  1.450520

Sorting a MultiIndex

For MultiIndex-ed objects to be indexed & sliced effectively, they need to be sorted. As with any index, you can use sort_index.

In [87]: import random; random.shuffle(tuples)

In [88]: s = pd.Series(np.random.randn(8), index=pd.MultiIndex.from_tuples(tuples))

In [89]: s
Out[89]: 
baz  one    0.206053
foo  one   -0.251905
bar  two   -2.213588
foo  two    1.063327
qux  two    1.266143
baz  two    0.299368
qux  one   -0.863838
bar  one    0.408204
dtype: float64

In [90]: s.sort_index()
Out[90]: 
bar  one    0.408204
     two   -2.213588
baz  one    0.206053
     two    0.299368
foo  one   -0.251905
     two    1.063327
qux  one   -0.863838
     two    1.266143
dtype: float64

In [91]: s.sort_index(level=0)
Out[91]: 
bar  one    0.408204
     two   -2.213588
baz  one    0.206053
     two    0.299368
foo  one   -0.251905
     two    1.063327
qux  one   -0.863838
     two    1.266143
dtype: float64

In [92]: s.sort_index(level=1)
Out[92]: 
bar  one    0.408204
baz  one    0.206053
foo  one   -0.251905
qux  one   -0.863838
bar  two   -2.213588
baz  two    0.299368
foo  two    1.063327
qux  two    1.266143
dtype: float64

You may also pass a level name to sort_index if the MultiIndex levels are named.

In [93]: s.index.set_names(['L1', 'L2'], inplace=True)

In [94]: s.sort_index(level='L1')
Out[94]: 
L1   L2 
bar  one    0.408204
     two   -2.213588
baz  one    0.206053
     two    0.299368
foo  one   -0.251905
     two    1.063327
qux  one   -0.863838
     two    1.266143
dtype: float64

In [95]: s.sort_index(level='L2')
Out[95]: 
L1   L2 
bar  one    0.408204
baz  one    0.206053
foo  one   -0.251905
qux  one   -0.863838
bar  two   -2.213588
baz  two    0.299368
foo  two    1.063327
qux  two    1.266143
dtype: float64

On higher dimensional objects, you can sort any of the other axes by level if they have a MultiIndex:

In [96]: df.T.sort_index(level=1, axis=1)
Out[96]: 
       zero       one      zero       one
          x         x         y         y
0  2.410179  0.600178  0.132885  1.519970
1  1.450520  0.274230 -0.023688 -0.493662

Indexing will work even if the data are not sorted, but will be rather inefficient (and show a PerformanceWarning). It will also return a copy of the data rather than a view:

In [97]: dfm = pd.DataFrame({'jim': [0, 0, 1, 1],
   ....:                     'joe': ['x', 'x', 'z', 'y'],
   ....:                     'jolie': np.random.rand(4)})
   ....: 

In [98]: dfm = dfm.set_index(['jim', 'joe'])

In [99]: dfm
Out[99]: 
            jolie
jim joe          
0   x    0.490671
    x    0.120248
1   z    0.537020
    y    0.110968
In [4]: dfm.loc[(1, 'z')]
PerformanceWarning: indexing past lexsort depth may impact performance.

Out[4]:
           jolie
jim joe
1   z    0.64094

Furthermore if you try to index something that is not fully lexsorted, this can raise:

In [5]: dfm.loc[(0,'y'):(1, 'z')]
UnsortedIndexError: 'Key length (2) was greater than MultiIndex lexsort depth (1)'

The is_lexsorted() method on an Index show if the index is sorted, and the lexsort_depth property returns the sort depth:

In [100]: dfm.index.is_lexsorted()
Out[100]: False

In [101]: dfm.index.lexsort_depth
Out[101]: 1
In [102]: dfm = dfm.sort_index()

In [103]: dfm
Out[103]: 
            jolie
jim joe          
0   x    0.490671
    x    0.120248
1   y    0.110968
    z    0.537020

In [104]: dfm.index.is_lexsorted()
Out[104]: True

In [105]: dfm.index.lexsort_depth
Out[105]: 2

And now selection works as expected.

In [106]: dfm.loc[(0,'y'):(1, 'z')]
Out[106]: 
            jolie
jim joe          
1   y    0.110968
    z    0.537020

Take Methods

Similar to numpy ndarrays, pandas Index, Series, and DataFrame also provides the take method that retrieves elements along a given axis at the given indices. The given indices must be either a list or an ndarray of integer index positions. take will also accept negative integers as relative positions to the end of the object.

In [107]: index = pd.Index(np.random.randint(0, 1000, 10))

In [108]: index
Out[108]: Int64Index([214, 502, 712, 567, 786, 175, 993, 133, 758, 329], dtype='int64')

In [109]: positions = [0, 9, 3]

In [110]: index[positions]
Out[110]: Int64Index([214, 329, 567], dtype='int64')

In [111]: index.take(positions)
Out[111]: Int64Index([214, 329, 567], dtype='int64')

In [112]: ser = pd.Series(np.random.randn(10))

In [113]: ser.iloc[positions]
Out[113]: 
0   -0.179666
9    1.824375
3    0.392149
dtype: float64

In [114]: ser.take(positions)
Out[114]: 
0   -0.179666
9    1.824375
3    0.392149
dtype: float64

For DataFrames, the given indices should be a 1d list or ndarray that specifies row or column positions.

In [115]: frm = pd.DataFrame(np.random.randn(5, 3))

In [116]: frm.take([1, 4, 3])
Out[116]: 
          0         1         2
1 -1.237881  0.106854 -1.276829
4  0.629675 -1.425966  1.857704
3  0.979542 -1.633678  0.615855

In [117]: frm.take([0, 2], axis=1)
Out[117]: 
          0         2
0  0.595974  0.601544
1 -1.237881 -1.276829
2 -0.767101  1.499591
3  0.979542  0.615855
4  0.629675  1.857704

It is important to note that the take method on pandas objects are not intended to work on boolean indices and may return unexpected results.

In [118]: arr = np.random.randn(10)

In [119]: arr.take([False, False, True, True])
Out[119]: array([-1.1935, -1.1935,  0.6775,  0.6775])

In [120]: arr[[0, 1]]
Out[120]: array([-1.1935,  0.6775])

In [121]: ser = pd.Series(np.random.randn(10))

In [122]: ser.take([False, False, True, True])
Out[122]: 
0    0.233141
0    0.233141
1   -0.223540
1   -0.223540
dtype: float64

In [123]: ser.iloc[[0, 1]]
Out[123]: 
0    0.233141
1   -0.223540
dtype: float64

Finally, as a small note on performance, because the take method handles a narrower range of inputs, it can offer performance that is a good deal faster than fancy indexing.

Index Types

We have discussed MultiIndex in the previous sections pretty extensively. DatetimeIndex and PeriodIndex are shown here. TimedeltaIndex are here.

In the following sub-sections we will highlite some other index types.

CategoricalIndex

New in version 0.16.1.

We introduce a CategoricalIndex, a new type of index object that is useful for supporting indexing with duplicates. This is a container around a Categorical (introduced in v0.15.0) and allows efficient indexing and storage of an index with a large number of duplicated elements. Prior to 0.16.1, setting the index of a DataFrame/Series with a category dtype would convert this to regular object-based Index.

In [124]: df = pd.DataFrame({'A': np.arange(6),
   .....:                    'B': list('aabbca')})
   .....: 

In [125]: df['B'] = df['B'].astype('category', categories=list('cab'))

In [126]: df
Out[126]: 
   A  B
0  0  a
1  1  a
2  2  b
3  3  b
4  4  c
5  5  a

In [127]: df.dtypes
Out[127]: 
A       int64
B    category
dtype: object

In [128]: df.B.cat.categories
Out[128]: Index(['c', 'a', 'b'], dtype='object')

Setting the index, will create create a CategoricalIndex

In [129]: df2 = df.set_index('B')

In [130]: df2.index
Out[130]: CategoricalIndex(['a', 'a', 'b', 'b', 'c', 'a'], categories=['c', 'a', 'b'], ordered=False, name='B', dtype='category')

Indexing with __getitem__/.iloc/.loc works similarly to an Index with duplicates. The indexers MUST be in the category or the operation will raise.

In [131]: df2.loc['a']
Out[131]: 
   A
B   
a  0
a  1
a  5

These PRESERVE the CategoricalIndex

In [132]: df2.loc['a'].index
Out[132]: CategoricalIndex(['a', 'a', 'a'], categories=['c', 'a', 'b'], ordered=False, name='B', dtype='category')

Sorting will order by the order of the categories

In [133]: df2.sort_index()
Out[133]: 
   A
B   
c  4
a  0
a  1
a  5
b  2
b  3

Groupby operations on the index will preserve the index nature as well

In [134]: df2.groupby(level=0).sum()
Out[134]: 
   A
B   
c  4
a  6
b  5

In [135]: df2.groupby(level=0).sum().index
Out[135]: CategoricalIndex(['c', 'a', 'b'], categories=['c', 'a', 'b'], ordered=False, name='B', dtype='category')

Reindexing operations, will return a resulting index based on the type of the passed indexer, meaning that passing a list will return a plain-old-Index; indexing with a Categorical will return a CategoricalIndex, indexed according to the categories of the PASSED Categorical dtype. This allows one to arbitrarly index these even with values NOT in the categories, similarly to how you can reindex ANY pandas index.

In [136]: df2.reindex(['a','e'])
Out[136]: 
     A
B     
a  0.0
a  1.0
a  5.0
e  NaN

In [137]: df2.reindex(['a','e']).index
Out[137]: Index(['a', 'a', 'a', 'e'], dtype='object', name='B')

In [138]: df2.reindex(pd.Categorical(['a','e'],categories=list('abcde')))
Out[138]: 
     A
B     
a  0.0
a  1.0
a  5.0
e  NaN

In [139]: df2.reindex(pd.Categorical(['a','e'],categories=list('abcde'))).index
Out[139]: CategoricalIndex(['a', 'a', 'a', 'e'], categories=['a', 'b', 'c', 'd', 'e'], ordered=False, name='B', dtype='category')

Warning

Reshaping and Comparison operations on a CategoricalIndex must have the same categories or a TypeError will be raised.

In [9]: df3 = pd.DataFrame({'A' : np.arange(6),
                            'B' : pd.Series(list('aabbca')).astype('category')})

In [11]: df3 = df3.set_index('B')

In [11]: df3.index
Out[11]: CategoricalIndex([u'a', u'a', u'b', u'b', u'c', u'a'], categories=[u'a', u'b', u'c'], ordered=False, name=u'B', dtype='category')

In [12]: pd.concat([df2, df3]
TypeError: categories must match existing categories when appending

Int64Index and RangeIndex

Warning

Indexing on an integer-based Index with floats has been clarified in 0.18.0, for a summary of the changes, see here.

Int64Index is a fundamental basic index in pandas. This is an Immutable array implementing an ordered, sliceable set. Prior to 0.18.0, the Int64Index would provide the default index for all NDFrame objects.

RangeIndex is a sub-class of Int64Index added in version 0.18.0, now providing the default index for all NDFrame objects. RangeIndex is an optimized version of Int64Index that can represent a monotonic ordered set. These are analagous to python range types.

Float64Index

Note

As of 0.14.0, Float64Index is backed by a native float64 dtype array. Prior to 0.14.0, Float64Index was backed by an object dtype array. Using a float64 dtype in the backend speeds up arithmetic operations by about 30x and boolean indexing operations on the Float64Index itself are about 2x as fast.

New in version 0.13.0.

By default a Float64Index will be automatically created when passing floating, or mixed-integer-floating values in index creation. This enables a pure label-based slicing paradigm that makes [],ix,loc for scalar indexing and slicing work exactly the same.

In [140]: indexf = pd.Index([1.5, 2, 3, 4.5, 5])

In [141]: indexf
Out[141]: Float64Index([1.5, 2.0, 3.0, 4.5, 5.0], dtype='float64')

In [142]: sf = pd.Series(range(5), index=indexf)

In [143]: sf
Out[143]: 
1.5    0
2.0    1
3.0    2
4.5    3
5.0    4
dtype: int64

Scalar selection for [],.loc will always be label based. An integer will match an equal float index (e.g. 3 is equivalent to 3.0)

In [144]: sf[3]
Out[144]: 2

In [145]: sf[3.0]
Out[145]: 2

In [146]: sf.loc[3]
Out[146]: 2

In [147]: sf.loc[3.0]
Out[147]: 2

The only positional indexing is via iloc

In [148]: sf.iloc[3]
Out[148]: 3

A scalar index that is not found will raise KeyError

Slicing is ALWAYS on the values of the index, for [],ix,loc and ALWAYS positional with iloc

In [149]: sf[2:4]
Out[149]: 
2.0    1
3.0    2
dtype: int64

In [150]: sf.loc[2:4]
Out[150]: 
2.0    1
3.0    2
dtype: int64

In [151]: sf.iloc[2:4]
Out[151]: 
3.0    2
4.5    3
dtype: int64

In float indexes, slicing using floats is allowed

In [152]: sf[2.1:4.6]
Out[152]: 
3.0    2
4.5    3
dtype: int64

In [153]: sf.loc[2.1:4.6]
Out[153]: 
3.0    2
4.5    3
dtype: int64

In non-float indexes, slicing using floats will raise a TypeError

In [1]: pd.Series(range(5))[3.5]
TypeError: the label [3.5] is not a proper indexer for this index type (Int64Index)

In [1]: pd.Series(range(5))[3.5:4.5]
TypeError: the slice start [3.5] is not a proper indexer for this index type (Int64Index)

Warning

Using a scalar float indexer for .iloc has been removed in 0.18.0, so the following will raise a TypeError

In [3]: pd.Series(range(5)).iloc[3.0]
TypeError: cannot do positional indexing on <class 'pandas.indexes.range.RangeIndex'> with these indexers [3.0] of <type 'float'>

Here is a typical use-case for using this type of indexing. Imagine that you have a somewhat irregular timedelta-like indexing scheme, but the data is recorded as floats. This could for example be millisecond offsets.

In [154]: dfir = pd.concat([pd.DataFrame(np.random.randn(5,2),
   .....:                                index=np.arange(5) * 250.0,
   .....:                                columns=list('AB')),
   .....:                   pd.DataFrame(np.random.randn(6,2),
   .....:                                index=np.arange(4,10) * 250.1,
   .....:                                columns=list('AB'))])
   .....: 

In [155]: dfir
Out[155]: 
               A         B
0.0     0.997289 -1.693316
250.0  -0.179129 -1.598062
500.0   0.936914  0.912560
750.0  -1.003401  1.632781
1000.0 -0.724626  0.178219
1000.4  0.310610 -0.108002
1250.5 -0.974226 -1.147708
1500.6 -2.281374  0.760010
1750.7 -0.742532  1.533318
2000.8  2.495362 -0.432771
2250.9 -0.068954  0.043520

Selection operations then will always work on a value basis, for all selection operators.

In [156]: dfir[0:1000.4]
Out[156]: 
               A         B
0.0     0.997289 -1.693316
250.0  -0.179129 -1.598062
500.0   0.936914  0.912560
750.0  -1.003401  1.632781
1000.0 -0.724626  0.178219
1000.4  0.310610 -0.108002

In [157]: dfir.loc[0:1001,'A']
Out[157]: 
0.0       0.997289
250.0    -0.179129
500.0     0.936914
750.0    -1.003401
1000.0   -0.724626
1000.4    0.310610
Name: A, dtype: float64

In [158]: dfir.loc[1000.4]
Out[158]: 
A    0.310610
B   -0.108002
Name: 1000.4, dtype: float64

You could then easily pick out the first 1 second (1000 ms) of data then.

In [159]: dfir[0:1000]
Out[159]: 
               A         B
0.0     0.997289 -1.693316
250.0  -0.179129 -1.598062
500.0   0.936914  0.912560
750.0  -1.003401  1.632781
1000.0 -0.724626  0.178219

Of course if you need integer based selection, then use iloc

In [160]: dfir.iloc[0:5]
Out[160]: 
               A         B
0.0     0.997289 -1.693316
250.0  -0.179129 -1.598062
500.0   0.936914  0.912560
750.0  -1.003401  1.632781
1000.0 -0.724626  0.178219

IntervalIndex

New in version 0.20.0.

Warning

These indexing behaviors are provisional and may change in a future version of pandas.

In [161]: df = pd.DataFrame({'A': [1, 2, 3, 4]},
   .....:                    index=pd.IntervalIndex.from_breaks([0, 1, 2, 3, 4]))
   .....: 

In [162]: df
Out[162]: 
        A
(0, 1]  1
(1, 2]  2
(2, 3]  3
(3, 4]  4

Label based indexing via .loc along the edges of an interval works as you would expect, selecting that particular interval.

In [163]: df.loc[2]
Out[163]: 
A    2
Name: (1, 2], dtype: int64

In [164]: df.loc[[2, 3]]
Out[164]: 
        A
(1, 2]  2
(2, 3]  3

If you select a lable contained within an interval, this will also select the interval.

In [165]: df.loc[2.5]
Out[165]: 
A    3
Name: (2, 3], dtype: int64

In [166]: df.loc[[2.5, 3.5]]
Out[166]: 
        A
(2, 3]  3
(3, 4]  4

Miscellaneous indexing FAQ

Integer indexing

Label-based indexing with integer axis labels is a thorny topic. It has been discussed heavily on mailing lists and among various members of the scientific Python community. In pandas, our general viewpoint is that labels matter more than integer locations. Therefore, with an integer axis index only label-based indexing is possible with the standard tools like .loc. The following code will generate exceptions:

s = pd.Series(range(5))
s[-1]
df = pd.DataFrame(np.random.randn(5, 4))
df
df.loc[-2:]

This deliberate decision was made to prevent ambiguities and subtle bugs (many users reported finding bugs when the API change was made to stop “falling back” on position-based indexing).

Non-monotonic indexes require exact matches

If the index of a Series or DataFrame is monotonically increasing or decreasing, then the bounds of a label-based slice can be outside the range of the index, much like slice indexing a normal Python list. Monotonicity of an index can be tested with the is_monotonic_increasing and is_monotonic_decreasing attributes.

In [167]: df = pd.DataFrame(index=[2,3,3,4,5], columns=['data'], data=list(range(5)))

In [168]: df.index.is_monotonic_increasing
Out[168]: True

# no rows 0 or 1, but still returns rows 2, 3 (both of them), and 4:
In [169]: df.loc[0:4, :]
Out[169]: 
   data
2     0
3     1
3     2
4     3

# slice is are outside the index, so empty DataFrame is returned
In [170]: df.loc[13:15, :]
Out[170]: 
Empty DataFrame
Columns: [data]
Index: []

On the other hand, if the index is not monotonic, then both slice bounds must be unique members of the index.

In [171]: df = pd.DataFrame(index=[2,3,1,4,3,5], columns=['data'], data=list(range(6)))

In [172]: df.index.is_monotonic_increasing
Out[172]: False

# OK because 2 and 4 are in the index
In [173]: df.loc[2:4, :]
Out[173]: 
   data
2     0
3     1
1     2
4     3
# 0 is not in the index
In [9]: df.loc[0:4, :]
KeyError: 0

# 3 is not a unique label
In [11]: df.loc[2:3, :]
KeyError: 'Cannot get right slice bound for non-unique label: 3'

Index.is_monotonic_increasing() and Index.is_monotonic_decreasing() only check that an index is weakly monotonic. To check for strict montonicity, you can combine one of those with Index.is_unique()

In [174]: weakly_monotonic = pd.Index(['a', 'b', 'c', 'c'])

In [175]: weakly_monotonic
Out[175]: Index(['a', 'b', 'c', 'c'], dtype='object')

In [176]: weakly_monotonic.is_monotonic_increasing
Out[176]: True

In [177]: weakly_monotonic.is_monotonic_increasing & weakly_monotonic.is_unique
Out[177]: False

Endpoints are inclusive

Compared with standard Python sequence slicing in which the slice endpoint is not inclusive, label-based slicing in pandas is inclusive. The primary reason for this is that it is often not possible to easily determine the “successor” or next element after a particular label in an index. For example, consider the following Series:

In [178]: s = pd.Series(np.random.randn(6), index=list('abcdef'))

In [179]: s
Out[179]: 
a    0.112246
b    0.871721
c   -0.816064
d   -0.784880
e    1.030659
f    0.187483
dtype: float64

Suppose we wished to slice from c to e, using integers this would be

In [180]: s[2:5]
Out[180]: 
c   -0.816064
d   -0.784880
e    1.030659
dtype: float64

However, if you only had c and e, determining the next element in the index can be somewhat complicated. For example, the following does not work:

s.loc['c':'e'+1]

A very common use case is to limit a time series to start and end at two specific dates. To enable this, we made the design design to make label-based slicing include both endpoints:

In [181]: s.loc['c':'e']
Out[181]: 
c   -0.816064
d   -0.784880
e    1.030659
dtype: float64

This is most definitely a “practicality beats purity” sort of thing, but it is something to watch out for if you expect label-based slicing to behave exactly in the way that standard Python integer slicing works.

Indexing potentially changes underlying Series dtype

The different indexing operation can potentially change the dtype of a Series.

In [182]: series1 = pd.Series([1, 2, 3])

In [183]: series1.dtype
Out[183]: dtype('int64')

In [184]: res = series1[[0,4]]

In [185]: res.dtype
Out[185]: dtype('float64')

In [186]: res
Out[186]: 
0    1.0
4    NaN
dtype: float64
In [187]: series2 = pd.Series([True])

In [188]: series2.dtype
Out[188]: dtype('bool')

In [189]: res = series2.reindex_like(series1)

In [190]: res.dtype
Out[190]: dtype('O')

In [191]: res
Out[191]: 
0    True
1     NaN
2     NaN
dtype: object

This is because the (re)indexing operations above silently inserts NaNs and the dtype changes accordingly. This can cause some issues when using numpy ufuncs such as numpy.logical_and.

See the this old issue for a more detailed discussion.

Scroll To Top