This section covers indexing with a MultiIndex and other 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.
chained assignment
See the cookbook for some advanced strategies.
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).
Series
DataFrame
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.
Changed in version 0.24.0: MultiIndex.labels has been renamed to MultiIndex.codes and MultiIndex.set_labels to MultiIndex.set_codes.
MultiIndex.labels
MultiIndex.codes
MultiIndex.set_labels
MultiIndex.set_codes
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()), a crossed set of iterables (using MultiIndex.from_product()), or a DataFrame (using MultiIndex.from_frame()). The Index constructor will attempt to return a MultiIndex when it is passed a list of tuples. The following examples demonstrate different ways to initialize MultiIndexes.
MultiIndex
Index
MultiIndex.from_arrays()
MultiIndex.from_tuples()
MultiIndex.from_product()
MultiIndex.from_frame()
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([('bar', 'one'), ('bar', 'two'), ('baz', 'one'), ('baz', 'two'), ('foo', 'one'), ('foo', 'two'), ('qux', 'one'), ('qux', 'two')], 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() method:
In [8]: iterables = [['bar', 'baz', 'foo', 'qux'], ['one', 'two']] In [9]: pd.MultiIndex.from_product(iterables, names=['first', 'second']) Out[9]: MultiIndex([('bar', 'one'), ('bar', 'two'), ('baz', 'one'), ('baz', 'two'), ('foo', 'one'), ('foo', 'two'), ('qux', 'one'), ('qux', 'two')], names=['first', 'second'])
You can also construct a MultiIndex from a DataFrame directly, using the method MultiIndex.from_frame(). This is a complementary method to MultiIndex.to_frame().
MultiIndex.to_frame()
New in version 0.24.0.
In [10]: df = pd.DataFrame([['bar', 'one'], ['bar', 'two'], ....: ['foo', 'one'], ['foo', 'two']], ....: columns=['first', 'second']) ....: In [11]: pd.MultiIndex.from_frame(df) Out[11]: MultiIndex([('bar', 'one'), ('bar', 'two'), ('foo', 'one'), ('foo', 'two')], names=['first', 'second'])
As a convenience, you can pass a list of arrays directly into Series or DataFrame to construct a MultiIndex automatically:
In [12]: arrays = [np.array(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux']), ....: np.array(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'])] ....: In [13]: s = pd.Series(np.random.randn(8), index=arrays) In [14]: s Out[14]: 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 [15]: df = pd.DataFrame(np.random.randn(8, 4), index=arrays) In [16]: df Out[16]: 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:
names
None
In [17]: df.index.names Out[17]: 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 [18]: df = pd.DataFrame(np.random.randn(3, 8), index=['A', 'B', 'C'], columns=index) In [19]: df Out[19]: first bar baz foo qux second one two one two one two one two A 0.895717 0.805244 -1.206412 2.565646 1.431256 1.340309 -1.170299 -0.226169 B 0.410835 0.813850 0.132003 -0.827317 -0.076467 -1.187678 1.130127 -1.436737 C -1.413681 1.607920 1.024180 0.569605 0.875906 -2.211372 0.974466 -2.006747 In [20]: pd.DataFrame(np.random.randn(6, 6), index=index[:6], columns=index[:6]) Out[20]: 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. Note that how the index is displayed can be controlled using the multi_sparse option in pandas.set_options():
multi_sparse
pandas.set_options()
In [21]: with pd.option_context('display.multi_sparse', False): ....: df ....:
It’s worth keeping in mind that there’s nothing preventing you from using tuples as atomic labels on an axis:
In [22]: pd.Series(np.random.randn(8), index=tuples) Out[22]: (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.
The method get_level_values() will return a vector of the labels for each location at a particular level:
get_level_values()
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')
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.
The MultiIndex keeps all the defined levels of an index, even if they are not actually used. When slicing an index, you may notice this. For example:
In [29]: df.columns.levels # original MultiIndex Out[29]: FrozenList([['bar', 'baz', 'foo', 'qux'], ['one', 'two']]) In [30]: df[['foo','qux']].columns.levels # sliced Out[30]: FrozenList([['bar', 'baz', 'foo', 'qux'], ['one', 'two']])
This is done to avoid a recomputation of the levels in order to make slicing highly performant. If you want to see only the used levels, you can use the get_level_values() method.
In [31]: df[['foo', 'qux']].columns.to_numpy() 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, the remove_unused_levels() method may be used.
remove_unused_levels()
In [33]: new_mi = df[['foo', 'qux']].columns.remove_unused_levels() In [34]: new_mi.levels Out[34]: FrozenList([['foo', 'qux'], ['one', 'two']])
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 [35]: s + s[:-2] Out[35]: 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 [36]: s + s[::2] Out[36]: 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
The reindex() method of Series/DataFrames can be called with another MultiIndex, or even a list or array of tuples:
reindex()
DataFrames
In [37]: s.reindex(index[:3]) Out[37]: first second bar one -0.861849 two -2.104569 baz one -0.494929 dtype: float64 In [38]: s.reindex([('foo', 'two'), ('bar', 'one'), ('qux', 'one'), ('baz', 'one')]) Out[38]: foo two -0.706771 bar one -0.861849 qux one -1.039575 baz one -0.494929 dtype: float64
Syntactically integrating MultiIndex in advanced indexing with .loc is a bit challenging, but we’ve made every effort to do so. In general, MultiIndex keys take the form of tuples. For example, the following works as you would expect:
.loc
In [39]: df = df.T In [40]: df Out[40]: 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 [41]: df.loc[('bar', 'two')] Out[41]: A 0.805244 B 0.813850 C 1.607920 Name: (bar, two), dtype: float64
Note that df.loc['bar', 'two'] would also work in this example, but this shorthand notation can lead to ambiguity in general.
df.loc['bar', 'two']
If you also want to index a specific column with .loc, you must use a tuple like this:
In [42]: df.loc[('bar', 'two'), 'A'] Out[42]: 0.8052440253863785
You don’t have to specify all levels of the MultiIndex by passing only the first elements of the tuple. For example, you can use “partial” indexing to get all elements with bar in the first level as follows:
bar
df.loc[‘bar’]
This is a shortcut for the slightly more verbose notation df.loc[('bar',),] (equivalent to df.loc['bar',] in this example).
df.loc[('bar',),]
df.loc['bar',]
“Partial” slicing also works quite nicely.
In [43]: df.loc['baz':'foo'] Out[43]: 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 [44]: df.loc[('baz', 'two'):('qux', 'one')] 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 qux one -1.170299 1.130127 0.974466 In [45]: df.loc[('baz', 'two'):'foo'] Out[45]: 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 [46]: df.loc[[('bar', 'two'), ('qux', 'one')]] Out[46]: A B C first second bar two 0.805244 0.813850 1.607920 qux one -1.170299 1.130127 0.974466
Note
It is important to note that tuples and lists are not treated identically in pandas when it comes to indexing. Whereas a tuple is interpreted as one multi-level key, a list is used to specify several keys. Or in other words, tuples go horizontally (traversing levels), lists go vertically (scanning levels).
Importantly, a list of tuples indexes several complete MultiIndex keys, whereas a tuple of lists refer to several values within a level:
In [47]: s = pd.Series([1, 2, 3, 4, 5, 6], ....: index=pd.MultiIndex.from_product([["A", "B"], ["c", "d", "e"]])) ....: In [48]: s.loc[[("A", "c"), ("B", "d")]] # list of tuples Out[48]: A c 1 B d 5 dtype: int64 In [49]: s.loc[(["A", "B"], ["c", "d"])] # tuple of lists Out[49]: A c 1 d 2 B c 4 d 5 dtype: int64
You can slice a MultiIndex 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).
slice(None)
As usual, both sides of the slicers are included as this is label indexing.
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 MultiIndex for the rows.
You should do this:
df.loc[(slice('A1', 'A3'), ...), :] # noqa: E999
You should not do this:
df.loc[(slice('A1', 'A3'), ...)] # noqa: E999
In [50]: def mklbl(prefix, n): ....: return ["%s%s" % (prefix, i) for i in range(n)] ....: In [51]: miindex = pd.MultiIndex.from_product([mklbl('A', 4), ....: mklbl('B', 2), ....: mklbl('C', 4), ....: mklbl('D', 2)]) ....: In [52]: micolumns = pd.MultiIndex.from_tuples([('a', 'foo'), ('a', 'bar'), ....: ('b', 'foo'), ('b', 'bah')], ....: names=['lvl0', 'lvl1']) ....: In [53]: 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 [54]: dfmi Out[54]: 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 ... ... ... ... ... A3 B1 C1 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 MultiIndex slicing using slices, lists, and labels.
In [55]: dfmi.loc[(slice('A1', 'A3'), slice(None), ['C1', 'C3']), :] Out[55]: 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 ... ... ... ... ... A3 B0 C3 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 pandas.IndexSlice to facilitate a more natural syntax using :, rather than using slice(None).
pandas.IndexSlice
:
In [56]: idx = pd.IndexSlice In [57]: dfmi.loc[idx[:, :, ['C1', 'C3']], idx[:, 'foo']] Out[57]: 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 ... ... ... A3 B0 C3 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 [58]: dfmi.loc['A1', (slice(None), 'foo')] Out[58]: 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 ... ... ... B1 C1 D1 108 110 C2 D0 112 114 D1 116 118 C3 D0 120 122 D1 124 126 [16 rows x 2 columns] In [59]: dfmi.loc[idx[:, :, ['C1', 'C3']], idx[:, 'foo']] Out[59]: 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 ... ... ... A3 B0 C3 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 [60]: mask = dfmi[('a', 'foo')] > 200 In [61]: dfmi.loc[idx[mask, :, ['C1', 'C3']], idx[:, 'foo']] Out[61]: 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.
axis
In [62]: dfmi.loc(axis=0)[:, :, ['C1', 'C3']] Out[62]: 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 ... ... ... ... ... A3 B0 C3 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 the following methods.
In [63]: df2 = dfmi.copy() In [64]: df2.loc(axis=0)[:, :, ['C1', 'C3']] = -10 In [65]: df2 Out[65]: 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 ... ... ... ... ... A3 B1 C1 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 [66]: df2 = dfmi.copy() In [67]: df2.loc[idx[:, :, ['C1', 'C3']], :] = df2 * 1000 In [68]: df2 Out[68]: 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 ... ... ... ... ... A3 B1 C1 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]
The xs() method of DataFrame additionally takes a level argument to make selecting data at a particular level of a MultiIndex easier.
xs()
In [69]: df Out[69]: 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 [70]: df.xs('one', level='second') Out[70]: 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 In [71]: df.loc[(slice(None), 'one'), :] Out[71]: 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.
xs
In [72]: df = df.T In [73]: df.xs('one', level='second', axis=1) Out[73]: 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 In [74]: df.loc[:, (slice(None), 'one')] Out[74]: 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 [75]: df.xs(('one', 'bar'), level=('second', 'first'), axis=1) Out[75]: first bar second one A 0.895717 B 0.410835 C -1.413681
# using the slicers In [76]: df.loc[:, ('bar', 'one')] Out[76]: A 0.895717 B 0.410835 C -1.413681 Name: (bar, one), dtype: float64
You can pass drop_level=False to xs to retain the level that was selected.
drop_level=False
In [77]: df.xs('one', level='second', axis=1, drop_level=False) Out[77]: 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
Compare the above with the result using drop_level=True (the default value).
drop_level=True
In [78]: df.xs('one', level='second', axis=1, drop_level=True) Out[78]: 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 parameter level in the reindex() and align() methods of pandas objects is useful to broadcast values across a level. For instance:
level
align()
In [79]: midx = pd.MultiIndex(levels=[['zero', 'one'], ['x', 'y']], ....: codes=[[1, 1, 0, 0], [1, 0, 1, 0]]) ....: In [80]: df = pd.DataFrame(np.random.randn(4, 2), index=midx) In [81]: df Out[81]: 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 [82]: df2 = df.mean(level=0) In [83]: df2 Out[83]: 0 1 one 1.060074 -0.109716 zero 1.271532 0.713416 In [84]: df2.reindex(df.index, level=0) Out[84]: 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 [85]: df_aligned, df2_aligned = df.align(df2, level=0) In [86]: df_aligned Out[86]: 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 [87]: df2_aligned Out[87]: 0 1 one y 1.060074 -0.109716 x 1.060074 -0.109716 zero y 1.271532 0.713416 x 1.271532 0.713416
swaplevel
The swaplevel() method can switch the order of two levels:
swaplevel()
In [88]: df[:5] Out[88]: 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 [89]: df[:5].swaplevel(0, 1, axis=0) Out[89]: 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
reorder_levels
The reorder_levels() method generalizes the swaplevel method, allowing you to permute the hierarchical index levels in one step:
reorder_levels()
In [90]: df[:5].reorder_levels([1, 0], axis=0) Out[90]: 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
The rename() method is used to rename the labels of a MultiIndex, and is typically used to rename the columns of a DataFrame. The columns argument of rename allows a dictionary to be specified that includes only the columns you wish to rename.
rename()
columns
rename
In [91]: df.rename(columns={0: "col0", 1: "col1"}) Out[91]: col0 col1 one y 1.519970 -0.493662 x 0.600178 0.274230 zero y 0.132885 -0.023688 x 2.410179 1.450520
This method can also be used to rename specific labels of the main index of the DataFrame.
In [92]: df.rename(index={"one": "two", "y": "z"}) Out[92]: 0 1 two z 1.519970 -0.493662 x 0.600178 0.274230 zero z 0.132885 -0.023688 x 2.410179 1.450520
The rename_axis() method is used to rename the name of a Index or MultiIndex. In particular, the names of the levels of a MultiIndex can be specified, which is useful if reset_index() is later used to move the values from the MultiIndex to a column.
rename_axis()
reset_index()
In [93]: df.rename_axis(index=['abc', 'def']) Out[93]: 0 1 abc def one y 1.519970 -0.493662 x 0.600178 0.274230 zero y 0.132885 -0.023688 x 2.410179 1.450520
Note that the columns of a DataFrame are an index, so that using rename_axis with the columns argument will change the name of that index.
rename_axis
In [94]: df.rename_axis(columns="Cols").columns Out[94]: RangeIndex(start=0, stop=2, step=1, name='Cols')
Both rename and rename_axis support specifying a dictionary, Series or a mapping function to map labels/names to new values.
When working with an Index object directly, rather than via a DataFrame, Index.set_names() can be used to change the names.
Index.set_names()
In [95]: mi = pd.MultiIndex.from_product([[1, 2], ['a', 'b']], names=['x', 'y']) In [96]: mi.names Out[96]: FrozenList(['x', 'y']) In [97]: mi2 = mi.rename("new name", level=0) In [98]: mi2 Out[98]: MultiIndex([(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b')], names=['new name', 'y'])
You cannot set the names of the MultiIndex via a level.
In [99]: mi.levels[0].name = "name via level" --------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) <ipython-input-99-35d32a9a5218> in <module> ----> 1 mi.levels[0].name = "name via level" /pandas/pandas/core/indexes/base.py in name(self, value) 1189 # Used in MultiIndex.levels to avoid silently ignoring name updates. 1190 raise RuntimeError( -> 1191 "Cannot set name on a level of a MultiIndex. Use " 1192 "'MultiIndex.set_names' instead." 1193 ) RuntimeError: Cannot set name on a level of a MultiIndex. Use 'MultiIndex.set_names' instead.
Use Index.set_names() instead.
For MultiIndex-ed objects to be indexed and sliced effectively, they need to be sorted. As with any index, you can use sort_index().
sort_index()
In [100]: import random In [101]: random.shuffle(tuples) In [102]: s = pd.Series(np.random.randn(8), index=pd.MultiIndex.from_tuples(tuples)) In [103]: s Out[103]: foo one 0.206053 two -0.251905 baz one -2.213588 bar one 1.063327 baz two 1.266143 bar two 0.299368 qux one -0.863838 two 0.408204 dtype: float64 In [104]: s.sort_index() Out[104]: bar one 1.063327 two 0.299368 baz one -2.213588 two 1.266143 foo one 0.206053 two -0.251905 qux one -0.863838 two 0.408204 dtype: float64 In [105]: s.sort_index(level=0) Out[105]: bar one 1.063327 two 0.299368 baz one -2.213588 two 1.266143 foo one 0.206053 two -0.251905 qux one -0.863838 two 0.408204 dtype: float64 In [106]: s.sort_index(level=1) Out[106]: bar one 1.063327 baz one -2.213588 foo one 0.206053 qux one -0.863838 bar two 0.299368 baz two 1.266143 foo two -0.251905 qux two 0.408204 dtype: float64
You may also pass a level name to sort_index if the MultiIndex levels are named.
sort_index
In [107]: s.index.set_names(['L1', 'L2'], inplace=True) In [108]: s.sort_index(level='L1') Out[108]: L1 L2 bar one 1.063327 two 0.299368 baz one -2.213588 two 1.266143 foo one 0.206053 two -0.251905 qux one -0.863838 two 0.408204 dtype: float64 In [109]: s.sort_index(level='L2') Out[109]: L1 L2 bar one 1.063327 baz one -2.213588 foo one 0.206053 qux one -0.863838 bar two 0.299368 baz two 1.266143 foo two -0.251905 qux two 0.408204 dtype: float64
On higher dimensional objects, you can sort any of the other axes by level if they have a MultiIndex:
In [110]: df.T.sort_index(level=1, axis=1) Out[110]: one zero one zero x x y y 0 0.600178 2.410179 1.519970 0.132885 1 0.274230 1.450520 -0.493662 -0.023688
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:
PerformanceWarning
In [111]: dfm = pd.DataFrame({'jim': [0, 0, 1, 1], .....: 'joe': ['x', 'x', 'z', 'y'], .....: 'jolie': np.random.rand(4)}) .....: In [112]: dfm = dfm.set_index(['jim', 'joe']) In [113]: dfm Out[113]: 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 a MultiIndex shows if the index is sorted, and the lexsort_depth property returns the sort depth:
is_lexsorted()
lexsort_depth
In [114]: dfm.index.is_lexsorted() Out[114]: False In [115]: dfm.index.lexsort_depth Out[115]: 1
In [116]: dfm = dfm.sort_index() In [117]: dfm Out[117]: jolie jim joe 0 x 0.490671 x 0.120248 1 y 0.110968 z 0.537020 In [118]: dfm.index.is_lexsorted() Out[118]: True In [119]: dfm.index.lexsort_depth Out[119]: 2
And now selection works as expected.
In [120]: dfm.loc[(0, 'y'):(1, 'z')] Out[120]: jolie jim joe 1 y 0.110968 z 0.537020
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.
take()
take
In [121]: index = pd.Index(np.random.randint(0, 1000, 10)) In [122]: index Out[122]: Int64Index([214, 502, 712, 567, 786, 175, 993, 133, 758, 329], dtype='int64') In [123]: positions = [0, 9, 3] In [124]: index[positions] Out[124]: Int64Index([214, 329, 567], dtype='int64') In [125]: index.take(positions) Out[125]: Int64Index([214, 329, 567], dtype='int64') In [126]: ser = pd.Series(np.random.randn(10)) In [127]: ser.iloc[positions] Out[127]: 0 -0.179666 9 1.824375 3 0.392149 dtype: float64 In [128]: ser.take(positions) Out[128]: 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 [129]: frm = pd.DataFrame(np.random.randn(5, 3)) In [130]: frm.take([1, 4, 3]) Out[130]: 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 [131]: frm.take([0, 2], axis=1) Out[131]: 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 [132]: arr = np.random.randn(10) In [133]: arr.take([False, False, True, True]) Out[133]: array([-1.1935, -1.1935, 0.6775, 0.6775]) In [134]: arr[[0, 1]] Out[134]: array([-1.1935, 0.6775]) In [135]: ser = pd.Series(np.random.randn(10)) In [136]: ser.take([False, False, True, True]) Out[136]: 0 0.233141 0 0.233141 1 -0.223540 1 -0.223540 dtype: float64 In [137]: ser.iloc[[0, 1]] Out[137]: 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.
In [138]: arr = np.random.randn(10000, 5) In [139]: indexer = np.arange(10000) In [140]: random.shuffle(indexer) In [141]: %timeit arr[indexer] .....: %timeit arr.take(indexer, axis=0) .....: 149 us +- 1.22 us per loop (mean +- std. dev. of 7 runs, 10000 loops each) 50.1 us +- 133 ns per loop (mean +- std. dev. of 7 runs, 10000 loops each)
In [142]: ser = pd.Series(arr[:, 0]) In [143]: %timeit ser.iloc[indexer] .....: %timeit ser.take(indexer) .....: 142 us +- 4.95 us per loop (mean +- std. dev. of 7 runs, 10000 loops each) 128 us +- 1.48 us per loop (mean +- std. dev. of 7 runs, 10000 loops each)
We have discussed MultiIndex in the previous sections pretty extensively. Documentation about DatetimeIndex and PeriodIndex are shown here, and documentation about TimedeltaIndex is found here.
DatetimeIndex
PeriodIndex
TimedeltaIndex
In the following sub-sections we will highlight some other index types.
CategoricalIndex is a type of index that is useful for supporting indexing with duplicates. This is a container around a Categorical and allows efficient indexing and storage of an index with a large number of duplicated elements.
CategoricalIndex
Categorical
In [144]: from pandas.api.types import CategoricalDtype In [145]: df = pd.DataFrame({'A': np.arange(6), .....: 'B': list('aabbca')}) .....: In [146]: df['B'] = df['B'].astype(CategoricalDtype(list('cab'))) In [147]: df Out[147]: A B 0 0 a 1 1 a 2 2 b 3 3 b 4 4 c 5 5 a In [148]: df.dtypes Out[148]: A int64 B category dtype: object In [149]: df['B'].cat.categories Out[149]: Index(['c', 'a', 'b'], dtype='object')
Setting the index will create a CategoricalIndex.
In [150]: df2 = df.set_index('B') In [151]: df2.index Out[151]: 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 a KeyError.
__getitem__/.iloc/.loc
KeyError
In [152]: df2.loc['a'] Out[152]: A B a 0 a 1 a 5
The CategoricalIndex is preserved after indexing:
In [153]: df2.loc['a'].index Out[153]: CategoricalIndex(['a', 'a', 'a'], categories=['c', 'a', 'b'], ordered=False, name='B', dtype='category')
Sorting the index will sort by the order of the categories (recall that we created the index with CategoricalDtype(list('cab')), so the sorted order is cab).
CategoricalDtype(list('cab'))
cab
In [154]: df2.sort_index() Out[154]: 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 [155]: df2.groupby(level=0).sum() Out[155]: A B c 4 a 6 b 5 In [156]: df2.groupby(level=0).sum().index Out[156]: 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. 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 arbitrarily index these even with values not in the categories, similarly to how you can reindex any pandas index.
In [157]: df3 = pd.DataFrame({'A': np.arange(3), .....: 'B': pd.Series(list('abc')).astype('category')}) .....: In [158]: df3 = df3.set_index('B') In [159]: df3 Out[159]: A B a 0 b 1 c 2
In [160]: df3.reindex(['a', 'e']) Out[160]: A B a 0.0 e NaN In [161]: df3.reindex(['a', 'e']).index Out[161]: Index(['a', 'e'], dtype='object', name='B') In [162]: df3.reindex(pd.Categorical(['a', 'e'], categories=list('abe'))) Out[162]: A B a 0.0 e NaN In [163]: df3.reindex(pd.Categorical(['a', 'e'], categories=list('abe'))).index Out[163]: CategoricalIndex(['a', 'e'], categories=['a', 'b', 'e'], ordered=False, name='B', dtype='category')
Reshaping and Comparison operations on a CategoricalIndex must have the same categories or a TypeError will be raised.
TypeError
In [164]: df4 = pd.DataFrame({'A': np.arange(2), .....: 'B': list('ba')}) .....: In [165]: df4['B'] = df4['B'].astype(CategoricalDtype(list('ab'))) In [166]: df4 = df4.set_index('B') In [167]: df4.index Out[167]: CategoricalIndex(['b', 'a'], categories=['a', 'b'], ordered=False, name='B', dtype='category') In [168]: df5 = pd.DataFrame({'A': np.arange(2), .....: 'B': list('bc')}) .....: In [169]: df5['B'] = df5['B'].astype(CategoricalDtype(list('bc'))) In [170]: df5 = df5.set_index('B') In [171]: df5.index Out[171]: CategoricalIndex(['b', 'c'], categories=['b', 'c'], ordered=False, name='B', dtype='category')
In [1]: pd.concat([df4, df5]) TypeError: categories must match existing categories when appending
Int64Index is a fundamental basic index in pandas. This is an immutable array implementing an ordered, sliceable set.
Int64Index
RangeIndex is a sub-class of Int64Index that provides the default index for all NDFrame objects. RangeIndex is an optimized version of Int64Index that can represent a monotonic ordered set. These are analogous to Python range types.
RangeIndex
NDFrame
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.
Float64Index
[],ix,loc
In [172]: indexf = pd.Index([1.5, 2, 3, 4.5, 5]) In [173]: indexf Out[173]: Float64Index([1.5, 2.0, 3.0, 4.5, 5.0], dtype='float64') In [174]: sf = pd.Series(range(5), index=indexf) In [175]: sf Out[175]: 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).
[],.loc
3
3.0
In [176]: sf[3] Out[176]: 2 In [177]: sf[3.0] Out[177]: 2 In [178]: sf.loc[3] Out[178]: 2 In [179]: sf.loc[3.0] Out[179]: 2
The only positional indexing is via iloc.
iloc
In [180]: sf.iloc[3] Out[180]: 3
A scalar index that is not found will raise a KeyError. Slicing is primarily on the values of the index when using [],ix,loc, and always positional when using iloc. The exception is when the slice is boolean, in which case it will always be positional.
In [181]: sf[2:4] Out[181]: 2.0 1 3.0 2 dtype: int64 In [182]: sf.loc[2:4] Out[182]: 2.0 1 3.0 2 dtype: int64 In [183]: sf.iloc[2:4] Out[183]: 3.0 2 4.5 3 dtype: int64
In float indexes, slicing using floats is allowed.
In [184]: sf[2.1:4.6] Out[184]: 3.0 2 4.5 3 dtype: int64 In [185]: sf.loc[2.1:4.6] Out[185]: 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)
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 [186]: 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 [187]: dfir Out[187]: A B 0.0 -0.435772 -1.188928 250.0 -0.808286 -0.284634 500.0 -1.815703 1.347213 750.0 -0.243487 0.514704 1000.0 1.162969 -0.287725 1000.4 -0.179734 0.993962 1250.5 -0.212673 0.909872 1500.6 -0.733333 -0.349893 1750.7 0.456434 -0.306735 2000.8 0.553396 0.166221 2250.9 -0.101684 -0.734907
Selection operations then will always work on a value basis, for all selection operators.
In [188]: dfir[0:1000.4] Out[188]: A B 0.0 -0.435772 -1.188928 250.0 -0.808286 -0.284634 500.0 -1.815703 1.347213 750.0 -0.243487 0.514704 1000.0 1.162969 -0.287725 1000.4 -0.179734 0.993962 In [189]: dfir.loc[0:1001, 'A'] Out[189]: 0.0 -0.435772 250.0 -0.808286 500.0 -1.815703 750.0 -0.243487 1000.0 1.162969 1000.4 -0.179734 Name: A, dtype: float64 In [190]: dfir.loc[1000.4] Out[190]: A -0.179734 B 0.993962 Name: 1000.4, dtype: float64
You could retrieve the first 1 second (1000 ms) of data as such:
In [191]: dfir[0:1000] Out[191]: A B 0.0 -0.435772 -1.188928 250.0 -0.808286 -0.284634 500.0 -1.815703 1.347213 750.0 -0.243487 0.514704 1000.0 1.162969 -0.287725
If you need integer based selection, you should use iloc:
In [192]: dfir.iloc[0:5] Out[192]: A B 0.0 -0.435772 -1.188928 250.0 -0.808286 -0.284634 500.0 -1.815703 1.347213 750.0 -0.243487 0.514704 1000.0 1.162969 -0.287725
IntervalIndex together with its own dtype, IntervalDtype as well as the Interval scalar type, allow first-class support in pandas for interval notation.
IntervalIndex
IntervalDtype
Interval
The IntervalIndex allows some unique indexing and is also used as a return type for the categories in cut() and qcut().
cut()
qcut()
An IntervalIndex can be used in Series and in DataFrame as the index.
In [193]: df = pd.DataFrame({'A': [1, 2, 3, 4]}, .....: index=pd.IntervalIndex.from_breaks([0, 1, 2, 3, 4])) .....: In [194]: df Out[194]: 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 [195]: df.loc[2] Out[195]: A 2 Name: (1, 2], dtype: int64 In [196]: df.loc[[2, 3]] Out[196]: A (1, 2] 2 (2, 3] 3
If you select a label contained within an interval, this will also select the interval.
In [197]: df.loc[2.5] Out[197]: A 3 Name: (2, 3], dtype: int64 In [198]: df.loc[[2.5, 3.5]] Out[198]: A (2, 3] 3 (3, 4] 4
Selecting using an Interval will only return exact matches (starting from pandas 0.25.0).
In [199]: df.loc[pd.Interval(1, 2)] Out[199]: A 2 Name: (1, 2], dtype: int64
Trying to select an Interval that is not exactly contained in the IntervalIndex will raise a KeyError.
In [7]: df.loc[pd.Interval(0.5, 2.5)] --------------------------------------------------------------------------- KeyError: Interval(0.5, 2.5, closed='right')
Selecting all Intervals that overlap a given Interval can be performed using the overlaps() method to create a boolean indexer.
Intervals
overlaps()
In [200]: idxr = df.index.overlaps(pd.Interval(0.5, 2.5)) In [201]: idxr Out[201]: array([ True, True, True, False]) In [202]: df[idxr] Out[202]: A (0, 1] 1 (1, 2] 2 (2, 3] 3
cut
qcut
cut() and qcut() both return a Categorical object, and the bins they create are stored as an IntervalIndex in its .categories attribute.
.categories
In [203]: c = pd.cut(range(4), bins=2) In [204]: c Out[204]: [(-0.003, 1.5], (-0.003, 1.5], (1.5, 3.0], (1.5, 3.0]] Categories (2, interval[float64]): [(-0.003, 1.5] < (1.5, 3.0]] In [205]: c.categories Out[205]: IntervalIndex([(-0.003, 1.5], (1.5, 3.0]], closed='right', dtype='interval[float64]')
cut() also accepts an IntervalIndex for its bins argument, which enables a useful pandas idiom. First, We call cut() with some data and bins set to a fixed number, to generate the bins. Then, we pass the values of .categories as the bins argument in subsequent calls to cut(), supplying new data which will be binned into the same bins.
bins
In [206]: pd.cut([0, 3, 5, 1], bins=c.categories) Out[206]: [(-0.003, 1.5], (1.5, 3.0], NaN, (-0.003, 1.5]] Categories (2, interval[float64]): [(-0.003, 1.5] < (1.5, 3.0]]
Any value which falls outside all bins will be assigned a NaN value.
NaN
If we need intervals on a regular frequency, we can use the interval_range() function to create an IntervalIndex using various combinations of start, end, and periods. The default frequency for interval_range is a 1 for numeric intervals, and calendar day for datetime-like intervals:
interval_range()
start
end
periods
interval_range
In [207]: pd.interval_range(start=0, end=5) Out[207]: IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]], closed='right', dtype='interval[int64]') In [208]: pd.interval_range(start=pd.Timestamp('2017-01-01'), periods=4) Out[208]: IntervalIndex([(2017-01-01, 2017-01-02], (2017-01-02, 2017-01-03], (2017-01-03, 2017-01-04], (2017-01-04, 2017-01-05]], closed='right', dtype='interval[datetime64[ns]]') In [209]: pd.interval_range(end=pd.Timedelta('3 days'), periods=3) Out[209]: IntervalIndex([(0 days 00:00:00, 1 days 00:00:00], (1 days 00:00:00, 2 days 00:00:00], (2 days 00:00:00, 3 days 00:00:00]], closed='right', dtype='interval[timedelta64[ns]]')
The freq parameter can used to specify non-default frequencies, and can utilize a variety of frequency aliases with datetime-like intervals:
freq
In [210]: pd.interval_range(start=0, periods=5, freq=1.5) Out[210]: IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0], (6.0, 7.5]], closed='right', dtype='interval[float64]') In [211]: pd.interval_range(start=pd.Timestamp('2017-01-01'), periods=4, freq='W') Out[211]: IntervalIndex([(2017-01-01, 2017-01-08], (2017-01-08, 2017-01-15], (2017-01-15, 2017-01-22], (2017-01-22, 2017-01-29]], closed='right', dtype='interval[datetime64[ns]]') In [212]: pd.interval_range(start=pd.Timedelta('0 days'), periods=3, freq='9H') Out[212]: IntervalIndex([(0 days 00:00:00, 0 days 09:00:00], (0 days 09:00:00, 0 days 18:00:00], (0 days 18:00:00, 1 days 03:00:00]], closed='right', dtype='interval[timedelta64[ns]]')
Additionally, the closed parameter can be used to specify which side(s) the intervals are closed on. Intervals are closed on the right side by default.
closed
In [213]: pd.interval_range(start=0, end=4, closed='both') Out[213]: IntervalIndex([[0, 1], [1, 2], [2, 3], [3, 4]], closed='both', dtype='interval[int64]') In [214]: pd.interval_range(start=0, end=4, closed='neither') Out[214]: IntervalIndex([(0, 1), (1, 2), (2, 3), (3, 4)], closed='neither', dtype='interval[int64]')
New in version 0.23.0.
Specifying start, end, and periods will generate a range of evenly spaced intervals from start to end inclusively, with periods number of elements in the resulting IntervalIndex:
In [215]: pd.interval_range(start=0, end=6, periods=4) Out[215]: IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]], closed='right', dtype='interval[float64]') In [216]: pd.interval_range(pd.Timestamp('2018-01-01'), .....: pd.Timestamp('2018-02-28'), periods=3) .....: Out[216]: IntervalIndex([(2018-01-01, 2018-01-20 08:00:00], (2018-01-20 08:00:00, 2018-02-08 16:00:00], (2018-02-08 16:00:00, 2018-02-28]], closed='right', dtype='interval[datetime64[ns]]')
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:
In [217]: s = pd.Series(range(5)) In [218]: s[-1] --------------------------------------------------------------------------- KeyError Traceback (most recent call last) <ipython-input-218-76c3dce40054> in <module> ----> 1 s[-1] /pandas/pandas/core/series.py in __getitem__(self, key) 869 key = com.apply_if_callable(key, self) 870 try: --> 871 result = self.index.get_value(self, key) 872 873 if not is_scalar(result): /pandas/pandas/core/indexes/base.py in get_value(self, series, key) 4402 k = self._convert_scalar_indexer(k, kind="getitem") 4403 try: -> 4404 return self._engine.get_value(s, k, tz=getattr(series.dtype, "tz", None)) 4405 except KeyError as e1: 4406 if len(self) > 0 and (self.holds_integer() or self.is_boolean()): /pandas/pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_value() /pandas/pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_value() /pandas/pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc() /pandas/pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.Int64HashTable.get_item() /pandas/pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.Int64HashTable.get_item() KeyError: -1 In [219]: df = pd.DataFrame(np.random.randn(5, 4)) In [220]: df Out[220]: 0 1 2 3 0 -0.130121 -0.476046 0.759104 0.213379 1 -0.082641 0.448008 0.656420 -1.051443 2 0.594956 -0.151360 -0.069303 1.221431 3 -0.182832 0.791235 0.042745 2.069775 4 1.446552 0.019814 -1.389212 -0.702312 In [221]: df.loc[-2:] Out[221]: 0 1 2 3 0 -0.130121 -0.476046 0.759104 0.213379 1 -0.082641 0.448008 0.656420 -1.051443 2 0.594956 -0.151360 -0.069303 1.221431 3 -0.182832 0.791235 0.042745 2.069775 4 1.446552 0.019814 -1.389212 -0.702312
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).
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.
list
is_monotonic_increasing()
is_monotonic_decreasing()
In [222]: df = pd.DataFrame(index=[2, 3, 3, 4, 5], columns=['data'], data=list(range(5))) In [223]: df.index.is_monotonic_increasing Out[223]: True # no rows 0 or 1, but still returns rows 2, 3 (both of them), and 4: In [224]: df.loc[0:4, :] Out[224]: data 2 0 3 1 3 2 4 3 # slice is are outside the index, so empty DataFrame is returned In [225]: df.loc[13:15, :] Out[225]: 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 [226]: df = pd.DataFrame(index=[2, 3, 1, 4, 3, 5], .....: columns=['data'], data=list(range(6))) .....: In [227]: df.index.is_monotonic_increasing Out[227]: False # OK because 2 and 4 are in the index In [228]: df.loc[2:4, :] Out[228]: 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 monotonicity, you can combine one of those with the is_unique() attribute.
Index.is_monotonic_increasing
Index.is_monotonic_decreasing
is_unique()
In [229]: weakly_monotonic = pd.Index(['a', 'b', 'c', 'c']) In [230]: weakly_monotonic Out[230]: Index(['a', 'b', 'c', 'c'], dtype='object') In [231]: weakly_monotonic.is_monotonic_increasing Out[231]: True In [232]: weakly_monotonic.is_monotonic_increasing & weakly_monotonic.is_unique Out[232]: False
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 [233]: s = pd.Series(np.random.randn(6), index=list('abcdef')) In [234]: s Out[234]: a 0.301379 b 1.240445 c -0.846068 d -0.043312 e -1.658747 f -0.819549 dtype: float64
Suppose we wished to slice from c to e, using integers this would be accomplished as such:
c
e
In [235]: s[2:5] Out[235]: c -0.846068 d -0.043312 e -1.658747 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 choice to make label-based slicing include both endpoints:
In [236]: s.loc['c':'e'] Out[236]: c -0.846068 d -0.043312 e -1.658747 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.
The different indexing operation can potentially change the dtype of a Series.
In [237]: series1 = pd.Series([1, 2, 3]) In [238]: series1.dtype Out[238]: dtype('int64') In [239]: res = series1.reindex([0, 4]) In [240]: res.dtype Out[240]: dtype('float64') In [241]: res Out[241]: 0 1.0 4 NaN dtype: float64
In [242]: series2 = pd.Series([True]) In [243]: series2.dtype Out[243]: dtype('bool') In [244]: res = series2.reindex_like(series1) In [245]: res.dtype Out[245]: dtype('O') In [246]: res Out[246]: 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.
NaNs
dtype
numpy
ufuncs
numpy.logical_and
See the this old issue for a more detailed discussion.