.. currentmodule:: pandas
.. ipython:: python :suppress: import numpy as np import pandas as pd np.random.seed(123456) np.set_printoptions(precision=4, suppress=True) pd.options.display.max_rows=15
This section covers indexing with a MultiIndex and more advanced indexing features.
See the :ref:`Indexing and Selecting Data <indexing>` 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 :ref:`Returning a View versus Copy
<indexing.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 :ref:`Internal Refactoring <whatsnew_0150.refactoring>`)
See the :ref:`cookbook<cookbook.selection>` 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).
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 :ref:`group by <groupby>` and :ref:`pivoting and reshaping data <reshaping>`, we'll show non-trivial applications to illustrate how it aids in structuring data for analysis.
See the :ref:`cookbook<cookbook.multi_index>` for some advanced strategies
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.
.. ipython:: python
arrays = [['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux'],
['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two']]
tuples = list(zip(*arrays))
tuples
index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
index
s = pd.Series(np.random.randn(8), index=index)
s
When you want every pairing of the elements in two iterables, it can be easier
to use the MultiIndex.from_product function:
.. ipython:: python iterables = [['bar', 'baz', 'foo', 'qux'], ['one', 'two']] pd.MultiIndex.from_product(iterables, names=['first', 'second'])
As a convenience, you can pass a list of arrays directly into Series or DataFrame to construct a MultiIndex automatically:
.. ipython:: python
arrays = [np.array(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux']),
np.array(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'])]
s = pd.Series(np.random.randn(8), index=arrays)
s
df = pd.DataFrame(np.random.randn(8, 4), index=arrays)
df
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:
.. ipython:: python df.index.names
This index can back any axis of a pandas object, and the number of levels of the index is up to you:
.. ipython:: python df = pd.DataFrame(np.random.randn(3, 8), index=['A', 'B', 'C'], columns=index) df pd.DataFrame(np.random.randn(6, 6), index=index[:6], columns=index[:6])
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:
.. ipython:: python pd.Series(np.random.randn(8), index=tuples)
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_printoptions:
.. ipython:: python
pd.set_option('display.multi_sparse', False)
df
pd.set_option('display.multi_sparse', True)
The method get_level_values will return a vector of the labels for each
location at a particular level:
.. ipython:: python
index.get_level_values(0)
index.get_level_values('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:
.. ipython:: python df['bar'] df['bar', 'one'] df['bar']['one'] s['qux']
See :ref:`Cross-section with hierarchical index <advanced.xs>` for how to select on a deeper level.
Note
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:
.. ipython:: python # original multi-index df.columns # sliced df[['foo','qux']].columns
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.
.. ipython:: python df[['foo','qux']].columns.values # for a specific level df[['foo','qux']].columns.get_level_values(0)
To reconstruct the multiindex with only the used levels
.. ipython:: python pd.MultiIndex.from_tuples(df[['foo','qux']].columns.values)
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:
.. ipython:: python s + s[:-2] s + s[::2]
reindex can be called with another MultiIndex or even a list or array
of tuples:
.. ipython:: python
s.reindex(index[:3])
s.reindex([('foo', 'two'), ('bar', 'one'), ('qux', 'one'), ('baz', 'one')])
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:
.. ipython:: python df = df.T df df.loc['bar'] df.loc['bar', 'two']
"Partial" slicing also works quite nicely.
.. ipython:: python df.loc['baz':'foo']
You can slice with a 'range' of values, by providing a slice of tuples.
.. ipython:: python
df.loc[('baz', 'two'):('qux', 'one')]
df.loc[('baz', 'two'):'foo']
Passing a list of labels or tuples works similar to reindexing:
.. ipython:: python
df.loc[[('bar', 'two'), ('qux', 'one')]]
.. versionadded:: 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 :ref:`Selection by Label <indexing.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'),.....)].. ipython:: python
def mklbl(prefix,n):
return ["%s%s" % (prefix,i) for i in range(n)]
miindex = pd.MultiIndex.from_product([mklbl('A',4),
mklbl('B',2),
mklbl('C',4),
mklbl('D',2)])
micolumns = pd.MultiIndex.from_tuples([('a','foo'),('a','bar'),
('b','foo'),('b','bah')],
names=['lvl0', 'lvl1'])
dfmi = pd.DataFrame(np.arange(len(miindex)*len(micolumns)).reshape((len(miindex),len(micolumns))),
index=miindex,
columns=micolumns).sort_index().sort_index(axis=1)
dfmi
Basic multi-index slicing using slices, lists, and labels.
.. ipython:: python
dfmi.loc[(slice('A1','A3'),slice(None), ['C1','C3']),:]
You can use a pd.IndexSlice to have a more natural syntax using : rather than using slice(None)
.. ipython:: python idx = pd.IndexSlice dfmi.loc[idx[:,:,['C1','C3']],idx[:,'foo']]
It is possible to perform quite complicated selections using this method on multiple axes at the same time.
.. ipython:: python dfmi.loc['A1',(slice(None),'foo')] dfmi.loc[idx[:,:,['C1','C3']],idx[:,'foo']]
Using a boolean indexer you can provide selection related to the values.
.. ipython:: python
mask = dfmi[('a','foo')]>200
dfmi.loc[idx[mask,:,['C1','C3']],idx[:,'foo']]
You can also specify the axis argument to .loc to interpret the passed
slicers on a single axis.
.. ipython:: python dfmi.loc(axis=0)[:,:,['C1','C3']]
Furthermore you can set the values using these methods
.. ipython:: python df2 = dfmi.copy() df2.loc(axis=0)[:,:,['C1','C3']] = -10 df2
You can use a right-hand-side of an alignable object as well.
.. ipython:: python df2 = dfmi.copy() df2.loc[idx[:,:,['C1','C3']],:] = df2*1000 df2
The xs method of DataFrame additionally takes a level argument to make
selecting data at a particular level of a MultiIndex easier.
.. ipython:: python
df
df.xs('one', level='second')
.. ipython:: python # using the slicers (new in 0.14.0) df.loc[(slice(None),'one'),:]
You can also select on the columns with :meth:`~pandas.MultiIndex.xs`, by providing the axis argument
.. ipython:: python
df = df.T
df.xs('one', level='second', axis=1)
.. ipython:: python # using the slicers (new in 0.14.0) df.loc[:,(slice(None),'one')]
:meth:`~pandas.MultiIndex.xs` also allows selection with multiple keys
.. ipython:: python
df.xs(('one', 'bar'), level=('second', 'first'), axis=1)
.. ipython:: python
# using the slicers (new in 0.14.0)
df.loc[:,('bar','one')]
.. versionadded:: 0.13.0
You can pass drop_level=False to :meth:`~pandas.MultiIndex.xs` to retain
the level that was selected
.. ipython:: python
df.xs('one', level='second', axis=1, drop_level=False)
versus the result with drop_level=True (the default value)
.. ipython:: python
df.xs('one', level='second', axis=1, drop_level=True)
.. ipython:: python :suppress: df = df.T
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:
.. ipython:: python
midx = pd.MultiIndex(levels=[['zero', 'one'], ['x','y']],
labels=[[1,1,0,0],[1,0,1,0]])
df = pd.DataFrame(np.random.randn(4,2), index=midx)
df
df2 = df.mean(level=0)
df2
df2.reindex(df.index, level=0)
# aligning
df_aligned, df2_aligned = df.align(df2, level=0)
df_aligned
df2_aligned
Swapping levels with :meth:`~pandas.MultiIndex.swaplevel`
The swaplevel function can switch the order of two levels:
.. ipython:: python df[:5] df[:5].swaplevel(0, 1, axis=0)
Reordering levels with :meth:`~pandas.MultiIndex.reorder_levels`
The reorder_levels function generalizes the swaplevel function,
allowing you to permute the hierarchical index levels in one step:
.. ipython:: python df[:5].reorder_levels([1,0], axis=0)
Sorting a :class:`~pandas.MultiIndex`
For MultiIndex-ed objects to be indexed & sliced effectively, they need
to be sorted. As with any index, you can use sort_index.
.. ipython:: python import random; random.shuffle(tuples) s = pd.Series(np.random.randn(8), index=pd.MultiIndex.from_tuples(tuples)) s s.sort_index() s.sort_index(level=0) s.sort_index(level=1)
You may also pass a level name to sort_index if the MultiIndex levels
are named.
.. ipython:: python s.index.set_names(['L1', 'L2'], inplace=True) s.sort_index(level='L1') s.sort_index(level='L2')
On higher dimensional objects, you can sort any of the other axes by level if they have a MultiIndex:
.. ipython:: python df.T.sort_index(level=1, axis=1)
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:
.. ipython:: python
dfm = pd.DataFrame({'jim': [0, 0, 1, 1],
'joe': ['x', 'x', 'z', 'y'],
'jolie': np.random.rand(4)})
dfm = dfm.set_index(['jim', 'joe'])
dfm
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:
.. ipython:: python dfm.index.is_lexsorted() dfm.index.lexsort_depth
.. ipython:: python dfm = dfm.sort_index() dfm dfm.index.is_lexsorted() dfm.index.lexsort_depth
And now selection works as expected.
.. ipython:: python dfm.loc[(0,'y'):(1, 'z')]
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.
.. ipython:: python index = pd.Index(np.random.randint(0, 1000, 10)) index positions = [0, 9, 3] index[positions] index.take(positions) ser = pd.Series(np.random.randn(10)) ser.iloc[positions] ser.take(positions)
For DataFrames, the given indices should be a 1d list or ndarray that specifies row or column positions.
.. ipython:: python frm = pd.DataFrame(np.random.randn(5, 3)) frm.take([1, 4, 3]) frm.take([0, 2], axis=1)
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.
.. ipython:: python arr = np.random.randn(10) arr.take([False, False, True, True]) arr[[0, 1]] ser = pd.Series(np.random.randn(10)) ser.take([False, False, True, True]) ser.iloc[[0, 1]]
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.
.. ipython:: arr = np.random.randn(10000, 5) indexer = np.arange(10000) random.shuffle(indexer) timeit arr[indexer] timeit arr.take(indexer, axis=0) ser = pd.Series(arr[:, 0]) timeit ser.iloc[indexer] timeit ser.take(indexer)
We have discussed MultiIndex in the previous sections pretty extensively. DatetimeIndex and PeriodIndex
are shown :ref:`here <timeseries.overview>`. TimedeltaIndex are :ref:`here <timedeltas.timedeltas>`.
In the following sub-sections we will highlite some other index types.
.. versionadded:: 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.
.. ipython:: python
df = pd.DataFrame({'A': np.arange(6),
'B': list('aabbca')})
df['B'] = df['B'].astype('category', categories=list('cab'))
df
df.dtypes
df.B.cat.categories
Setting the index, will create create a CategoricalIndex
.. ipython:: python
df2 = df.set_index('B')
df2.index
Indexing with __getitem__/.iloc/.loc works similarly to an Index with duplicates.
The indexers MUST be in the category or the operation will raise.
.. ipython:: python df2.loc['a']
These PRESERVE the CategoricalIndex
.. ipython:: python df2.loc['a'].index
Sorting will order by the order of the categories
.. ipython:: python df2.sort_index()
Groupby operations on the index will preserve the index nature as well
.. ipython:: python df2.groupby(level=0).sum() df2.groupby(level=0).sum().index
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.
.. ipython :: python
df2.reindex(['a','e'])
df2.reindex(['a','e']).index
df2.reindex(pd.Categorical(['a','e'],categories=list('abcde')))
df2.reindex(pd.Categorical(['a','e'],categories=list('abcde'))).index
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 appendingWarning
Indexing on an integer-based Index with floats has been clarified in 0.18.0, for a summary of the changes, see :ref:`here <whatsnew_0180.float_indexers>`.
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.
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.
.. versionadded:: 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.
.. ipython:: python indexf = pd.Index([1.5, 2, 3, 4.5, 5]) indexf sf = pd.Series(range(5), index=indexf) sf
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)
.. ipython:: python sf[3] sf[3.0] sf.loc[3] sf.loc[3.0]
The only positional indexing is via iloc
.. ipython:: python sf.iloc[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
.. ipython:: python sf[2:4] sf.loc[2:4] sf.iloc[2:4]
In float indexes, slicing using floats is allowed
.. ipython:: python sf[2.1:4.6] sf.loc[2.1:4.6]
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.
.. ipython:: python
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'))])
dfir
Selection operations then will always work on a value basis, for all selection operators.
.. ipython:: python dfir[0:1000.4] dfir.loc[0:1001,'A'] dfir.loc[1000.4]
You could then easily pick out the first 1 second (1000 ms) of data then.
.. ipython:: python dfir[0:1000]
Of course if you need integer based selection, then use iloc
.. ipython:: python dfir.iloc[0:5]
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).
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.
.. ipython:: python
df = pd.DataFrame(index=[2,3,3,4,5], columns=['data'], data=list(range(5)))
df.index.is_monotonic_increasing
# no rows 0 or 1, but still returns rows 2, 3 (both of them), and 4:
df.loc[0:4, :]
# slice is are outside the index, so empty DataFrame is returned
df.loc[13:15, :]
On the other hand, if the index is not monotonic, then both slice bounds must be unique members of the index.
.. ipython:: python
df = pd.DataFrame(index=[2,3,1,4,3,5], columns=['data'], data=list(range(6)))
df.index.is_monotonic_increasing
# OK because 2 and 4 are in the index
df.loc[2:4, :]
# 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'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:
.. ipython:: python
s = pd.Series(np.random.randn(6), index=list('abcdef'))
s
Suppose we wished to slice from c to e, using integers this would be
.. ipython:: python s[2:5]
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:
.. ipython:: python
s.loc['c':'e']
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.
.. ipython:: python series1 = pd.Series([1, 2, 3]) series1.dtype res = series1[[0,4]] res.dtype res
.. ipython:: python series2 = pd.Series([True]) series2.dtype res = series2.reindex_like(series1) res.dtype res
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.