pandas
python
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 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 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 Internal Refactoring <whatsnew_0150.refactoring>)
See the 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 the all of the pandas indexing functionality described above and in prior sections. Later, when discussing group by
<groupby> and pivoting and reshaping data <reshaping>, we'll show non-trivial applications to illustrate how it aids in structuring data for analysis.
See the 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 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.
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:
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:
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:
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:
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:
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:
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:
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:
python
df['bar'] df['bar', 'one'] df['bar']['one'] s['qux']
See 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:
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.
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
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:
python
s + s[:-2] s + s[::2]
reindex can be called with another MultiIndex or even a list or array of tuples:
python
s.reindex(index[:3]) s.reindex([('foo', 'two'), ('bar', 'one'), ('qux', 'one'), ('baz', 'one')])
Syntactically integrating MultiIndex in advanced indexing with .loc/.ix is a bit challenging, but we've made every effort to do so. for example the following works as you would expect:
python
df = df.T df df.loc['bar'] df.loc['bar', 'two']
"Partial" slicing also works quite nicely.
python
df.loc['baz':'foo']
You can slice with a 'range' of values, by providing a slice of tuples.
python
df.loc[('baz', 'two'):('qux', 'one')] df.loc[('baz', 'two'):'foo']
Passing a list of labels or tuples works similar to reindexing:
python
df.ix[[('bar', 'two'), ('qux', 'one')]]
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 <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'),.....)]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.
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)
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.
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.
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.
python
dfmi.loc(axis=0)[:,:,['C1','C3']]
Furthermore you can set the values using these methods
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.
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.
python
df df.xs('one', level='second')
python
# using the slicers (new in 0.14.0) df.loc[(slice(None),'one'),:]
You can also select on the columns with ~pandas.MultiIndex.xs, by providing the axis argument
python
df = df.T df.xs('one', level='second', axis=1)
python
# using the slicers (new in 0.14.0) df.loc[:,(slice(None),'one')]
~pandas.MultiIndex.xs also allows selection with multiple keys
python
df.xs(('one', 'bar'), level=('second', 'first'), axis=1)
python
# using the slicers (new in 0.14.0) df.loc[:,('bar','one')]
0.13.0
You can pass drop_level=False to ~pandas.MultiIndex.xs to retain the level that was selected
python
df.xs('one', level='second', axis=1, drop_level=False)
versus the result with drop_level=True (the default value)
python
df.xs('one', level='second', axis=1, drop_level=True)
python
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:
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
The swaplevel function can switch the order of two levels:
python
df[:5] df[:5].swaplevel(0, 1, axis=0)
The reorder_levels function generalizes the swaplevel function, allowing you to permute the hierarchical index levels in one step:
python
df[:5].reorder_levels([1,0], axis=0)
For MultiIndex-ed objects to be indexed & sliced effectively, they need to be sorted. As with any index, you can use sort_index.
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.
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:
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:
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 0.64094Furthermore if you try to index something that is not fully lexsorted, this can raise:
In [5]: dfm.loc[(0,'y'):(1, 'z')]
KeyError: '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:
python
dfm.index.is_lexsorted() dfm.index.lexsort_depth
python
dfm = dfm.sort_index() dfm dfm.index.is_lexsorted() dfm.index.lexsort_depth
And now selection works as expected.
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.
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.
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.
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.ix[[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.
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.ix[indexer] timeit ser.take(indexer)
We have discussed MultiIndex in the previous sections pretty extensively. DatetimeIndex and PeriodIndex are shown here <timeseries.overview>. TimedeltaIndex are here <timedeltas.timedeltas>.
In the following sub-sections we will highlite some other index types.
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.
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
python
df2 = df.set_index('B') df2.index
Indexing with __getitem__/.iloc/.loc/.ix works similarly to an Index with duplicates. The indexers MUST be in the category or the operation will raise.
python
df2.loc['a']
These PRESERVE the CategoricalIndex
python
df2.loc['a'].index
Sorting will order by the order of the categories
python
df2.sort_index()
Groupby operations on the index will preserve the index nature as well
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.
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 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.
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.
python
indexf = pd.Index([1.5, 2, 3, 4.5, 5]) indexf sf = pd.Series(range(5), index=indexf) sf
Scalar selection for [],.ix,.loc will always be label based. An integer will match an equal float index (e.g. 3 is equivalent to 3.0)
python
sf[3] sf[3.0] sf.ix[3] sf.ix[3.0] sf.loc[3] sf.loc[3.0]
The only positional indexing is via iloc
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
python
sf[2:4] sf.ix[2:4] sf.loc[2:4] sf.iloc[2:4]
In float indexes, slicing using floats is allowed
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'>Further the treatment of .ix with a float indexer on a non-float index, will be label based, and thus coerce the index.
python
s2 = pd.Series([1, 2, 3], index=list('abc')) s2 s2.ix[1.0] = 10 s2
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.
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.
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.
python
dfir[0:1000]
Of course if you need integer based selection, then use iloc
python
dfir.iloc[0:5]