Sparse data structures#
pandas provides data structures for efficiently storing sparse data.
These are not necessarily sparse in the typical “mostly 0”. Rather, you can view these
objects as being “compressed” where any data matching a specific value (NaN / missing value, though any value
can be chosen, including 0) is omitted. The compressed values are not actually stored in the array.
In [1]: arr = np.random.randn(10)
In [2]: arr[2:-2] = np.nan
In [3]: ts = pd.Series(pd.arrays.SparseArray(arr))
In [4]: ts
Out[4]:
0 0.469112
1 -0.282863
2 NaN
3 NaN
4 NaN
5 NaN
6 NaN
7 NaN
8 -0.861849
9 -2.104569
dtype: Sparse[float64, nan]
Notice the dtype, Sparse[float64, nan]. The nan means that elements in the
array that are nan aren’t actually stored, only the non-nan elements are.
Those non-nan elements have a float64 dtype.
The sparse objects exist for memory efficiency reasons. Suppose you had a
large, mostly NA DataFrame:
In [5]: df = pd.DataFrame(np.random.randn(10000, 4))
In [6]: df.iloc[:9998] = np.nan
In [7]: sdf = df.astype(pd.SparseDtype("float", np.nan))
In [8]: sdf.head()
Out[8]:
0 1 2 3
0 NaN NaN NaN NaN
1 NaN NaN NaN NaN
2 NaN NaN NaN NaN
3 NaN NaN NaN NaN
4 NaN NaN NaN NaN
In [9]: sdf.dtypes
Out[9]:
0 Sparse[float64, nan]
1 Sparse[float64, nan]
2 Sparse[float64, nan]
3 Sparse[float64, nan]
dtype: object
In [10]: sdf.sparse.density
Out[10]: 0.0002
As you can see, the density (% of values that have not been “compressed”) is extremely low. This sparse object takes up much less memory on disk (pickled) and in the Python interpreter.
In [11]: 'dense : {:0.2f} bytes'.format(df.memory_usage().sum() / 1e3)
Out[11]: 'dense : 320.13 bytes'
In [12]: 'sparse: {:0.2f} bytes'.format(sdf.memory_usage().sum() / 1e3)
Out[12]: 'sparse: 0.22 bytes'
Functionally, their behavior should be nearly identical to their dense counterparts.
SparseArray#
arrays.SparseArray is a ExtensionArray
for storing an array of sparse values (see dtypes for more
on extension arrays). It is a 1-dimensional ndarray-like object storing
only values distinct from the fill_value:
In [13]: arr = np.random.randn(10)
In [14]: arr[2:5] = np.nan
In [15]: arr[7:8] = np.nan
In [16]: sparr = pd.arrays.SparseArray(arr)
In [17]: sparr
Out[17]:
[-1.9556635297215477, -1.6588664275960427, nan, nan, nan, 1.1589328886422277, 0.14529711373305043, nan, 0.6060271905134522, 1.3342113401317768]
Fill: nan
IntIndex
Indices: array([0, 1, 5, 6, 8, 9], dtype=int32)
A sparse array can be converted to a regular (dense) ndarray with numpy.asarray()
In [18]: np.asarray(sparr)
Out[18]:
array([-1.9557, -1.6589, nan, nan, nan, 1.1589, 0.1453,
nan, 0.606 , 1.3342])
SparseDtype#
The SparseArray.dtype property stores two pieces of information
The dtype of the non-sparse values
The scalar fill value
In [19]: sparr.dtype
Out[19]: Sparse[float64, nan]
A SparseDtype may be constructed by passing only a dtype
In [20]: pd.SparseDtype(np.dtype('datetime64[ns]'))
Out[20]: Sparse[datetime64[ns], numpy.datetime64('NaT')]
in which case a default fill value will be used (for NumPy dtypes this is often the “missing” value for that dtype). To override this default an explicit fill value may be passed instead
In [21]: pd.SparseDtype(np.dtype('datetime64[ns]'),
....: fill_value=pd.Timestamp('2017-01-01'))
....:
Out[21]: Sparse[datetime64[ns], Timestamp('2017-01-01 00:00:00')]
Finally, the string alias 'Sparse[dtype]' may be used to specify a sparse dtype
in many places
In [22]: pd.array([1, 0, 0, 2], dtype='Sparse[int]')
Out[22]:
[1, 0, 0, 2]
Fill: 0
IntIndex
Indices: array([0, 3], dtype=int32)
Sparse accessor#
pandas provides a .sparse accessor, similar to .str for string data, .cat
for categorical data, and .dt for datetime-like data. This namespace provides
attributes and methods that are specific to sparse data.
In [23]: s = pd.Series([0, 0, 1, 2], dtype="Sparse[int]")
In [24]: s.sparse.density
Out[24]: 0.5
In [25]: s.sparse.fill_value
Out[25]: 0
This accessor is available only on data with SparseDtype, and on the Series
class itself for creating a Series with sparse data from a scipy COO matrix with.
A .sparse accessor has been added for DataFrame as well.
See Sparse accessor for more.
Sparse calculation#
You can apply NumPy ufuncs
to arrays.SparseArray and get a arrays.SparseArray as a result.
In [26]: arr = pd.arrays.SparseArray([1., np.nan, np.nan, -2., np.nan])
In [27]: np.abs(arr)
Out[27]:
[1.0, nan, nan, 2.0, nan]
Fill: nan
IntIndex
Indices: array([0, 3], dtype=int32)
The ufunc is also applied to fill_value. This is needed to get
the correct dense result.
In [28]: arr = pd.arrays.SparseArray([1., -1, -1, -2., -1], fill_value=-1)
In [29]: np.abs(arr)
Out[29]:
[1, 1, 1, 2.0, 1]
Fill: 1
IntIndex
Indices: array([3], dtype=int32)
In [30]: np.abs(arr).to_dense()
Out[30]: array([1., 1., 1., 2., 1.])
Migrating#
Note
SparseSeries and SparseDataFrame were removed in pandas 1.0.0. This migration
guide is present to aid in migrating from previous versions.
In older versions of pandas, the SparseSeries and SparseDataFrame classes (documented below)
were the preferred way to work with sparse data. With the advent of extension arrays, these subclasses
are no longer needed. Their purpose is better served by using a regular Series or DataFrame with
sparse values instead.
Note
There’s no performance or memory penalty to using a Series or DataFrame with sparse values, rather than a SparseSeries or SparseDataFrame.
This section provides some guidance on migrating your code to the new style. As a reminder, you can use the Python warnings module to control warnings. But we recommend modifying your code, rather than ignoring the warning.
Construction
From an array-like, use the regular Series or
DataFrame constructors with arrays.SparseArray values.
# Previous way
>>> pd.SparseDataFrame({"A": [0, 1]})
# New way
In [31]: pd.DataFrame({"A": pd.arrays.SparseArray([0, 1])})
Out[31]:
A
0 0
1 1
From a SciPy sparse matrix, use DataFrame.sparse.from_spmatrix(),
# Previous way
>>> from scipy import sparse
>>> mat = sparse.eye(3)
>>> df = pd.SparseDataFrame(mat, columns=['A', 'B', 'C'])
# New way
In [32]: from scipy import sparse
In [33]: mat = sparse.eye(3)
In [34]: df = pd.DataFrame.sparse.from_spmatrix(mat, columns=['A', 'B', 'C'])
In [35]: df.dtypes
Out[35]:
A Sparse[float64, 0]
B Sparse[float64, 0]
C Sparse[float64, 0]
dtype: object
Conversion
From sparse to dense, use the .sparse accessors
In [36]: df.sparse.to_dense()
Out[36]:
A B C
0 1.0 0.0 0.0
1 0.0 1.0 0.0
2 0.0 0.0 1.0
In [37]: df.sparse.to_coo()
Out[37]:
<3x3 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>
From dense to sparse, use DataFrame.astype() with a SparseDtype.
In [38]: dense = pd.DataFrame({"A": [1, 0, 0, 1]})
In [39]: dtype = pd.SparseDtype(int, fill_value=0)
In [40]: dense.astype(dtype)
Out[40]:
A
0 1
1 0
2 0
3 1
Sparse Properties
Sparse-specific properties, like density, are available on the .sparse accessor.
In [41]: df.sparse.density
Out[41]: 0.3333333333333333
General differences
In a SparseDataFrame, all columns were sparse. A DataFrame can have a mixture of
sparse and dense columns. As a consequence, assigning new columns to a DataFrame with sparse
values will not automatically convert the input to be sparse.
# Previous Way
>>> df = pd.SparseDataFrame({"A": [0, 1]})
>>> df['B'] = [0, 0] # implicitly becomes Sparse
>>> df['B'].dtype
Sparse[int64, nan]
Instead, you’ll need to ensure that the values being assigned are sparse
In [42]: df = pd.DataFrame({"A": pd.arrays.SparseArray([0, 1])})
In [43]: df['B'] = [0, 0] # remains dense
In [44]: df['B'].dtype
Out[44]: dtype('int64')
In [45]: df['B'] = pd.arrays.SparseArray([0, 0])
In [46]: df['B'].dtype
Out[46]: Sparse[int64, 0]
The SparseDataFrame.default_kind and SparseDataFrame.default_fill_value attributes
have no replacement.
Interaction with scipy.sparse#
Use DataFrame.sparse.from_spmatrix() to create a DataFrame with sparse values from a sparse matrix.
In [47]: from scipy.sparse import csr_matrix
In [48]: arr = np.random.random(size=(1000, 5))
In [49]: arr[arr < .9] = 0
In [50]: sp_arr = csr_matrix(arr)
In [51]: sp_arr
Out[51]:
<1000x5 sparse matrix of type '<class 'numpy.float64'>'
with 517 stored elements in Compressed Sparse Row format>
In [52]: sdf = pd.DataFrame.sparse.from_spmatrix(sp_arr)
In [53]: sdf.head()
Out[53]:
0 1 2 3 4
0 0.956380 0.0 0.0 0.000000 0.0
1 0.000000 0.0 0.0 0.000000 0.0
2 0.000000 0.0 0.0 0.000000 0.0
3 0.000000 0.0 0.0 0.000000 0.0
4 0.999552 0.0 0.0 0.956153 0.0
In [54]: sdf.dtypes
Out[54]:
0 Sparse[float64, 0]
1 Sparse[float64, 0]
2 Sparse[float64, 0]
3 Sparse[float64, 0]
4 Sparse[float64, 0]
dtype: object
All sparse formats are supported, but matrices that are not in COOrdinate format will be converted, copying data as needed.
To convert back to sparse SciPy matrix in COO format, you can use the DataFrame.sparse.to_coo() method:
In [55]: sdf.sparse.to_coo()
Out[55]:
<1000x5 sparse matrix of type '<class 'numpy.float64'>'
with 517 stored elements in COOrdinate format>
Series.sparse.to_coo() is implemented for transforming a Series with sparse values indexed by a MultiIndex to a scipy.sparse.coo_matrix.
The method requires a MultiIndex with two or more levels.
In [56]: s = pd.Series([3.0, np.nan, 1.0, 3.0, np.nan, np.nan])
In [57]: s.index = pd.MultiIndex.from_tuples(
....: [
....: (1, 2, "a", 0),
....: (1, 2, "a", 1),
....: (1, 1, "b", 0),
....: (1, 1, "b", 1),
....: (2, 1, "b", 0),
....: (2, 1, "b", 1),
....: ],
....: names=["A", "B", "C", "D"],
....: )
....:
In [58]: ss = s.astype('Sparse')
In [59]: ss
Out[59]:
A B C D
1 2 a 0 3.0
1 NaN
1 b 0 1.0
1 3.0
2 1 b 0 NaN
1 NaN
dtype: Sparse[float64, nan]
In the example below, we transform the Series to a sparse representation of a 2-d array by specifying that the first and second MultiIndex levels define labels for the rows and the third and fourth levels define labels for the columns. We also specify that the column and row labels should be sorted in the final sparse representation.
In [60]: A, rows, columns = ss.sparse.to_coo(
....: row_levels=["A", "B"], column_levels=["C", "D"], sort_labels=True
....: )
....:
In [61]: A
Out[61]:
<3x4 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>
In [62]: A.todense()
Out[62]:
matrix([[0., 0., 1., 3.],
[3., 0., 0., 0.],
[0., 0., 0., 0.]])
In [63]: rows
Out[63]: [(1, 1), (1, 2), (2, 1)]
In [64]: columns
Out[64]: [('a', 0), ('a', 1), ('b', 0), ('b', 1)]
Specifying different row and column labels (and not sorting them) yields a different sparse matrix:
In [65]: A, rows, columns = ss.sparse.to_coo(
....: row_levels=["A", "B", "C"], column_levels=["D"], sort_labels=False
....: )
....:
In [66]: A
Out[66]:
<3x2 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>
In [67]: A.todense()
Out[67]:
matrix([[3., 0.],
[1., 3.],
[0., 0.]])
In [68]: rows
Out[68]: [(1, 2, 'a'), (1, 1, 'b'), (2, 1, 'b')]
In [69]: columns
Out[69]: [(0,), (1,)]
A convenience method Series.sparse.from_coo() is implemented for creating a Series with sparse values from a scipy.sparse.coo_matrix.
In [70]: from scipy import sparse
In [71]: A = sparse.coo_matrix(([3.0, 1.0, 2.0], ([1, 0, 0], [0, 2, 3])), shape=(3, 4))
In [72]: A
Out[72]:
<3x4 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>
In [73]: A.todense()
Out[73]:
matrix([[0., 0., 1., 2.],
[3., 0., 0., 0.],
[0., 0., 0., 0.]])
The default behaviour (with dense_index=False) simply returns a Series containing
only the non-null entries.
In [74]: ss = pd.Series.sparse.from_coo(A)
In [75]: ss
Out[75]:
0 2 1.0
3 2.0
1 0 3.0
dtype: Sparse[float64, nan]
Specifying dense_index=True will result in an index that is the Cartesian product of the
row and columns coordinates of the matrix. Note that this will consume a significant amount of memory
(relative to dense_index=False) if the sparse matrix is large (and sparse) enough.
In [76]: ss_dense = pd.Series.sparse.from_coo(A, dense_index=True)
In [77]: ss_dense
Out[77]:
1 0 3.0
2 NaN
3 NaN
0 0 NaN
2 1.0
3 2.0
0 NaN
2 1.0
3 2.0
dtype: Sparse[float64, nan]