# Sparse data structures¶

Note

The SparsePanel class has been removed in 0.19.0

We have implemented “sparse” versions of Series and DataFrame. These are not 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) is omitted. A special SparseIndex object tracks where data has been “sparsified”. This will make much more sense in an example. All of the standard pandas data structures have a to_sparse method:

In [1]: ts = pd.Series(randn(10))

In [2]: ts[2:-2] = np.nan

In [3]: sts = ts.to_sparse()

In [4]: sts
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: float64
BlockIndex
Block locations: array([0, 8], dtype=int32)
Block lengths: array([2, 2], dtype=int32)


The to_sparse method takes a kind argument (for the sparse index, see below) and a fill_value. So if we had a mostly zero Series, we could convert it to sparse with fill_value=0:

In [5]: ts.fillna(0).to_sparse(fill_value=0)
Out[5]:
0    0.469112
1   -0.282863
2    0.000000
3    0.000000
4    0.000000
5    0.000000
6    0.000000
7    0.000000
8   -0.861849
9   -2.104569
dtype: float64
BlockIndex
Block locations: array([0, 8], dtype=int32)
Block lengths: array([2, 2], dtype=int32)


The sparse objects exist for memory efficiency reasons. Suppose you had a large, mostly NA DataFrame:

In [6]: df = pd.DataFrame(randn(10000, 4))

In [7]: df.iloc[:9998] = np.nan

In [8]: sdf = df.to_sparse()

In [9]: sdf
Out[9]:
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
5          NaN       NaN       NaN       NaN
6          NaN       NaN       NaN       NaN
...        ...       ...       ...       ...
9993       NaN       NaN       NaN       NaN
9994       NaN       NaN       NaN       NaN
9995       NaN       NaN       NaN       NaN
9996       NaN       NaN       NaN       NaN
9997       NaN       NaN       NaN       NaN
9998  0.509184 -0.774928 -1.369894 -0.382141
9999  0.280249 -1.648493  1.490865 -0.890819

[10000 rows x 4 columns]

In [10]: sdf.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. Functionally, their behavior should be nearly identical to their dense counterparts.

Any sparse object can be converted back to the standard dense form by calling to_dense:

In [11]: sts.to_dense()
Out[11]:
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: float64


## SparseArray¶

SparseArray is the base layer for all of the sparse indexed data structures. It is a 1-dimensional ndarray-like object storing only values distinct from the fill_value:

In [12]: arr = np.random.randn(10)

In [13]: arr[2:5] = np.nan; arr[7:8] = np.nan

In [14]: sparr = pd.SparseArray(arr)

In [15]: sparr
Out[15]:
[-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)


Like the indexed objects (SparseSeries, SparseDataFrame), a SparseArray can be converted back to a regular ndarray by calling to_dense:

In [16]: sparr.to_dense()
Out[16]:
array([-1.9557, -1.6589,     nan,     nan,     nan,  1.1589,  0.1453,
nan,  0.606 ,  1.3342])


## SparseList¶

The SparseList class has been deprecated and will be removed in a future version. See the docs of a previous version for documentation on SparseList.

## SparseIndex objects¶

Two kinds of SparseIndex are implemented, block and integer. We recommend using block as it’s more memory efficient. The integer format keeps an arrays of all of the locations where the data are not equal to the fill value. The block format tracks only the locations and sizes of blocks of data.

## Sparse Dtypes¶

Sparse data should have the same dtype as its dense representation. Currently, float64, int64 and bool dtypes are supported. Depending on the original dtype, fill_value default changes:

• float64: np.nan
• int64: 0
• bool: False
In [17]: s = pd.Series([1, np.nan, np.nan])

In [18]: s
Out[18]:
0    1.0
1    NaN
2    NaN
dtype: float64

In [19]: s.to_sparse()
Out[19]:
0    1.0
1    NaN
2    NaN
dtype: float64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([1], dtype=int32)

In [20]: s = pd.Series([1, 0, 0])

In [21]: s
Out[21]:
0    1
1    0
2    0
dtype: int64

In [22]: s.to_sparse()
Out[22]:
0    1
1    0
2    0
dtype: int64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([1], dtype=int32)

In [23]: s = pd.Series([True, False, True])

In [24]: s
Out[24]:
0     True
1    False
2     True
dtype: bool

In [25]: s.to_sparse()
Out[25]:
0     True
1    False
2     True
dtype: bool
BlockIndex
Block locations: array([0, 2], dtype=int32)
Block lengths: array([1, 1], dtype=int32)


You can change the dtype using .astype(), the result is also sparse. Note that .astype() also affects to the fill_value to keep its dense representation.

In [26]: s = pd.Series([1, 0, 0, 0, 0])

In [27]: s
Out[27]:
0    1
1    0
2    0
3    0
4    0
dtype: int64

In [28]: ss = s.to_sparse()

In [29]: ss
Out[29]:
0    1
1    0
2    0
3    0
4    0
dtype: int64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([1], dtype=int32)

In [30]: ss.astype(np.float64)
Out[30]:
0    1.0
1    0.0
2    0.0
3    0.0
4    0.0
dtype: float64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([1], dtype=int32)


It raises if any value cannot be coerced to specified dtype.

In [1]: ss = pd.Series([1, np.nan, np.nan]).to_sparse()
0    1.0
1    NaN
2    NaN
dtype: float64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([1], dtype=int32)

In [2]: ss.astype(np.int64)
ValueError: unable to coerce current fill_value nan to int64 dtype


## Sparse Calculation¶

You can apply NumPy ufuncs to SparseArray and get a SparseArray as a result.

In [31]: arr = pd.SparseArray([1., np.nan, np.nan, -2., np.nan])

In [32]: np.abs(arr)
Out[32]:
[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 [33]: arr = pd.SparseArray([1., -1, -1, -2., -1], fill_value=-1)

In [34]: np.abs(arr)
Out[34]:
[1.0, 1.0, 1.0, 2.0, 1.0]
Fill: 1
IntIndex
Indices: array([0, 3], dtype=int32)

In [35]: np.abs(arr).to_dense()
Out[35]: array([ 1.,  1.,  1.,  2.,  1.])


## Interaction with scipy.sparse¶

### SparseDataFrame¶

New in version 0.20.0.

Pandas supports creating sparse dataframes directly from scipy.sparse matrices.

In [36]: from scipy.sparse import csr_matrix

In [37]: arr = np.random.random(size=(1000, 5))

In [38]: arr[arr < .9] = 0

In [39]: sp_arr = csr_matrix(arr)

In [40]: sp_arr
Out[40]:
<1000x5 sparse matrix of type '<class 'numpy.float64'>'
with 517 stored elements in Compressed Sparse Row format>

In [41]: sdf = pd.SparseDataFrame(sp_arr)

In [42]: sdf
Out[42]:
0   1        2         3   4
0    0.956380 NaN      NaN       NaN NaN
1         NaN NaN      NaN       NaN NaN
2         NaN NaN      NaN       NaN NaN
3         NaN NaN      NaN       NaN NaN
4    0.999552 NaN      NaN  0.956153 NaN
5         NaN NaN      NaN       NaN NaN
6    0.913638 NaN      NaN       NaN NaN
..        ...  ..      ...       ...  ..
993       NaN NaN      NaN       NaN NaN
994       NaN NaN      NaN       NaN NaN
995       NaN NaN      NaN  0.998834 NaN
996       NaN NaN      NaN       NaN NaN
997       NaN NaN      NaN       NaN NaN
998       NaN NaN  0.95659       NaN NaN
999       NaN NaN      NaN       NaN NaN

[1000 rows x 5 columns]


All sparse formats are supported, but matrices that are not in COOrdinate format will be converted, copying data as needed. To convert a SparseDataFrame back to sparse SciPy matrix in COO format, you can use the SparseDataFrame.to_coo() method:

In [43]: sdf.to_coo()
Out[43]:
<1000x5 sparse matrix of type '<class 'numpy.float64'>'
with 517 stored elements in COOrdinate format>


### SparseSeries¶

A SparseSeries.to_coo() method is implemented for transforming a SparseSeries indexed by a MultiIndex to a scipy.sparse.coo_matrix.

The method requires a MultiIndex with two or more levels.

In [44]: s = pd.Series([3.0, np.nan, 1.0, 3.0, np.nan, np.nan])

In [45]: 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 [46]: s
Out[46]:
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: float64

# SparseSeries
In [47]: ss = s.to_sparse()

In [48]: ss
Out[48]:
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: float64
BlockIndex
Block locations: array([0, 2], dtype=int32)
Block lengths: array([1, 2], dtype=int32)


In the example below, we transform the SparseSeries 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 [49]: A, rows, columns = ss.to_coo(row_levels=['A', 'B'],
....:                              column_levels=['C', 'D'],
....:                              sort_labels=True)
....:

In [50]: A
Out[50]:
<3x4 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>

In [51]: A.todense()
Out[51]:
matrix([[ 0.,  0.,  1.,  3.],
[ 3.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.]])

In [52]: rows
Out[52]: [(1, 1), (1, 2), (2, 1)]

In [53]: columns
Out[53]: [('a', 0), ('a', 1), ('b', 0), ('b', 1)]


Specifying different row and column labels (and not sorting them) yields a different sparse matrix:

In [54]: A, rows, columns = ss.to_coo(row_levels=['A', 'B', 'C'],
....:                              column_levels=['D'],
....:                              sort_labels=False)
....:

In [55]: A
Out[55]:
<3x2 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>

In [56]: A.todense()
Out[56]:
matrix([[ 3.,  0.],
[ 1.,  3.],
[ 0.,  0.]])

In [57]: rows
Out[57]: [(1, 2, 'a'), (1, 1, 'b'), (2, 1, 'b')]

In [58]: columns
Out[58]: [0, 1]


A convenience method SparseSeries.from_coo() is implemented for creating a SparseSeries from a scipy.sparse.coo_matrix.

In [59]: from scipy import sparse

In [60]: A = sparse.coo_matrix(([3.0, 1.0, 2.0], ([1, 0, 0], [0, 2, 3])),
....:                       shape=(3, 4))
....:

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.,  2.],
[ 3.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.]])


The default behaviour (with dense_index=False) simply returns a SparseSeries containing only the non-null entries.

In [63]: ss = pd.SparseSeries.from_coo(A)

In [64]: ss
Out[64]:
0  2    1.0
3    2.0
1  0    3.0
dtype: float64
BlockIndex
Block locations: array([0], dtype=int32)
Block lengths: array([3], dtype=int32)


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 [65]: ss_dense = pd.SparseSeries.from_coo(A, dense_index=True)

In [66]: ss_dense
Out[66]:
0  0    NaN
1    NaN
2    1.0
3    2.0
1  0    3.0
1    NaN
2    NaN
3    NaN
2  0    NaN
1    NaN
2    NaN
3    NaN
dtype: float64
BlockIndex
Block locations: array([2], dtype=int32)
Block lengths: array([3], dtype=int32)

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