# Sparse data structures¶

We have implemented “sparse” versions of Series, DataFrame, and Panel. These are not sparse in the typical “mostly 0”. You can view these objects as being “compressed” where any data matching a specific value (NaN/missing by default, 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.ix[: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       NaN       NaN       NaN       NaN
9999  0.280249 -1.648493  1.490865 -0.890819

[10000 rows x 4 columns]

In [10]: sdf.density
Out[10]: 0.0001
```

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]:
[-1.95566352972, -1.6588664276, nan, nan, nan, 1.15893288864, 0.145297113733, nan, 0.606027190513, 1.33421134013]
Fill: nan
IntIndex
Indices: array([0, 1, 5, 6, 8, 9], dtype=int32)
```

Like the indexed objects (SparseSeries, SparseDataFrame, SparsePanel), 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¶

SparseList is a list-like data structure for managing a dynamic collection of SparseArrays. To create one, simply call the SparseList constructor with a fill_value (defaulting to NaN):

```In [17]: spl = pd.SparseList()

In [18]: spl
Out[18]: <pandas.sparse.list.SparseList object at 0x12df89e50>
```

The two important methods are append and to_array. append can accept scalar values or any 1-dimensional sequence:

```In [19]: spl.append(np.array([1., np.nan, np.nan, 2., 3.]))

In [20]: spl.append(5)

In [21]: spl.append(sparr)

In [22]: spl
Out[22]:
<pandas.sparse.list.SparseList object at 0x12df89e50>
[1.0, nan, nan, 2.0, 3.0]
Fill: nan
IntIndex
Indices: array([0, 3, 4], dtype=int32)

[5.0]
Fill: nan
IntIndex
Indices: array([0], dtype=int32)

[-1.95566352972, -1.6588664276, nan, nan, nan, 1.15893288864, 0.145297113733, nan, 0.606027190513, 1.33421134013]
Fill: nan
IntIndex
Indices: array([0, 1, 5, 6, 8, 9], dtype=int32)
```

As you can see, all of the contents are stored internally as a list of memory-efficient SparseArray objects. Once you’ve accumulated all of the data, you can call to_array to get a single SparseArray with all the data:

```In [23]: spl.to_array()
Out[23]:
[1.0, nan, nan, 2.0, 3.0, 5.0, -1.95566352972, -1.6588664276, nan, nan, nan, 1.15893288864, 0.145297113733, nan, 0.606027190513, 1.33421134013]
Fill: nan
IntIndex
Indices: array([ 0,  3,  4,  5,  6,  7, 11, 12, 14, 15], dtype=int32)
```

## 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.

## Interaction with scipy.sparse¶

Experimental api to transform between sparse pandas and scipy.sparse structures.

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

In [25]: 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 [26]: s
Out[26]:
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 [27]: ss = s.to_sparse()

In [28]: ss
Out[28]:
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 [29]: A, rows, columns = ss.to_coo(row_levels=['A', 'B'],
....:                              column_levels=['C', 'D'],
....:                              sort_labels=True)
....:

In [30]: A
Out[30]:
<3x4 sparse matrix of type '<type 'numpy.float64'>'
with 3 stored elements in COOrdinate format>

In [31]: A.todense()
Out[31]:
matrix([[ 0.,  0.,  1.,  3.],
[ 3.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.]])

In [32]: rows
Out[32]: [(1, 1), (1, 2), (2, 1)]

In [33]: columns
Out[33]: [('a', 0), ('a', 1), ('b', 0), ('b', 1)]
```

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

```In [34]: A, rows, columns = ss.to_coo(row_levels=['A', 'B', 'C'],
....:                              column_levels=['D'],
....:                              sort_labels=False)
....:

In [35]: A
Out[35]:
<3x2 sparse matrix of type '<type 'numpy.float64'>'
with 3 stored elements in COOrdinate format>

In [36]: A.todense()
Out[36]:
matrix([[ 3.,  0.],
[ 1.,  3.],
[ 0.,  0.]])

In [37]: rows
Out[37]: [(1, 2, 'a'), (1, 1, 'b'), (2, 1, 'b')]

In [38]: columns
Out[38]: [0, 1]
```

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

```In [39]: from scipy import sparse

In [40]: A = sparse.coo_matrix(([3.0, 1.0, 2.0], ([1, 0, 0], [0, 2, 3])),
....:                       shape=(3, 4))
....:

In [41]: A
Out[41]:
<3x4 sparse matrix of type '<type 'numpy.float64'>'
with 3 stored elements in COOrdinate format>

In [42]: A.todense()
Out[42]:
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 [43]: ss = pd.SparseSeries.from_coo(A)

In [44]: ss
Out[44]:
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 [45]: ss_dense = pd.SparseSeries.from_coo(A, dense_index=True)

In [46]: ss_dense
Out[46]:
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)
```