List of Lists Format (LIL)¶

row-based linked list
- each row is a Python list (sorted) of column indices of non-zero elements
- rows stored in a NumPy array (dtype=np.object)
- non-zero values data stored analogously
efficient for constructing sparse matrices incrementally
constructor accepts:
- dense matrix (array)
- sparse matrix
- shape tuple (create empty matrix)
flexible slicing, changing sparsity structure is efficient
slow arithmetics, slow column slicing due to being row-based
use:
- when sparsity pattern is not known apriori or changes
- example: reading a sparse matrix from a text file

Examples¶

create an empty LIL matrix:
```
>>> mtx = sparse.lil_matrix((4, 5))
```

prepare random data:

>>> fromnumpy.randomimportrand
>>> data=np.round(rand(2,3))
>>> data
array([[ 1.,  1.,  1.],
       [ 1.,  0.,  1.]])

assign the data using fancy indexing:

>>> mtx[:2,[1,2,3]]=data
>>> mtx
<4x5 sparse matrix of type '<... 'numpy.float64'>'
        with 5 stored elements in LInked List format>
>>> print(mtx)
  (0, 1)  1.0
  (0, 2)  1.0
  (0, 3)  1.0
  (1, 1)  1.0
  (1, 3)  1.0
>>> mtx.todense()
matrix([[ 0.,  1.,  1.,  1.,  0.],
        [ 0.,  1.,  0.,  1.,  0.],
        [ 0.,  0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.,  0.]])
>>> mtx.toarray()
array([[ 0.,  1.,  1.,  1.,  0.],
       [ 0.,  1.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.]])

more slicing and indexing:

>>> mtx=sparse.lil_matrix([[0,1,2,0],[3,0,1,0],[1,0,0,1]])
>>> mtx.todense()
matrix([[0, 1, 2, 0],
        [3, 0, 1, 0],
        [1, 0, 0, 1]]...)
>>> print(mtx)
  (0, 1)    1
  (0, 2)    2
  (1, 0)    3
  (1, 2)    1
  (2, 0)    1
  (2, 3)    1
>>> mtx[:2,:]
<2x4 sparse matrix of type '<... 'numpy.int64'>'
  with 4 stored elements in LInked List format>
>>> mtx[:2,:].todense()
matrix([[0, 1, 2, 0],
        [3, 0, 1, 0]]...)
>>> mtx[1:2,[0,2]].todense()
matrix([[3, 1]]...)
>>> mtx.todense()
matrix([[0, 1, 2, 0],
        [3, 0, 1, 0],
        [1, 0, 0, 1]]...)