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 arrays incrementally

• constructor accepts:

  • dense array/matrix

  • sparse array/matrix

  • shape tuple (create empty array)

• flexible slicing, changing sparsity structure is efficient

• slow arithmetic, slow column slicing due to being row-based

• use:

  • when sparsity pattern is not known apriori or changes

  • example: reading a sparse array from a text file

Examples

• create an empty LIL array:

  >>> mtx = sp.sparse.lil_array((4, 5))
  

• prepare random data:

  >>> rng = np.random.default_rng(27446968)
  >>> data = np.round(rng.random((2, 3)))
  >>> data
  array([[1.,  0.,  1.],
         [0.,  0.,  1.]])
  

• assign the data using fancy indexing:

  >>> mtx[:2, [1, 2, 3]] = data
  >>> mtx
  <List of Lists sparse array of dtype 'float64'
          with 3 stored elements and shape (4, 5)>
  >>> print(mtx)
  <List of Lists sparse array of dtype 'float64'
          with 3 stored elements and shape (4, 5)>
    Coords    Values
    (0, 1)    1.0
    (0, 3)    1.0
    (1, 3)    1.0
  >>> mtx.toarray()
  array([[0., 1., 0., 1., 0.],
         [0., 0., 0., 1., 0.],
         [0., 0., 0., 0., 0.],
         [0., 0., 0., 0., 0.]])
  >>> mtx.toarray()
  array([[0., 1., 0., 1., 0.],
         [0., 0., 0., 1., 0.],
         [0., 0., 0., 0., 0.],
         [0., 0., 0., 0., 0.]])
  

• more slicing and indexing:

  >>> mtx = sp.sparse.lil_array([[0, 1, 2, 0], [3, 0, 1, 0], [1, 0, 0, 1]])
  >>> mtx.toarray()
  array([[0, 1, 2, 0],
         [3, 0, 1, 0],
         [1, 0, 0, 1]]...)
  >>> print(mtx)
  <List of Lists sparse array of dtype 'int64'
          with 6 stored elements and shape (3, 4)>
    Coords    Values
    (0, 1)    1
    (0, 2)    2
    (1, 0)    3
    (1, 2)    1
    (2, 0)    1
    (2, 3)    1
  >>> mtx[:2, :]
  <List of Lists sparse array of dtype 'int64'
          with 4 stored elements and shape (2, 4)>
  >>> mtx[:2, :].toarray()
  array([[0, 1, 2, 0],
         [3, 0, 1, 0]]...)
  >>> mtx[1:2, [0,2]].toarray()
  array([[3, 1]]...)
  >>> mtx.toarray()
  array([[0, 1, 2, 0],
         [3, 0, 1, 0],
         [1, 0, 0, 1]]...)