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]]...)