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:

    >>> from numpy.random import rand
    
    >>> 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]]...)