2.5.2.2.6. Compressed Sparse Column Format (CSC)

  • column oriented
    • three NumPy arrays: indices, indptr, data
      • indices is array of row indices
      • data is array of corresponding nonzero values
      • indptr points to column starts in indices and data
      • length is n_col + 1, last item = number of values = length of both indices and data
      • nonzero values of the i-th column are data[indptr[i]:indptr[i+1]] with row indices indices[indptr[i]:indptr[i+1]]
      • item (i, j) can be accessed as data[indptr[j]+k], where k is position of i in indices[indptr[j]:indptr[j+1]]
    • subclass of _cs_matrix (common CSR/CSC functionality)
      • subclass of _data_matrix (sparse matrix classes with .data attribute)

  • fast matrix vector products and other arithmetics (sparsetools)

  • constructor accepts:
    • dense matrix (array)
    • sparse matrix
    • shape tuple (create empty matrix)
    • (data, ij) tuple
    • (data, indices, indptr) tuple

  • efficient column slicing, column-oriented operations

  • slow row slicing, expensive changes to the sparsity structure

  • use:
    • actual computations (most linear solvers support this format)

2.5.2.2.6.1. Examples

  • create empty CSC matrix:

    >>> mtx = sparse.csc_matrix((3, 4), dtype=np.int8)

    >>> mtx.todense()

    matrix([[0, 0, 0, 0],

            [0, 0, 0, 0],

            [0, 0, 0, 0]], dtype=int8)

  • create using (data, ij) tuple:

    >>> row = np.array([0, 0, 1, 2, 2, 2])

    >>> col = np.array([0, 2, 2, 0, 1, 2])

    >>> data = np.array([1, 2, 3, 4, 5, 6])

    >>> mtx = sparse.csc_matrix((data, (row, col)), shape=(3, 3))

    >>> mtx         

    <3x3 sparse matrix of type '<... 'numpy.int64'>'

            with 6 stored elements in Compressed Sparse Column format>

    >>> mtx.todense()   

    matrix([[1, 0, 2],

            [0, 0, 3],

            [4, 5, 6]]...)

    >>> mtx.data   

    array([1, 4, 5, 2, 3, 6]...)

    >>> mtx.indices

    array([0, 2, 2, 0, 1, 2], dtype=int32)

    >>> mtx.indptr

    array([0, 2, 3, 6], dtype=int32)

  • create using (data, indices, indptr) tuple:

    >>> data = np.array([1, 4, 5, 2, 3, 6])

    >>> indices = np.array([0, 2, 2, 0, 1, 2])

    >>> indptr = np.array([0, 2, 3, 6])

    >>> mtx = sparse.csc_matrix((data, indices, indptr), shape=(3, 3))

    >>> mtx.todense()

    matrix([[1, 0, 2],

            [0, 0, 3],

            [4, 5, 6]])