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 array classes with .data attribute)

  • fast matrix vector products and other arithmetic (sparsetools)

  • constructor accepts:

    • dense array/matrix

    • sparse array/matrix

    • shape tuple (create empty array)

    • (data, coords) 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)

Examples

  • create empty CSC array:

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

    >>> mtx.toarray()

    array([[0, 0, 0, 0],

           [0, 0, 0, 0],

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

  • create using (data, coords) 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 = sp.sparse.csc_array((data, (row, col)), shape=(3, 3))

    >>> mtx

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

            with 6 stored elements in Compressed Sparse Column format>

    >>> mtx.toarray()

    array([[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])

    >>> mtx.indptr

    array([0, 2, 3, 6])

  • 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 = sp.sparse.csc_array((data, indices, indptr), shape=(3, 3))

    >>> mtx.toarray()

    array([[1, 0, 2],

           [0, 0, 3],

           [4, 5, 6]])