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]])