Coordinate Format (COO)

• also known as the ‘ijv’ or ‘triplet’ format

  • three NumPy arrays: row, col, data
  • data[i] is value at (row[i], col[i]) position
  • permits duplicate entries
  • subclass of _data_matrix (sparse matrix classes with .data attribute)

• fast format for constructing sparse matrices

• constructor accepts:

  • dense matrix (array)
  • sparse matrix
  • shape tuple (create empty matrix)
  • (data, ij) tuple

• very fast conversion to and from CSR/CSC formats

• fast matrix * vector (sparsetools)

• fast and easy item-wise operations

  • manipulate data array directly (fast NumPy machinery)

• no slicing, no arithmetics (directly)

• use:

  • facilitates fast conversion among sparse formats

  • when converting to other format (usually CSR or CSC), duplicate entries are summed together

    • facilitates efficient construction of finite element matrices

Examples

• create empty COO matrix:

  >>> mtx = sparse.coo_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, 3, 1, 0])
  >>> col = np.array([0, 3, 1, 2])
  >>> data = np.array([4, 5, 7, 9])
  >>> mtx = sparse.coo_matrix((data, (row, col)), shape=(4, 4))
  >>> mtx     
  <4x4 sparse matrix of type '<... 'numpy.int64'>'
          with 4 stored elements in COOrdinate format>
  >>> mtx.todense()
  matrix([[4, 0, 9, 0],
          [0, 7, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 0, 5]])
  

• duplicates entries are summed together:

  >>> row = np.array([0, 0, 1, 3, 1, 0, 0])
  >>> col = np.array([0, 2, 1, 3, 1, 0, 0])
  >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
  >>> mtx = sparse.coo_matrix((data, (row, col)), shape=(4, 4))
  >>> mtx.todense()
  matrix([[3, 0, 1, 0],
          [0, 2, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 0, 1]])
  

• no slicing…:

  >>> mtx[2, 3]   
  Traceback (most recent call last):
  ...
  TypeError: 'coo_matrix' object ...