Dictionary of Keys Format (DOK)

  • subclass of Python dict
    • keys are (row, column) index tuples (no duplicate entries allowed)
    • values are corresponding non-zero values
  • efficient for constructing sparse matrices incrementally
  • constructor accepts:
    • dense matrix (array)
    • sparse matrix
    • shape tuple (create empty matrix)
  • efficient O(1) access to individual elements
  • flexible slicing, changing sparsity structure is efficient
  • can be efficiently converted to a coo_matrix once constructed
  • slow arithmetics (for loops with dict.iteritems())
  • use:
    • when sparsity pattern is not known apriori or changes

Examples

  • create a DOK matrix element by element:

    >>> mtx = sparse.dok_matrix((5, 5), dtype=np.float64)
    
    >>> mtx
    <5x5 sparse matrix of type '<... 'numpy.float64'>'
    with 0 stored elements in Dictionary Of Keys format>
    >>> for ir in range(5):
    ... for ic in range(5):
    ... mtx[ir, ic] = 1.0 * (ir != ic)
    >>> mtx
    <5x5 sparse matrix of type '<... 'numpy.float64'>'
    with 20 stored elements in Dictionary Of Keys format>
    >>> mtx.todense()
    matrix([[ 0., 1., 1., 1., 1.],
    [ 1., 0., 1., 1., 1.],
    [ 1., 1., 0., 1., 1.],
    [ 1., 1., 1., 0., 1.],
    [ 1., 1., 1., 1., 0.]])
  • slicing and indexing:

    >>> mtx[1, 1]
    
    0.0
    >>> mtx[1, 1:3]
    <1x2 sparse matrix of type '<... 'numpy.float64'>'
    with 1 stored elements in Dictionary Of Keys format>
    >>> mtx[1, 1:3].todense()
    matrix([[ 0., 1.]])
    >>> mtx[[2,1], 1:3].todense()
    matrix([[ 1., 0.],
    [ 0., 1.]])