2.5.2.2.3. 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

2.5.2.2.3.1. 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.]])