Compressed Sparse Column Format (CSC)

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import numpy as np
import scipy as sp

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

<Compressed Sparse Column sparse array of dtype 'int64'
	with 6 stored elements and shape (3, 3)>

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]])
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