Compressed Sparse formats CSR and CSC in Python

Compressed sparse row (CSR) and compressed sparse column (CSC) are widely known and most used formats of sparse data structures. Mainly, they are used for write-once-read-many tasks.

Compressed Sparse Column (CSC) format is almost identical, except that values are indexed first by column with a column-major order. Usually, the CSC is used when there are more rows than columns. On the contrary, the CSR works better for a ‘wide’ format. So, her is taking CSR as an example here.

Internally, CSR is based on three NumPy arrays:

• data is an array of corresponding nonzero values
• indices is array of column indices
• indptr points to row starts in data and indices

~ length of indptr is number of rows + 1, last item in indptr = number of nonvalues = length of both data and indices

~ nonzero items of the i-th row are located data[indptr[i]:indptr[i+1]] with column indices indices[indptr[i]:indptr[i+1]]

If you’re new to the SciPy sparse matrix game, you might find yourself stymied by the ‘indptr’ array, which can be used to instantiate a csc_matrix or a csr_matrix object. Here I give an example to explain how to compute matrix through NumPy arrays.

Example: create using (data, indices, indptr) tuple as below:

>>> data = np.array([1,2,3,4,5,6])

>>> indices = np.array([0,2,2,0,1,2])

>>> indptr = np.array([0,2,3,6])

>>> mtx = sparse.csr_matrix((data, indices, indptr), shape=(3, 3))

>>> mtx.todense()

matrix([1,0,2], [0,0,3],[4,5,6])

How to get result matrix through the given (data, indices, indptr) tuple? Here is what it is going:

i = 0 -> indptr[0] = 0, indptr[0 + 1] = 2 -> data[0:2] = 1,2 and indices[0:2] = 0,2 -> first row of matrix is [1,0,2]

i = 1 -> indptr[1] = 2, indptr[1 + 1] = 3 -> data[2:3] = 3 and indices[2:3] = 2 -> second row of matrix is [0,0,3]

i = 2 -> indptr[2] = 3, indptr[2 + 1] = 6 -> data[3:6] = 4,5,6 and indices[3:6] = 4,5,6 -> third row of matrix is [4,5,6]

Thanks for reading. Welcome to comment if you have doubts.