scipy csr_matrix: understand indptr

Maybe this explanation can help understand the concept:

• data is an array containing all the non zero elements of the sparse matrix.
• indices is an array mapping each element in data to its column in the sparse matrix.

• indptr then maps the elements of data and indices to the rows of the sparse matrix. This is done with the following reasoning:

  1. If the sparse matrix has M rows, indptr is an array containing M+1 elements
  2. for row i, [indptr[i]:indptr[i+1]] returns the indices of elements to take from data and indices corresponding to row i. So suppose indptr[i]=k and indptr[i+1]=l, the data corresponding to row i would be data[k:l] at columns indices[k:l]. This is the tricky part, and I hope the following example helps understanding it.

EDIT : I replaced the numbers in data by letters to avoid confusion in the following example.

Note: the values in indptr are necessarily increasing, because the next cell in indptr (the next row) is referring to the next values in data and indices corresponding to that row.