scipy csr_matrix: understand indptr

Question

Every once in a while, I get to manipulate a csr_matrix but I always forget how the parameters indices and indptr work together to build a sparse matrix.

I am looking for a clear and intuitive explanation on how the indptr interacts with both the data and indices parameters when defining a sparse matrix using the notation csr_matrix((data, indices, indptr), [shape=(M, N)]).

I can see from the scipy documentation that the data parameter contains all the non-zero data, and the indices parameter contains the columns associated to that data (as such, indices is equal to col in the example given in the documentation). But how can we explain in clear terms the indptr parameter?

Answer 1

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.