# Sparse

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:
• If the sparse matrix has M rows, indptr is an array containing M+1 elements
• 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.

https://stackoverflow.com/a/52299730/20148196

Represent the "data" in a 4 X 4 Matrix:

data = np.array([10,0,5,99,25,9,3,90,12,87,20,38,1,8])
indices = np.array([0,1,2,3,0,2,3,0,1,2,3,1,2,3])
indptr  = np.array([0,4,7,11,14])

• 'indptr'- Index pointers is linked list of pointers to 'indices' (Column index Pointers)...
• indptr[i:i+1] represents i to i+1 index of pointer
• 14 reprents len of Data len(data)... indptr = np.array([0,4,7,11,len(data)]) other way of represenint 'indptr'
• 0,4 → 0:4 represents pointers to indices 0,1,2,3
• 4,7 → 4:7 represents the pointers of indices 0,2,3
• 7,11 → 7:11 represents the pointers of 0,1,2,3
• 11,14 → 11:14 represents pointers 1,2,3
#  Representing the data in a 4,4 matrix

a = csr_matrix((data,indices,indptr),shape=(4,4),dtype=np.int)
a.todense()

matrix([[10,  0,  5, 99],
[25,  0,  9,  3],
[90, 12, 87, 20],
[ 0, 38,  1,  8]])

https://stackoverflow.com/a/62118005/20148196