can't understand scipy.sparse.csr_matrix example

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])

from the above arrays;

for k in 0~5
a[row_ind[k], col_ind[k]] = data[k]

 a row[0],col[0] = [0,0] = 1 (from data[0]) row[1],col[1] = [0,2] = 2 (from data[1]) row[2],col[2] = [1,2] = 3 (from data[2]) row[3],col[3] = [2,0] = 4 (from data[3]) row[4],col[4] = [2,1] = 5 (from data[4]) row[5],col[5] = [2,2] = 6 (from data[5]) 

so let's arrange matrix 'a' in shape(3X3)

a 0 1 2 0 [1, 0, 2] 1 [0, 0, 3] 2 [4, 5, 6] 

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]]) 

Another Stackoverflow explanation

As far as I understand, in row and col arrays we have indices which corrensponds to non-zero values in matrix. a[0, 0] = 1, a[0, 2] = 2, a[1, 2] = 3 and so on. As we have no indices for a[0, 1], a[1, 0], a[1, 1] so appropriate values in matrix are equal to 0.

Also, maybe this little intro will be helpful for you: https://www.youtube.com/watch?v=Lhef_jxzqCg

@Rohit Pandey stated correctly, I just want to add an example on that.

When most of the elements of a matrix have 0 values, then we call this a sparse matrix. The process includes removing zero elements from the matrix and thus saving memory space and computing time. We only store non-zero items with their respected row and column index. i.e.

0 3 0 4

0 5 7 0

0 0 0 0

0 2 6 0

We calculate the sparse matrix by putting non-zero items row index first, then column index, and finally non-zero values like the following:

By reversing the process we get the simple matrix form from the sparse form.