# Mathematica SparseArray Access Non-Default Values

• Mathematica
wima
Hi,

I am currently dealing with really huge (~ 80,000 x 80,000) sparse matrices. I this context I need to read the number of non-default values in each row.
When Accessing the i-th row of a SparseArray, this information is given.
E.g.
test = SparseArray[{{1, 1} -> 3, {1, 5} -> 2, {5, 3} -> 1}];
test[]
returns SparseArray[<2>, {5}]
However, I fail to access the number of entries (here 2) to assign it to a variable.
I did not find any information in the documentation so far.
Does anyone have an idea?

Thx

## Answers and Replies

Mentor
2021 Award
You can use Normal[test[]]

Gold Member
I could be wrong but is it :
test[][] in this case? its the only index that returns "2"

wima
@DaleSpam:
The problem is, that my matrices are too large to convert them into normal arrays. However, about only 1% of the matrix entries have non-zero values. For my computations, I need to construct a vector that stores the number of non-zero values that are in each row of the matrix. For the example I posted, that vector would be {2,0,0,0,1} because there are two entries in the first row and one in the fifth row. Iterating over all 80,000 x 80,000 = 6,400,000,000 values of the sparse matrix will not work...

@Hepth:
test[][] returns the value of the matrix in row 1 and column 5. That entry is 2. What I need to access is the number of nonzero values in every row.

It's really bothering, because it's obvious that the number of entries is easily accessible as you can see here:
test[]
test[]
test[]
returns
SparseArray[<2>, {5}]
SparseArray[<0>, {5}]
SparseArray[<1>, {5}]
namely 2, 0 and 1. However, it's not sufficient for me to read the values manually, but I need to assign them to a variable for storing them in the vector of size 80,000. So the probelm is to access the values in <>.

Anyway, thanks for your replies so far!

Mentor
2021 Award
Yes, I understand that it is too big to convert the whole matrix into a normal array. That is why I suggest Normal[test[]] rather than Normal[test][]. For your matrix that will be a vector with 80k entries, so not too big.

The values in the <> are not real values stored anywhere, they are just for display. If you really want those the only way to get them would be to use ToString[test[]] and then use some string manipulation to pull out the number between the <>.

Gold Member
Length[ArrayRules[test[]]] - 1

will give you the number of nonzero elements. But Array Rules itself might not be fast for something that large, it gives the list of all non zero components.

wima
Thank you for your replies! All of the suggested methods work. I am currently about to figure out, which of them are most efficient.