Delete zeros from a sparse array

Question

Why doesn't SparseArray automatically remove zero entries? The code

a = SparseArray[{2->22,3->33,5->55,7->77,11->1111,13->1313},13];
b = SparseArray[{1->11,3->33,5->55,7->77,9->99,11->1111},13];
r = DeleteCases[a-b,0]
r //ArrayRules

returns

{{1}->-11,{3}->0,{5}->0,{7}->0,{9}->-99,{11}->0,{2}->22,{13}->1313,{_}->0}

instead of

{{1}->-11,{9}->-99,{2}->22,{13}->1313,{_}->0}.

Is there a nice way to get rid of zero entries? For instance, when I perform Gaussian elimination on $A\!\in\!\mathbb{Z}^{m\times n}_2$, I use A = Mod[A, 2];, and suddenly many entries are zero. I don't want to waste memory on them.

Of course I could use

A = SparseArray[DeleteCases[ArrayRules[A], #[[2]] == 0&], {m,n}]

but it seems clumsy to use this often.

Also, when I have a very long sparse row that gets updated frequently and fills up somewhat (Gaussian elimination), is it better to use SparseArray with + or Association with Merge?

Answer 1

You can just apply SparseArray to a SparseArray object to normalize it. For your example:

a = SparseArray[{2->22,3->33,5->55,7->77,11->1111,13->1313},13];
b = SparseArray[{1->11,3->33,5->55,7->77,9->99,11->1111},13];
r = DeleteCases[a-b,0];

SparseArray[r] //ArrayRules

{{1} -> -11, {2} -> 22, {9} -> -99, {13} -> 1313, {_} -> 0}