Fastest way to check if array is zero

Question

What is the fastest way to check if an entire array is zero? For my case the elements of the array are either 1 or 0 but for reference purposes the general case can also be considered.

Maybe LinearAlgebra`Private`ZeroArrayQ? I recall that we had a similar question not long ago... — Henrik Schumacher, Oct 13 '20 at 13:40
Ah, here it is. Not a duplicate but related and thus maybe of interest: https://mathematica.stackexchange.com/q/230971 — Henrik Schumacher, Oct 13 '20 at 13:46
@Q.P. - Total@matrix returns a vector rather than a scalar. Even if you Flatten the matrix first, you would also need to use Abs to ensure that a zero result indicated that the matrix was all zeroes. — Bob Hanlon, Oct 13 '20 at 13:52
@Q.P. Total would work but I'm interested in speed. It might be the fastest but I don't know. — AccidentalTaylorExpansion, Oct 13 '20 at 18:53

Henrik Schumacher · Accepted Answer · 2020-10-13T13:58:50.937

14

LinearAlgebra`Private`ZeroArrayQ seems to do quite a good job. Curiously enough, Statistics`Library`ConstantVectorQ[#] && #[[1]] == 0 & tends to be a little bit faster on my machine.

edited Oct 13 '20 at 13:58

answered Oct 13 '20 at 13:51

Henrik Schumacher

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score 4 · Answer 2 · answered Oct 14 '20 at 11:44

I tested the methods from Henrik and got the following timings

linAlgZeroArrayQ = LinearAlgebra`Private`ZeroArrayQ;
statZeroArrayQ = 
  Statistics`Library`ConstantVectorQ[#] && #[[1]] == 0 &;
totalZeroArrayQ = Total[#] == 0 &;
n = 10^5;
exactZeros = ConstantArray[0, n];
numericalZeros = ConstantArray[0., n];
exactSparse = exactZeros; exactSparse[[n/2]] = 1;
numericalSparse = numericalZeros; numericalSparse[[n/2]] = 1.;
exactRandom = RandomChoice[{0, 1}, n];
numericalRandom = RandomChoice[{0., 1.}, n];
functions = {linAlgZeroArrayQ, statZeroArrayQ, totalZeroArrayQ};
tests = {exactZeros, numericalZeros, exactSparse, numericalSparse, 
   exactRandom, numericalRandom};
results = Table[
   AbsoluteTiming[Do[functions[[j]]@tests[[i]], {10000}]][[1]], {i, 1,
     Length@tests}, {j, 1, Length@functions}
   ];
TableForm[results, 
 TableHeadings -> {{"Exact zeros", "Numerical zeros", "Exact sparse", 
    "Numerical sparse", "Exact random", 
    "Numerical random"}, {"Linear Algebra method", 
    "Statistics method", "Total"}}]

For the cases I tested the LinearAlgebra`Private`ZeroArrayQ seems like a clear winner but there might be cases/machines where Statistics`Library`ConstantVectorQ[#] && #[[1]] == 0 & wins.

score 2 · Answer 3 · answered Mar 11 '23 at 07:27

2

You can try the following

AA = {{0, 0}, {0, 0}};
AllTrue[Flatten[AA], PossibleZeroQ]

answered Mar 11 '23 at 07:27

William Wang

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Fastest way to check if array is zero

3 Answers3