How to perform logical AND on intervals of contiguous locations
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Arturo Camacho Lozano
on 23 Sep 2020
Commented: Arturo Camacho Lozano
on 30 Sep 2020
I have the following problem. Let's say I have the arrays
x = logical([0, 1, 0,0, 1,1, 0,0,0, 1,1,1, 0])
y = logical([0, 1, 1,0, 1,1, 0,1,0, 1,0,1, 0])
Array X has three intervals of 1's with indices 2:2, 5:6, and 10:12. I want to apply an "interval AND" operation to X, based on Y, in the following sense: for each interval of ones in X, if any element in Y is zero in that interval, the whole interval is zeroed, i.e., Z = intervalAND(X,Y) should be the same as
z = logical([0, 1, 0,0, 1,1, 0,0,0, 0,0,0, 0])
Let me explain. Since all(Y(2:2)) = 1, it produces ones in Z(2:2). The same happens in the second interval (5:6): Both Y(5) and Y(6) are true, producing ones in Z. However, there is a zero in Y(10:12) which zeroes the whole interval Z(10:12).
I know how to do it with a for loop:
d = diff(x);
pos = find(d == 1);
neg = find(d == -1);
z = x;
for k = 1:length(neg)
interval = pos(k)+1 : neg(k);
if ~all(y(interval))
z(interval) = false;
end
end
However, I need to vectorize it to make it run faster (I am working with huge arrays). Does someone know how to compute Z without using a for/while loop?
4 Comments
James Tursa
on 24 Sep 2020
Is the algorithm running on each column individually, or running across the entire matrix as a whole? I.e., does the 1's logic extend across columns?
Accepted Answer
Bruno Luong
on 24 Sep 2020
Edited: Bruno Luong
on 25 Sep 2020
x = logical([0, 1, 0,0, 1,1, 0,0,0, 1,1,1, 0])
y = logical([0, 1, 1,0, 1,1, 0,1,0, 1,0,1, 0])
code without loop or groupping, on my bench test about 3 time faster than Stephen's accumarray solution
i = find(diff([0 x 0]));
n = histc(find(~y), i);
j = [1;-1]*(n(1:2:end)==0);
if x(end)
i(end)=[];
j(end)=[];
end
z = logical(cumsum(accumarray(i(:),j(:),[length(x),1])));
10 Comments
Bruno Luong
on 26 Sep 2020
Edited: Bruno Luong
on 26 Sep 2020
Faster. It does not create unecessary elements to accumulate then removed.
The one before is still OK if you prefer readable code.
More Answers (2)
Mohammad Sami
on 24 Sep 2020
You can group based on the values of x.
gid = cumsum(x ~= circshift(x,1));
if(gid(1) == 0)
gid = gid + 1;
end
a = splitapply(@min,y,gid);
z = a(gid);
1 Comment
Matt J
on 25 Sep 2020
Using group1s from
>> xg=group1s(x)+1;
>> yg=splitapply(@all,y,xg);
>> z=yg(xg)
z =
1×13 logical array
0 1 0 0 1 1 0 0 0 0 0 0 0
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