MATLAB: How to perform logical AND on intervals of contiguous locations

for looplogical operationsvectorization

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?

Best Answer

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])));
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