How to perform logical AND on intervals of contiguous locations

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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 comentarios
James Tursa
James Tursa el 24 de Sept. de 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?
Arturo Camacho Lozano
Arturo Camacho Lozano el 24 de Sept. de 2020
Each column is independant. The same column vector Y is applied to all columns, though.

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Respuesta aceptada

Bruno Luong
Bruno Luong el 24 de Sept. de 2020
Editada: Bruno Luong el 25 de Sept. de 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 comentarios
Bruno Luong
Bruno Luong el 26 de Sept. de 2020
Editada: Bruno Luong el 26 de Sept. de 2020
Faster. It does not create unecessary elements to accumulate then removed.
The one before is still OK if you prefer readable code.
Arturo Camacho Lozano
Arturo Camacho Lozano el 30 de Sept. de 2020
Thanks four answer. This implementation works way faster than other proposed implementations that use "splitapply". Besides, it was easy to port to the target language (Python).

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Más respuestas (2)

Mohammad Sami
Mohammad Sami el 24 de Sept. de 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 comentario
Arturo Camacho Lozano
Arturo Camacho Lozano el 25 de Sept. de 2020
Editada: Arturo Camacho Lozano el 25 de Sept. de 2020
Great! It needs a small adjusment, though. The second argument to splitapply should be x&y:
a = splitapply(@min, x&y, gid);
Let me clarify. If we change the fourth element of Y to 1, i.e.
x = logical([0, 1, 0,0, 1,1, 0,0,0, 1,1,1, 0])
y = logical([0, 1, 1,1, 1,1, 0,1,0, 1,0,1, 0])
the output should be the same as before:
z = logical([0, 1, 0,0, 1,1, 0,0,0, 0,0,0, 0])
because there was already a 0 in that position of X.
(Please edit the answer to accept it).

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Matt J
Matt J el 25 de Sept. de 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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