How to perform logical AND on intervals of contiguous locations

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Arturo Camacho Lozano
评论： Arturo Camacho Lozano 2020-9-30
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?
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James Tursa
James Tursa 2020-9-24
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 2020-9-24
Each column is independant. The same column vector Y is applied to all columns, though.

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采纳的回答

Bruno Luong
Bruno Luong 2020-9-24
编辑：Bruno Luong 2020-9-25
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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Bruno Luong
Bruno Luong 2020-9-26
编辑：Bruno Luong 2020-9-26
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 2020-9-30
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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更多回答（2 个）

Mohammad Sami
Mohammad Sami 2020-9-24
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 个评论
Arturo Camacho Lozano
Arturo Camacho Lozano 2020-9-25
编辑：Arturo Camacho Lozano 2020-9-25
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 2020-9-25
Using group1s from
https://www.mathworks.com/matlabcentral/fileexchange/78008-group1s
>> 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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