Turning iteratively all elements after and above a '1' into '0'-s starting from the left bottom corner
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I have logical square matrices consisting of non-intersecting rectangular patches of '1'-s with no gaps and otherwise '0'-s. 'No gaps' in particular means that two different rectangular patches are not allowed to share horizontal or vertical coordinates. Moreover, the rectangular patches are strictly monotone increasing from the POV of the bottom left corner. For example:
A = [0 0 0 0 1;
0 0 0 0 1;
0 1 1 1 0;
0 1 1 1 0;
1 0 0 0 0]
I would like to perform the following operation on A in a fast way, possibly on GPU. Starting from the left bottom corner, I would like to iteratively turn all elements above and after a '1' into '0'. For example:
B = [0 0 0 0 0;
0 0 0 0 1;
0 0 1 0 0;
0 1 0 0 0;
1 0 0 0 0]
That is, B(3,3) = 1 because after the iteration at A(4,2), A(4,3) turns into a '0'.
My logical matrices are of size at most 15 and I would like to perform this operation on a 3D-array of many such square matrices stacked upon each other in a fast way, hence the request for vectorizability if possible.
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DGM
il 13 Apr 2022
Modificato: DGM
il 13 Apr 2022
This might not be particularly efficient, but maybe it's one way (if i'm interpreting it right):
A = [0 0 0 0 0 0 1
0 0 0 0 0 0 1;
0 0 0 0 1 1 0;
0 0 0 0 1 1 0;
0 1 1 1 0 0 0;
0 1 1 1 0 0 0;
1 0 0 0 0 0 0];
D = rot90(hankel(size(A,1):-1:1),2).*A;
D(D==0) = NaN;
Dmin = min(D,[],2);
D = D - (flip(cummax(flip(Dmin)))-1);
output = D==1
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