Consider three row vectors in Matlab, A, B, C, each with size 1xJ. I want to construct a matrix D of size Kx3 listing every triplets (a,b,c) such that:

• a is the position in A of A(a).

• b is the position in B of B(b).

• A(a)-B(b) is an element of C.

• c is the position in C of A(a)-B(b).

• A(a) and B(b) are different from Inf, -Inf.

For example,

A=[-3 3 0 Inf -Inf];
B=[-2 2 0 Inf -Inf];
C=[Inf -Inf -1 1 0];
D=[1 1 3;   %-3-(-2)=-1
   2 2 4;   % 3-2=1
   3 3 5];  % 0-0=0

I would like this code to be efficient, because in my real example I have to repeat it many times.

This question relates to my previous question here, but now I'm looking for the positions of the elements.

CodePudding user response：

You can use combvec (or any number of alternatives) to get all pairings of indices a and b for the corresponding arrays A and B. Then it's simply a case of following your criteria

1. Find the differences
2. Check which differences are in C
3. Remove elements you don't care about

Like so:

% Generate all index pairings
D = combvec( 1:numel(A), 1:numel(B) ).';
% Calculate deltas
delta = A(D(:,1)) - B(D(:,2));
delta = delta(:); % make it a column
% Get delta index in C (0 if not present)
[~,D(:,3)] = ismember(delta,C);
% If A or B are inf then the delta is Inf or NaN, remove these
idxRemove = isinf(delta) | isnan(delta) | D(:,3) == 0;
D(idxRemove,:) = [];

For your example, this yields the expected results from the question.

You said that A and B are at most 7 elements long, so you have up to 49 pairings to check. This isn't too bad, but readers should be careful that the pairings can grow quickly for larger inputs.