How do I find the indices of a given array A1, *any* of whose values are practically equivalent to *any* of the values of a second array A2?

Question

By \"practically equivalent\", I mean that their distances are of order epsilon apart (or 0.000001). Equality in MATLAB often doesn\'t really work for long floating numbers.

Answer 1

You can get the answer by calculating distance between two vectors using MATLAB's pdist2 function.

dist=pdist2(A1,A2);
minDist=min(dist,[],2);
indices_A1=minDist<=0.000001;
desired_A1=A1(indices_A1);

Not tested, but should work.

Answer 2

Since you care about a distance from any element to any element, you can create a distance matrix from the vectorized matrices and probe that for the distance threshold. Example:

A = rand(10, 4); % (example) matrix A 
B = rand(3, 5);  % matrix B of different size 
minDist = 0.005; 

Solution: Repeat vectorized matrices, column- and row-wise to get same size matrices and apply matrix-based distance estimation:

Da = repmat(A(:), 1, length(B(:)));  % size 40 x 15
Db = repmat(B(:)', length(A(:)), 1); % size 40 x 15 
DD = Da - Db; 
indA = any(abs(DD) < minDist, 2); 

The use of any() will give you logical indices to any value of A that is close to any value of B). You can directly index/return the elements of A using indA.

The matrix DD (as @Shai also points out) can be equivalently estimated through bsxfun

DD = bsxfun(@minus, A(:), B(:)');

In addition: you can map from row-index (corresponding to A elements) back to matrix A indices using:

[iA, jA] = ind2sub(size(A), indA);

Assert/test that all the returned values are less than minDist,e.g. using:

for k = 1:length(iA); 
    d(k) = min(min(abs(A(iA(k), jA(k)) - B)));
end
all(d < minDist)

(tested in Octave 3.6.2)