How to find 3 elements from multiple vectors that meet a given condition 3 element condition?

I have several (more than 3) 1xN vectors. I am trying to find a column number i, and 3 vectors X, Y, Z, which satisfy the condition X_i -Y_i = Y_i -Z_i. An example of what I am trying to do is shown below:

W = [1 2 3];
X = [0 2 4];
Y = [1 3 5];
Z = [1 4 9];

%[i, A, B, C] = searchfunction(W,X,Y,Z);

find(W - X == X - Y)
find(W - Y == Y - Z)
find(X - Y == Y - Z)

I would like the search function to find the solutions:

i = 1, for W, Y, Z => because W(1) - Y(1) = Y(1) - Z(1)

i = 2, for W, Y, Z => because W(2) - Y(2) = Y(2) - Z(2)

i = 2, for X, Y, Z => because X(2) - Y(2) = Y(2) - Z(2)

i =3, for W, X, Y => because W(3) - X(3) = X(3) - Y(3)

My code above does this, but if I have N vectors I have to write N-1 find statements to get all the answers. I would like to have a more compact and efficient way of finding the solutions.

Answer 1

[Paras Gupta]

Hi,

It is my understanding that you are able to determine the solution using the “find” function but require a way to avoid manually writing down the code for iterating over the possible combination of vectors.

The following code illustrates one possible way to efficiently achieve the same.

W = [1 2 3]; % Vector 1
X = [0 2 4]; % Vector 2
Y = [1 3 5]; % Vector 3
Z = [1 4 9]; % Vector 4

%% Concatenate all vectors
concatTemp = [W;X;Y;Z];
n = size(concatTemp);

%% Find all combinations of 3 rows in the concatenated matrix
c = nchoosek(1:n,3);

%% For each combination, find the solution
for k=1:size(c)

    vectors = c(k, :);
    A = concatTemp(vectors(1), :);
    B = concatTemp(vectors(2), :);
    C = concatTemp(vectors(3), :);
    i = find( A - B == B - C);

    if isempty(i)
        i = "No Solution";
    end
        
    disp(['For vectors, ', num2str(vectors),', the solution, i = ', num2str(i)])
end

For vectors, 1  2  3, the solution, i = 3
For vectors, 1  2  4, the solution, i = No Solution
For vectors, 1  3  4, the solution, i = 1  2
For vectors, 2  3  4, the solution, i = 2

Please refer to nchoosek and Colon documentation for more information on computing the combinations and indexing a matrix respectively.

Hope it helps!