I understand that the goal is to create a function that performs linear interpolation for a fitness equation with two information states, considering all possible combinations of two integers that are closest to the given floating-point numbers. The approach is as follows:
- Identify the closest integers around the given floating-point numbers for both ‘j’ and ‘k’.
- Calculate the probabilities associated with each combination of those integers.
- Evaluate the fitness function ‘Ft(x, j, k, t)’ for each combination.
- Sum up these evaluations weighted by their respective probabilities.
Here is a MATLAB code implementing the above approach:
function fitness = interpolateFitness(Ft, x, j, k, t)
% Find the floor and ceiling for j and k
j_floor = floor(j);
j_ceil = ceil(j);
k_floor = floor(k);
k_ceil = ceil(k);
% Calculate probabilities based on the distance from the actual values
p_j_floor = j_ceil - j;
p_j_ceil = j - j_floor;
p_k_floor = k_ceil - k;
p_k_ceil = k - k_floor;
% Calculate the weighted fitness for each combination
fitness = 0;
fitness = fitness + p_j_floor * p_k_floor * Ft(x, j_floor, k_floor, t);
fitness = fitness + p_j_floor * p_k_ceil * Ft(x, j_floor, k_ceil, t);
fitness = fitness + p_j_ceil * p_k_floor * Ft(x, j_ceil, k_floor, t);
fitness = fitness + p_j_ceil * p_k_ceil * Ft(x, j_ceil, k_ceil, t);
end
NOTE: The above function calculates the interpolated fitness by considering the probabilities of ‘j’ and ‘k’ being at their floor or ceiling values. These probabilities are uses as weights for the fitness values calculated at these integer points around ‘j’ and ‘k’.
Hope it helps!
