hellingerDist.m

% Function to calculate Hellinger distance based on histograms
function distance = hellingerDist(x, y)

%     x = x(~isnan(x));
%     y = y(~isnan(y));

    % Return maximum distance if inputs are empty or invalid
    minV = min([x(:); y(:)]);
    maxV = max([x(:); y(:)]);
    if isempty(x) || isempty(y) || minV >= maxV
        distance = 1;
        return;
    end

    % Define number of bins and edges
    numBins = 10;
    edges = linspace(minV, maxV, numBins + 1);

    % Compute and normalize histograms
    histX = histcounts(x, edges);
    histX = histX./sum(histX);
    histY = histcounts(y, edges);
    histY = histY./sum(histY);
%     histX = histcounts(x, edges, 'Normalization','probability');
%     histY = histcounts(y, edges, 'Normalization', 'probability');

    % Compute Hellinger distance
    sqrtDiff = sqrt(histX) - sqrt(histY);
    distance = sqrt(sum(sqrtDiff.^2)) / sqrt(2);
end