write a function that calculates the total variation distance of two probability distributions in matlab

Here's an implementation of a function in MATLAB that calculates the total variation distance of two probability distributions:

main.m
function TVD = totalVariationDistance(P, Q)
% Calculates the total variation distance of two probability distributions
% P and Q.

% Check that P and Q are valid probability distributions.
if any(P < 0) || any(Q < 0) || abs(sum(P) - 1) > eps || abs(sum(Q) - 1) > eps
    error('Invalid probability distribution.');
end

% Calculate the total variation distance.
TVD = 0.5 * sum(abs(P - Q));

end
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The function takes in two probability distributions P and Q, and checks that they are valid probability distributions (i.e., they contain only non-negative values and their sum is equal to 1 within a small tolerance eps).

If the distributions are valid, the function calculates the total variation distance as half the sum of the absolute differences between their corresponding elements. The function returns the total variation distance as TVD.