Reduced Potential Definition in pymbar's FES Implementation

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Hello to all the community, I am writing to you because I have been using the FES implementation of pymbar to calculate the PMF from an umbrella sampling, but I have encountered some issues with the definition of the reduced potential.

The documentation explains that the reduced potential, or u_kn, used to initialize the FES object, is an array of shape K,N where K is the number of simulations or states and N is the number of configurations of each state. However, in the umbrella sampling example code on GitHub, the u_kln matrix, which is an array of shape K,K,N, is used to initialize the FES object. I am wondering why this matrix is used instead.

Additionally, to generate the PMF, the u_kn matrix is used, but the documentation mentions that the reduced potential of one state can be used. Could you help me understand these discrepancies?