API Reference

Primary data structure of the library. Holds all the information needed to run all of the functions provided. The constructor provided for this will precompute all the required datasets to ensure fastest interpolation. The fields are

• observables::Vector{Symbol}: A vector of symbols comprising of all the observables of the system. For instance, for an Ising system, this will be the internal energy and magnetization. It is mandatory that the column for internal energy be labelled with :U. Magnetization can be labelled whatever, so for instance a valid observables vector is Symbol[:U, :M].
• parameter_values::Vector{pType}: List of parameters at which the system was simulated. For instnace, this can be the temperatures at which MCMC simulations were done.
• simulated_histograms::Vector{DataFrame}: Flattened vector of all simulated histograms. The DataFrame must have a column for internal energy labelled :U and the frequency of occurance labelled :f. Other columns can be named whatever.
• observable_ranges::Vector{orType}: Vector of the ranges spanned by the observables.
• marginal_energy_histograms::Vector{ehType}: Dictionary of marginal energy histograms, mapping energy to frequency of occurance.
• marginal_energy_histiters::Vector{ehiType}: Array of collected pairs of marginal_energy_histograms. Collected they take less memory.
• nEbins::Int64: Number of energy bins sampled in total.
• nbins::Int64: Number of histogram bins in total.
• free_energies::Vector{pType}: Current best guess of free energies.
• tuple_iterators::{ntiType}: Named tuple iterators from the histograms for fast iterations.

Iterate the free energy multihistogram equation until the error is below a threshold. Error is calculated as.

\[\Delta^2 = \sum_{i} \left(\frac{F^(m)_i - F^(m-1)_i}{F^(m-1)_i}\right)^2\]

Inputs are

• data::MultihistogramData: Multihistogram dataset.
• rtol (default 1e-10): Tolerance until the error is minimized. Value of $\Delta$.
• logsum (default false): Use the logsum method. Recommended for systems with energies larger than 300.

One iteration of the multihistogram (wham) free energy equations. Inputs are

• u: One dimensional array-like type. Guess for the free energies.
• data::MultihistogramData: Dataset for Multihistogram interpolation.

One iteration of the multihistogram (wham) free energy equations with the logsum trick. Inputs are

• u: One dimensional array-like type. Guess for the free energies.
• data::MultihistogramData: Dataset for Multihistogram interpolation.