geomm.free_energy module

geomm.free_energy.free_energy(weights, max_energy=None, zero_point_energy=1e-12, supermax_value=nan)

Perform a transformation of probability weights to free energies.

The free energy of probabilities is a transformation of -ln(p) where p is the properly normalized probability.

In addition to this simple transformation we set a maximum free energy (max_energy) and a mask value (supermax_value) for values greater than the max energy. This is to account for missing observations or extreme outliers. This can be disabled by setting max_energy to None.

Free energy values are relative to a zero-point energy, which in the absence of a theoretically determined value can be simply determined by the minimum value in the dataset. If the zero_point_energy value is given this simply fixes this minimum free energy to the zero-point energy so that the rest of the values have some meaningful value. Typically, we set this to something to close to but greater than 0. Because a 0 free energy is equivalent to a probability of 1.0, which would make the dataset non-normalized.

Parameters

• weights (arraylike of float) – The normalized weights to transform

• max_energy (float or None) –

  Sets a maximum value for free energies. Free energies larger

  than this will be replaced by the ‘supermax_value’. If None the masking is not performed.

  (Default = None)

• supermax_value (numpy scalar) –

  The value that replaces free energies that are larger than the

  max energy. Typically is a numpy NaN so as to omit the data.

  (Default = np.nan)

• zero_point_energy (float or None) –

  Free energies are relative and the minimum value will be set

  to this zero point energy. This is to avoid having 0 free energy values. If None this is not done.

  (Default = 1.0e-12)

Returns

free_energies – The free energy for each weight.

Return type

arraylike