CheckEnergy

class CheckEnergy : public feasst::ModifyUpdateOnly

Check if the running energy from criteria is equivalent, within tolerance, to an (unoptimized) calculation over the entire configuration.

The origin of the energy deviation is different rounding at the level of numerical precision due to adding up the energy terms in different orders. For example, when an entire configuration energy is calculated, each pairwise energy term may be added in a different order than the sum of the contribution of each molecule. And each Monte Carlo trial may only calculate the energy change of one randomly chosen molecule.

The energy check tolerance parameter is extensive, so it may be reasonable if the error happens when you increase the size. Thus, the tolerance parameter may need to be adjusted with system size. It is not very surprising to see a difference in the 6th or 7th decimal place in some cases.

The size of the deviation can depend not only on the system size but the potential function and the number of trials between each check. For example, if the system undergoes a random walk deviation of size delta, it may deviate by the square root of the number of trials, where the size delta may be related to the number of interaction sites.

An alternative metric is the number of decimal places. In practice, this is implemented as follows for two energies U1 and U2.

\(\frac{|U_1-U_2|}{\mathrm{max}(|U_1|, |U_2|)} < 10^{-decimal\_places}\)

For this alternative metric, special consideration is made for small or near zero values of energy. In this special case, the check passes as long as

\(\mathrm{max}(|U_1|, |U_2|) < 10^{-decimal\_places}\)

Otherwise, the differences about zero to numerical precision would almost always fail the test.

Although this class does not change the System beyond the specified tolerance, the energy is recomputed and therefore the class is a Modify, not an Analyze.

Public Functions

void update(MonteCarlo *mc)

Perform update.

Arguments

• tolerance: absolute difference between running energy and recomputed energy (default: 1e-10).

• decimal_places: If decimal places > 0 (default: 0), ignore the tolerance parameter and instead check if the difference between the two energies exceeds is within a the given number of decimal places.

• Stepper arguments.