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36 * \brief Implements internal functionality for expanded ensemble
38 * \author Pascal Merz <pascal.merz@me.com>
39 * \author Michael Shirts <michael.shirts@colorado.edu>
40 * \ingroup module_mdlib
44 #include "expanded_internal.h"
48 #include "gromacs/mdtypes/md_enums.h"
49 #include "gromacs/utility/exceptions.h"
53 real calculateAcceptanceWeight(LambdaWeightCalculation calculationMode, real lambdaEnergyDifference)
55 if (calculationMode == LambdaWeightCalculation::Barker
56 || calculationMode == LambdaWeightCalculation::Minvar)
58 /* Barker acceptance rule forumula is used for accumulation of probability for
59 * both the Barker variant of the weight accumulation algorithm and the
60 * minimum variance variant of the weight accumulation algorithm.
62 * Barker acceptance rule for a jump from state i -> j is defined as
63 * exp(-E_i)/exp(-Ei)+exp(-Ej) = 1 / (1 + exp(dE_ij))
64 * where dE_ij is the potential energy difference between the two states
65 * plus a constant offset that can be removed at the end for numerical stability.
66 * dE_ij = FE_j - FE_i + offset
67 * Numerically, this computation can be unstable if dE gets large. (See #3304)
68 * To avoid numerical instability, we're calculating it as
69 * 1 / (1 + exp(dE_ij)) (if dE < 0)
70 * exp(-dE_ij) / (exp(-dE_ij) + 1) (if dE > 0)
72 if (lambdaEnergyDifference < 0)
74 return 1.0 / (1.0 + std::exp(lambdaEnergyDifference));
78 return std::exp(-lambdaEnergyDifference) / (1.0 + std::exp(-lambdaEnergyDifference));
81 else if (calculationMode == LambdaWeightCalculation::Metropolis)
83 /* Metropolis acceptance rule for a jump from state i -> j is defined as
85 * exp(-dE_ij) (if dE_ij >= 0)
86 * where dE_ij is the potential energy difference between the two states
87 * plus a free energy offset that can be subtracted off later:
88 * dE_ij = FE_j - FE_i + offset
90 if (lambdaEnergyDifference < 0)
96 return std::exp(-lambdaEnergyDifference);
100 GMX_THROW(NotImplementedError("Unknown acceptance calculation mode"));