dimod.BinaryQuadraticModel.energy

BinaryQuadraticModel.energy(sample)

Determine the energy of the specified sample of a binary quadratic model.

Energy of a sample for a binary quadratic model is defined as a sum, offset by the constant energy offset associated with the binary quadratic model, of the sample multipled by the linear bias of the variable and all its interactions; that is,

\[E(\mathbf{s}) = \sum_v h_v s_v + \sum_{u,v} J_{u,v} s_u s_v + c\]

where \(s_v\) is the sample, \(h_v\) is the linear bias, \(J_{u,v}\) the quadratic bias (interactions), and \(c\) the energy offset.

Code for the energy calculation might look like the following:

energy = model.offset  # doctest: +SKIP
for v in model:  # doctest: +SKIP
    energy += model.linear[v] * sample[v]
for u, v in model.quadratic:  # doctest: +SKIP
    energy += model.quadratic[(u, v)] * sample[u] * sample[v]

Parameters:sample (dict) – Sample for which to calculate the energy, formatted as a dict where keys are variables and values are the value associated with each variable. Returns:Energy for the sample. Return type:float

Examples

This example creates a binary quadratic model and returns the energies for a couple of samples.

>>> import dimod
>>> bqm = dimod.BinaryQuadraticModel({1: 1, 2: 1}, {(1, 2): 1}, 0.5, dimod.SPIN)
>>> bqm.energy({1: -1, 2: -1})
-0.5
>>> bqm.energy({1: 1, 2: 1})
3.5