# dimod.utilities.ising_energy#

ising_energy(sample, h, J, offset=0.0)[source]#

Calculate the energy for the specified sample of an Ising model.

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

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

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

Parameters:
• sample (dict[variable, spin]) – Sample for a binary quadratic model as a dict of form {v: spin, …}, where keys are variables of the model and values are spins (either -1 or 1).

• h (dict[variable, bias]) – Linear biases as a dict of the form {v: bias, …}, where keys are variables of the model and values are biases.

• J (dict[(variable, variable), bias]) – Quadratic biases as a dict of the form {(u, v): bias, …}, where keys are 2-tuples of variables of the model and values are quadratic biases associated with the pair of variables (the interaction).

• offset (numeric, optional, default=0) – Constant offset to be applied to the energy. Default 0.

Returns:

The induced energy.

Return type:

float

Notes

No input checking is performed.

Examples

This example calculates the energy of a sample representing two down spins for an Ising model of two variables that have positive biases of value 1 and are positively coupled with an interaction of value 1.

>>> sample = {1: -1, 2: -1}
>>> h = {1: 1, 2: 1}
>>> J = {(1, 2): 1}
>>> dimod.ising_energy(sample, h, J, 0.5)
-0.5


References

Ising model on Wikipedia