# Utilities¶

Utility functions.

 common_working_graph(graph0, graph1) Creates a graph using the common nodes and edges of two given graphs.
 coupling_groups(hardware_graph) Generate groups of couplers for which a limit on total coupling applies for each group.

## Temperature Utilities¶

The following effective temperature estimators are provided:

• Maximum pseudo-likelihood is an efficient estimator for the temperature describing a classical Boltzmann distribution P(x) = exp(-H(x)/T)/Z(T) given samples from that distribution, where H(x) is the classical energy function. The following links describe features of the estimator in application to equilibrium distribution drawn from binary quadratic models and non-equilibrium distributions generated by annealing: https://www.jstor.org/stable/25464568 https://doi.org/10.3389/fict.2016.00023

• An effective temperature can be inferred assuming freeze-out during the anneal at s=t/t_a, an annealing schedule, and a device physical temperature. Necessary device-specific properties are published for online solvers: https://docs.dwavesys.com/docs/latest/doc_physical_properties.html

 effective_field(bqm[, samples, ...]) Returns the effective field for all variables and all samples. maximum_pseudolikelihood_temperature([bqm, ...]) Returns a sampling-based temperature estimate. freezeout_effective_temperature(freezeout_B, ...) Provides an effective temperature as a function of freezeout information. fast_effective_temperature([sampler, ...]) Provides an estimate to the effective temperature, $$T$$, of a sampler.
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