Target Accuracy Requirements

The sensitivities and covariances can be also used for computing target accuracy requirements. Before looking for the requirements, it is necessary to provide the target values for the functionals as a dictionary. Here is an example how the values are defined.

tars = {'Eigenvalue' : 0.003,
        'beta-eff'   : 0.030,
        'lambda-eff' : 0.040}

Next, it is necessary to provide a list of sensitivities to be used in solving the optimization problem. Each instance relates to a single core model, and the $\texttt{tars}$ values are used for each functional of each model.

sensitivities = [sensitivities_1, sensitivities_2, sensitivities_3]

The following step is to call the $\texttt{tars()}$ method for getting an updated $\texttt{Covariances}$ instance. The first argument takes a list of sensitivities. The second one is the covariances that is going to be tweaked to achieve the target accuracies. Next argument takes the functional target accuracy requirements. defines the number of symmetric covariance matrices to be used in the optimization together with an additional number of channel-channel matrices that corresponds to the symmetric ones. That is why the final number of the changed matrices is larger than the number provided. The last argument of interest is , which defines the minimal achievable value of uncertainty to account limitations of measurement tools.

target_covariances = sauna.Analysis.tars(sensitivities, covariances, tars, number_of_reactions=5, lower_boundary=5e-3)

There are more advanced parameters to provide for the method: and . The first parameter takes one of the three values {'A', 'B', 'C'}, defining the relative cost for each reaction. The values are set in accordance with the WPEC/SG26 analysis though the bottom was only intended for $(n,n')$ there, the implementation here relates all the other reactions that are not mentioned above. The values are provided below, and the default value is 'A'.

Nuclide	Reaction	A	B	C
		1	1	1
Fuel		1	2	2
Non-Fuel		1	1	1
The others		1	1	1
The others	The others	1	3	10

The second parameter allows one to set the energy dependence for the cost parameter. This parameter takes a list of values with the number equal to the number of energy groups. The values are provided from the lower energies to the higher energies. How these two types of parameters are used is provided below.

weights = [6.9, 9.2, 14.4, 19.5, 7.1, 2.4, 1.0][::-1]
target_covariances = sauna.Analysis.tars(sensitivities,
                                         covariances,
                                         tars,
                                         number_of_reactions=20,
                                         lower_boundary=5e-3,
                                         cost_type = 'B',
                                         energy_costs = weights)