pyesmda.compute_ensemble_average_normalized_objective_function

pyesmda.compute_ensemble_average_normalized_objective_function(pred_ensemble: ndarray[Any, dtype[float64]], obs: ndarray[Any, dtype[float64]], cov_obs: Union[ndarray[Any, dtype[float64]], csr_matrix]) → float

Compute the ensemble average normalized objective function.

\[\overline{O}_{N_{d}} = \frac{1}{N_{e}} \sum_{j=1}^{N_{e}} O_{N_{d}, j}\]

\[\begin{split}\textrm{with } O_{N_{d}, j} = \frac{1}{2N_{d}} \sum_{j=1}^{N_{e}}\left(d^{l}_{j} - {d_{obs}} \right)^{T}C_{D}^{-1}\left(d^{l}_{j} - {d_{obs}} \right)\\\end{split}\]

Parameters:

• pred_ensemble (NDArrayFloat) – Vector of predicted values.

• obs (NDArrayFloat) – Vector of observed values.

• cov_obs (Union[NDArrayFloat, csr_matrix]) – Covariance matrix of observed data measurement errors with dimensions (\(N_{obs}\), \(N_{obs}\)). Also denoted \(R\). This can be a sparse matrix.

Returns:

The objective function.

Return type:

float