pyesmda.compute_ensemble_average_normalized_objective_function¶
- pyesmda.compute_ensemble_average_normalized_objective_function(pred_ensemble: numpy.ndarray[Any, numpy.dtype[numpy.float64]], obs: numpy.ndarray[Any, numpy.dtype[numpy.float64]], cov_obs: Union[numpy.ndarray[Any, numpy.dtype[numpy.float64]], scipy.sparse._csr.csr_matrix]) float [source]¶
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