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

float