pyesmda.compute_normalized_objective_function

pyesmda.compute_normalized_objective_function(pred: ndarray[Any, dtype[float64]], obs: ndarray[Any, dtype[float64]], cov_obs: ndarray[Any, dtype[float64]]) → float

Compute the normalized objective function for a given member \(j\).

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

Parameters:

• pred (npt.NDArray[np.float64]) – Vector of predicted values.

• obs (npt.NDArray[np.float64]) – Vector of observed values.

• cov_obs (npt.NDArray[np.float64]) – Covariance matrix of observed data measurement errors with dimensions (\(N_{obs}\), \(N_{obs}\)). Also denoted \(R\).

Returns:

The objective function.

Return type:

float