py__prodrinva_pdaf()

Provide \(\mathbf{R}^{-1} \times \mathbf{A}\).

Here, one should compute \(\mathbf{R}^{-1} \times \mathbf{A}\) where \(\mathbf{R}\) is observation error covariance matrix. The matrix \(\mathbf{A}\) depends on the filter algorithm. In ESTKF, \(\mathbf{R}\) can is ensemble perturbation in observation space.

Parameters

stepint

Current time step

dim_obs_pint

Dimension of observation vector

rank: int

Rank of the matrix A (second dimension of A) This is ensemble size for ETKF and ensemble size - 1 for ESTKF.

obs_p: np.ndarray[np.float, dim=1]

Observation vector. shape: (dim_obs_p,)

a_p: np.ndarray[np.float, dim=2]

Input matrix A. shape: (dim_obs_p, rank)

c_p: np.ndarray[np.float, dim=2]

Output matrix \(\mathbf{C} = \mathbf{R}^{-1} \times \mathbf{A}\). shape: (dim_obs_p, rank)

Returns

c_p: np.ndarray[np.float64, dim=2]

Output matrix \(\mathbf{C} = \mathbf{R}^{-1} \times \mathbf{A}\). shape: (dim_obs_p, rank)