PetscDALETKFGetLocalizationMatrix#

Compute localization weight matrix for LETKF [move to ml/da/interface]

Synopsis#

PetscErrorCode PetscDALETKFGetLocalizationMatrix(const PetscInt n_obs_vertex, const PetscInt n_dof, Vec Vecxyz[3], PetscReal bd[3], Mat H, Mat *Q)

Collective

Input Parameters#

n_obs_vertex - Number of observations to localize to per vertex
n_dof - Number of degrees of freedom
Vecxyz - Array of vectors containing the vertex coordinates
bd - Array of boundary extents per dimension (used for periodicity)
H - Observation operator matrix

Output Parameter#

Q - Localization weight matrix (sparse, AIJ format)

Notes#

The output matrix Q has dimensions (n_vert_global x n_obs_global) where n_vert_global is the number of vertices in the DMPlex. Each row contains exactly n_obs_vertex non-zero entries corresponding to the nearest observations, weighted by the Gaspari-Cohn fifth-order piecewise rational function.

The observation locations are computed as H * V where V is the vector of vertex coordinates. The localization weights ensure smooth tapering of observation influence with distance.

Kokkos is required for this routine.