Localization matrix Q created using PetscDALETKFGetLocalizationMatrix
PetscDA Object: 1 MPI process
  type: letkf
  State size: 160
  Observation size: 40
  Ensemble size: 5
  Assembled: true
  Inflation: 1.
  Square root type: eigen
  Local analysis: CPU
  Local observations per vertex: 7
  GPU batch size: auto
  Localization matrix: set
Shallow Water [L]ETKF Example
============================
  Test case             : Traveling wave
  Flux scheme           : Rusanov (1st order)
  State dimension       : 160 (80 grid points x 2 DOF)
  Observation dimension : 40
  Ensemble size         : 5
  Domain length (L)     : 80.0000
  Gravitational const   : 9.8100
  Time step (dt)        : 0.0200
  Total steps           : 10
  Observation frequency : 2
  Observation noise std : 0.030
  Random seed           : 12345
  Localization          : None/Global (7 obs per vertex)

Step    0, time  0.000  RMSE_forecast 0.00000  RMSE_analysis 0.00000 [initial]
Step   10, time  0.200  RMSE_forecast 0.00997  RMSE_analysis 0.01006

Statistics (10 steps):
==================================================
  Mean RMSE (forecast) : 0.00996
  Mean RMSE (analysis) : 0.01089
  Observations used    : 5

