PetscDAEnsembleApplySqrtTInverse#
Apply T^{-1/2} to a matrix U [Alg 6.4 line 9]
Synopsis#
Collective
Input Parameters#
da - the
PetscDAcontextU - input matrix (usually Identity, but can be general)
Output Parameter#
Y - output matrix Y = T^{-1/2} * U
Notes#
This function applies the inverse square root of T = I + S^T * S using the stored factorization.
For CHOLESKY mode: Computes Y = L^{-T} U
For EIGEN mode: Computes Y = V D^{-1/2} V^T U
Both results satisfy Y^T * T * Y = U^T * U, preserving the metric.
See Also#
PetscDA: Data Assimilation, PetscDA, PETSCDAETKF, PETSCDALETKF, PetscDAEnsembleTFactor(), PetscDAEnsembleApplyTInverse()
Level#
advanced
Location#
src/ml/da/impls/ensemble/daensemble.c
Index of all PetscDA routines
Table of Contents for all manual pages
Index of all manual pages