PetscDAEnsembleApplySqrtTInverse#

Apply T^{-1/2} to a matrix U [Alg 6.4 line 9]

Synopsis#

Collective

Input Parameters#

  • da - the PetscDA context

  • U - 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
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Index of all manual pages