PetscDAEnsembleApplySqrtTInverse#

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

Synopsis#

PetscErrorCode PetscDAEnsembleApplySqrtTInverse(PetscDA da, Mat U, Mat Y)

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 symmetric inverse square root of \(T = (1/\rho) I + S^T * S\) (with \(\rho\) the inflation factor) using the stored eigendecomposition: \(Y = V D^{-1/2} V^T U\). The result satisfies \(Y^T * T * Y = U^T * U\), preserving the metric.

Level#

advanced

Location#

src/ml/da/impls/ensemble/daensemble.c

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