gemseo_umdo / statistics / multilevel / mlmc_mlcv / pilots

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pilot module

The base pilot class for the MLMC-MLCV algorithm.

class gemseo_umdo.statistics.multilevel.mlmc_mlcv.pilots.pilot.MLMCMLCVPilot(sampling_ratios, costs)[source]

Bases: Pilot

The base pilot class for the MLMC-MLCV algorithm.

See also

El Amri et al., Algo. 1, Multilevel Surrogate-based Control Variates, 2023.

Parameters:

  • sampling_ratios (NDArray[float]) – The sampling ratios $r_0,ldots,r_L$; the sampling ratio $r_ell$ is the factor by which $n_ell$ is increased between two sampling steps on the level $ell$.

  • costs (NDArray[float]) – The unit sampling costs of each level of the telescopic sum. Namely, $(mathcal{C}_{ell-1}+mathcal{C}_ell)_{ellin{0,ldots,L}}$ with $mathcal{C}_{-1}=0$.

V_l: NDArray[float]

The terms variances $mathcal{V}_0,ldots,mathcal{V}_L$.