allocate_samples_mlmc

pyapprox.control_variate_monte_carlo.allocate_samples_mlmc(cov, costs, target_cost, standardize=True)

Determine the samples to be allocated to each model when using MLMC

Parameters

covnp.ndarray (nmodels,nmodels)

The covariance C between each of the models. The highest fidelity model is the first model, i.e its variance is cov[0,0]

costsnp.ndarray (nmodels)

The relative costs of evaluating each model

target_costfloat

The total cost budget

standardizeboolean

If true make sure that nhf_samples is an integer and that nhf_samples*nsamples_ratios are integers. False is only ever used for testing.

Returns

nhf_samplesinteger

The number of samples of the high fidelity model

nsample_ratiosnp.ndarray (nmodels-1)

The sample ratios r used to specify the number of samples of the lower fidelity models, e.g. N_i = r_i*nhf_samples, i=1,…,nmodels-1. For model i>0 nsample_ratio*nhf_samples equals the number of samples in the two different discrepancies involving the ith model.

log10_variancefloat

The base 10 logarithm of the variance of the estimator