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#' @export
print.mlmc.test <- function(x, ...) {
with(x, {
cat("\n")
cat("**********************************************************\n")
cat("*** Convergence tests, kurtosis, telescoping sum check ***\n")
cat("*** using N =", N, "samples ", paste0(rep(' ', 21 - nchar(as.character(N))), collapse = ''), " ***\n")
cat("**********************************************************\n")
cat("\n l ave(Pf-Pc) ave(Pf) var(Pf-Pc) var(Pf)")
cat(" kurtosis check cost\n-------------------------")
cat("--------------------------------------------------------------\n")
for(l in 0:L) {
cat(sprintf("%2d %8.4e %8.4e %8.4e %8.4e %8.4e %8.4e %8.4e \n",
l, del1[l+1], del2[l+1], var1[l+1], var2[l+1], kur1[l+1], chk1[l+1], cost[l+1]))
}
if( kur1[length(kur1)] > 100.0 ) {
cat(sprintf("\n WARNING: kurtosis on finest level = %f \n", kur1[length(kur1)]))
cat(" indicates MLMC correction dominated by a few rare paths; \n")
cat(" for information on the connection to variance of sample variances,\n")
cat(" see http://mathworld.wolfram.com/SampleVarianceDistribution.html\n\n")
}
if( max(chk1) > 1.0 ) {
cat(sprintf("\n WARNING: maximum consistency error = %f \n", max(chk1)))
cat(" indicates identity E[Pf-Pc] = E[Pf] - E[Pc] not satisfied; \n")
cat(" to be more certain, re-run mlmc.test with larger N \n\n")
}
cat("\n******************************************************\n")
cat("*** Linear regression estimates of MLMC parameters ***\n")
cat("******************************************************\n")
cat(sprintf("\n alpha = %f (exponent for MLMC weak convergence)\n", alpha))
cat(sprintf(" beta = %f (exponent for MLMC variance) \n", beta))
cat(sprintf(" gamma = %f (exponent for MLMC cost) \n", gamma))
cat("\n")
cat("***************************** \n")
cat("*** MLMC complexity tests *** \n")
cat("***************************** \n\n")
cat(" eps value mlmc_cost std_cost savings N_l \n")
cat("----------------------------------------------------------- \n")
for(i in 1:length(eps.v)) {
cat(sprintf("%.4f %.4e %.3e %.3e %7.2f ",
eps.v[i], P[i], mlmc_cost[i], std_cost[i], std_cost[i]/mlmc_cost[i]))
cat(sprintf("%9d", Nl[[i]]))
cat("\n")
}
cat("\n")
})
}
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