def test_ACVMC_objective_jacobian(self):
cov = np.asarray([[1.00, 0.50, 0.25], [0.50, 1.00, 0.50],
[0.25, 0.50, 4.00]])
costs = [4, 2, 1]
target_cost = 20
nhf_samples, nsample_ratios = pya.allocate_samples_mlmc(
cov, costs, target_cost)[:2]
estimator = ACVMF(cov, costs)
errors = pya.check_gradients(
partial(acv_sample_allocation_objective, estimator),
partial(acv_sample_allocation_jacobian_torch, estimator),
nsample_ratios[:, np.newaxis],
disp=False)
#print(errors.min())
assert errors.min() < 1e-8
def test_mlmc_sample_allocation(self):
# The following will give mlmc with unit variance
# and discrepancy variances 1,4,4
target_cost = 81
cov = np.asarray([[1.00,0.50,0.25],
[0.50,1.00,0.50],
[0.25,0.50,4.00]])
# ensure cov is positive definite
np.linalg.cholesky(cov)
#print(np.linalg.inv(cov))
costs = [6,3,1]
nmodels = len(costs)
nhf_samples,nsample_ratios, log10_var = pya.allocate_samples_mlmc(
cov, costs, target_cost)
assert np.allclose(10**log10_var,1)
nsamples = np.concatenate([[1],nsample_ratios])*nhf_samples
lamda = 9
nsamples_discrepancy = 9*np.sqrt(np.asarray([1/(6+3),4/(3+1),4]))
nsamples_true = [
nsamples_discrepancy[0],nsamples_discrepancy[:2].sum(),
nsamples_discrepancy[1:3].sum()]
assert np.allclose(nsamples,nsamples_true)
short_column_model = ShortColumnModelEnsemble()
model_ensemble = pya.ModelEnsemble(
[short_column_model.m0,short_column_model.m1,short_column_model.m2])
costs = np.asarray([100, 50, 5])
target_cost = int(1e4)
idx = [0,1,2]
cov = short_column_model.get_covariance_matrix()[np.ix_(idx,idx)]
# generate pilot samples to estimate correlation
# npilot_samples = int(1e4)
# cov = pya.estimate_model_ensemble_covariance(
# npilot_samples,short_column_model.generate_samples,model_ensemble)[0]
# define the sample allocation
nhf_samples,nsample_ratios = pya.allocate_samples_mlmc(
cov, costs, target_cost)[:2]
# generate sample sets
samples,values =pya.generate_samples_and_values_mlmc(
nhf_samples,nsample_ratios,model_ensemble,
short_column_model.generate_samples)
# compute mean using only hf data
hf_mean = values[0][0].mean()
# compute mlmc control variate weights
eta = pya.get_mlmc_control_variate_weights(cov.shape[0])
# compute MLMC mean
mlmc_mean = pya.compute_approximate_control_variate_mean_estimate(eta,values)
# get the true mean of the high-fidelity model
true_mean = short_column_model.get_means()[0]
print('MLMC error',abs(mlmc_mean-true_mean))
print('MC error',abs(hf_mean-true_mean))