def test_estimate_for_monte_carlo(num_models, num_samples,
mc_sample_allocation):
mc_outputs = [np.empty(0) for _ in range(num_models)]
mc_outputs[0] = np.random.random(num_samples)
covariance = np.eye(num_models)
est = Estimator(mc_sample_allocation, covariance)
expected_estimate = np.mean(mc_outputs[0])
assert est.get_estimate(mc_outputs) == pytest.approx(expected_estimate)
def test_two_model_estimate():
compressed_allocation = np.array([[1, 1, 1, 1], [5, 1, 1, 0],
[10, 0, 0, 1]])
allocation = MLMCSampleAllocation(compressed_allocation)
model_outputs = [np.arange(1, 7), np.arange(1, 17)]
covariance = np.array([[1, 0.5], [0.5, 1]])
est = Estimator(allocation, covariance)
expected_estimate = 10.545454545454547
assert est.get_estimate(model_outputs) == pytest.approx(expected_estimate)
def test_three_model_approximate_variance():
compressed_allocation = np.array([[1, 1, 1, 1, 0, 0], [5, 0, 1, 1, 1, 1],
[10, 0, 0, 0, 1, 1]])
sample_allocation = MLMCSampleAllocation(compressed_allocation)
covariance = np.array([[1, 0.5, 0.25], [0.5, 1, 0.5], [0.25, 0.5, 1]])
est = Estimator(sample_allocation, covariance)
assert est.approximate_variance == pytest.approx(1)
def test_two_model_approximate_variance():
compressed_allocation = np.array([[3, 1, 1, 1], [57, 0, 0, 1]], dtype=int)
allocation = MLMCSampleAllocation(compressed_allocation)
covariance = np.array([[1, 0.5], [0.5, 1]])
est = Estimator(allocation, covariance)
assert est.approximate_variance == pytest.approx(1 / 3.)
def _assert_opt_result_is_consistent(covariance, model_costs, opt_result):
sample_allocation = opt_result.allocation
estimator = Estimator(sample_allocation, covariance)
estimator_approx_variance = estimator.approximate_variance
optimizer_approx_variance = opt_result.variance
assert estimator_approx_variance \
== pytest.approx(optimizer_approx_variance)
actual_cost = _calculate_costs_from_allocation(opt_result.allocation,
model_costs)
assert opt_result.cost == pytest.approx(actual_cost)
def test_decreases_variance(two_model_compressed_allocation,
two_model_costs):
# Ignore warning regarding variance in BaseSampleAllocation.
warnings.filterwarnings(action="ignore", category=UserWarning)
# This allocation and model costs have a total cost of 200.
covariance = np.array([[1., 0.3],
[0.3, 1.]])
target_cost = 215
base_allocation = MLMCSampleAllocation(two_model_compressed_allocation)
base_estimate = Estimator(base_allocation, covariance)
base_variance = base_estimate._get_approximate_variance()
adjusted_allocation = adjust_sample_allocation_to_cost(base_allocation,
target_cost,
two_model_costs,
covariance)
adjusted_estimate = Estimator(adjusted_allocation, covariance)
adjusted_variance = adjusted_estimate._get_approximate_variance()
assert adjusted_variance < base_variance
def _get_estimator_variance(sample_allocation, covariance):
estimator = Estimator(sample_allocation, covariance)
return estimator._get_approximate_variance()