def initialize_component_surrogates(self, component_options):
"""
Initialize a surrogate of each system component.
Parameters
----------
component_options : iterable
List of dictionary of options containing the arguments necessary to
initialize each surrogate
See documentation of
:func:`pyapprox.approximate.adaptive_approximate_sparse_grid`
"""
# self.random_samples_for_refinement_test = \
# generate_independent_random_samples(
# self.variables, self.nrefinement_samples)
marginal_icdfs = [v.ppf for v in self.variables.all_variables()]
self.random_samples_for_refinement_test = \
transformed_halton_sequence(
marginal_icdfs, len(marginal_icdfs), self.nrefinement_samples)
surr_graph = self.surrogate_network.graph
functions = []
for nid in surr_graph.nodes:
options = component_options[nid]
functions.append(
self.initialize_surrogate(surr_graph.nodes[nid], **options))
self.surrogate_network.set_functions(functions)
# Add first index of each variable to active set of respective grid
self.component_output_ranges = []
for nid in surr_graph.nodes:
if self.verbose > 0:
print('------------------------------------')
print(f'Refining component {surr_graph.nodes[nid]["label"]}')
surr_graph.nodes[nid]['functions'].refine()
if self.verbose > 0:
print('------------------------------------')
def generate_samples(num_samples):
from pyapprox.low_discrepancy_sequences import \
transformed_halton_sequence
samples = transformed_halton_sequence(None, num_vars, num_samples)
samples = samples*2.-1.
return samples
def plot_lognormal_example_exact_quantities(
num_samples=int(2e5), plot=False, mu=0, sigma=1):
num_vars = 1
if plot:
assert num_samples <= 1e5
else:
assert num_samples >= 1e4
f, f_cdf, f_pdf, VaR, CVaR, ssd, ssd_disutil = \
get_lognormal_example_exact_quantities(mu, sigma)
from pyapprox.low_discrepancy_sequences import transformed_halton_sequence
#samples = np.random.normal(mu,sigma,(num_vars,num_samples))
#values = f(samples)[:,0]
samples = transformed_halton_sequence(
[partial(stats.norm.ppf, loc=mu, scale=sigma)], num_vars, num_samples)
values = f(samples)[:, 0]
fig, axs = plt.subplots(1, 6, sharey=False, figsize=(16, 6))
from pyapprox.density import EmpiricalCDF
if plot:
ygrid = np.linspace(-1, 5, 100)
#ecdf = EmpiricalCDF(values)
# axs[0].plot(ygrid,ecdf(ygrid),'-')
axs[0].plot(ygrid, f_cdf(ygrid), '--')
# axs[0].set_xlim(ygrid.min(),ygrid.max())
axs[0].set_title('CDF')
#ecdf = EmpiricalCDF(-values)
# axs[0].plot(-ygrid,ecdf(-ygrid),'-')
ygrid = np.linspace(-1, 20, 100)
# axs[1].hist(values,bins='auto',density=True)
axs[1].plot(ygrid, f_pdf(ygrid), '--')
axs[1].set_xlim(ygrid.min(), ygrid.max())
axs[1].set_title('PDF')
pgrid = np.linspace(1e-2, 1 - 1e-2, 100)
evar = np.array([value_at_risk(values, p)[0] for p in pgrid])
# print(np.linalg.norm(evar.squeeze()-VaR(pgrid),ord=np.inf))
if plot:
axs[2].plot(pgrid, evar, '-')
axs[2].plot(pgrid, VaR(pgrid), '--')
axs[2].set_title('VaR')
else:
assert np.allclose(evar.squeeze(), VaR(pgrid), atol=2e-1)
pgrid = np.linspace(1e-2, 1 - 1e-2, 100)
ecvar = np.array([conditional_value_at_risk(values, y) for y in pgrid])
# print(np.linalg.norm(ecvar.squeeze()-CVaR(pgrid).squeeze(),ord=np.inf))
print(CVaR(0.8))
if plot:
axs[3].plot(pgrid, ecvar, '-')
axs[3].plot(pgrid, CVaR(pgrid), '--')
axs[3].set_xlim(pgrid.min(), pgrid.max())
axs[3].set_title('CVaR')
else:
assert np.allclose(ecvar.squeeze(), CVaR(pgrid).squeeze(), rtol=4e-2)
#ygrid = np.linspace(-1,10,100)
ygrid = np.linspace(logstats.norm.ppf(0.0, np.exp(mu), sigma),
logstats.norm.ppf(0.9, np.exp(mu), sigma), 101)
essd = compute_conditional_expectations(ygrid, values, False)
# print(np.linalg.norm(essd.squeeze()-ssd(ygrid),ord=np.inf))
if plot:
axs[4].plot(ygrid, essd, '-')
axs[4].plot(ygrid, ssd(ygrid), '--')
axs[4].set_xlim(ygrid.min(), ygrid.max())
axs[4].set_title(r'$E[(\eta-Y)^+]$')
axs[4].set_xlabel(r'$\eta$')
else:
assert np.allclose(essd.squeeze(), ssd(ygrid), atol=1e-3)
# zoom into ygrid over high probability region of -Y
ygrid = -ygrid[::-1]
disutil_essd = compute_conditional_expectations(ygrid, values, True)
assert np.allclose(disutil_essd,
compute_conditional_expectations(ygrid, -values, False))
# print(np.linalg.norm(disutil_essd.squeeze()-ssd_disutil(ygrid),ord=np.inf))
if plot:
axs[5].plot(ygrid, disutil_essd, '-', label='Empirical')
axs[5].plot(ygrid, ssd_disutil(ygrid), '--', label='Exact')
axs[5].set_xlim((ygrid).min(), (ygrid).max())
axs[5].set_title(r'$E[(\eta-(-Y))^+]$')
axs[5].set_xlabel(r'$\eta$')
axs[5].plot([0], [np.exp(mu + sigma**2 / 2)], 'o')
axs[5].legend()
plt.show()
else:
assert np.allclose(disutil_essd.squeeze(),
ssd_disutil(ygrid),
atol=1e-3)