def test_derivatives_scalarQoI(self):
systemsize = 3
mu = mean_3dim # np.random.randn(systemsize)
std_dev = std_dev_3dim # np.diag(np.random.rand(systemsize))
jdist = cp.MvNormal(mu, std_dev)
# Create QoI Object
QoI = examples.Paraboloid3D(systemsize)
# Create the Stochastic Collocation object
deriv_dict = {
'xi': {
'dQoI_func': QoI.eval_QoIGradient,
'output_dimensions': systemsize
}
}
QoI_dict = {
'paraboloid': {
'quadrature_degree': 3,
'reduced_collocation': False,
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
'include_derivs': True,
'deriv_dict': deriv_dict
}
}
sc_obj = StochasticCollocation3(jdist, 'MvNormal', QoI_dict)
sc_obj.evaluateQoIs(jdist)
dmu_j = sc_obj.dmean(of=['paraboloid'], wrt=['xi'])
# dvar_j = sc_obj.dvariance(of=['paraboloid'], wrt=['xi'])
# Analytical dmu_j
dmu_j_analytical = np.array([100 * mu[0], 50 * mu[1], 2 * mu[2]])
err = abs(
(dmu_j['paraboloid']['xi'] - dmu_j_analytical) / dmu_j_analytical)
self.assertTrue((err < 1.e-12).all())
def test_reduced_normalStochasticCollocation3D(self):
# This is not a very good test because we are comparing the reduced collocation
# against the analytical expected value. The only hting it tells us is that
# the solution is within the ball park of actual value. We still need to
# come up with a better test.
systemsize = 3
mu = mean_3dim # np.random.randn(systemsize)
std_dev = std_dev_3dim # abs(np.diag(np.random.randn(systemsize)))
jdist = cp.MvNormal(mu, std_dev)
# Create QoI Object
QoI = examples.Paraboloid3D(systemsize)
dominant_dir = np.array([[1.0, 0.0], [0.0, 1.0], [0.0, 0.0]],
dtype=np.float)
# Create the Stochastic Collocation object
deriv_dict = {
'xi': {
'dQoI_func': QoI.eval_QoIGradient,
'output_dimensions': systemsize
}
}
QoI_dict = {
'paraboloid': {
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
'deriv_dict': deriv_dict
}
}
sc_obj = StochasticCollocation2(jdist,
3,
'MvNormal',
QoI_dict,
reduced_collocation=True,
dominant_dir=dominant_dir)
sc_obj.evaluateQoIs(jdist)
mu_js = sc_obj.mean(of=['paraboloid'])
var_js = sc_obj.variance(of=['paraboloid'])
# Analytical mean
mu_j_analytical = QoI.eval_QoI_analyticalmean(mu, cp.Cov(jdist))
err = abs((mu_js['paraboloid'][0] - mu_j_analytical) / mu_j_analytical)
self.assertTrue(err < 1e-1)
# Analytical variance
var_j_analytical = QoI.eval_QoI_analyticalvariance(mu, cp.Cov(jdist))
err = abs(
(var_js['paraboloid'][0, 0] - var_j_analytical) / var_j_analytical)
self.assertTrue(err < 0.01)
def test_central_difference(self):
systemsize = 3
QoI = examples.Paraboloid3D(systemsize)
def func(x):
return QoI.eval_QoI(x, np.zeros(systemsize))
x_location = np.random.randn(3)
# Do the finite difference
dfval = utils.central_fd(func,
x_location,
output_dimensions=1,
fd_pert=1.e-6)
# Get the analytical gradient
dfval_analytical = QoI.eval_QoIGradient(x_location, np.zeros(3))
err = abs(dfval - dfval_analytical)
self.assertTrue((err < 1.e-6).all())
def test_normalStochasticCollocation3D(self):
systemsize = 3
mu = mean_3dim # np.random.randn(systemsize)
std_dev = std_dev_3dim # np.diag(np.random.rand(systemsize))
jdist = cp.MvNormal(mu, std_dev)
# Create QoI Object
QoI = examples.Paraboloid3D(systemsize)
# Create the Stochastic Collocation object
deriv_dict = {
'xi': {
'dQoI_func': QoI.eval_QoIGradient,
'output_dimensions': systemsize
}
}
QoI_dict = {
'paraboloid': {
'quadrature_degree': 3,
'reduced_collocation': False,
'QoI_func': QoI.eval_QoI,
'output_dimensions': 1,
'include_derivs': False,
'deriv_dict': deriv_dict
}
}
sc_obj = StochasticCollocation3(jdist, 'MvNormal', QoI_dict)
sc_obj.evaluateQoIs(jdist)
mu_js = sc_obj.mean(of=['paraboloid'])
var_js = sc_obj.variance(of=['paraboloid'])
# Analytical mean
mu_j_analytical = QoI.eval_QoI_analyticalmean(mu, cp.Cov(jdist))
err = abs((mu_js['paraboloid'][0] - mu_j_analytical) / mu_j_analytical)
self.assertTrue(err < 1.e-15)
# Analytical variance
var_j_analytical = QoI.eval_QoI_analyticalvariance(mu, cp.Cov(jdist))
err = abs(
(var_js['paraboloid'][0, 0] - var_j_analytical) / var_j_analytical)
self.assertTrue(err < 1.e-15)
from smt.surrogate_models import QP # Surrogate Modeling
from pystatreduce.new_stochastic_collocation import StochasticCollocation2
from pystatreduce.stochastic_collocation import StochasticCollocation
from pystatreduce.quantity_of_interest import QuantityOfInterest
from pystatreduce.dimension_reduction import DimensionReduction
import pystatreduce.examples as examples
import pystatreduce.utils as utils
# Create the actual QoI
systemsize = 3
mu = np.random.randn(3)
std_dev = abs(np.diag(np.random.randn(3)))
jdist = cp.MvNormal(mu, std_dev)
QoI = examples.Paraboloid3D(systemsize)
# Generate the samples for surrogate
n_surrogate_samples = int(0.5 * (systemsize + 1) * (systemsize + 2))
surrogate_samples = jdist.sample(5000, rule='R')
std_dev_vec = np.diagonal(std_dev)
new_samples = utils.check_std_dev_violation(surrogate_samples, mu, std_dev_vec, scale=1.0)
print('orig_shape = ', new_samples.shape)
new_samples = new_samples[:,0:1000]
print('new_shape = ', new_samples.shape)
"""
fval_arr = np.zeros(n_surrogate_samples)
for i in range(n_surrogate_samples):
fval_arr[i] = QoI.eval_QoI(surrogate_samples[:,i], np.zeros(systemsize))
