def test_fekete_rosenblatt_interpolation(self):
np.random.seed(2)
degree=3
__,__,joint_density,limits = rosenblatt_example_2d(num_samples=1)
num_vars=len(limits)//2
rosenblatt_opts = {'limits':limits,'num_quad_samples_1d':20}
var_trans_1 = RosenblattTransformation(
joint_density,num_vars,rosenblatt_opts)
# rosenblatt maps to [0,1] but polynomials of bounded variables
# are in [-1,1] so add second transformation for this second mapping
var_trans_2 = define_iid_random_variable_transformation(
uniform(),num_vars)
var_trans = TransformationComposition([var_trans_1, var_trans_2])
poly = PolynomialChaosExpansion()
poly.configure({'poly_type':'jacobi','alpha_poly':0.,
'beta_poly':0.,'var_trans':var_trans})
indices = compute_hyperbolic_indices(num_vars,degree,1.0)
poly.set_indices(indices)
num_candidate_samples = 10000
generate_candidate_samples=lambda n: np.cos(
np.random.uniform(0.,np.pi,(num_vars,n)))
precond_func = lambda matrix, samples: christoffel_weights(matrix)
canonical_samples, data_structures = get_fekete_samples(
poly.canonical_basis_matrix,generate_candidate_samples,
num_candidate_samples,preconditioning_function=precond_func)
samples = var_trans.map_from_canonical_space(canonical_samples)
assert np.allclose(
canonical_samples,var_trans.map_to_canonical_space(samples))
assert samples.max()<=1 and samples.min()>=0.
c = np.random.uniform(0.,1.,num_vars)
c*=20/c.sum()
w = np.zeros_like(c); w[0] = np.random.uniform(0.,1.,1)
genz_function = GenzFunction('oscillatory',num_vars,c=c,w=w)
values = genz_function(samples)
# function = lambda x: np.sum(x**2,axis=0)[:,np.newaxis]
# values = function(samples)
# Ensure coef produce an interpolant
coef = interpolate_fekete_samples(
canonical_samples,values,data_structures)
poly.set_coefficients(coef)
assert np.allclose(poly(samples),values)
# compare mean computed using quadrature and mean computed using
# first coefficient of expansion. This is not testing that mean
# is correct because rosenblatt transformation introduces large error
# which makes it hard to compute accurate mean from pce or quadrature
quad_w = get_quadrature_weights_from_fekete_samples(
canonical_samples,data_structures)
values_at_quad_x = values[:,0]
assert np.allclose(
np.dot(values_at_quad_x,quad_w),poly.mean())
def test_rosenblatt_transformation(self):
true_samples, true_canonical_samples, joint_density, limits = \
rosenblatt_example_2d(num_samples=10)
num_vars = 2
opts = {'limits': limits, 'num_quad_samples_1d': 100}
var_trans = RosenblattTransformation(joint_density, num_vars, opts)
samples = var_trans.map_from_canonical_space(true_canonical_samples)
assert np.allclose(true_samples, samples)
canonical_samples = var_trans.map_to_canonical_space(samples)
assert np.allclose(true_canonical_samples, canonical_samples)
def test_pickle_rosenblatt_transformation(self):
import pickle, os
true_samples, true_canonical_samples, joint_density, limits = \
rosenblatt_example_2d(num_samples=10)
num_vars = 2
opts = {'limits': limits, 'num_quad_samples_1d': 100}
var_trans = RosenblattTransformation(joint_density, num_vars, opts)
filename = 'rv_trans.pkl'
with open(filename, 'wb') as f:
pickle.dump(var_trans, f)
with open(filename, 'rb') as f:
file_var_trans = pickle.load(f)
os.remove(filename)
def test_transformation_composition_I(self):
np.random.seed(2)
true_samples, true_canonical_samples, joint_density, limits = \
rosenblatt_example_2d(num_samples=10)
# rosenblatt_example_2d is defined on [0,1] remap to [-1,1]
true_canonical_samples = true_canonical_samples * 2 - 1
num_vars = 2
opts = {'limits': limits, 'num_quad_samples_1d': 100}
var_trans_1 = RosenblattTransformation(joint_density, num_vars, opts)
var_trans_2 = define_iid_random_variable_transformation(
uniform(0, 1), num_vars)
var_trans = TransformationComposition([var_trans_1, var_trans_2])
samples = var_trans.map_from_canonical_space(true_canonical_samples)
assert np.allclose(true_samples, samples)
canonical_samples = var_trans.map_to_canonical_space(samples)
assert np.allclose(true_canonical_samples, canonical_samples)