def test_identity_map_subset(self):
num_vars = 3
var_trans = define_iid_random_variable_transformation(
stats.uniform(0, 1), num_vars)
var_trans.set_identity_maps([1])
samples = np.random.uniform(0, 1, (num_vars, 4))
canonical_samples = var_trans.map_to_canonical_space(samples)
assert np.allclose(canonical_samples[1, :], samples[1, :])
assert np.allclose(
var_trans.map_from_canonical_space(canonical_samples), samples)
univariate_variables = [
stats.uniform(-1, 2),
stats.beta(1, 1, -1, 2),
stats.norm(-1, np.sqrt(4)),
stats.uniform(),
stats.uniform(-1, 2),
stats.beta(2, 1, -2, 3)
]
var_trans = AffineRandomVariableTransformation(univariate_variables)
var_trans.set_identity_maps([4, 2])
from pyapprox.probability_measure_sampling import \
generate_independent_random_samples
samples = generate_independent_random_samples(var_trans.variable, 10)
canonical_samples = var_trans.map_to_canonical_space(samples)
assert np.allclose(canonical_samples[[2, 4], :], samples[[2, 4], :])
assert np.allclose(
var_trans.map_from_canonical_space(canonical_samples), samples)
def test_pce_product_of_beta_variables(self):
def fun(x):
return np.sqrt(x.prod(axis=0))[:, None]
dist_alpha1, dist_beta1 = 1, 1
dist_alpha2, dist_beta2 = dist_alpha1 + 0.5, dist_beta1
nvars = 2
x_1d, w_1d = [], []
nquad_samples_1d = 100
x, w = gauss_jacobi_pts_wts_1D(nquad_samples_1d, dist_beta1 - 1,
dist_alpha1 - 1)
x = (x + 1) / 2
x_1d.append(x)
w_1d.append(w)
x, w = gauss_jacobi_pts_wts_1D(nquad_samples_1d, dist_beta2 - 1,
dist_alpha2 - 1)
x = (x + 1) / 2
x_1d.append(x)
w_1d.append(w)
quad_samples = cartesian_product(x_1d)
quad_weights = outer_product(w_1d)
mean = fun(quad_samples)[:, 0].dot(quad_weights)
variance = (fun(quad_samples)[:, 0]**2).dot(quad_weights) - mean**2
assert np.allclose(mean, beta(dist_alpha1 * 2, dist_beta1 * 2).mean())
assert np.allclose(variance,
beta(dist_alpha1 * 2, dist_beta1 * 2).var())
degree = 10
poly = PolynomialChaosExpansion()
# the distribution and ranges of univariate variables is ignored
# when var_trans.set_identity_maps([0]) is used
univariate_variables = [uniform(0, 1)]
variable = IndependentMultivariateRandomVariable(univariate_variables)
var_trans = AffineRandomVariableTransformation(variable)
# the following means do not map samples
var_trans.set_identity_maps([0])
quad_rules = [(x, w) for x, w in zip(x_1d, w_1d)]
poly.configure({
'poly_types': {
0: {
'poly_type': 'function_indpnt_vars',
'var_nums': [0],
'fun': fun,
'quad_rules': quad_rules
}
},
'var_trans': var_trans
})
from pyapprox.indexing import tensor_product_indices
poly.set_indices(tensor_product_indices([degree]))
train_samples = (np.linspace(0, np.pi, 101)[None, :] + 1) / 2
train_vals = train_samples.T
coef = np.linalg.lstsq(poly.basis_matrix(train_samples),
train_vals,
rcond=None)[0]
poly.set_coefficients(coef)
assert np.allclose(poly.mean(),
beta(dist_alpha1 * 2, dist_beta1 * 2).mean())
assert np.allclose(poly.variance(),
beta(dist_alpha1 * 2, dist_beta1 * 2).var())
poly = PolynomialChaosExpansion()
# the distribution and ranges of univariate variables is ignored
# when var_trans.set_identity_maps([0]) is used
univariate_variables = [uniform(0, 1)]
variable = IndependentMultivariateRandomVariable(univariate_variables)
var_trans = AffineRandomVariableTransformation(variable)
# the following means do not map samples
var_trans.set_identity_maps([0])
funs = [lambda x: np.sqrt(x)] * nvars
quad_rules = [(x, w) for x, w in zip(x_1d, w_1d)]
poly.configure({
'poly_types': {
0: {
'poly_type': 'product_indpnt_vars',
'var_nums': [0],
'funs': funs,
'quad_rules': quad_rules
}
},
'var_trans': var_trans
})
from pyapprox.indexing import tensor_product_indices
poly.set_indices(tensor_product_indices([degree]))
train_samples = (np.linspace(0, np.pi, 101)[None, :] + 1) / 2
train_vals = train_samples.T
coef = np.linalg.lstsq(poly.basis_matrix(train_samples),
train_vals,
rcond=None)[0]
poly.set_coefficients(coef)
assert np.allclose(poly.mean(),
beta(dist_alpha1 * 2, dist_beta1 * 2).mean())
assert np.allclose(poly.variance(),
beta(dist_alpha1 * 2, dist_beta1 * 2).var())
