def test_discrete_induced_sampling(self):
degree = 3
nmasses1 = 10
mass_locations1 = np.geomspace(1.0, 512.0, num=nmasses1)
#mass_locations1 = np.arange(0,nmasses1)
masses1 = np.ones(nmasses1, dtype=float) / nmasses1
var1 = float_rv_discrete(name='float_rv_discrete',
values=(mass_locations1, masses1))()
nmasses2 = 10
mass_locations2 = np.arange(0, nmasses2)
# if increase from 16 unmodififed becomes ill conditioned
masses2 = np.geomspace(1.0, 16.0, num=nmasses2)
#masses2 = np.ones(nmasses2,dtype=float)/nmasses2
masses2 /= masses2.sum()
var2 = float_rv_discrete(name='float_rv_discrete',
values=(mass_locations2, masses2))()
var_trans = AffineRandomVariableTransformation([var1, var2])
pce_opts = define_poly_options_from_variable_transformation(var_trans)
pce = PolynomialChaosExpansion()
pce.configure(pce_opts)
indices = compute_hyperbolic_indices(pce.num_vars(), degree, 1.0)
pce.set_indices(indices)
num_samples = int(1e4)
np.random.seed(1)
canonical_samples = generate_induced_samples(pce, num_samples)
samples = var_trans.map_from_canonical_space(canonical_samples)
np.random.seed(1)
canonical_xk = [
2 * get_distribution_info(var1)[2]['xk'] - 1,
2 * get_distribution_info(var2)[2]['xk'] - 1
]
basis_matrix_generator = partial(basis_matrix_generator_1d, pce,
degree)
canonical_samples1 = discrete_induced_sampling(
basis_matrix_generator, pce.indices, canonical_xk,
[var1.dist.pk, var2.dist.pk], num_samples)
samples1 = var_trans.map_from_canonical_space(canonical_samples1)
def density(x):
return var1.pdf(x[0, :]) * var2.pdf(x[1, :])
envelope_factor = 30
def generate_proposal_samples(n):
samples = np.vstack([var1.rvs(n), var2.rvs(n)])
return samples
proposal_density = density
# unlike fekete and leja sampling can and should use
# pce.basis_matrix here. If use canonical_basis_matrix then
# densities must be mapped to this space also which can be difficult
samples2 = random_induced_measure_sampling(num_samples, pce.num_vars(),
pce.basis_matrix, density,
proposal_density,
generate_proposal_samples,
envelope_factor)
def induced_density(x):
vals = density(x) * christoffel_function(x, pce.basis_matrix, True)
return vals
from pyapprox.utilities import cartesian_product, outer_product
from pyapprox.polynomial_sampling import christoffel_function
quad_samples = cartesian_product([var1.dist.xk, var2.dist.xk])
quad_weights = outer_product([var1.dist.pk, var2.dist.pk])
#print(canonical_samples.min(axis=1),canonical_samples.max(axis=1))
#print(samples.min(axis=1),samples.max(axis=1))
#print(canonical_samples1.min(axis=1),canonical_samples1.max(axis=1))
#print(samples1.min(axis=1),samples1.max(axis=1))
# import matplotlib.pyplot as plt
# plt.plot(quad_samples[0,:],quad_samples[1,:],'s')
# plt.plot(samples[0,:],samples[1,:],'o')
# plt.plot(samples1[0,:],samples1[1,:],'*')
# plt.show()
rtol = 1e-2
assert np.allclose(quad_weights, density(quad_samples))
assert np.allclose(density(quad_samples).sum(), 1)
assert np.allclose(
christoffel_function(quad_samples, pce.basis_matrix,
True).dot(quad_weights), 1.0)
true_induced_mean = quad_samples.dot(induced_density(quad_samples))
print(true_induced_mean)
print(samples.mean(axis=1))
print(samples1.mean(axis=1))
print(samples2.mean(axis=1))
print(
samples1.mean(axis=1) - true_induced_mean,
true_induced_mean * rtol)
#print(samples2.mean(axis=1))
assert np.allclose(samples.mean(axis=1), true_induced_mean, rtol=rtol)
assert np.allclose(samples1.mean(axis=1), true_induced_mean, rtol=rtol)
assert np.allclose(samples2.mean(axis=1), true_induced_mean, rtol=rtol)
def help_discrete_induced_sampling(self, var1, var2, envelope_factor):
degree = 3
var_trans = AffineRandomVariableTransformation([var1, var2])
pce_opts = define_poly_options_from_variable_transformation(var_trans)
pce = PolynomialChaosExpansion()
pce.configure(pce_opts)
indices = compute_hyperbolic_indices(pce.num_vars(), degree, 1.0)
pce.set_indices(indices)
num_samples = int(3e4)
np.random.seed(1)
canonical_samples = generate_induced_samples(pce, num_samples)
samples = var_trans.map_from_canonical_space(canonical_samples)
np.random.seed(1)
#canonical_xk = [2*get_distribution_info(var1)[2]['xk']-1,
# 2*get_distribution_info(var2)[2]['xk']-1]
xk = np.array([
get_probability_masses(var)[0]
for var in var_trans.variable.all_variables()
])
pk = np.array([
get_probability_masses(var)[1]
for var in var_trans.variable.all_variables()
])
canonical_xk = var_trans.map_to_canonical_space(xk)
basis_matrix_generator = partial(basis_matrix_generator_1d, pce,
degree)
canonical_samples1 = discrete_induced_sampling(basis_matrix_generator,
pce.indices,
canonical_xk, pk,
num_samples)
samples1 = var_trans.map_from_canonical_space(canonical_samples1)
def univariate_pdf(var, x):
if hasattr(var.dist, 'pdf'):
return var.pdf(x)
else:
return var.pmf(x)
xk, pk = get_probability_masses(var)
x = np.atleast_1d(x)
vals = np.zeros(x.shape[0])
for jj in range(x.shape[0]):
for ii in range(xk.shape[0]):
if xk[ii] == x[jj]:
vals[jj] = pk[ii]
break
return vals
def density(x):
# some issue with native scipy.pmf
#assert np.allclose(var1.pdf(x[0, :]),var1.pmf(x[0, :]))
return univariate_pdf(var1, x[0, :]) * univariate_pdf(
var2, x[1, :])
def generate_proposal_samples(n):
samples = np.vstack([var1.rvs(n), var2.rvs(n)])
return samples
proposal_density = density
# unlike fekete and leja sampling can and should use
# pce.basis_matrix here. If use canonical_basis_matrix then
# densities must be mapped to this space also which can be difficult
samples2 = random_induced_measure_sampling(num_samples, pce.num_vars(),
pce.basis_matrix, density,
proposal_density,
generate_proposal_samples,
envelope_factor)
def induced_density(x):
vals = density(x) * christoffel_function(x, pce.basis_matrix, True)
return vals
from pyapprox.utilities import cartesian_product, outer_product
from pyapprox.polynomial_sampling import christoffel_function
quad_samples = cartesian_product([xk[0], xk[1]])
quad_weights = outer_product([pk[0], pk[1]])
# print(canonical_samples.min(axis=1),canonical_samples.max(axis=1))
# print(samples.min(axis=1),samples.max(axis=1))
# print(canonical_samples1.min(axis=1),canonical_samples1.max(axis=1))
# print(samples1.min(axis=1),samples1.max(axis=1))
# import matplotlib.pyplot as plt
# plt.plot(quad_samples[0,:],quad_samples[1,:],'s')
# plt.plot(samples[0,:],samples[1,:],'o')
# plt.plot(samples1[0,:],samples1[1,:],'*')
# plt.show()
rtol = 1e-2
assert np.allclose(quad_weights, density(quad_samples))
assert np.allclose(density(quad_samples).sum(), 1)
assert np.allclose(
christoffel_function(quad_samples, pce.basis_matrix,
True).dot(quad_weights), 1.0)
true_induced_mean = quad_samples.dot(induced_density(quad_samples))
# print(true_induced_mean)
# print(samples.mean(axis=1))
# print(samples1.mean(axis=1))
# print(samples2.mean(axis=1))
# print(samples1.mean(axis=1)-true_induced_mean, true_induced_mean*rtol)
# print(samples2.mean(axis=1))
assert np.allclose(samples.mean(axis=1), true_induced_mean, rtol=rtol)
assert np.allclose(samples1.mean(axis=1), true_induced_mean, rtol=rtol)
assert np.allclose(samples2.mean(axis=1), true_induced_mean, rtol=rtol)