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_define_mixed_tensor_product_random_variable(self):
"""
Construct a multivariate random variable from the tensor-product of
different one-dimensional variables assuming that a given variable
type the distribution parameters ARE NOT the same
"""
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)
# first sample is on left boundary of all bounded variables
# and one standard deviation to left of mean for gaussian variable
# second sample is on right boundary of all bounded variables
# and one standard deviation to right of mean for gaussian variable
true_user_samples = np.asarray([[-1, -1, -3, 0, -1, -2],
[1, 1, 1, 1, 1, 1]]).T
canonical_samples = var_trans.map_to_canonical_space(true_user_samples)
true_canonical_samples = np.ones_like(true_user_samples)
true_canonical_samples[:, 0] = -1
assert np.allclose(true_canonical_samples, canonical_samples)
user_samples = var_trans.map_from_canonical_space(canonical_samples)
assert np.allclose(user_samples, true_user_samples)
def test_define_mixed_tensor_product_random_variable_contin_discrete(self):
"""
Construct a multivariate random variable from the tensor-product of
different one-dimensional variables assuming that a given variable
type the distribution parameters ARE NOT the same
"""
# parameters of binomial distribution
num_trials = 10
prob_success = 0.5
univariate_variables = [
stats.uniform(),
stats.norm(-1, np.sqrt(4)),
stats.norm(-1, np.sqrt(4)),
stats.binom(num_trials, prob_success),
stats.norm(-1, np.sqrt(4)),
stats.uniform(0, 1),
stats.uniform(0, 1),
stats.binom(num_trials, prob_success)
]
var_trans = AffineRandomVariableTransformation(univariate_variables)
# first sample is on left boundary of all bounded variables
# and one standard deviation to left of mean for gaussian variables
# second sample is on right boundary of all bounded variables
# and one standard deviation to right of mean for gaussian variable
true_user_samples = np.asarray([[0, -3, -3, 0, -3, 0, 0, 0],
[1, 1, 1, num_trials, 1, 1, 1, 10]]).T
canonical_samples = var_trans.map_to_canonical_space(true_user_samples)
true_canonical_samples = np.ones_like(true_user_samples)
true_canonical_samples[:, 0] = -1
true_canonical_samples[5, 0] = -1
true_canonical_samples[3, :] = [-1, 1]
true_canonical_samples[7, :] = [-1, 1]
assert np.allclose(true_canonical_samples, canonical_samples)
user_samples = var_trans.map_from_canonical_space(canonical_samples)
assert np.allclose(user_samples, true_user_samples)
def test_map_rv_discrete(self):
nvars = 2
mass_locs = np.arange(5, 501, step=50)
nmasses = mass_locs.shape[0]
mass_probs = np.ones(nmasses, dtype=float) / float(nmasses)
univariate_variables = [
float_rv_discrete(name='float_rv_discrete',
values=(mass_locs, mass_probs))()
] * nvars
variables = IndependentMultivariateRandomVariable(univariate_variables)
var_trans = AffineRandomVariableTransformation(variables)
samples = np.vstack(
[mass_locs[np.newaxis, :], mass_locs[0] * np.ones((1, nmasses))])
canonical_samples = var_trans.map_to_canonical_space(samples)
assert (canonical_samples[0].min() == -1)
assert (canonical_samples[0].max() == 1)
recovered_samples = var_trans.map_from_canonical_space(
canonical_samples)
assert np.allclose(recovered_samples, samples)
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)
