def sampling_total_degree_indices(N, d, k):
"""
Chooses N random multi-indices (with the uniform probability law) from the
set of d-variate multi-indices whose total degree is k and less
Parameters
------
param1: N
Numebr of chosen random multi-indices
param2: d
dimension of variables
param3L k
total degree of variables
Returns
------
The output lambdas is an N x d matrix, with each row containing one of
these multi-indices
"""
lambdas = np.zeros((N, d))
degrees = discrete_sampling(N, pdjk(d, k), np.arange(k+1)).T
for i in range(1, d):
for n in range(1, N+1):
lambdas[n-1, i-1] = \
discrete_sampling(1, pdjk(d-i, degrees[n-1]),
np.arange(degrees[n-1], 0-1e-8, -1))
degrees = degrees - lambdas[:, i-1]
lambdas[:, d-1] = degrees
return lambdas
def idist_mixture_sampling(self, M, Lambdas, weights=None,
fast_sampler=True):
"""
Performs tensorial inverse transform sampling from an additive mixture
of tensorial induced distributions, generating M samples
The measure this samples from is the order-Lambdas induced measure,
which is an additive mixture of tensorial measures
Each tensorial measure is defined a row of Lambdas
Parameters
------
param1: M
Number of samples to generate
param2: Lambdas
Sample from the order-Lambdas induced measure
Returns
------
"""
from UncertainSCI.utils.prob import discrete_sampling
K, d = Lambdas.shape
assert M > 0 and d == self.dim
if weights is None:
weights = np.ones(K)/K
else:
assert weights.size == K
assert np.all(weights >= 0)
weights = weights/np.sum(weights)
ks = discrete_sampling(M, weights, np.arange(K, dtype=int))
Lambdas = Lambdas[ks, :]
if self.isotropic:
fidistinv = getattr(self.polys1d, "fidistinv", None)
if callable(fidistinv):
has_fidistinv = True
else:
has_fidistinv = False
if fast_sampler and has_fidistinv:
idistinv = self.polys1d.fidistinv
else:
idistinv = self.polys1d.idistinv
return idistinv(np.random.random([M, d]), Lambdas)
else:
x = np.zeros([M, d])
for qd in range(self.dim):
fidistinv = getattr(self.polys1d[qd], "fidistinv", None)
if callable(fidistinv):
has_fidistinv = True
else:
has_fidistinv = False
if fast_sampler and has_fidistinv:
idistinv = self.polys1d[qd].fidistinv
else:
idistinv = self.polys1d[qd].idistinv
x[:, qd] = idistinv(np.random.random(M), Lambdas[:, qd])
return x