import logging
import chaospy as cp
from .base import BaseSamplingElement, Vary
__author__ = "Jalal Lakhlili"
__copyright__ = """
Copyright 2018 Robin A. Richardson, David W. Wright
This file is part of EasyVVUQ
EasyVVUQ is free software: you can redistribute it and/or modify
it under the terms of the Lesser GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
EasyVVUQ is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
Lesser GNU General Public License for more details.
You should have received a copy of the Lesser GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
__license__ = "LGPL"
[docs]class PCESampler(BaseSamplingElement, sampler_name="PCE_sampler"):
def __init__(self,
vary=None,
count=0,
polynomial_order=4,
regression=False,
rule="G",
sparse=False,
growth=False):
"""
Create the sampler for the Polynomial Chaos Expansion using
pseudo-spectral projection or regression (Point Collocation).
Parameters
----------
vary: dict or None
keys = parameters to be sampled, values = distributions.
count : int, optional
Specified counter for Fast forward, default is 0.
polynomial_order : int, optional
The polynomial order, default is 4.
regression : bool, optional
If True, regression variante (point collecation) will be used,
otherwise projection variante (pseud-spectral) will be used.
Default value is False.
rule : char, optional
The quadrature method, in case of projection (default is Gaussian "G").
The sequence sampler in case of regression (default is Hammersley "M")
sparse : bool, optional
If True, use Smolyak sparse grid instead of normal tensor product
grid. Default value is False.
growth (bool, None), optional
If True, quadrature point became nested.
"""
if vary is None:
msg = ("'vary' cannot be None. RandomSampler must be passed a "
"dict of the names of the parameters you want to vary, "
"and their corresponding distributions.")
logging.error(msg)
raise Exception(msg)
if not isinstance(vary, dict):
msg = ("'vary' must be a dictionary of the names of the "
"parameters you want to vary, and their corresponding "
"distributions.")
logging.error(msg)
raise Exception(msg)
if len(vary) == 0:
msg = "'vary' cannot be empty."
logging.error(msg)
raise Exception(msg)
self.vary = Vary(vary)
self.polynomial_order = polynomial_order
# List of the probability distributions of uncertain parameters
params_distribution = list(vary.values())
# Multivariate distribution
self.distribution = cp.J(*params_distribution)
# The orthogonal polynomials corresponding to the joint distribution
self.P = cp.expansion.stieltjes(polynomial_order, self.distribution, normed=True)
# The quadrature information
self.quad_sparse = sparse
self.rule = rule
# Clenshaw-Curtis should be nested if sparse (#139 chaospy issue)
self.quad_growth = growth
cc = ['c', 'C', 'clenshaw_curtis', 'Clenshaw_Curtis']
if sparse and rule in cc:
self.quad_growth = True
# To determinate the PCE vrainte to use
self.regression = regression
# Regression variante (Point collocation method)
if regression:
# Change the default rule
if rule == "G":
self.rule = "M"
# Generates samples
self._n_samples = 2 * len(self.P)
self._nodes = cp.generate_samples(order=self._n_samples,
domain=self.distribution,
rule=self.rule)
self._weights = None
# Projection variante (Pseudo-spectral method)
else:
# Nodes and weights for the integration
self._nodes, self._weights = cp.generate_quadrature(order=polynomial_order,
dist=self.distribution,
rule=self.rule,
sparse=sparse,
growth=self.quad_growth)
# Number of samples
self._n_samples = len(self._nodes[0])
# Fast forward to specified count, if possible
self.count = 0
if self.count >= self._n_samples:
msg = (f"Attempt to start sampler fastforwarded to count {self.count}, "
f"but sampler only has {self.n_samples} samples, therefore"
f"this sampler will not provide any more samples.")
logging.warning(msg)
else:
for i in range(count):
self.__next__()
[docs] def is_finite(self):
return True
@property
def n_samples(self):
"""
Number of samples (Ns) of PCE method.
- When using pseudo-spectral projection method with tensored
quadrature: Ns = (p + 1)**d
- When using pseudo-spectral projection method with sparce grid
quadratue: Ns = bigO((p + 1)*log(p + 1)**(d-1))
- When using regression method: Ns = 2*(p + d)!/p!*d!
Where: p is the polynomial degree and d is the number of
uncertain parameters.
Ref: Eck et al. 'A guide to uncertainty quantification and
sensitivity analysis for cardiovascular applications' [2016].
"""
return self._n_samples
@property
def analysis_class(self):
"""Return a corresponding analysis class.
"""
from easyvvuq.analysis import PCEAnalysis
return PCEAnalysis
def __next__(self):
if self.count < self._n_samples:
run_dict = {}
for i, param_name in enumerate(self.vary.vary_dict):
run_dict[param_name] = self._nodes[i][self.count]
self.count += 1
return run_dict
else:
raise StopIteration
