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quadrature_sampler.py
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Sat, May 4, 23:57

quadrature_sampler.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy 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
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import numpy as np
from rrompy.utilities.parameter_sampling.generic_sampler import GenericSampler
from rrompy.utilities.base.types import Np1D, Tuple, List
__all__ = ['QuadratureSampler']
class QuadratureSampler(GenericSampler):
"""Generator of quadrature sample points."""
allowedKinds = ["UNIFORM", "CHEBYSHEV", "GAUSSLEGENDRE"]
def __init__(self, lims:Tuple[Np1D, Np1D], kind : str = "UNIFORM",
scaling : List[callable] = None,
scalingInv : List[callable] = None):
super().__init__(lims = lims, scaling = scaling,
scalingInv = scalingInv)
self.kind = kind
def __str__(self) -> str:
return "{}_{}".format(super().__str__(), self.kind)
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
@property
def kind(self):
"""Value of kind."""
return self._kind
@kind.setter
def kind(self, kind):
if kind.upper() not in self.allowedKinds:
raise Exception("Generator kind not recognized.")
self._kind = kind.upper()
def generatePoints(self, n:Np1D) -> Tuple[List[Np1D], Np1D]:
"""Array of quadrature points and array of weights."""
super().generatePoints(n)
d = len(self.lims[0])
try:
len(n)
except:
n = np.array([n])
if len(n) != d:
raise Exception(("Numbers of points must have same dimension as"
"limits."))
for j in range(d):
a, b = self.lims[0][j], self.lims[1][j]
if self.scaling is not None:
a, b = self.scaling[j](a), self.scaling[j](b)
if self.kind == "UNIFORM":
xj = np.linspace(a, b, n[j])[:, None]
wj = np.abs(a - b) / (n[j] - 1) * np.ones(n[j])
elif self.kind == "CHEBYSHEV":
nodes, weights = np.polynomial.chebyshev.chebgauss(n[j])
xj = (a + b) / 2 + (a - b) / 2 * nodes[:, None]
wj = np.abs(a - b) / np.pi * weights
elif self.kind == "GAUSSLEGENDRE":
nodes, weights = np.polynomial.legendre.leggauss(n[j])
xj = (a + b) / 2 + (a - b) / 2 * nodes[:, None]
wj = np.abs(a - b) * weights
if self.scalingInv is not None:
xj = self.scalingInv[j](xj)
if j == 0:
x = xj
w = wj
xsize = n[0]
else:
x = np.concatenate((np.kron(np.ones(n[j])[:, None], x),
np.kron(xj, np.ones(xsize)[:, None])),
axis = 1)
w = np.multiply(np.kron(np.ones(n[j]), w),
np.kron(wj, np.ones(xsize)))
xsize = xsize * n[j]
return [y.flatten() for y in np.split(x, xsize)], w
def refine(self, n:int) -> Tuple[List[Np1D], Np1D]:
"""
Apply refinement. If points are not nested, equivalent to
generatePoints([2 * x - 1 for x in n]).
"""
if self.kind != "UNIFORM": return super().refine(n)
super().generatePoints(n)
d = len(self.lims[0])
try:
len(n)
except:
n = np.array([n])
if len(n) != d:
raise Exception(("Numbers of points must have same dimension as"
"limits."))
for j in range(d):
a, b = self.lims[0][j], self.lims[1][j]
if self.scaling is not None:
a, b = self.scaling[j](a), self.scaling[j](b)
xj = np.linspace(a + (b - a) / 2. / (n[j] - 1),
b + (a - b) / 2. / (n[j] - 1), n[j] - 1)[:, None]
wj = np.abs(a - b) / (n[j] - 2) * np.ones(n[j] - 1)
if self.scalingInv is not None:
xj = self.scalingInv[j](xj)
if j == 0:
x = xj
w = wj
xsize = n[0] - 1
else:
x = np.concatenate((np.kron(np.ones(n[j] - 1)[:, None], x),
np.kron(xj, np.ones(xsize)[:, None])),
axis = 1)
w = np.multiply(np.kron(np.ones(n[j] - 1), w),
np.kron(wj, np.ones(xsize)))
xsize = xsize * (n[j] - 1)
return [y.flatten() for y in np.split(x, xsize)], w

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