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import abc
import math
import numpy as np
class ExpansionBasis1D(object):
"""
A family of one-dimensional functions that make up a basis.
"""
__metaclass__ = abc.ABCMeta
@abc.abstractmethod
def eval(self, idx, coord, diff_order = 0):
"""
Evaluate the diff_order-th derivative of the idx-th basis function at
the specified coordinates (where zeroth derivative means evaluating the
function itself).
"""
pass
@abc.abstractmethod
def colloc_grid(self, order):
"""
Get the coordinates of the optimal collocation grid of the specified
order (i.e. exactly order coordinates will be returned).
"""
pass
class CosBasis(ExpansionBasis1D):
PARITY_NONE = 0
PARITY_EVEN = 1
PARITY_ODD = 2
_diff_fact = [(1, np.cos), (-1, np.sin), (-1, np.cos), (1, np.sin)]
_parity = None
def __init__(self, parity = PARITY_NONE):
self._parity = parity
def eval(self, idx, coord, diff_order = 0):
fact, f = self._diff_fact[diff_order % 4]
if self._parity == self.PARITY_EVEN:
idx *= 2
elif self._parity == self.PARITY_ODD:
idx = 2 * idx + 1
fact *= idx ** diff_order
return fact * f(idx * coord)
def colloc_grid(self, order):
if self._parity == self.PARITY_NONE:
return (np.array(range(0, order)) + 1) * 2 * np.pi / (order + 1)
else:
return (np.array(range(0, order)) + 1) * np.pi / (2 * (order + 1))
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