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import numpy as np
class SeriesExpansion(object):
"""
An N-dimensional function approximated as a series expansion in some chosen
basis
"""
_dim = None
_coeffs = None
_basis = None
def __init__(self, coeffs, basis):
self._dim = coeffs.ndim
self._coeffs = coeffs
# for 1D, allow passing just the basis object itself
# without being wrapped in an iterable
if self._dim == 1:
try:
basis[0]
except (TypeError, IndexError):
basis = [basis]
if len(basis) != coeffs.ndim:
raise ValueError('Mismatching number of coefficient and basis functions')
self._basis = basis
@property
def coeffs(self):
return self._coeffs
@property
def basis(self):
return self._basis
def eval(self, coords, diff_order = None):
# for 1D, allow passing just the plain array of coords
# without being wrapped in an iterable
if self._dim == 1:
try:
coords[0][0]
except (TypeError, IndexError):
coords = [coords]
if diff_order is not None:
try:
diff_order[0]
except (TypeError, IndexError):
diff_order = [diff_order]
if diff_order is None:
diff_order = [0] * len(coords)
shape = [len(c) for c in coords]
ret = np.zeros(shape)
basis_vals = []
for i, (b, c, d) in enumerate(zip(self._basis, coords, diff_order)):
val = []
for idx in range(self._coeffs.shape[i]):
val.append(b.eval(idx, c, d))
basis_vals.append(val)
if self._dim == 1:
for c, val in zip(self._coeffs, basis_vals[0]):
ret += val * c
return ret
elif self._dim == 2:
for i in range(self._coeffs.shape[0]):
for j in range(self._coeffs.shape[1]):
ret += self._coeffs[i, j] * np.outer(basis_vals[0][i], basis_vals[1][j])
return ret
else:
raise NotImplementedError('Unsupported number of dimensions')
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