def cand(divisions, orders):
if len(divisions) == 0:
assert len(orders) == 1
return Mesh1D((a, b), (order + orders[0],))
elif len(divisions) == 1:
assert len(orders) == 2
return Mesh1D((a, _fekete.get_x_phys(divisions[0], a, b), b),
(order + orders[0], order + orders[1]))
else:
raise NotImplementedError()
def cand(divisions, orders):
if len(divisions) == 0:
assert len(orders) == 1
return Mesh1D((a, b), (order + orders[0], ))
elif len(divisions) == 1:
assert len(orders) == 2
return Mesh1D((a, _fekete.get_x_phys(divisions[0], a, b), b),
(order + orders[0], order + orders[1]))
else:
raise NotImplementedError()
def get_polynomial(self, x, values, a, b):
"""
Returns the interpolating polynomial's coeffs.
The len(values) specifies the order and we work in the element <a, b>
"""
# Note: the version in _fekete is 2.6x faster
n = len(values)
A = empty((n, n), dtype="double")
y = empty((n,), dtype="double")
assert len(x) == n
for i in range(n):
for j in range(n):
A[i, j] = _fekete.get_x_phys(x[i], a, b)**(n-j-1)
y[i] = values[i]
a = solve(A, y)
return a
def get_polynomial(self, x, values, a, b):
"""
Returns the interpolating polynomial's coeffs.
The len(values) specifies the order and we work in the element <a, b>
"""
# Note: the version in _fekete is 2.6x faster
n = len(values)
A = empty((n, n), dtype="double")
y = empty((n, ), dtype="double")
assert len(x) == n
for i in range(n):
for j in range(n):
A[i, j] = _fekete.get_x_phys(x[i], a, b)**(n - j - 1)
y[i] = values[i]
a = solve(A, y)
return a