def __call__(self, x):
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
if b < x:
continue
y = _fekete.eval_poly(array([float(x)]), self._values[n],
a, b)[0]
return y
def __call__(self, x):
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
if b < x:
continue
y = _fekete.eval_poly(array([float(x)]), self._values[n],
a, b)[0]
return y
def get_values_in_element(self, n, x):
"""
Return the values in points 'x' in the element 'n'.
'x' is a numpy array of points
'n' is an element id
It returns a numpy array of values of the function in points 'x'.
All points 'x' must be in the element 'n'.
"""
a, b, order = self._mesh.get_element_by_id(n)
assert (a<=x).all()
assert (x<=b).all()
return _fekete.eval_poly(x, self._values[n], a, b)
def get_values_in_element(self, n, x):
"""
Return the values in points 'x' in the element 'n'.
'x' is a numpy array of points
'n' is an element id
It returns a numpy array of values of the function in points 'x'.
All points 'x' must be in the element 'n'.
"""
a, b, order = self._mesh.get_element_by_id(n)
assert (a <= x).all()
assert (x <= b).all()
return _fekete.eval_poly(x, self._values[n], a, b)
def __pow__(self, o):
if isinstance(o, (int, long)):
pts = self._mesh._points
orders = empty(len(self._mesh._orders), dtype="int")
values = []
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
order = o*order
x = _fekete.get_fekete_points_phys(order, a, b)
vals = _fekete.eval_poly(x, self._values[n], a, b)**o
values.append(vals)
orders[n] = order
mesh = Mesh1D(pts, orders)
return Function(values, mesh)
else:
return NotImplemented
def __pow__(self, o):
if isinstance(o, (int, long)):
pts = self._mesh._points
orders = empty(len(self._mesh._orders), dtype="int")
values = []
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
order = o * order
x = _fekete.get_fekete_points_phys(order, a, b)
vals = _fekete.eval_poly(x, self._values[n], a, b)**o
values.append(vals)
orders[n] = order
mesh = Mesh1D(pts, orders)
return Function(values, mesh)
else:
return NotImplemented
def l2_norm(self, method="Fekete"):
"""
Calculates the L2 norm of the function.
method == "Fekete" or "FE": Use Legendre interpolation, or first
project to a FE basis and then calculate the L2 norm
"""
if method=="Fekete":
r = 0
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
x, w = _fekete.get_gauss_points_phys(a, b, order+1)
vals = _fekete.eval_poly(x, self._values[n], a, b)
r += _fekete.int_f2(w, vals)
return sqrt(r)
elif method=="FE":
self.calculate_FE_coeffs()
return self._fe_sol.l2_norm()
def l2_norm(self, method="Fekete"):
"""
Calculates the L2 norm of the function.
method == "Fekete" or "FE": Use Legendre interpolation, or first
project to a FE basis and then calculate the L2 norm
"""
if method == "Fekete":
r = 0
for n, (a, b, order) in enumerate(self._mesh.iter_elems()):
x, w = _fekete.get_gauss_points_phys(a, b, order + 1)
vals = _fekete.eval_poly(x, self._values[n], a, b)
r += _fekete.int_f2(w, vals)
return sqrt(r)
elif method == "FE":
self.calculate_FE_coeffs()
return self._fe_sol.l2_norm()
