def lobatto_shape_functions(points):
"""Returns a list of Polynomial objects representing the Lobatto
shape functions for a set of Gauss-Lobatto quadrature points."""
f = []
for point in points:
# The Lobatto shape function corresponding to a point is simply a
# Lagrange basis polynomial with roots at all the other points:
other_points = points[points!=point]
f_i = Polynomial.fromroots(other_points)/np.prod(point - other_points)
f.append(f_i)
return f
def update(self):
if len(self.roots)>0:
self.poly = Polynomial.fromroots(self.roots)
else:
self.poly = Polynomial([0])
