def __init__(self, ref_el, m):
if m < 2:
raise ValueError(
"Gauss-Labotto-Legendre quadrature invalid for fewer than 2 points")
Ref1 = reference_element.DefaultLine()
verts = Ref1.get_vertices()
if m > 2:
# Calculate the recursion coefficients.
alpha, beta = orthopoly.rec_jacobi(m, 0, 0)
xs_ref, ws_ref = orthopoly.lobatto(alpha, beta, verts[0][0], verts[1][0])
else:
# Special case for lowest order.
xs_ref = [v[0] for v in verts[:]]
ws_ref = (0.5 * (xs_ref[1] - xs_ref[0]), ) * 2
A, b = reference_element.make_affine_mapping(Ref1.get_vertices(),
ref_el.get_vertices())
mapping = lambda x: numpy.dot(A, x) + b
scale = numpy.linalg.det(A)
xs = tuple([tuple(mapping(x_ref)[0]) for x_ref in xs_ref])
ws = tuple([scale * w for w in ws_ref])
QuadratureRule.__init__(self, ref_el, xs, ws)
def __init__(self, ref_el):
if ref_el.get_spatial_dimension() != 1:
raise Exception("Must have a line")
self.ref_el = ref_el
self.base_ref_el = reference_element.DefaultLine()
v1 = ref_el.get_vertices()
v2 = self.base_ref_el.get_vertices()
self.A, self.b = reference_element.make_affine_mapping(v1, v2)
self.mapping = lambda x: numpy.dot(self.A, x) + self.b
self.scale = numpy.sqrt(numpy.linalg.det(self.A))
def __init__(self, ref_el, m):
# this gives roots on the default (-1,1) reference element
# (xs_ref, ws_ref) = compute_gauss_jacobi_rule(a, b, m)
(xs_ref, ws_ref) = compute_gauss_jacobi_rule(0., 0., m)
Ref1 = reference_element.DefaultLine()
A, b = reference_element.make_affine_mapping(Ref1.get_vertices(),
ref_el.get_vertices())
mapping = lambda x: numpy.dot(A, x) + b
scale = numpy.linalg.det(A)
xs = tuple([tuple(mapping(x_ref)[0]) for x_ref in xs_ref])
ws = tuple([scale * w for w in ws_ref])
QuadratureRule.__init__(self, ref_el, xs, ws)
def create_data():
ps = polynomial_set.ONPolynomialSet(
ref_el=reference_element.DefaultLine(), degree=3)
return ps.dmats