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, 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)