def create_quadrature(shape, num_points):
"""
Generate quadrature rule (points, weights) for given shape with
num_points points in each direction.
"""
if isinstance(shape, int) and shape == 0:
return ([()], array([1.0,]))
if shape in cellname2dim and cellname2dim[shape] == 0:
return ([()], array([1.0,]))
quad_rule = FIAT.make_quadrature(reference_cell(shape), num_points)
return quad_rule.get_points(), quad_rule.get_weights()
def create_quadrature(cell, num_points):
"""
Generate quadrature rule (points, weights) for given shape with
num_points points in each direction.
"""
if isinstance(cell, int) and cell == 0:
return ([()], array([1.0,]))
if isinstance(cell, str):
cellname = cell
else:
cellname = cell.cellname()
if cellname == "vertex":
return ([()], array([1.0,]))
quad_rule = FIAT.make_quadrature(reference_cell(cell), num_points)
return quad_rule.get_points(), quad_rule.get_weights()
def __init__(self, L, order):
assert L.ref_el == FIAT.ufc_simplex(1)
for ell in L.dual.nodes:
assert isinstance(ell, FIAT.functional.PointEvaluation)
c = numpy.asarray([list(ell.pt_dict.keys())[0][0]
for ell in L.dual.nodes])
num_stages = len(c)
Q = FIAT.make_quadrature(L.ref_el, 2*num_stages)
qpts = Q.get_points()
qwts = Q.get_weights()
Lvals = L.tabulate(0, qpts)[0, ]
# integrates them all!
b = Lvals @ qwts
# now for A, which means we have to adjust the interval
A = numpy.zeros((num_stages, num_stages))
for i in range(num_stages):
qpts_i = qpts * c[i]
qwts_i = qwts * c[i]
Lvals_i = L.tabulate(0, qpts_i)[0, ]
A[i, :] = Lvals_i @ qwts_i
Aexplicit = numpy.zeros((num_stages, num_stages))
for i in range(num_stages):
qpts_i = 1 + qpts * c[i]
qwts_i = qwts * c[i]
Lvals_i = L.tabulate(0, qpts_i)[0, ]
Aexplicit[i, :] = Lvals_i @ qwts_i
self.Aexplicit = Aexplicit
V = vander(c, increasing=True)
rhs = numpy.array([1.0/(s+1) for s in range(num_stages-1)] + [0])
btilde = numpy.linalg.solve(V.T, rhs)
super(CollocationButcherTableau, self).__init__(A, b, btilde, c, order)
def create_quadrature(cell, num_points):
"""
Generate quadrature rule (points, weights) for given shape with
num_points points in each direction.
"""
if isinstance(cell, int) and cell == 0:
return ([()], array([
1.0,
]))
if isinstance(cell, str):
cellname = cell
else:
cellname = cell.cellname()
if cellname == "vertex":
return ([()], array([
1.0,
]))
quad_rule = FIAT.make_quadrature(reference_cell(cell), num_points)
return quad_rule.get_points(), quad_rule.get_weights()
