def __init__(self):
def tensor_points(P):
PP0, PP1 = np.array(np.meshgrid(P, P))
return np.array((PP0.ravel(), PP1.ravel())).T
def tensor_weights(W):
return np.dot(W[:, np.newaxis], W[np.newaxis, :]).ravel()
self._quadrature_points = [tensor_points(GaussQuadratures.quadrature(npoints=p + 1)[0])
for p in range(GaussQuadratures.maxpoints())]
self._quadrature_weights = [tensor_weights(GaussQuadratures.quadrature(npoints=p + 1)[1])
for p in range(GaussQuadratures.maxpoints())]
self._quadrature_npoints = np.arange(1, GaussQuadratures.maxpoints() + 1) ** 2
self._quadrature_orders = GaussQuadratures.orders
self._quadrature_order_map = GaussQuadratures.order_map
def test_quadrature_other_functions():
order = GaussQuadratures.orders[-1]
for name, function, integral in FUNCTIONS:
Q = GaussQuadratures.iter_quadrature(order)
ret = sum([function(p) * w for (p, w) in Q])
assert float_cmp(ret, integral), \
f'{name} integral wrong: {integral} vs {ret} (quadrature order {order})'
def __init__(self, flux, flux_derivative, gausspoints=5, intervals=1):
self.__auto_init(locals())
points, weights = GaussQuadratures.quadrature(npoints=self.gausspoints)
points = points / intervals
points = ((np.arange(self.intervals, dtype=np.float)[:, np.newaxis] * (1 / intervals))
+ points[np.newaxis, :]).ravel()
weights = np.tile(weights, intervals) * (1 / intervals)
self.points = points
self.weights = weights
def test_quadrature_polynomials():
for n, function, _, integral in polynomials(GaussQuadratures.orders[-1]):
name = f'x^{n}'
for order in GaussQuadratures.orders:
if n > order / 2:
continue
Q = GaussQuadratures.iter_quadrature(order)
ret = sum([function(p) * w for (p, w) in Q])
assert float_cmp(ret, integral), \
f'{name} integral wrong: {integral} vs {ret} (quadrature order {order})'
def quadrature(self, order=None, npoints=None, quadrature_type='default'):
if quadrature_type == 'default' or quadrature_type == 'gauss':
P, W = GaussQuadratures.quadrature(order, npoints)
return P[:, np.newaxis], W
else:
raise NotImplementedError('quadrature_type must be "default" or "gauss"')
def test_quadrature_points():
for order in GaussQuadratures.orders:
P, _ = GaussQuadratures.quadrature(order)
assert float_cmp_all(P, np.sort(P))
assert 0.0 < P[0]
assert P[-1] < 1.0
def test_quadrature_weights():
for order in GaussQuadratures.orders:
_, W = GaussQuadratures.quadrature(order)
assert float_cmp(sum(W), 1)
