def laplace_basis(self, point, cellidx=None, p=None):
if p is None:
p = self.p
area = self.area
ldof = self.number_of_local_dofs()
shape = point.shape[:-1] + (ldof, )
lphi = np.zeros(shape, dtype=np.float)
if p > 1:
start = 3
r = np.arange(1, p + 1)
r = r[0:-1] * r[1:]
phi = self.basis(point, cellidx=cellidx)
for i in range(2, p + 1):
lphi[..., start:start + i - 1] += np.einsum(
'i, ...i->...i', r[i - 2::-1],
phi[..., start - 2 * i + 1:start - i])
lphi[..., start + 2:start + i + 1] += np.eisum(
'i, ...i->...i', r[0:i - 1],
phi[..., start - 2 * i + 1:start - i])
start += i + 1
if cellidx is None:
return lphi / area.reshape(-1, 1)
else:
assert (point.shape[-2] == len(cellidx))
return lphi / area[cellidx].reshape(-1, 1)
def basis(self, bc):
bc0 = bc[0]
bc1 = bc[1]
phi0 = self.lagranian_basis(bc0, 2)
phi1 = self.lagranian_basis(bc1, 1)
phi = np.eisum('', phi0, phi1)
return phi
