def subtest_biotsavart_d2A_by_dXdX_taylortest(self, idx):
coil = get_coil()
bs = BiotSavart([coil], [1e4])
points = np.asarray(
17 * [[-1.41513202e-03, 8.99999382e-01, -3.14473221e-04]])
bs.set_points(points)
dA_by_dX, d2A_by_dXdX = bs.dA_by_dX(), bs.d2A_by_dXdX()
for d1 in range(3):
for d2 in range(3):
second_deriv = d2A_by_dXdX[idx, d1, d2]
err = 1e6
for i in range(5, 10):
eps = 0.5**i
ed2 = np.zeros((1, 3))
ed2[0, d2] = 1.
bs.set_points(points + eps * ed2)
dA_dXp = bs.dA_by_dX()[idx, d1]
bs.set_points(points - eps * ed2)
dA_dXm = bs.dA_by_dX()[idx, d1]
second_deriv_est = (dA_dXp - dA_dXm) / (2. * eps)
new_err = np.linalg.norm(second_deriv - second_deriv_est)
print("new_err", new_err)
assert new_err < 0.30 * err
err = new_err
def subtest_biotsavart_dAdX_taylortest(self, idx):
coil = get_coil()
bs = BiotSavart([coil], [1e4])
points = np.asarray(
17 * [[-1.41513202e-03, 8.99999382e-01, -3.14473221e-04]])
points += 0.001 * (np.random.rand(*points.shape) - 0.5)
bs.set_points(points)
A0 = bs.A()[idx]
dA = bs.dA_by_dX()[idx]
for direction in [
np.asarray((1., 0, 0)),
np.asarray((0, 1., 0)),
np.asarray((0, 0, 1.))
]:
deriv = dA.T.dot(direction)
err = 1e6
for i in range(5, 10):
eps = 0.5**i
bs.set_points(points + eps * direction)
Aeps = bs.A()[idx]
deriv_est = (Aeps - A0) / (eps)
new_err = np.linalg.norm(deriv - deriv_est)
assert new_err < 0.55 * err
err = new_err
def test_biotsavart_B_is_curlA(self):
coil = get_coil()
bs = BiotSavart([coil], [1e4])
points = np.asarray(
17 * [[-1.41513202e-03, 8.99999382e-01, -3.14473221e-04]])
bs.set_points(points)
B, dA_by_dX = bs.B(), bs.dA_by_dX()
curlA1 = dA_by_dX[:, 1, 2] - dA_by_dX[:, 2, 1]
curlA2 = dA_by_dX[:, 2, 0] - dA_by_dX[:, 0, 2]
curlA3 = dA_by_dX[:, 0, 1] - dA_by_dX[:, 1, 0]
curlA = np.concatenate(
(curlA1[:, None], curlA2[:, None], curlA3[:, None]), axis=1)
err = np.max(np.abs(curlA - B))
assert err < 1e-14