def test_biotsavart_coil_current_taylortest(self):
coil0 = get_coil()
current0 = 1e4
coil1 = get_coil(perturb=True)
current1 = 1e3
bs = BiotSavart([coil0, coil1], [current0, current1])
points = np.asarray(
17 * [[-1.41513202e-03, 8.99999382e-01, -3.14473221e-04]])
bs.set_points(points)
B = bs.B()
J = bs.dB_by_dX()
H = bs.d2B_by_dXdX()
dB = bs.dB_by_dcoilcurrents()
dJ = bs.d2B_by_dXdcoilcurrents()
dH = bs.d3B_by_dXdXdcoilcurrents()
h = 1.
bs.currents_optim[0].set_dofs(1e4 + h)
bs.invalidate_cache()
Bp = bs.B()
Jp = bs.dB_by_dX()
Hp = bs.d2B_by_dXdX()
bs.currents_optim[0].set_dofs(1e4 - h)
bs.invalidate_cache()
Bm = bs.B()
Jm = bs.dB_by_dX()
Hm = bs.d2B_by_dXdX()
dB_approx = (Bp - Bm) / (2 * h)
dJ_approx = (Jp - Jm) / (2 * h)
dH_approx = (Hp - Hm) / (2 * h)
assert np.linalg.norm(dB[0] - dB_approx) < 1e-15
assert np.linalg.norm(dJ[0] - dJ_approx) < 1e-15
assert np.linalg.norm(dH[0] - dH_approx) < 1e-13
def subtest_biotsavart_d2B_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)
dB_by_dX, d2B_by_dXdX = bs.dB_by_dX(), bs.d2B_by_dXdX()
for d1 in range(3):
for d2 in range(3):
second_deriv = d2B_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)
dB_dXp = bs.dB_by_dX()[idx, d1]
bs.set_points(points - eps * ed2)
dB_dXm = bs.dB_by_dX()[idx, d1]
second_deriv_est = (dB_dXp - dB_dXm) / (2. * eps)
new_err = np.linalg.norm(second_deriv - second_deriv_est)
assert new_err < 0.30 * err
err = new_err
def subtest_d2B_by_dXdX_is_symmetric(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)
d2B_by_dXdX = bs.d2B_by_dXdX()
for i in range(3):
assert np.allclose(d2B_by_dXdX[idx, :, :, i],
d2B_by_dXdX[idx, :, :, i].T)