def base_init(self, magParameters=None, steps=1000, p_start=pi / 18):
if magParameters is None:
self.mag_params = utils.MagParameters()
else:
self.mag_params = magParameters
(self.sphs, self.times) = generate_dynamics(self.mag_params,
steps=steps)
def partial_energy(sph):
energy.llg_state_energy(sph, self.mag_params)
self.energys = map(partial_energy, self.sphs)
def check_dfdm(m_cart):
"""Compare dfdm function with finite differenced dfdm."""
# Some parameters
magnetic_parameters = utils.MagParameters()
t = 0.3
# Use LL to get dmdt:
alpha = magnetic_parameters.alpha
gamma = magnetic_parameters.gamma
Hvec = magnetic_parameters.Hvec
Ms = magnetic_parameters.Ms
h_eff = Hvec
dmdt_cart = (gamma/(1+alpha**2)) * sp.cross(m_cart, h_eff) \
- (alpha*gamma/((1+alpha**2)*Ms)) * sp.cross(m_cart, sp.cross(
m_cart, h_eff))
# Calculate with function
dfdm_func = llg_cartesian_dfdm(magnetic_parameters, t, m_cart, dmdt_cart)
def f(t, m_cart, dmdt_cart):
# f is the residual + dm/dt (see notes 27/2/13)
return llg_cartesian_residual(magnetic_parameters, t, m_cart,
dmdt_cart) + dmdt_cart
# FD it
dfdm_fd = sp.zeros((3, 3))
r = f(t, m_cart, dmdt_cart)
delta = 1e-8
for i, m in enumerate(m_cart):
m_temp = sp.array(m_cart).copy() # Must force a copy here
m_temp[i] += delta
r_temp = f(t, m_temp, dmdt_cart)
r_diff = (r_temp - r) / delta
for j, r_diff_j in enumerate(r_diff):
dfdm_fd[i][j] = r_diff_j
print dfdm_fd
# Check the max of the difference
utils.assert_almost_zero(sp.amax(dfdm_func - dfdm_fd), 1e-6)
def check_residual(residual, initial_m):
mag_params = utils.MagParameters()
tmax = 3.0
f_residual = ft.partial(residual, mag_params)
# Timestep to a solution + convert to spherical
m_list, result_times = ode.odeint(f_residual,
sp.array(initial_m),
tmax,
dt=0.01)
m_sph = [utils.array2sph(m) for m in m_list]
result_pols = [m.pol for m in m_sph]
result_azis = [m.azi for m in m_sph]
# Calculate exact solutions
exact_times, exact_azis = \
mlsn.calculate_equivalent_dynamics(mag_params, result_pols)
# Check
utils.assert_list_almost_equal(exact_azis, result_azis, 1e-3)
utils.assert_list_almost_equal(exact_times, result_times, 1e-3)
def check_zeeman(m, H, ans):
"""Helper function for test_zeeman."""
mag_params = utils.MagParameters()
mag_params.Hvec = H
utils.assert_almost_equal(zeeman_energy(m, mag_params), ans(mag_params))
def setUp(self):
mag_params = utils.MagParameters()
mag_params.alpha = 0.1
self.base_init(mag_params, steps=10000)
def setUp(self):
mag_params = utils.MagParameters()
mag_params.K1 = 0.6
self.base_init(mag_params)