def in_plane_indices(normal, magnitude=1, decimal_places=5):
""" Returns an array of Miller indices which lie in the
plane specified by a surface normal vector. The magnitude
specifies the maximum magnitude of the Miller indice searched.
"""
indices = all_miller_indices(magnitude)
return indices[np.where(
np.round(normalize(indices).dot(normal), decimal_places) == 0)]
def euler_step(dt, m, torque):
"""Takes one step using the Euler method
dt: time step
m: moment unit vector
torque: function to calculate torque from m
"""
t = torque(m)
return normalize(m + dt * t)
def rk23_step(dt, m, torque):
""" Takes one step using the Bogacki-Shampine method (Runga-Kutta RK23)
dt: time step
m: moment unit vector
torque: function to calculate torque from m
"""
k1 = torque(m)
k2 = torque(m + dt * k1 / 2.0)
k3 = torque(m + 3.0 * dt * k2 / 2.0)
m = m + 2.0 * dt * k1 / 9.0 + dt * k2 / 3.0 + 4 * dt * k3 / 9.0
return normalize(m)
def huen_step(dt, m, torque):
""" Takes one step using Huen's method
dt: time step
m: moment unit vector
torque: function to calculate torque from m
"""
k1 = torque(m)
m1 = m + dt * k1
k2 = torque(m1)
m = m + dt * (k1 + k2) / 2.0
return normalize(m)
def in_plane_indices_and_angles(start,
normal,
rotation='right',
magnitude=1,
decimal_places=5):
""" Returns the Miller indices and angles in degrees for in-plane
directions, based on a surface normal and a starting vector in the plane
"""
indices = in_plane_indices(normal, magnitude, decimal_places)
angles = angle_between_directions(start, normal, normalize(indices))
mask = angles.argsort()
return in_plane_indices[mask], angles[mask]
def rk4_step(dt, m, torque):
""" Takes one step using the Classic 4th order Runga-Kutta method
dt: time step
m: moment unit vector
torque: function to calculate torque from m
"""
k1 = torque(m)
k2 = torque(m + dt * k1 / 2.0)
k3 = torque(m + dt * k2 / 2.0)
k4 = torque(m + dt * k3)
m = m + dt * (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0
return normalize(m)