def euler_step(torque, dt, m, hext, Jc):
"""Takes one step using the Euler method
torque: function to calculate torque from m, hext and Jc
dt: time step
m: moment unit vector
hext: external field
Jc: current density
"""
t = torque(m, hext, Jc)
return normalize(m + dt * t)
def rk23_step(torque, dt, m, hext, Jc):
""" Takes one step using the Bogacki-Shampine method (Runga-Kutta RK23)
torque: function to calculate torque from m, hext and Jc
dt: time step
m: moment unit vector
hext: external field
Jc: current density
"""
k1 = torque(m, hext, Jc)
k2 = torque(m + dt * k1 / 2.0, hext, Jc)
k3 = torque(m + 3.0 * dt * k2 / 2.0, hext, Jc)
m = m + 2.0 * dt * k1 / 9.0 + dt * k2 / 3.0 + 4 * dt * k3 / 9.0
return normalize(m)
def huen_step(torque, dt, m, hext, Jc):
""" Takes one step using Huen's method
torque: function to calculate torque from m, hext and Jc
dt: time step
m: moment unit vector
hext: external field
Jc: current density
"""
k1 = torque(m)
m1 = m + dt * k1
k2 = torque(m1)
m = m + dt * (k1 + k2) / 2.0
return normalize(m)
def rk4_step(torque, dt, m, hext, Jc):
""" Takes one step using the Classic 4th order Runga-Kutta method
torque: function to calculate torque from m, hext and Jc
dt: time step
m: moment unit vector
hext: external field
Jc: current density
"""
k1 = torque(m, hext, Jc)
k2 = torque(m + dt * k1 / 2.0, hext, Jc)
k3 = torque(m + dt * k2 / 2.0, hext, Jc)
k4 = torque(m + dt * k3, hext, Jc)
m = m + dt * (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0
return normalize(m)
def reset(self):
""" Resets the kernel to the initial conditions
"""
self.m = normalize(self.m0)
self.t = 0.0