def __init__(self, mesh, name='unnamed'):
self.mesh = mesh
self.name = name
self.n = mesh.n
self.n_nonzero = self.n
self.ngbs = mesh.neighbours
self._mu_s = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self.random_spin = np.zeros(3 * self.n, dtype=np.float)
self._H = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.create_tablewriter()
self.vtk = SaveVTK(self.mesh, name=name)
self.hexagonal_mesh = False
if mesh.mesh_type == 'hexagonal':
self.hexagonal_mesh = True
#FIX ME !!!!
self.nngbs = np.copy(mesh.neighbours)
else:
self.nngbs = mesh.next_neighbours
self.step = 0
self.skx_num = 0
self.mc = clib.monte_carlo()
self.set_options()
def __init__(self, mesh, name='unnamed'):
self.mesh = mesh
self.name = name
self.n = mesh.n
self.n_nonzero = self.n
self.ngbs = mesh.neighbours
self._mu_s = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self.random_spin = np.zeros(3 * self.n, dtype=np.float)
self._H = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.create_tablewriter()
self.vtk = SaveVTK(self.mesh, name=name)
self.step = 0
self.skx_num = 0
self.set_options()
def __init__(self, mesh, name='unnamed'):
self.mesh = mesh
self.name = name
self.n = mesh.n
self.n_nonzero = self.n
self.ngbs = mesh.neighbours
self._mu_s = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self.random_spin = np.zeros(3 * self.n, dtype=np.float)
self._H = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.create_tablewriter()
self.vtk = SaveVTK(self.mesh, name=name)
self.hexagnoal_mesh = False
if mesh.mesh_type == 'hexagonal':
self.hexagnoal_mesh = True
#FIX ME !!!!
self.nngbs = np.copy(mesh.neighbours)
else:
self.nngbs = mesh.next_neighbours
self.step = 0
self.skx_num = 0
self.mc = clib.monte_carlo()
self.set_options()
def __init__(self, mesh, name="unnamed", use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + ".txt")
self.saver.entities["E_total"] = {"unit": "<J>", "get": lambda sim: sim.compute_energy(), "header": "E_total"}
self.saver.entities["m_error"] = {
"unit": "<>",
"get": lambda sim: sim.compute_spin_error(),
"header": "m_error",
}
self.saver.entities["skx_num"] = {"unit": "<>", "get": lambda sim: sim.skyrmion_number(), "header": "skx_num"}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs, self.sundials_jtn)
self.set_default_options()
self.set_tols()
class LLG(object):
def __init__(self, mesh, name="unnamed", use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + ".txt")
self.saver.entities["E_total"] = {"unit": "<J>", "get": lambda sim: sim.compute_energy(), "header": "E_total"}
self.saver.entities["m_error"] = {
"unit": "<>",
"get": lambda sim: sim.compute_spin_error(),
"header": "m_error",
}
self.saver.entities["skx_num"] = {"unit": "<>", "get": lambda sim: sim.skyrmion_number(), "header": "skx_num"}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs, self.sundials_jtn)
self.set_default_options()
self.set_tols()
def set_default_options(self, gamma=1, mu_s=1, alpha=0.1):
self.default_c = -1
self._alpha[:] = alpha
self._mu_s[:] = mu_s
self.gamma = gamma
self.do_procession = True
def set_tols(self, rtol=1e-8, atol=1e-10):
self.vode.set_options(rtol, atol)
def set_options(self, rtol=1e-8, atol=1e-10):
self.set_tols(rtol, atol)
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._mu_s[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
self.vode.set_initial_value(self.spin, self.t)
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_mu_s(self):
return self._mu_s
def set_mu_s(self, value):
self._mu_s[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._mu_s[i] > 0.0:
self._mu_s_inv[i] = 1.0 / self._mu_s[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
mu_s = property(get_mu_s, set_mu_s)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, self._mu_s)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + "_2"
self.interactions.append(interaction)
energy_name = "E_{0}".format(interaction.name)
self.saver.entities[energy_name] = {
"unit": "<J>",
"get": lambda sim: sim.get_interaction(interaction.name).compute_energy(),
"header": energy_name,
}
if save_field:
fn = "{0}".format(interaction.name)
self.saver.entities[fn] = {
"unit": "<>",
"get": lambda sim: sim.get_interaction(interaction.name).average_field(),
"header": ("%s_x" % fn, "%s_y" % fn, "%s_z" % fn),
}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError(
"Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(name, [x.name for x in self.interactions])
)
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
ode = self.vode
self.spin_last[:] = self.spin[:]
flag = ode.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = ode.y[:]
self.t = t
self.step += 1
# update field before saving data
self.compute_effective_field(t)
self.saver.save()
def compute_effective_field(self, t):
# self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def compute_effective_field_jac(self, t, spin):
# self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
if obj.jac is True:
self.field += obj.compute_field(t, spin=spin)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(
ydot, self.spin, self.field, self.alpha, self._pins, self.gamma, self.n, self.do_procession, self.default_c
)
# ydot[:] = self.dm_dt[:]
return 0
def sundials_jtn(self, mp, Jmp, t, m, fy):
# we can not copy mp to self.spin since m and self.spin is one object.
# self.spin[:] = mp[:]
print "NO jac..........."
self.compute_effective_field_jac(t, mp)
clib.compute_llg_jtimes(
Jmp, m, fy, mp, self.field, self.alpha, self._pins, self.gamma, self.n, self.do_procession, self.default_c
)
return 0
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (-1,)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skymrion_number(self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
"""
Returns the spin components of the spin at
i-th position in the z direction, j-th position in the
y direction and k-th position in x direction
"""
nxyz = self.mesh.n
index = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[index], self.spin[index + 1], self.spin[index + 2]])
def add_monitor_at(self, i, j, k, name="p"):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
"unit": "<>",
"get": lambda sim: sim.spin_at(i, j, k),
"header": (name + "_x", name + "_y", name + "_z"),
}
self.saver.update_entity_order()
def save_vtk(self):
self.vtk.save_vtk(self.spin.reshape(-1, 3), self._mu_s, step=self.step)
def save_m(self):
if not os.path.exists("%s_npys" % self.name):
os.makedirs("%s_npys" % self.name)
name = "%s_npys/m_%g.npy" % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self, vtk=False):
if not os.path.exists("%s_skx_npys" % self.name):
os.makedirs("%s_skx_npys" % self.name)
name = "%s_skx_npys/m_%g.npy" % (self.name, self.step)
np.save(name, self._skx_number)
if vtk is True:
self.vtk.save_vtk_scalar(self._skx_number, self.step)
def stat(self):
return self.vode.stat()
def spin_length(self):
self.spin.shape = (-1, 3)
length = np.sqrt(np.sum(self.spin ** 2, axis=1))
self.spin.shape = (-1,)
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((-1, 3))
max_dm = np.max(np.sqrt(np.sum(dm ** 2, axis=1)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self, dt=1e-11, stopping_dmdt=0.01, max_steps=1000, save_m_steps=100, save_vtk_steps=100):
for i in range(0, max_steps + 1):
cvode_dt = self.vode.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print "step=%d, time=%g, max_dmdt=%g ode_step=%g" % (self.step, self.t, dmdt, cvode_dt)
if dmdt < stopping_dmdt:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
class MonteCarlo(object):
def __init__(self, mesh, name='unnamed'):
self.mesh = mesh
self.name = name
self.n = mesh.n
self.n_nonzero = self.n
self.ngbs = mesh.neighbours
self._mu_s = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self.random_spin = np.zeros(3 * self.n, dtype=np.float)
self._H = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.create_tablewriter()
self.vtk = SaveVTK(self.mesh, name=name)
self.hexagonal_mesh = False
if mesh.mesh_type == 'hexagonal':
self.hexagonal_mesh = True
#FIX ME !!!!
self.nngbs = np.copy(mesh.neighbours)
else:
self.nngbs = mesh.next_neighbours
self.step = 0
self.skx_num = 0
self.mc = clib.monte_carlo()
self.set_options()
def set_options(self,
J=50.0 * const.k_B,
J1=0,
D=0,
D1=0,
Kc=0,
H=None,
seed=100,
T=10.0,
S=1):
"""
J, D and Kc in units of Joule
H in units of Tesla.
S is the spin length
"""
self.mc.set_seed(seed)
self.J = J / const.k_B
self.J1 = J1 / const.k_B
self.D = D / const.k_B
self.D1 = D1 / const.k_B
self.T = T
self.Kc = Kc / const.k_B
self.mu_s = 1.0
if H is not None:
self._H[:] = helper.init_vector(H, self.mesh)
self._H[:] = self._H[:] * const.mu_s_1 * S / const.k_B
def create_tablewriter(self):
entities = {
'step': {
'unit': '<>',
'get': lambda sim: sim.step,
'header': 'step'
},
'm': {
'unit': '<>',
'get': lambda sim: sim.compute_average(),
'header': ('m_x', 'm_y', 'm_z')
},
'skx_num': {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'
}
}
self.saver = DataSaver(self, self.name + '.txt', entities=entities)
self.saver.update_entity_order()
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._mu_s[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1, )
def get_mu_s(self):
return self._mu_s
def set_mu_s(self, value):
self._mu_s[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._mu_s[i] > 0.0:
nonzero += 1
self.n_nonzero = nonzero
mu_s = property(get_mu_s, set_mu_s)
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (-1, )
return average
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skyrmion_number(self.spin, self._skx_number, nx,
ny, nz, self.mesh.neighbours,
self.mesh.n_ngbs)
self.skx_num = number
return number
def save_vtk(self):
"""
Save a VTK file with the magnetisation vector field and magnetic
moments as cell data. Magnetic moments are saved in units of
Bohr magnetons
NOTE: It is recommended to use a *cell to point data* filter in
Paraview or Mayavi to plot the vector field
"""
self.vtk.save_vtk(self.spin.reshape(-1, 3), self._mu_s, step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def run(self,
steps=1000,
save_m_steps=100,
save_vtk_steps=100,
save_data_steps=1):
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
for step in range(1, steps + 1):
self.step = step
self.mc.run_step(self.spin, self.random_spin, self.ngbs,
self.nngbs, self.mesh.n_ngbs, self.J, self.J1,
self.D, self.D1, self._H, self.Kc, self.n, self.T,
self.hexagonal_mesh)
if save_data_steps is not None:
if step % save_data_steps == 0:
self.saver.save()
print("step=%d, skyrmion number=%0.9g" %
(self.step, self.skx_num))
if save_vtk_steps is not None:
if step % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if step % save_m_steps == 0:
self.save_m()
def __init__(self, mesh, name='unnamed', use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'
}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'
}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'
}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[
1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs,
self.sundials_jtn)
self.set_default_options()
self.set_tols()
# When initialising the integrator in the self.vode call, the CVOde
# class calls the set_initial_value function (with flag_m=0), which
# initialises a new integrator and allocates memory in this process.
# Now, when we set the magnetisation, we will use the same memory
# setting this flag_m to 1, so instead of calling CVodeInit we call
# CVodeReInit. If don't, memory is allocated in every call of set_m
self.flag_m = 1
class LLG(object):
def __init__(self, mesh, name='unnamed', integrator='sundials'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
if integrator == "sundials":
self.integrator = SundialsIntegrator(self.spin, self.sundials_rhs)
elif integrator == "euler" or integrator == "rk4":
self.integrator = StepIntegrator(self.spin, self.step_rhs, integrator)
else:
raise NotImplemented("integrator must be sundials, euler or rk4")
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.integrator.rhs_evals,
'header': 'rhs_evals'}
self.saver.entities['real_time'] = {
'unit': '<s>',
'get': lambda _: time.time(), # seconds since epoch
'header': 'real_time'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.set_default_options()
def set_default_options(self, gamma=2.21e5, Ms=8.0e5, alpha=0.1):
self.default_c = 1e11
self._alpha[:] = alpha
self._Ms[:] = Ms
self.gamma = gamma
self.do_procession = True
def reset_integrator(self, t=0):
self.integrator.reset(self.spin, t)
self.t = t # also reinitialise the simulation time and step
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10, max_ord=None, reset=True):
if max_ord is not None:
self.integrator.set_tols(rtol=rtol, atol=atol, max_ord=max_ord)
else:
# not all integrators have max_ord (only VODE does)
# and we don't want to encode a default value here either
self.integrator.set_tols(rtol=rtol, atol=atol)
if reset:
self.reset_integrator(self.t)
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._Ms[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
self.integrator.set_initial_value(self.spin, self.t)
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_Ms(self):
return self._Ms
def set_Ms(self, value):
self._Ms[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._Ms[i] > 0.0:
self._Ms_inv = 1.0 / self._Ms[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
self.Ms_const = np.max(self._Ms)
Ms = property(get_Ms, set_Ms)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, Ms=self._Ms)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit': '<J>',
'get': lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header': energy_name}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit': '<>',
'get': lambda sim: sim.get_interaction(interaction.name).average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
self.spin_last[:] = self.spin[:]
flag = self.integrator.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = self.integrator.y[:]
self.t = t
self.step += 1
self.compute_effective_field(t) # update fields before saving data
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_procession,
self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def step_rhs(self, t, y):
self.t = t
self.compute_effective_field(t)
clib.compute_llg_rhs(self.dm_dt,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_procession,
self.default_c)
return self.dm_dt
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (3 * self.n)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skymrion_number(
self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
i1 = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[i1],
self.spin[i1 + 1],
self.spin[i1 + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')}
self.saver.update_entity_order()
def save_vtk(self):
self.vtk.save_vtk(self.spin.reshape(-1, 3), self.Ms, step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
def stat(self):
return self.integrator.stat()
def spin_length(self):
self.spin.shape = (3, -1)
length = np.sqrt(np.sum(self.spin**2, axis=0))
self.spin.shape = (-1,)
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((3, -1))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=0)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self, dt=1e-11, stopping_dmdt=0.01, max_steps=1000,
save_m_steps=100, save_vtk_steps=100):
ONE_DEGREE_PER_NS = 17453292.52
for i in range(0, max_steps + 1):
cvode_dt = self.integrator.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print 'step=%d, time=%g, max_dmdt=%g ode_step=%g' % (self.step,
self.t,
dmdt / ONE_DEGREE_PER_NS,
cvode_dt)
if dmdt < stopping_dmdt * ONE_DEGREE_PER_NS:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
def __init__(self, mesh, name='unnamed', use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(
self.spin, self.sundials_rhs, self.sundials_jtn)
self.set_default_options()
self.set_tols()
# When initialising the integrator in the self.vode call, the CVOde
# class calls the set_initial_value function (with flag_m=0), which
# initialises a new integrator and allocates memory in this process.
# Now, when we set the magnetisation, we will use the same memory
# setting this flag_m to 1, so instead of calling CVodeInit we call
# CVodeReInit. If don't, memory is allocated in every call of set_m
self.flag_m = 1
class LLG(object):
def __init__(self, mesh, name='unnamed', use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(
self.spin, self.sundials_rhs, self.sundials_jtn)
self.set_default_options()
self.set_tols()
# When initialising the integrator in the self.vode call, the CVOde
# class calls the set_initial_value function (with flag_m=0), which
# initialises a new integrator and allocates memory in this process.
# Now, when we set the magnetisation, we will use the same memory
# setting this flag_m to 1, so instead of calling CVodeInit we call
# CVodeReInit. If don't, memory is allocated in every call of set_m
self.flag_m = 1
def set_default_options(self, gamma=1, mu_s=1, alpha=0.1):
self.default_c = -1
self._alpha[:] = alpha
self._mu_s[:] = mu_s
self.gamma = gamma
self.do_precession = True
def reset_integrator(self, t=0):
self.vode.reset(self.spin, t)
self.t = t # also reinitialise the simulation time and step
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10):
self.vode.set_options(rtol, atol)
def set_options(self, rtol=1e-8, atol=1e-10):
self.set_tols(rtol, atol)
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._mu_s[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
self.vode.set_initial_value(self.spin, self.t)
if not self.flag_m:
self.flag_m = 1
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_mu_s(self):
return self._mu_s
def set_mu_s(self, value):
self._mu_s[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._mu_s[i] > 0.0:
self._mu_s_inv[i] = 1.0 / self._mu_s[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
mu_s = property(get_mu_s, set_mu_s)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, self._mu_s)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit': '<J>',
'get': lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header': energy_name}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit': '<>',
'get': lambda sim: sim.get_interaction(interaction.name).average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
ode = self.vode
self.spin_last[:] = self.spin[:]
flag = ode.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = ode.y[:]
self.t = t
self.step += 1
# update field before saving data
self.compute_effective_field(t)
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def compute_effective_field_jac(self, t, spin):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
if obj.jac is True:
self.field += obj.compute_field(t, spin=spin)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_precession,
self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def sundials_jtn(self, mp, Jmp, t, m, fy):
# we can not copy mp to self.spin since m and self.spin is one object.
#self.spin[:] = mp[:]
print('NO jac...........')
self.compute_effective_field_jac(t, mp)
clib.compute_llg_jtimes(Jmp,
m, fy,
mp, self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_precession,
self.default_c)
return 0
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (-1,)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skyrmion_number(
self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
"""
Returns the spin components of the spin at
i-th position in the z direction, j-th position in the
y direction and k-th position in x direction
"""
nxyz = self.mesh.n
index = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[index],
self.spin[index + 1],
self.spin[index + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')}
self.saver.update_entity_order()
def save_vtk(self):
"""
Save a VTK file with the magnetisation vector field and magnetic
moments as cell data. Magnetic moments are saved in units of
Bohr magnetons
NOTE: It is recommended to use a *cell to point data* filter in
Paraview or Mayavi to plot the vector field
"""
self.vtk.save_vtk(self.spin.reshape(-1, 3),
self._mu_s / const.mu_B,
step=self.step
)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self, vtk=False):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
if vtk is True:
self.vtk.save_vtk_scalar(self._skx_number, self.step)
def stat(self):
return self.vode.stat()
def spin_length(self):
self.spin.shape = (-1, 3)
length = np.sqrt(np.sum(self.spin**2, axis=1))
self.spin.shape = (-1,)
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((-1, 3))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=1)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self, dt=1e-11, stopping_dmdt=0.01,
max_steps=1000, save_m_steps=100, save_vtk_steps=100):
for i in range(0, max_steps + 1):
cvode_dt = self.vode.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print('step=%d, time=%0.3g, max_dmdt=%0.3g ode_step=%0.3g' % (self.step,self.t, dmdt,cvode_dt))
if dmdt < stopping_dmdt:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
class MonteCarlo(object):
def __init__(self, mesh, name='unnamed'):
self.mesh = mesh
self.name = name
self.n = mesh.n
self.n_nonzero = self.n
self.ngbs = mesh.neighbours
self._mu_s = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self.random_spin = np.zeros(3 * self.n, dtype=np.float)
self._H = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.create_tablewriter()
self.vtk = SaveVTK(self.mesh, name=name)
self.hexagnoal_mesh = False
if mesh.mesh_type == 'hexagonal':
self.hexagnoal_mesh = True
#FIX ME !!!!
self.nngbs = np.copy(mesh.neighbours)
else:
self.nngbs = mesh.next_neighbours
self.step = 0
self.skx_num = 0
self.mc = clib.monte_carlo()
self.set_options()
def set_options(self, J=50.0, J1=0, D=0, D1=0, Kc=0, H=None, seed=100, T=10.0, S=1):
"""
J, D and Kc in units of k_B
H in units of Tesla.
S is the spin length
"""
self.mc.set_seed(seed)
self.J = J
self.J1 = J1
self.D = D
self.D1 = D1
self.T = T
self.Kc = Kc
self.mu_s = 1.0
if H is not None:
self._H[:] = helper.init_vector(H, self.mesh)
self._H[:] = self._H[:]*const.mu_s_1*S/const.k_B #We have set k_B = 1
def create_tablewriter(self):
entities = {
'step': {'unit': '<>',
'get': lambda sim: sim.step,
'header': 'step'},
'm': {'unit': '<>',
'get': lambda sim: sim.compute_average(),
'header': ('m_x', 'm_y', 'm_z')},
'skx_num':{'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
}
self.saver = DataSaver(self, self.name + '.txt', entities=entities)
self.saver.update_entity_order()
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._mu_s[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
def get_mu_s(self):
return self._mu_s
def set_mu_s(self, value):
self._mu_s[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._mu_s[i] > 0.0:
nonzero += 1
self.n_nonzero = nonzero
mu_s = property(get_mu_s, set_mu_s)
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (-1,)
return average
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skyrmion_number(
self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
self.skx_num = number
return number
def save_vtk(self):
"""
Save a VTK file with the magnetisation vector field and magnetic
moments as cell data. Magnetic moments are saved in units of
Bohr magnetons
NOTE: It is recommended to use a *cell to point data* filter in
Paraview or Mayavi to plot the vector field
"""
self.vtk.save_vtk(self.spin.reshape(-1, 3),
self._mu_s,
step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def run(self, steps=1000, save_m_steps=100, save_vtk_steps=100, save_data_steps=1):
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
for step in range(1, steps + 1):
self.step = step
self.mc.run_step(self.spin, self.random_spin, self.ngbs, self.nngbs,
self.J, self.J1, self.D, self.D1, self._H, self.Kc, self.n, self.T, self.hexagnoal_mesh)
if save_data_steps is not None:
if step % save_data_steps == 0:
self.saver.save()
print("step=%d, skyrmion number=%0.9g"%(self.step, self.skx_num))
if save_vtk_steps is not None:
if step % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if step % save_m_steps == 0:
self.save_m()
class LLG(object):
def __init__(self, mesh, name='unnamed'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'
}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'
}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'
}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.cvode_stat_output(sim),
'header': 'rhs_evals'
}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
self.set_default_options()
self.set_tols()
def set_default_options(self, gamma=2.21e5, Ms=8.0e5, alpha=0.1):
self.default_c = 1e11
self._alpha[:] = alpha
self._Ms[:] = Ms
self.gamma = gamma
self.do_procession = True
def reset_integrator(self, t=0):
self.vode.reset(self.spin, t)
# Also reinitialise the simulation time and step
self.t = t
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10):
if self.integrator_tolerances_set is True:
self.reset_integrator(self.t)
self.vode.set_options(rtol, atol)
self.integrator_tolerances_set = True
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._Ms[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1, )
self.vode.set_initial_value(self.spin, self.t)
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_Ms(self):
return self._Ms
def set_Ms(self, value):
self._Ms[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._Ms[i] > 0.0:
self._Ms_inv = 1.0 / self._Ms[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
self.Ms_const = np.max(self._Ms)
Ms = property(get_Ms, set_Ms)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, Ms=self._Ms)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit':
'<J>',
'get':
lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header':
energy_name
}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit':
'<>',
'get':
lambda sim: sim.get_interaction(interaction.name).
average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)
}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
ode = self.vode
self.spin_last[:] = self.spin[:]
flag = ode.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = ode.y[:]
self.t = t
self.step += 1
# update field before saving data
self.compute_effective_field(t)
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot, self.spin, self.field, self.alpha,
self._pins, self.gamma, self.n,
self.do_procession, self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (3 * self.n)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skymrion_number(self.spin, self._skx_number, nx,
ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
i1 = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[i1], self.spin[i1 + 1], self.spin[i1 + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')
}
self.saver.update_entity_order()
def save_vtk(self):
self.vtk.save_vtk(self.spin.reshape(-1, 3), self.Ms, step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
def stat(self):
return self.vode.stat()
def spin_length(self):
self.spin.shape = (3, -1)
length = np.sqrt(np.sum(self.spin**2, axis=0))
self.spin.shape = (-1, )
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((3, -1))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=0)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self,
dt=1e-11,
stopping_dmdt=0.01,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=100):
ONE_DEGREE_PER_NS = 17453292.52
for i in range(0, max_steps + 1):
cvode_dt = self.vode.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print 'step=%d, time=%g, max_dmdt=%g ode_step=%g' % (
self.step, self.t, dmdt / ONE_DEGREE_PER_NS, cvode_dt)
if dmdt < stopping_dmdt * ONE_DEGREE_PER_NS:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
def cvode_stat_output(self, sim):
"""
This function tries to get the values from the CVODE statistics. For a
'sim' simulation object, this is done starting from calling
sim.vode.stats()
According to the CVODE version, this call can generate a string:
CvodeSolver(nsteps = 18,
nfevals = 32,
njevals = 14.
)
where:
nsteps --> number of steps taken by CVODE
nfevals --> number of calls to the user's f function
(I guess this is what we need)
njevals --> the cumulative number of calls to the Jacobian function
So, for example, we can regex search any number preceded by
"nfevals = "
to get the number of evaluations of the RHS and convert the
result to an integer
OR it can give a tuple with 3 values, which must be in the same
order than before
For now, we are only interested in the RHS evaluations, so we
return a single value
"""
cvode_stat = sim.vode.stat()
if isinstance(cvode_stat, str):
out = int(
re.search(r'(?<=nfevals\s=\s)[0-9]*', cvode_stat).group(0))
elif isinstance(cvode_stat, tuple):
out = cvode_stat[1]
else:
raise NotImplementedError('Cannot retrieve the values'
'from CVODE stats')
return out
def __init__(self, mesh, name='unnamed'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.cvode_stat_output(sim),
'header': 'rhs_evals'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
self.set_default_options()
self.set_tols()
class LLG(object):
def __init__(self, mesh, name='unnamed'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.cvode_stat_output(sim),
'header': 'rhs_evals'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
self.set_default_options()
self.set_tols()
def set_default_options(self, gamma=2.21e5, Ms=8.0e5, alpha=0.1):
self.default_c = 1e11
self._alpha[:] = alpha
self._Ms[:] = Ms
self.gamma = gamma
self.do_procession = True
def reset_integrator(self, t=0):
self.vode.reset(self.spin, t)
# Also reinitialise the simulation time and step
self.t = t
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10):
if self.integrator_tolerances_set is True:
self.reset_integrator(self.t)
self.vode.set_options(rtol, atol)
self.integrator_tolerances_set = True
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._Ms[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
self.vode.set_initial_value(self.spin, self.t)
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_Ms(self):
return self._Ms
def set_Ms(self, value):
self._Ms[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._Ms[i] > 0.0:
self._Ms_inv = 1.0 / self._Ms[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
self.Ms_const = np.max(self._Ms)
Ms = property(get_Ms, set_Ms)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, Ms=self._Ms)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit': '<J>',
'get': lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header': energy_name}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit': '<>',
'get': lambda sim: sim.get_interaction(interaction.name).average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
ode = self.vode
self.spin_last[:] = self.spin[:]
flag = ode.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = ode.y[:]
self.t = t
self.step += 1
# update field before saving data
self.compute_effective_field(t)
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_procession,
self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (3 * self.n)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skymrion_number(
self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
i1 = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[i1],
self.spin[i1 + 1],
self.spin[i1 + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')}
self.saver.update_entity_order()
def save_vtk(self):
self.vtk.save_vtk(self.spin.reshape(-1, 3), self.Ms, step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
def stat(self):
return self.vode.stat()
def spin_length(self):
self.spin.shape = (3, -1)
length = np.sqrt(np.sum(self.spin**2, axis=0))
self.spin.shape = (-1,)
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((3, -1))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=0)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self, dt=1e-11, stopping_dmdt=0.01, max_steps=1000,
save_m_steps=100, save_vtk_steps=100):
ONE_DEGREE_PER_NS = 17453292.52
for i in range(0, max_steps + 1):
cvode_dt = self.vode.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print 'step=%d, time=%g, max_dmdt=%g ode_step=%g' % (self.step,
self.t,
dmdt / ONE_DEGREE_PER_NS,
cvode_dt)
if dmdt < stopping_dmdt * ONE_DEGREE_PER_NS:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
def cvode_stat_output(self, sim):
"""
This function tries to get the values from the CVODE statistics. For a
'sim' simulation object, this is done starting from calling
sim.vode.stats()
According to the CVODE version, this call can generate a string:
CvodeSolver(nsteps = 18,
nfevals = 32,
njevals = 14.
)
where:
nsteps --> number of steps taken by CVODE
nfevals --> number of calls to the user's f function
(I guess this is what we need)
njevals --> the cumulative number of calls to the Jacobian function
So, for example, we can regex search any number preceded by
"nfevals = "
to get the number of evaluations of the RHS and convert the
result to an integer
OR it can give a tuple with 3 values, which must be in the same
order than before
For now, we are only interested in the RHS evaluations, so we
return a single value
"""
cvode_stat = sim.vode.stat()
if isinstance(cvode_stat, str):
out = int(re.search(r'(?<=nfevals\s=\s)[0-9]*',
cvode_stat).group(0)
)
elif isinstance(cvode_stat, tuple):
out = cvode_stat[1]
else:
raise NotImplementedError('Cannot retrieve the values'
'from CVODE stats')
return out
class LLG(object):
def __init__(self, mesh, name='unnamed', integrator='sundials'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
if integrator == "sundials":
self.integrator = SundialsIntegrator(self.spin, self.sundials_rhs)
elif integrator == "euler" or integrator == "rk4":
self.integrator = StepIntegrator(self.spin, self.step_rhs, integrator)
else:
raise NotImplemented("integrator must be sundials, euler or rk4")
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.integrator.rhs_evals,
'header': 'rhs_evals'}
self.saver.entities['real_time'] = {
'unit': '<s>',
'get': lambda _: time.time(), # seconds since epoch
'header': 'real_time'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.set_default_options()
def set_default_options(self, gamma=2.21e5, Ms=8.0e5, alpha=0.1):
self.default_c = 1e11
self._alpha[:] = alpha
self._Ms[:] = Ms
self.gamma = gamma
self.do_precession = True
def reset_integrator(self, t=0):
self.integrator.reset(self.spin, t)
self.t = t # also reinitialise the simulation time and step
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10, max_ord=None, reset=True):
if max_ord is not None:
self.integrator.set_tols(rtol=rtol, atol=atol, max_ord=max_ord)
else:
# not all integrators have max_ord (only VODE does)
# and we don't want to encode a default value here either
self.integrator.set_tols(rtol=rtol, atol=atol)
if reset:
self.reset_integrator(self.t)
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._Ms[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1,)
self.integrator.set_initial_value(self.spin, self.t)
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_Ms(self):
return self._Ms
def set_Ms(self, value):
self._Ms[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._Ms[i] > 0.0:
self._Ms_inv = 1.0 / self._Ms[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._Ms)):
if self._Ms[i] == 0.0:
self._pins[i] = 1
self.Ms_const = np.max(self._Ms)
Ms = property(get_Ms, set_Ms)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, Ms=self._Ms)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit': '<J>',
'get': lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header': energy_name}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit': '<>',
'get': lambda sim: sim.get_interaction(interaction.name).average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
self.spin_last[:] = self.spin[:]
flag = self.integrator.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = self.integrator.y[:]
self.t = t
self.step += 1
self.compute_effective_field(t) # update fields before saving data
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_precession,
self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def step_rhs(self, t, y):
self.t = t
self.compute_effective_field(t)
clib.compute_llg_rhs(self.dm_dt,
self.spin,
self.field,
self.alpha,
self._pins,
self.gamma,
self.n,
self.do_precession,
self.default_c)
return self.dm_dt
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (3 * self.n)
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skymrion_number(
self.spin, self._skx_number, nx, ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
i1 = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array([self.spin[i1],
self.spin[i1 + 1],
self.spin[i1 + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')}
self.saver.update_entity_order()
def save_vtk(self):
self.vtk.save_vtk(self.spin.reshape(-1, 3), self.Ms, step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
def stat(self):
return self.integrator.stat()
def spin_length(self):
self.spin.shape = (3, -1)
length = np.sqrt(np.sum(self.spin**2, axis=0))
self.spin.shape = (-1,)
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((3, -1))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=0)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self, dt=1e-11, stopping_dmdt=0.01, max_steps=1000,
save_m_steps=100, save_vtk_steps=100):
ONE_DEGREE_PER_NS = 17453292.52
for i in range(0, max_steps + 1):
cvode_dt = self.integrator.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print 'step=%d, time=%g, max_dmdt=%g ode_step=%g' % (self.step,
self.t,
dmdt / ONE_DEGREE_PER_NS,
cvode_dt)
if dmdt < stopping_dmdt * ONE_DEGREE_PER_NS:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
def __init__(self, mesh, name='unnamed', use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'
}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'
}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'
}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[
1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs,
self.sundials_jtn)
self.set_default_options()
self.set_tols()
def __init__(self, mesh, name='unnamed', integrator='sundials'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
if integrator == "sundials":
self.integrator = SundialsIntegrator(self.spin, self.sundials_rhs)
elif integrator == "euler" or integrator == "rk4":
self.integrator = StepIntegrator(self.spin, self.step_rhs, integrator)
else:
raise NotImplemented("integrator must be sundials, euler or rk4")
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.integrator.rhs_evals,
'header': 'rhs_evals'}
self.saver.entities['real_time'] = {
'unit': '<s>',
'get': lambda _: time.time(), # seconds since epoch
'header': 'real_time'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.set_default_options()
class LLG(object):
def __init__(self, mesh, name='unnamed', use_jac=False):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._mu_s = np.zeros(self.n, dtype=np.float)
self._mu_s_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.step = 0
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'
}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'
}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'
}
self.saver.update_entity_order()
# This is only for old C files using the xperiodic variable
self.xperiodic, self.yperiodic = mesh.periodicity[0], mesh.periodicity[
1]
self.vtk = SaveVTK(self.mesh, name=name)
if use_jac is not True:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs)
else:
self.vode = cvode.CvodeSolver(self.spin, self.sundials_rhs,
self.sundials_jtn)
self.set_default_options()
self.set_tols()
# When initialising the integrator in the self.vode call, the CVOde
# class calls the set_initial_value function (with flag_m=0), which
# initialises a new integrator and allocates memory in this process.
# Now, when we set the magnetisation, we will use the same memory
# setting this flag_m to 1, so instead of calling CVodeInit we call
# CVodeReInit. If don't, memory is allocated in every call of set_m
self.flag_m = 1
def set_default_options(self, gamma=1, mu_s=1, alpha=0.1):
self.default_c = -1
self._alpha[:] = alpha
self._mu_s[:] = mu_s
self.gamma = gamma
self.do_precession = True
def reset_integrator(self, t=0):
self.vode.reset(self.spin, t)
self.t = t # also reinitialise the simulation time and step
self.step = 0
def set_tols(self, rtol=1e-8, atol=1e-10):
self.vode.set_options(rtol, atol)
def set_options(self, rtol=1e-8, atol=1e-10):
self.set_tols(rtol, atol)
def set_m(self, m0=(1, 0, 0), normalise=True):
self.spin[:] = helper.init_vector(m0, self.mesh, normalise)
# TODO: carefully checking and requires to call set_mu first
self.spin.shape = (-1, 3)
for i in range(self.spin.shape[0]):
if self._mu_s[i] == 0:
self.spin[i, :] = 0
self.spin.shape = (-1, )
self.vode.set_initial_value(self.spin, self.t)
if not self.flag_m:
self.flag_m = 1
def get_pins(self):
return self._pins
def set_pins(self, pin):
self._pins[:] = helper.init_scalar(pin, self.mesh)
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
pins = property(get_pins, set_pins)
def get_alpha(self):
return self._alpha
def set_alpha(self, value):
self._alpha[:] = helper.init_scalar(value, self.mesh)
alpha = property(get_alpha, set_alpha)
def get_mu_s(self):
return self._mu_s
def set_mu_s(self, value):
self._mu_s[:] = helper.init_scalar(value, self.mesh)
nonzero = 0
for i in range(self.n):
if self._mu_s[i] > 0.0:
self._mu_s_inv[i] = 1.0 / self._mu_s[i]
nonzero += 1
self.n_nonzero = nonzero
for i in range(len(self._mu_s)):
if self._mu_s[i] == 0.0:
self._pins[i] = 1
mu_s = property(get_mu_s, set_mu_s)
def add(self, interaction, save_field=False):
interaction.setup(self.mesh, self.spin, self._mu_s)
# TODO: FIX
for i in self.interactions:
if i.name == interaction.name:
interaction.name = i.name + '_2'
self.interactions.append(interaction)
energy_name = 'E_{0}'.format(interaction.name)
self.saver.entities[energy_name] = {
'unit':
'<J>',
'get':
lambda sim: sim.get_interaction(interaction.name).compute_energy(),
'header':
energy_name
}
if save_field:
fn = '{0}'.format(interaction.name)
self.saver.entities[fn] = {
'unit':
'<>',
'get':
lambda sim: sim.get_interaction(interaction.name).
average_field(),
'header': ('%s_x' % fn, '%s_y' % fn, '%s_z' % fn)
}
self.saver.update_entity_order()
def get_interaction(self, name):
for interaction in self.interactions:
if interaction.name == name:
return interaction
else:
raise ValueError("Failed to find the interaction with name '{0}', "
"available interactions: {1}.".format(
name, [x.name for x in self.interactions]))
def run_until(self, t):
if t <= self.t:
if t == self.t and self.t == 0.0:
self.compute_effective_field(t)
self.saver.save()
return
ode = self.vode
self.spin_last[:] = self.spin[:]
flag = ode.run_until(t)
if flag < 0:
raise Exception("Run cython run_until failed!!!")
self.spin[:] = ode.y[:]
self.t = t
self.step += 1
# update field before saving data
self.compute_effective_field(t)
self.saver.save()
def compute_effective_field(self, t):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
self.field += obj.compute_field(t)
def compute_effective_field_jac(self, t, spin):
#self.spin[:] = y[:]
self.field[:] = 0
for obj in self.interactions:
if obj.jac is True:
self.field += obj.compute_field(t, spin=spin)
def sundials_rhs(self, t, y, ydot):
self.t = t
# already synchronized when call this funciton
# self.spin[:]=y[:]
self.compute_effective_field(t)
clib.compute_llg_rhs(ydot, self.spin, self.field, self.alpha,
self._pins, self.gamma, self.n,
self.do_precession, self.default_c)
#ydot[:] = self.dm_dt[:]
return 0
def sundials_jtn(self, mp, Jmp, t, m, fy):
# we can not copy mp to self.spin since m and self.spin is one object.
#self.spin[:] = mp[:]
print('NO jac...........')
self.compute_effective_field_jac(t, mp)
clib.compute_llg_jtimes(Jmp, m, fy, mp, self.field, self.alpha,
self._pins, self.gamma, self.n,
self.do_precession, self.default_c)
return 0
def compute_average(self):
self.spin.shape = (-1, 3)
average = np.sum(self.spin, axis=0) / self.n_nonzero
self.spin.shape = (-1, )
return average
def compute_energy(self):
energy = 0
for obj in self.interactions:
energy += obj.compute_energy()
return energy
def skyrmion_number(self):
nx = self.mesh.nx
ny = self.mesh.ny
nz = self.mesh.nz
number = clib.compute_skyrmion_number(self.spin, self._skx_number, nx,
ny, nz, self.mesh.neighbours)
return number
def spin_at(self, i, j, k):
"""
Returns the spin components of the spin at
i-th position in the z direction, j-th position in the
y direction and k-th position in x direction
"""
nxyz = self.mesh.n
index = 3 * self.mesh.index(i, j, k)
# print self.spin.shape,nxy,nx,i1,i2,i3
return np.array(
[self.spin[index], self.spin[index + 1], self.spin[index + 2]])
def add_monitor_at(self, i, j, k, name='p'):
"""
Save site spin with index (i,j,k) to txt file.
"""
self.saver.entities[name] = {
'unit': '<>',
'get': lambda sim: sim.spin_at(i, j, k),
'header': (name + '_x', name + '_y', name + '_z')
}
self.saver.update_entity_order()
def save_vtk(self):
"""
Save a VTK file with the magnetisation vector field and magnetic
moments as cell data. Magnetic moments are saved in units of
Bohr magnetons
NOTE: It is recommended to use a *cell to point data* filter in
Paraview or Mayavi to plot the vector field
"""
self.vtk.save_vtk(self.spin.reshape(-1, 3),
self._mu_s / const.mu_B,
step=self.step)
def save_m(self):
if not os.path.exists('%s_npys' % self.name):
os.makedirs('%s_npys' % self.name)
name = '%s_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self.spin)
def save_skx(self, vtk=False):
if not os.path.exists('%s_skx_npys' % self.name):
os.makedirs('%s_skx_npys' % self.name)
name = '%s_skx_npys/m_%g.npy' % (self.name, self.step)
np.save(name, self._skx_number)
if vtk is True:
self.vtk.save_vtk_scalar(self._skx_number, self.step)
def stat(self):
return self.vode.stat()
def spin_length(self):
self.spin.shape = (-1, 3)
length = np.sqrt(np.sum(self.spin**2, axis=1))
self.spin.shape = (-1, )
return length
def compute_spin_error(self):
length = self.spin_length() - 1.0
length[self._pins > 0] = 0
return np.max(abs(length))
def compute_dmdt(self, dt):
m0 = self.spin_last
m1 = self.spin
dm = (m1 - m0).reshape((-1, 3))
max_dm = np.max(np.sqrt(np.sum(dm**2, axis=1)))
max_dmdt = max_dm / dt
return max_dmdt
def relax(self,
dt=1e-11,
stopping_dmdt=0.01,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=100):
for i in range(0, max_steps + 1):
cvode_dt = self.vode.get_current_step()
increment_dt = dt
if cvode_dt > dt:
increment_dt = cvode_dt
self.run_until(self.t + increment_dt)
if save_vtk_steps is not None:
if i % save_vtk_steps == 0:
self.save_vtk()
if save_m_steps is not None:
if i % save_m_steps == 0:
self.save_m()
dmdt = self.compute_dmdt(increment_dt)
print('step=%d, time=%0.3g, max_dmdt=%0.3g ode_step=%0.3g' %
(self.step, self.t, dmdt, cvode_dt))
if dmdt < stopping_dmdt:
break
if save_m_steps is not None:
self.save_m()
if save_vtk_steps is not None:
self.save_vtk()
def __init__(self, mesh, name='unnamed', integrator='sundials'):
"""Simulation object.
*Arguments*
name : the Simulation name (used for writing data files, for examples)
"""
self.t = 0
self.name = name
self.mesh = mesh
self.n = mesh.n
self.n_nonzero = mesh.n
self.unit_length = mesh.unit_length
self._alpha = np.zeros(self.n, dtype=np.float)
self._Ms = np.zeros(self.n, dtype=np.float)
self._Ms_inv = np.zeros(self.n, dtype=np.float)
self.spin = np.ones(3 * self.n, dtype=np.float)
self.spin_last = np.ones(3 * self.n, dtype=np.float)
self._pins = np.zeros(self.n, dtype=np.int32)
self.field = np.zeros(3 * self.n, dtype=np.float)
self.dm_dt = np.zeros(3 * self.n, dtype=np.float)
self._skx_number = np.zeros(self.n, dtype=np.float)
self.interactions = []
self.pin_fun = None
self.integrator_tolerances_set = False
self.step = 0
if integrator == "sundials":
self.integrator = SundialsIntegrator(self.spin, self.sundials_rhs)
elif integrator == "euler" or integrator == "rk4":
self.integrator = StepIntegrator(self.spin, self.step_rhs, integrator)
else:
raise NotImplemented("integrator must be sundials, euler or rk4")
self.saver = DataSaver(self, name + '.txt')
self.saver.entities['E_total'] = {
'unit': '<J>',
'get': lambda sim: sim.compute_energy(),
'header': 'E_total'}
self.saver.entities['m_error'] = {
'unit': '<>',
'get': lambda sim: sim.compute_spin_error(),
'header': 'm_error'}
self.saver.entities['skx_num'] = {
'unit': '<>',
'get': lambda sim: sim.skyrmion_number(),
'header': 'skx_num'}
self.saver.entities['rhs_evals'] = {
'unit': '<>',
'get': lambda sim: self.integrator.rhs_evals,
'header': 'rhs_evals'}
self.saver.entities['real_time'] = {
'unit': '<s>',
'get': lambda _: time.time(), # seconds since epoch
'header': 'real_time'}
self.saver.update_entity_order()
# This is for old C files codes using the xperiodic variables
self.xperiodic, self.yperiodic, self.zperiodic = mesh.periodicity
self.vtk = SaveVTK(self.mesh, name=name)
self.set_default_options()
# Number of images to be generated
number_images = 19
# -----------------------------------------------------------------------------
mu_s = 0.846 * const.mu_B
a = 0.125
nx = 320
ny = 185
# MESH
mesh = HexagonalMesh(a, nx, ny, alignment='square', unit_length=1e-9)
vtk_saver = SaveVTK(mesh, name='sk_displ')
centre_x = (np.max(mesh.coordinates[:, 0]) +
np.min(mesh.coordinates[:, 0])) * 0.5
centre_y = (np.max(mesh.coordinates[:, 1]) +
np.min(mesh.coordinates[:, 1])) * 0.5
lx = (np.max(mesh.coordinates[:, 0]) - np.min(mesh.coordinates[:, 0]))
ly = (np.max(mesh.coordinates[:, 1]) - np.min(mesh.coordinates[:, 1]))
# Create a simulation for the FM state and one for the skyrmion
sim = Sim(mesh, name='sk_displ')
sim.mu_s = mu_s
sim_sk = Sim(mesh)
sim_sk.mu_s = mu_s