#!/usr/bin/env python
# coding: utf-8

# # Derived fields and values
# 
# In this tutorial, we show how derived fields and values can be computed afetr the micromagnetic system is defined.
# 
# ## Simulation
# 
# First of all, as usual, we import `oommfc` and `discretisedfield`.

# In[1]:


import oommfc as oc
import discretisedfield as df


# We define the cube mesh with edge length $10 \,\text{nm}$ and cell discretisation edge $1 \,\text{nm}$.

# In[2]:


mesh = oc.Mesh(p1=(0, 0, 0), p2=(10e-9, 10e-9, 10e-9), cell=(1e-9, 1e-9, 1e-9))

# Plot the mesh.
get_ipython().run_line_magic('matplotlib', 'inline')
mesh


# Now we define the system object and its Hamiltonian.

# In[3]:


system = oc.System(name="system")

A = 1e-11
H = (0.1/oc.mu0, 0, 0)
K1 = 1e3
u = (1, 1, 1)
system.hamiltonian = oc.Exchange(A) + \
                     oc.Demag() + \
                     oc.Zeeman(H) + \
                     oc.UniaxialAnisotropy(K1=K1, u=u)


# We will now intialise the system in $(0, 0, 1)$ direction and relax the magnetisation.

# In[4]:


Ms = 8e5
system.m = df.Field(mesh, value=(0,0,1), norm=Ms)


# ## Effective field
# 
# Total effective field is:

# In[5]:


system.hamiltonian.effective_field.plot_plane("x")


# Whereas, the individual exchange effective field is:

# In[6]:


Hex_eff = system.hamiltonian.exchange.effective_field


# Because we initialised the system with the uniform state, we expect this effective field to be zero.

# In[7]:


Hex_eff.average


# ## Relax the system

# In[8]:


md = oc.MinDriver()
md.drive(system)


# Compute the energy (and demonstrate that the energy decreased) and plot its magnetisation:

# In[9]:


E = system.hamiltonian.energy
print("The system's energy is {} J.".format(E))

system.m.plot_plane("x")


# ## Computing energies of individual term

# For instance, the exchange energy is:

# In[10]:


system.hamiltonian.exchange.energy


# We can also chack the sum of all individual energy terms and check if it the same as the total energy.

# In[11]:


total_energy = 0
for term in system.hamiltonian.terms:
    total_energy += term.energy
    
print("The sum of energy terms is {} J.".format(total_energy))
print("The system's energy is {} J.".format(system.hamiltonian.energy))