def test_exchange_energy_density():
"""
Compare solution with nmag for now. Should derive the
analytical solution here as well.
Our initial magnetisation looks like this:
^ ~
| / ---> \ | (Hahahaha! :-D)
~ v
"""
TOL = 1e-7 # Should be lower when comparing with analytical solution
MODULE_DIR = os.path.dirname(os.path.abspath(__file__))
# run nmag
cmd = "nsim %s --clean" % os.path.join(MODULE_DIR, "run_nmag_Eexch.py")
status, output = commands.getstatusoutput(cmd)
if status != 0:
print output
sys.exit("Error %d: Running %s failed." % (status, cmd))
nmag_data = np.loadtxt(
os.path.join(MODULE_DIR, "nmag_exchange_energy_density.txt"))
# run finmag
mesh = df.IntervalMesh(100, 0, 10e-9)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
Ms = 42
m = Field(S3,
value=df.Expression(
("cos(x[0]*pi/10e-9)", "sin(x[0]*pi/10e-9)", "0"), degree=1))
exch = Exchange(1.3e-11)
Ms_field = Field(df.FunctionSpace(mesh, 'DG', 0), Ms)
exch.setup(m, Ms_field)
finmag_data = exch.energy_density()
rel_err = np.abs(nmag_data - finmag_data) / np.linalg.norm(nmag_data)
print("Nmag data = %g" % nmag_data[0])
print("Finmag data = %g" % finmag_data[0])
print "Relative error from nmag data (expect array of 0):"
print rel_err
print "Max relative error:", np.max(rel_err)
assert np.max(rel_err) < TOL, \
"Max relative error is %g, should be zero." % np.max(rel_err)
print("Work out average energy density and energy")
S1 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=1)
# only approximative -- using assemble would be better
average_energy_density = np.average(finmag_data)
w = df.TestFunction(S1)
vol = sum(df.assemble(df.dot(df.Constant([1]), w) * df.dx))
# finmag 'manually' computed, based on node values of energy density:
energy1 = average_energy_density * vol
# finmag computed by energy class
energy2 = exch.compute_energy()
# comparison with Nmag
energy3 = np.average(nmag_data) * vol
print energy1, energy2, energy3
assert abs(energy1 - energy2) < 1e-12 # actual value is 0, but
# that must be pure luck.
assert abs(energy1 - energy3) < 5e-8 # actual value
nd = np.load(os.path.join(MODULE_DIR, "nmag_hansconf.npy"))
# run finmag
mesh = df.IntervalMesh(100, 0, 10e-9)
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
DG0 = df.FunctionSpace(mesh, "DG", 0)
m = Field(
S3,
df.Expression(("cos(x[0]*pi/10e-9)", "sin(x[0]*pi/10e-9)", "0"), degree=1))
Ms = Field(DG0, 1.0)
exchange = Exchange(1.3e-11)
exchange.setup(m, Ms)
fd = exchange.energy_density()
# draw an ASCII table of the findings
table_border = "+" + "-" * 8 + "+" + "-" * 64 + "+"
table_entries = "| {:<6} | {:<20} {:<20} {:<20} |"
table_entries_f = "| {:<6} | {:<20.8f} {:<20.8f} {:<20g} |"
print table_border
print table_entries.format(" ", "min", "max", "delta")
print table_border
print table_entries_f.format("finmag", min(fd), max(fd), max(fd) - min(fd))
print table_entries_f.format("nmag", min(nd), max(nd), max(nd) - min(nd))
print table_border
# draw a plot of the two exchange energy densities
xs = mesh.coordinates().flatten()
figure, (upper_axis, lower_axis) = plt.subplots(2, 1, sharex=True)