def plot_results(o_potential_fitter):
import matplotlib.pyplot as plt
fig, ax = plt.subplots(3, 1)
rmax = o_potential_fitter.setfl_reader.n_r * o_potential_fitter.setfl_reader.d_r
rN = o_potential_fitter.setfl_reader.n_r
r = create_r(rmax, rN)
rhomax = o_potential_fitter.setfl_reader.n_rho * o_potential_fitter.setfl_reader.d_rho
rhoN = o_potential_fitter.setfl_reader.n_rho
rho = create_r(rhomax, rhoN)
ax[0].plot(r,
o_potential_fitter.setfl_reader.pair_function('NiNi'),
label='from_file')
ax[0].plot(r,
o_potential_fitter.formalisms['pair']['NiNi'](
r, **o.parameters['popt']['pair']['NiNi']),
label='fitted')
ax[0].set_xlim([1.5, 5.168])
ax[0].set_ylim([-1, 5])
ax[1].plot(r, o.setfl_reader.density_function('Ni'), label='from_file')
ax[1].plot(r,
o.formalisms['density']['Ni'](
r, **o.parameters['popt']['density']['Ni']),
label='fitted')
ax[1].set_xlim([1.5, 5.168])
#ax[0].set_ylim([-1,5])
#
ax[2].plot(rho, o.setfl_reader.embedding_function('Ni'), label='from_file')
ax[2].plot(rho,
o.formalisms['embedding']['Ni'](
r, **o.parameters['popt']['embedding']['Ni']),
label='fitted')
plt.show()
def fit_density_function(self,
func_density,
symbol,
param0,
bounds,
rlow=None,
rhigh=None):
if not isinstance(self.setfl_reader,SeatonSetflReader):
m = "the read_setfl_command method must be run before this method"
raise EamSetflFitterException(m)
arg_names = [k for k in inspect.getargspec(func_density)[0] if k!= 'r']
p0 = [param0[k] for k in arg_names]
bounds_ = [
[bounds[k][0] for k in arg_names],
[bounds[k][1] for k in arg_names]]
for i in range(len(arg_names)):
print(arg_names[i],p0[i],bounds_[0][i], bounds_[1][i])
# maximum interatomic spacing distance
rmax = self.setfl_reader.n_r * self.setfl_reader.d_r
# interatomic spacing distance step size
rN = self.setfl_reader.n_r
if rlow is None and rhigh is None:
r = create_r(rmax,rN)
rho = np.array(self.setfl_reader.density_function(symbol))
else:
r_ = create_r(rmax,rN)
rho_ = np.array(self.setfl_reader.density_function(symbol))
r = r_[np.all([r_>rlow,r_<rhigh],axis=0)]
rho = rho_[np.all([r_>rlow,r_<rhigh],axis=0)]
# iterate until convergence
while True:
popt,pcov = curve_fit(f=func_density,
xdata=r,
ydata=rho,
p0=p0,
check_finite=False,
bounds=bounds_,
method='trf')
if all([np.abs(k[1]/k[0]-1) < 0.01 for k in zip(popt,p0)]):
break
p0=popt
self.parameters['p0']['density'][symbol] = param0
self.parameters['popt']['density'][symbol] = OrderedDict(
[(k[0],k[1]) for k in zip(arg_names,popt)])
self.formalisms['density'][symbol] = func_density
def fit_potential_pair(self,
func_pair_potential,
symbol_pair,
param0,
rlow=None):
if not isinstance(self.setfl_reader, SeatonSetflReader):
m = "the read_setfl_command method must be run before this method"
raise EamSetflFitterException(m)
pair_name = "".join(symbol_pair)
arg_names = [
k for k in inspect.signature(func_pair_potential).parameters
if k != 'r'
]
p0 = [param0[k] for k in arg_names if k != 'r']
# maximum interatomic spacing distance
rmax = self.setfl_reader.n_r * self.setfl_reader.d_r
# interatomic spacing distance step size
rN = self.setfl_reader.n_r
if rlow is None:
r = create_r(rmax, rN)
phi = np.array(self.setfl_reader.pair_function(pair_name))
else:
r_ = create_r(rmax, rN)
phi_ = np.array(self.setfl_reader.pair_function(pair_name))
r = r_[r_ > rlow]
phi = phi_[r_ > rlow]
# iterate until convergence
while True:
popt, pcov = curve_fit(func_pair_potential,
r,
phi,
method='trf',
p0=p0)
if all([np.abs(k[1] / k[0] - 1) < 0.01 for k in zip(popt, p0)]):
break
p0 = popt
self.parameters['p0']['pair'][pair_name] = param0
self.parameters['popt']['pair'][pair_name] = OrderedDict([
(k[0], k[1]) for k in zip(arg_names, popt)
])
self.formalisms['pair'][pair_name] = func_pair_potential
def test__EquationOfStateSolver(symbols,pair_names):
rmax = 10
rN = 1000
r = create_r(rmax,rN)
rhomax = 10.
rhoN = 1000
rho = create_rho(rhomax,rN)
o = EquationOfStateSolver(symbols,r,rho)
assert o.symbols == symbols
assert np.array_equal(o.r,r)
assert np.array_equal(o.rho,rho)
assert isinstance(o.potentials,OrderedDict)
for k in EquationOfStateSolver.potential_types:
assert k in o.potentials
for pn in pair_names:
assert pn in o.potentials['pair']
assert isinstance(o.potentials['pair'][pn],OrderedDict)
assert 'formalism' in o.potentials['pair'][pn]
assert 'parameters' in o.potentials['pair'][pn]
assert 'evaluation' in o.potentials['pair'][pn]
for s in symbols:
assert s in o.potentials['density']
assert isinstance(o.potentials['density'][s],OrderedDict)
assert 'formalism' in o.potentials['density'][s]
assert 'parameters' in o.potentials['density'][s]
assert 'evaluation' in o.potentials['density'][s]
for s in symbols:
assert s in o.potentials['embedding']
assert isinstance(o.potentials['embedding'][s],OrderedDict)
assert 'formalism' in o.potentials['embedding'][s]
assert 'parameters' in o.potentials['embedding'][s]
assert 'evaluation' in o.potentials['embedding'][s]
def plot_results():
import matplotlib.pyplot as plt
fig, ax = plt.subplots(3, 1)
rmax = o.setfl_reader.n_r * o.setfl_reader.d_r
rN = o.setfl_reader.n_r
r = create_r(rmax, rN)
ax[0].plot(r, o.setfl_reader.pair_function('NiNi'), label='from_file')
ax[0].plot(r,
o.formalisms['pair']['NiNi'](
r, **o.parameters['popt']['pair']['NiNi']),
label='fitted')
ax[1].plot(r, o.setfl_reader.density_function('Ni'), label='from_file')
ax[1].plot(r,
o.formalisms['density']['Ni'](
r, **o.parameters['popt']['density']['Ni']),
label='fitted')
ax[2].plot(rho,
o.setfl.reader.embedding_function('NiNi'),
label='from_file')
ax[2].plot(rho,
o.formalism['embedding']['Ni'](
r, **o.parameters['popt']['density']['Ni']),
label='fitted')
plt.show()
def fit_density_function(self, func_density, symbol, param0, rlow=None):
if not isinstance(self.setfl_reader, SeatonSetflReader):
m = "the read_setfl_command method must be run before this method"
raise EamSetflFitterException(m)
arg_names = [
k for k in inspect.getargspec(func_density)[0] if k != 'r'
]
p0 = [param0[k] for k in arg_names]
# maximum interatomic spacing distance
rmax = self.setfl_reader.n_r * self.setfl_reader.d_r
# interatomic spacing distance step size
rN = self.setfl_reader.n_r
if rlow is None:
r = create_r(rmax, rN)
rho = np.array(self.setfl_reader.density_function(symbol))
else:
# temporary arrays
r_ = create_r(rmax, rN)
rho_ = np.array(self.setfl_reader.density_function(symbol))
# final arrays
r = r_[r_ > rlow]
rho = rho_[r_ > rlow]
# iterate until convergence
while True:
popt, pcov = curve_fit(func_density, r, rho, method='trf', p0=p0)
if all([np.abs(k[1] / k[0] - 1) < 0.01 for k in zip(popt, p0)]):
break
p0 = popt
self.parameters['p0']['density'][symbol] = param0
self.parameters['popt']['density'][symbol] = OrderedDict([
(k[0], k[1]) for k in zip(arg_names, popt)
])
self.formalisms['density'][symbol] = func_density
def test__create_r(rmax,rN):
r = create_r(rmax,rN)
assert isinstance(r,np.ndarray)
assert r.max() == rmax
assert r.size == rN
from pypospack.potential.pair_general_lj import (
func_cutoff_mishin2004, func_pair_generalized_lj,
func_pair_generalized_lj_w_cutoff)
parameters = {
'b1': 4.7067e-3,
'b2': 0.15106,
'r1': 3.8663e-4,
'V0': -3.5126e3,
'delta': 3.6046e3,
'rc': 5.168,
'hc': 3.323,
'h0': 1.500
}
r = create_r(6.0, 1000)
def test__func_cutoff_mishin2004__r_numpy():
param = [
parameters[v]
for v in inspect.signature(func_cutoff_mishin2004).parameters
if v != 'r'
]
psi = func_cutoff_mishin2004(r, *param)
assert isinstance(psi, np.ndarray)
def test__func_pair_generalized_lj__r_numpy():
param = [
parameters[v]
a[i] = brentq(f=get_density_at_a,
a=a_min,
b=a_max,
args=(rhostar, func_density, func_density_param),
xtol=a_tol)
E_eos = func_zopemishin_eos(a, a0, B, E0, beta)
E_pair = get_pair_energy_at_a(a, func_pair, func_pair_param)
E_embedding = E_eos - E_pair
return E_embedding
rhomax = o.setfl_reader.n_rho * o.setfl_reader.d_rho
rhoN = o.setfl_reader.n_rho
rho = create_r(rhomax, rhoN)
arg_names = [
k for k in inspect.getargspec(func_zopemishin_embedding_function)[0]
if k not in ['rho', 'lattice_type']
]
print(arg_names)
args = [potentials['embedding']['Ni']['param'][k] for k in arg_names]
embedding = func_zopemishin_embedding_function(rho, *args)
assert embedding.size == rho.size
o.fit_eos_embedding_function(func_embedding=func_zopemishin_embedding_function,
symbol='Ni',
param0=potentials['embedding']['Ni']['param'],
bounds=potentials['embedding']['Ni']['bounds'])
print(o.parameters['p0']['embedding']['Ni'])
import numpy as np
import matplotlib.pyplot as plt
from pypospack.eamtools import create_r
from pypospack.potential.pair_general_lj import func_cutoff_mishin2004
r = create_r(6.,5000)
rc = 5.168
hc = 0.332
xrc = (r-rc)/hc
psirc = (xrc**4)/(1+xrc**4)
rc_ind = np.ones(r.size)
rc_ind[r > rc] = 0
psirc = psirc * rc_ind
h0 = 0.332
x0 = r/h0
psi0 = (x0**4)/(1+x0**4)
fig, ax = plt.subplots(3, 1)
ax[0].plot(r,psirc,label=r'$\Psi_{c}$')
ax[0].set_ylabel(r'$\Psi_{c}$')
ax[1].plot(r,psi0,label=r'$\Psi_{0}$')
ax[1].set_ylabel(r'$\Psi_{0}$')
ax[2].plot(r,psirc*psi0,label=r'$\Psi_{c}*\Psi_{0}$')
ax[2].set_ylabel(r'$\Psi_{c}\Psi_{0}$')
for i in range(2):