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plagioclase_fit_eos.py
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plagioclase_fit_eos.py
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import numpy as np
from plagioclase_model import make_scalar_model, make_anisotropic_model
from plagioclase_data import get_C1_data
from scipy.optimize import minimize
from plagioclase_parameters import scalar_args, cell_args, elastic_args
from scipy.optimize import differential_evolution
data = get_C1_data()
min_chisqr = [1.0e18]
iteration = [0]
def misfit_scalar(args):
# For scalar EoS, fit isothermal compressibilities and volumes
ss = make_scalar_model(args)
molar_fractions = np.array([data["cell"]["p_an"], 1.0 - data["cell"]["p_an"]]).T
pressures = data["cell"]["P"]
temperatures = data["cell"]["T"]
V_obs = ss.evaluate(["V"], pressures, temperatures, molar_fractions)[0]
chisqr = np.sum(
np.power((V_obs - data["cell"]["V"]) / (data["cell"]["V_err"]), 2.0)
)
molar_fractions = np.array([data["beta"]["p_an"], 1.0 - data["beta"]["p_an"]]).T
pressures = data["beta"]["P"]
temperatures = data["beta"]["T"]
beta_model = ss.evaluate(
["isothermal_compressibility_reuss"], pressures, temperatures, molar_fractions
)[0]
chisqr += np.sum(
np.power((beta_model - data["beta"]["bTR"]) / (data["beta"]["bTR_err"]), 2.0)
)
# add a chisqr for extreme nonlinear mixing behaviour in K_T
# chisqr += np.power(args[5]/4., 2.)
if chisqr < min_chisqr[0]:
min_chisqr[0] = chisqr
print(repr(args))
print(chisqr)
print()
return chisqr
def misfit_cell(args, scalar_args, elastic_args):
# For cell EoS, fit cell parameters and isothermal compressibilities
cell_args = args
ss = make_anisotropic_model(scalar_args, cell_args, elastic_args)
# cell parameters
pressures = data["cell"]["P"]
temperatures = data["cell"]["T"]
molar_fractions = np.array([data["cell"]["p_an"], 1.0 - data["cell"]["p_an"]]).T
cell_model = ss.evaluate(
["cell_parameters"], pressures, temperatures, molar_fractions
)[0]
chisqr = 0.0
f_cell = 0.1 # cell and compressibility uncertainties are poorly scaled
for i, prm in enumerate(["a", "b", "c", "alpha", "beta", "gamma"]):
chi = (cell_model[:, i] - data["cell"][prm]) / data["cell"][prm + "_err"]
chisqr += f_cell * np.sum(np.power(chi, 2.0))
# isothermal compressibilities
if False:
pressures = data["beta"]["P"]
temperatures = data["beta"]["T"]
molar_fractions = np.array([data["beta"]["p_an"], 1.0 - data["beta"]["p_an"]]).T
beta_model = ss.evaluate(
["isothermal_compressibility_tensor"],
pressures,
temperatures,
molar_fractions,
)[0]
f_beta = 10.0 # cell and compressibility uncertainties are poorly scaled
for idx, (i, j) in enumerate([(0, 0), (1, 1), (2, 2), (1, 2), (0, 2), (0, 1)]):
beta_model_i = beta_model[:, i, j]
chi = (beta_model_i - data["beta"]["b"][:, idx]) / data["beta"]["b_err"][
:, idx
]
chisqr += f_beta * np.sum(np.power(chi, 2.0))
if False:
iteration[0] = iteration[0] + 1
if chisqr < min_chisqr[0]:
min_chisqr[0] = chisqr
print(repr(args))
print(chisqr)
else:
print(f"{iteration[0]}: {chisqr} \r")
return chisqr
def misfit_elastic(args, scalar_args, cell_args):
elastic_args = args
ss = make_anisotropic_model(scalar_args, cell_args, elastic_args)
pressures = data["CN"]["P"]
temperatures = data["CN"]["T"]
molar_fractions = np.array([data["CN"]["p_an"], 1.0 - data["CN"]["p_an"]]).T
CN_model = ss.evaluate(
["isentropic_stiffness_tensor"], pressures, temperatures, molar_fractions
)[0]
chi = (CN_model - data["CN"]["CN"]) / data["CN"]["CN_err"]
chisqr = np.sum(np.tri(6, 6) * np.power(chi, 2.0))
if False:
iteration[0] = iteration[0] + 1
if chisqr < min_chisqr[0]:
min_chisqr[0] = chisqr
print(repr(args))
print(chisqr)
else:
print(f"\r{iteration[0]}: {chisqr}", end="", flush=True)
return chisqr
def misfit_cell_and_elastic(args, scalar_args):
cell_args = args[:20]
elastic_args = args[20:]
chisqr = misfit_cell(cell_args, scalar_args, elastic_args)
chisqr += misfit_elastic(elastic_args, scalar_args, cell_args)
iteration[0] = iteration[0] + 1
if chisqr < min_chisqr[0]:
min_chisqr[0] = chisqr
print(repr(args[:20]))
print(repr(args[20:]))
print(chisqr)
else:
print(f"\r{iteration[0]}: {chisqr}", end="", flush=True)
return chisqr
def misfit_elastic_2(args, scalar_args, cell_args):
elastic_args = args
ss = make_anisotropic_model(scalar_args, cell_args, elastic_args)
pressures = data["CN"]["P"]
temperatures = data["CN"]["T"]
molar_fractions = np.array([data["CN"]["p_an"], 1.0 - data["CN"]["p_an"]]).T
SN_model, KNR_model = ss.evaluate(
["isentropic_compliance_tensor", "isentropic_bulk_modulus_reuss"],
pressures,
temperatures,
molar_fractions,
)
phi_model = np.einsum("ijk, i->ijk", SN_model, KNR_model)
chi = phi_model - data["CN"]["phiN"]
chisqr = np.sum(np.power(chi, 2.0))
iteration[0] = iteration[0] + 1
if chisqr < min_chisqr[0]:
min_chisqr[0] = chisqr
print(repr(args))
print(chisqr)
else:
print(f"\r{iteration[0]}: {chisqr}", end="", flush=True)
return chisqr
if False:
args = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
sol = minimize(misfit_scalar, args)
exit()
if False:
sol = minimize(
misfit_cell,
cell_args,
args=(scalar_args, elastic_args),
)
if False:
bounds = [(-20, 20) for i in range(30)]
sol = minimize(
misfit_elastic,
elastic_args,
args=(scalar_args, cell_args),
) # bounds=bounds)
if False:
bounds = [(-10, 10) for i in range(30)]
sol = differential_evolution(
misfit_elastic, bounds=bounds, x0=elastic_args, args=(scalar_args, cell_args)
)
if True:
ce_args = np.concatenate((cell_args, elastic_args))
sol = minimize(misfit_cell_and_elastic, ce_args, args=(scalar_args))
sol = minimize(
misfit_cell_and_elastic, sol.x, args=(scalar_args), method="Nelder-Mead"
)
sol = minimize(
misfit_cell_and_elastic, sol.x, args=(scalar_args), method="Nelder-Mead"
)
sol = minimize(misfit_cell_and_elastic, sol.x, args=(scalar_args))