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%cat 0Source_Citation.txt
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%matplotlib inline
# %matplotlib notebook # for interactive
For high dpi displays.
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%config InlineBackend.figure_format = 'retina'
This notebook shows an example of EOS fitting for static compression, focusing on converting pressure scales when the volume data for pressure standard is not available.
The notebook demonstrates easy ways to change the EOS for pressure standard.
We use data from Lundin et al. (2007, PEPI).
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import numpy as np
from uncertainties import unumpy as unp
import pandas as pd
import pytheos as eos
Setup dictionaries for pressure standard (au_eos) and equation to use (fit_model). This allows for eos fits with a wide range of different pressure scales.
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au_eos = {'Fei2007': eos.gold.Fei2007bm3(), 'Dorogokupets2007': eos.gold.Dorogokupets2007(),
'Yokoo2009': eos.gold.Yokoo2009(), 'Ye2017': eos.gold.Ye2017()}
fit_model = {'Fei2007': eos.BM3Model(), 'Dorogokupets2007': eos.VinetModel(),
'Yokoo2009': eos.BM3Model(), 'Ye2017': eos.VinetModel()}
Lundin et al. (2007) used the gold scale by Tsuchiya (2003). Since then many updates have been made by a few different authors.
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au_org = eos.gold.Tsuchiya2003()
Uncomment the following line to get some help.
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#help(eos.gold.Yokoo2009)
We set initial values for the EOS parameters.
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v0 = {'en100': 162.30, 'en91': 163.18, 'en85': 163.30}
k0 = {'en100': 260., 'en91': 260., 'en85': 260.}
k0p = {'en100': 4.0, 'en91': 4.0, 'en85': 4.0}
Read data file. Data points are stored in csv files.
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data = pd.read_csv('./data/Lundin2007.csv')
Make error propagation possible.
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v = {'en100': unp.uarray(data['v(en100)'][~np.isnan(data['v(en100)'])],
data['sv(en100)'][~np.isnan(data['v(en100)'])]),
'en91': unp.uarray(data['v(en91)'], data['sv(en91)']),
'en85': unp.uarray(data['v(en85)'], data['sv(en85)'])}
p_org= {'en100': unp.uarray(data['p(en100)'][~np.isnan(data['v(en100)'])],
data['sp(en100)'][~np.isnan(data['v(en100)'])]),
'en91': unp.uarray(data['p(en91)'], data['sp(en91)']),
'en85': unp.uarray(data['p(en85)'], data['sp(en85)'])}
v_std= {}
In order to understand the cell below, please try the 8_pv_eos_fit_multi-scales.ipynb file first.
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for key, value in v.items():
model = eos.BM3Model()
params = model.make_params(v0=v0[key], k0=k0[key], k0p=k0p[key])
params['v0'].vary = False
params['k0p'].vary = False
fitresult = model.fit(unp.nominal_values(p_org[key]), params, v=unp.nominal_values(v[key]))
print('***'+key)
print(fitresult.fit_report())
eos.plot.static_fit_result(fitresult, title=key)
In order to convert to different gold scale, we first invert the equation to get volume from pressure. The cell below iteratively perform this task for all three different compositions in Lundin et al.
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for key, value in p_org.items():
p_tempo = unp.nominal_values(value)
# filter out empty cells
p_norm = p_tempo[~np.isnan(p_tempo)]
# now we get volume of gold
v_std[key] = au_org.cal_v(p_norm,
np.ones_like(p_norm) * 300.)
We fix v0 and k0p in this fitting example
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for comp, value in v.items(): # iteration for different compositions
for key, value in au_eos.items(): # iteration for different gold scales
# set pressure scale to use
p = au_eos[key].cal_pst(v_std[comp])
# set equation to use
model = fit_model[key]
params = model.make_params(v0=v0[comp], k0=k0[comp], k0p=k0p[comp])
params['v0'].vary = False
params['k0p'].vary = False
# perform fitting
fitresult = model.fit(unp.nominal_values(p), params, v=unp.nominal_values(v[comp]))
print('***'+key+' '+comp)
print(fitresult.fit_report())
eos.plot.static_fit_result(fitresult, title=key)
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