Berman Standard State Code Generator + Birch-Murnaghan¶
Required system packages and initialization
import pandas as pd
import numpy as np
import sympy as sym
sym.init_printing()
from thermoengine import coder
model = coder.StdStateModel()
T = model.get_symbol_for_t()
P = model.get_symbol_for_p()
Tr = model.get_symbol_for_tr()
Pr = model.get_symbol_for_pr()
Define model expressions applicable over all of T,P space¶
An expression for the Gibbs free energy, \(G(T,P)\) or the Helmholtz energy \(A(T,V)\) is constructed. The expression may have multiple parts. Often the heat capacity function is postulated, then integrated to yield expressions for the entahlpy, entropy, and in combination the energy potential. Then, an equation of state (EOS) is adopted and that term is integrated in pressure or volume and added to the heat capacity integrals. This proceedure is follwed here. #### (1) \(C_P\) integrals The isobaric heat capacity terms parameterized as: $C_P = k_0 + k_1 / T^{1/2} + k_2 / T^2 + k_3 / T^3 $, and in addition the reference condition third law entropy, $ S_{Tr,Pr} $, and enthalpy of formation from the elements, $ :raw-latex:`Delta `H_{Tr,Pr} $, constitute additional parameters:
k0,k1,k2,k3 = sym.symbols('k0 k1 k2 k3')
CpPr = k0+k1/sym.sqrt(T)+k2/T**2+k3/T**3
STrPr,HTrPr = sym.symbols('S_TrPr H_TrPr')
Specify paramters …
params = [('H_TrPr','J',HTrPr), ('S_TrPr','J/K',STrPr), ('k0','J/K-m',k0), ('k1','J-K^(1/2)-m',k1),
('k2','J-K/m',k2), ('k3','J-K^2',k3)]
Define the heat capacity contribution to the Gibbs free energy …
GPr = HTrPr + sym.integrate(CpPr,(T,Tr,T)) - T*(STrPr + sym.integrate(CpPr/T,(T,Tr,T)))
… and add this expression to the model
model.add_expression_to_model(GPr, params)
(2) \(V\) (EOS) integrals¶
Next, define a volume-implicit equation of state applicable over the
whole of temperature and pressure space. We will use the 3rd order
Birch-Murnaghan expression:
\(P = \frac{{3K}}{2}\left[ {{{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{7}{3}}} - {{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{5}{3}}}} \right]\left\{ {\left( {\frac{{3{K_P}}}{4} - 3} \right)\left[ {{{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{2}{3}}} - 1} \right] + 1} \right\}\)
The parameters in this expression are:
VTrPr,K,Kp = sym.symbols('V_TrPr K K_P')
params = [('V_TrPr', 'J/bar-m', VTrPr), ('K','bar',K), ('K_P','',Kp)]
where V is an implicit function of T and P:
V = sym.Function('V')(T,P)
Define f, an implicit function derived from the Birch-Murnaghan
expression. f has a value zero for internally consistent V, T,
and P:
\(f = 0 = \frac{{3K}}{2}\left[ {{{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{7}{3}}} - {{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{5}{3}}}} \right]\left\{ {\left( {\frac{{3{K_P}}}{4} - 3} \right)\left[ {{{\left( {\frac{{{V_{{T_r}.{P_r}}}}}{V}} \right)}^{\frac{2}{3}}} - 1} \right] + 1} \right\} - P\)
f = (sym.S(3)*K/sym.S(2))*((VTrPr/V)**(sym.S(7)/sym.S(3))-(VTrPr/V)**(sym.S(5)/sym.S(3)))*(1+(sym.S(3)/sym.S(4))*(Kp-4)*((VTrPr/V)**(sym.S(2)/sym.S(3))-1))- P
f
\[\displaystyle \frac{3 K \left(\left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{7}{3}} - \left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{5}{3}}\right) \left(\left(\frac{3 K_{P}}{4} - 3\right) \left(\left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} - 1\right) + 1\right)}{2} - P\]
Because the EOS is explicit in P (and a function of T and V),
the natural thermodynamic potential to use is the Helmholtz energy,
A. A is obtained by integrating pressure from the reference volume
to the final volume:
\({A_{T,P}} - {A_{{T_r},{P_r}}} = \int_{{V_{{T_r},{P_r}}}}^{{V_{T,P}}} {PdV}\)
Note: To perform this integration in SymPy, first define a variable of
integration, \(V_{TP}\), substitute that variable for the function
\(V(T,P)\), and integrate \(f\) with respect to \(V_{TP}\)
over the limits \(V_{TrPr}\) to \(V(T,P)\). This procedure
generates an expression for the Helmholtz energy that is a function of
\(V(T,P)\).
Note: The integration is performed on the integrand \(f+P\), which
corresponds to the Birch-Murnaghan expression for \(P\).
VTP = sym.symbols('V_TP')
A = sym.integrate((f+P).subs(V,VTP),(VTP,VTrPr,V)).simplify()
A
\[\displaystyle \frac{9 K \left(- K_{P} V_{TrPr}^{3} + V_{TrPr}^{\frac{5}{3}} \left(3 K_{P} V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} - 3 K_{P} - 14 V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} + 16\right) \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{5}{3}} V^{3}{\left(T,P \right)} + 4 V_{TrPr}^{3} - \left(3 K_{P} V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} - 3 K_{P} V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} - K_{P} V_{TrPr} - 14 V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} + 16 V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} + 4 V_{TrPr}\right) V^{2}{\left(T,P \right)}\right)}{16 V^{2}{\left(T,P \right)}}\]
The Gibbs free energy contribution if given by the identity: \(G = A + PV\) and \({G_{T,P}} - {G_{{T_r},{P_r}}} = {A_{T,P}} + PV - {A_{{T_r},{P_r}}} - {P_r}{V_{{T_r},{P_r}}}\)
GTr = A+(f+P)*V-A.subs(V,VTrPr)-Pr*VTrPr
GTr
\[\displaystyle \frac{3 K \left(\left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{7}{3}} - \left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{5}{3}}\right) \left(\left(\frac{3 K_{P}}{4} - 3\right) \left(\left(\frac{V_{TrPr}}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} - 1\right) + 1\right) V{\left(T,P \right)}}{2} + \frac{9 K \left(- K_{P} V_{TrPr}^{3} + V_{TrPr}^{\frac{5}{3}} \left(3 K_{P} V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} - 3 K_{P} - 14 V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{2}{3}} + 16\right) \left(\frac{1}{V{\left(T,P \right)}}\right)^{\frac{5}{3}} V^{3}{\left(T,P \right)} + 4 V_{TrPr}^{3} - \left(3 K_{P} V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} - 3 K_{P} V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} - K_{P} V_{TrPr} - 14 V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} + 16 V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} + 4 V_{TrPr}\right) V^{2}{\left(T,P \right)}\right)}{16 V^{2}{\left(T,P \right)}} - \frac{9 K \left(- K_{P} V_{TrPr}^{3} + V_{TrPr}^{\frac{14}{3}} \left(3 K_{P} V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{2}{3}} - 3 K_{P} - 14 V_{TrPr}^{\frac{2}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{2}{3}} + 16\right) \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} + 4 V_{TrPr}^{3} - V_{TrPr}^{2} \left(3 K_{P} V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} - 3 K_{P} V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} - K_{P} V_{TrPr} - 14 V_{TrPr}^{\frac{10}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{7}{3}} + 16 V_{TrPr}^{\frac{8}{3}} \left(\frac{1}{V_{TrPr}}\right)^{\frac{5}{3}} + 4 V_{TrPr}\right)\right)}{16 V_{TrPr}^{2}} - P_{r} V_{TrPr}\]
The implicit_function argument of the add_expression_to_model method conveys information about how to compute a value for the implicit variable contained in the Gibbs free energy expression passed as the first argument. It is an array of tuples; each tuple has three components. The first is a sympy expression for the implicit function, which evaluates to zero for an internally consistent set of T, P, V. The second component is a symbol for the function definition of the implicit variable. The third component is is a sympy expression that initializes f in the iterative routine. This expression must be defined in terms of known parameters and Tr, Pr, T, P..
model.add_expression_to_model(GTr, params, implicit_functions=[(f,V,VTrPr/2.0)])
Note:
The implicit function will be utilized in code generation not only to
compute the value of V, given a T and P, but also to evaluate
derivatives of V, Since:
\(dP = {\left( {\frac{{\partial P}}{{\partial V}}} \right)_T}dV + {\left( {\frac{{\partial P}}{{\partial T}}} \right)_V}dT\),
\({d^2}P = d{\left( {\frac{{\partial P}}{{\partial V}}} \right)_T}dV + {\left( {\frac{{\partial P}}{{\partial V}}} \right)_T}{d^2}V + d{\left( {\frac{{\partial P}}{{\partial T}}} \right)_V}dT + {\left( {\frac{{\partial P}}{{\partial T}}} \right)_V}{d^2}T\), or
\({d^2}P = {\left( {\frac{{{\partial ^2}P}}{{\partial {V^2}}}} \right)_T}dVdV + 2\left( {\frac{{{\partial ^2}P}}{{\partial V\partial T}}} \right)dVdT + {\left( {\frac{{{\partial ^2}P}}{{\partial {T^2}}}} \right)_V}dTdT + {\left( {\frac{{\partial P}}{{\partial V}}} \right)_T}{d^2}V + {\left( {\frac{{\partial P}}{{\partial T}}} \right)_V}{d^2}T\)
Code Print the Model, compile the code and link a Python module¶
Name the model class
model.set_module_name('berman')
#model.get_berman_std_state_database()
Make a working sub-directory and move down into the directory. This is done so that generated files will not clash between alternate model configurations.
model_working_dir = "working"
!mkdir -p {model_working_dir}
%cd {model_working_dir}
/Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Codegen/working
Choose an existing phase from the Berman database
Generate an include file and code file for this phase
Note that the call to
model.create_code_module(phase=phase_name, formula=formula, params=param_dict)
generates fast code with unmodifiable model parameters and “calibration-” related functions. The call to:
model.create_code_module(phase=phase_name, formula=formula, params=param_dict, module_type='calib')
generates code suitable for model parameter calibration.
model_type='fast'
param_dict = model.get_berman_std_state_database(47, extend_defs=True)
#param_dict['K'] = 100.0
#param_dict['K_P'] = 4.0
phase_name = param_dict.pop('Phase', None).title()
formula = param_dict.pop('Formula', None)
result = model.create_code_module(phase=phase_name, formula=formula, params=param_dict, module_type=model_type)
Creating (once only) generic fast model code file string
Creating (once only) generic model fast code template include file string
Creating (once only) generic model fast code template code file string
Creating include file ...
... done!
Creating code file ...
... done
Writing include file to working directory ...
Writing code file to working directory ...
Writing pyxbld file to working directory ...
writing pyx file to working directory ...
Compiling code and Python bindings ...
Success! Import the module named berman
param_dict
{'H_TrPr': -3970790.781,
'S_TrPr': 214.145,
'k0': 381.37231,
'k1': -1941.045,
'k2': -12037252,
'k3': 1836425472,
'V_TrPr': 10.869,
'v1': -1.8045e-06,
'v2': 0,
'v3': 1.51451e-05,
'v4': 5.5000000000000004e-09,
'l1': 0.0,
'l2': 0.0,
'k_lambda': 0.0,
'T_lambda_Pr': 0.0,
'T_lambda_ref': 0.0,
'H_t': 0.0,
'd0': 282.98291,
'd1': -4831.375,
'd2': 3620706.0,
'd3': -0.15733000000000003,
'd4': 3.477e-05,
'd5': 410629.63,
'T_D': 1436.15,
'T_D_ref': 298.15,
'T_r': 298.15,
'P_r': 1.0,
'K': 554170.1302299806,
'K_P': 4.0}
Import the new module and test the model¶
import berman
%cd ..
/Users/ghiorso/anaconda3/lib/python3.7/site-packages/Cython/Compiler/Main.py:369: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Codegen/working/berman.pyx
tree = Parsing.p_module(s, pxd, full_module_name)
/Users/ghiorso/Documents/ARCHIVE_XCODE/ThermoEngine/Notebooks/Codegen
Evaluate functions at temperature (K) and pressure (bars)
t = 1000.0
p = 10000.0
Available in both “Fast” and “Calib” code versions¶
Execute the “fast” or “calibration” code metadata retrieval functions:
try:
print(berman.cy_Potassium_Feldspar_berman_identifier())
print(berman.cy_Potassium_Feldspar_berman_name())
print(berman.cy_Potassium_Feldspar_berman_formula())
print(berman.cy_Potassium_Feldspar_berman_mw())
print(berman.cy_Potassium_Feldspar_berman_elements())
except AttributeError:
pass
try:
print(berman.cy_Potassium_Feldspar_berman_calib_identifier())
print(berman.cy_Potassium_Feldspar_berman_calib_name())
print(berman.cy_Potassium_Feldspar_berman_calib_formula())
print(berman.cy_Potassium_Feldspar_berman_calib_mw())
print(berman.cy_Potassium_Feldspar_berman_calib_elements())
except AttributeError:
pass
Wed Sep 23 09:55:49 2020
Potassium_Feldspar
KAlSi3O8
278.33524
[0. 0. 0. 0. 0. 0. 0. 0. 8. 0. 0. 0. 0. 1. 3. 0. 0. 0. 0. 1. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
Execute the standard thermodynamic property retrieval functions:
fmt = "{0:<10.10s} {1:13.6e} {2:<10.10s}"
try:
print(fmt.format('G', berman.cy_Potassium_Feldspar_berman_g(t,p), 'J/m'))
print(fmt.format('dGdT', berman.cy_Potassium_Feldspar_berman_dgdt(t,p), 'J/K-m'))
print(fmt.format('dGdP', berman.cy_Potassium_Feldspar_berman_dgdp(t,p), 'J/bar-m'))
print(fmt.format('d2GdP2', berman.cy_Potassium_Feldspar_berman_d2gdt2(t,p), 'J/K^2-m'))
print(fmt.format('d2GdTdP', berman.cy_Potassium_Feldspar_berman_d2gdtdp(t,p), 'J/K-bar-m'))
print(fmt.format('d2GdP2', berman.cy_Potassium_Feldspar_berman_d2gdp2(t,p), 'J/bar^2-m'))
print(fmt.format('d3GdT3', berman.cy_Potassium_Feldspar_berman_d3gdt3(t,p), 'J/K^3-m'))
print(fmt.format('d3GdT2dP', berman.cy_Potassium_Feldspar_berman_d3gdt2dp(t,p), 'J/K^2-bar-m'))
print(fmt.format('d3GdTdP2', berman.cy_Potassium_Feldspar_berman_d3gdtdp2(t,p), 'J/K-bar^2-m'))
print(fmt.format('d3GdP3', berman.cy_Potassium_Feldspar_berman_d3gdp3(t,p), 'J/bar^3-m'))
print(fmt.format('S', berman.cy_Potassium_Feldspar_berman_s(t,p), 'J/K-m'))
print(fmt.format('V', berman.cy_Potassium_Feldspar_berman_v(t,p), 'J/bar-m'))
print(fmt.format('Cv', berman.cy_Potassium_Feldspar_berman_cv(t,p), 'J/K-m'))
print(fmt.format('Cp', berman.cy_Potassium_Feldspar_berman_cp(t,p), 'J/K-m'))
print(fmt.format('dCpdT', berman.cy_Potassium_Feldspar_berman_dcpdt(t,p), 'J/K^2-m'))
print(fmt.format('alpha', berman.cy_Potassium_Feldspar_berman_alpha(t,p), '1/K'))
print(fmt.format('beta', berman.cy_Potassium_Feldspar_berman_beta(t,p), '1/bar'))
print(fmt.format('K', berman.cy_Potassium_Feldspar_berman_K(t,p), 'bar'))
print(fmt.format('Kp', berman.cy_Potassium_Feldspar_berman_Kp(t,p), ''))
except AttributeError:
pass
try:
print(fmt.format('G', berman.cy_Potassium_Feldspar_berman_calib_g(t,p), 'J/m'))
print(fmt.format('dGdT', berman.cy_Potassium_Feldspar_berman_calib_dgdt(t,p), 'J/K-m'))
print(fmt.format('dGdP', berman.cy_Potassium_Feldspar_berman_calib_dgdp(t,p), 'J/bar-m'))
print(fmt.format('d2GdP2', berman.cy_Potassium_Feldspar_berman_calib_d2gdt2(t,p), 'J/K^2-m'))
print(fmt.format('d2GdTdP', berman.cy_Potassium_Feldspar_berman_calib_d2gdtdp(t,p), 'J/K-bar-m'))
print(fmt.format('d2GdP2', berman.cy_Potassium_Feldspar_berman_calib_d2gdp2(t,p), 'J/bar^2-m'))
print(fmt.format('d3GdT3', berman.cy_Potassium_Feldspar_berman_calib_d3gdt3(t,p), 'J/K^3-m'))
print(fmt.format('d3GdT2dP', berman.cy_Potassium_Feldspar_berman_calib_d3gdt2dp(t,p), 'J/K^2-bar-m'))
print(fmt.format('d3GdTdP2', berman.cy_Potassium_Feldspar_berman_calib_d3gdtdp2(t,p), 'J/K-bar^2-m'))
print(fmt.format('d3GdP3', berman.cy_Potassium_Feldspar_berman_calib_d3gdp3(t,p), 'J/bar^3-m'))
print(fmt.format('S', berman.cy_Potassium_Feldspar_berman_calib_s(t,p), 'J/K-m'))
print(fmt.format('V', berman.cy_Potassium_Feldspar_berman_calib_v(t,p), 'J/bar-m'))
print(fmt.format('Cv', berman.cy_Potassium_Feldspar_berman_calib_cv(t,p), 'J/K-m'))
print(fmt.format('Cp', berman.cy_Potassium_Feldspar_berman_calib_cp(t,p), 'J/K-m'))
print(fmt.format('dCpdT', berman.cy_Potassium_Feldspar_berman_calib_dcpdt(t,p), 'J/K^2-m'))
print(fmt.format('alpha', berman.cy_Potassium_Feldspar_berman_calib_alpha(t,p), '1/K'))
print(fmt.format('beta', berman.cy_Potassium_Feldspar_berman_calib_beta(t,p), '1/bar'))
print(fmt.format('K', berman.cy_Potassium_Feldspar_berman_calib_K(t,p), 'bar'))
print(fmt.format('Kp', berman.cy_Potassium_Feldspar_berman_calib_Kp(t,p), ''))
except AttributeError:
pass
G -4.206302e+06 J/m
dGdT -5.343985e+02 J/K-m
dGdP 1.032149e+01 J/bar-m
d2GdP2 -3.097903e-01 J/K^2-m
d2GdTdP 0.000000e+00 J/K-bar-m
d2GdP2 -5.097131e-05 J/bar^2-m
d3GdT3 2.605344e-04 J/K^3-m
d3GdT2dP 0.000000e+00 J/K^2-bar-
d3GdTdP2 0.000000e+00 J/K-bar^2-
d3GdP3 6.989655e-10 J/bar^3-m
S 5.343985e+02 J/K-m
V 1.032149e+01 J/bar-m
Cv 3.097903e+02 J/K-m
Cp 3.097903e+02 J/K-m
dCpdT 4.925584e-02 J/K^2-m
alpha 0.000000e+00 1/K
beta 4.938367e-06 1/bar
K 2.024961e+05 bar
Kp 1.776812e+00
Available only in the “Calib” versions of generated code¶
Execute the parameter value/metadata functions.
These functions are only defined for the “calibration” model code
implementation:
try:
np = berman.cy_Potassium_Feldspar_berman_get_param_number()
names = berman.cy_Potassium_Feldspar_berman_get_param_names()
units = berman.cy_Potassium_Feldspar_berman_get_param_units()
values = berman.cy_Potassium_Feldspar_berman_get_param_values()
fmt = "{0:<10.10s} {1:13.6e} {2:13.6e} {3:<10.10s}"
for i in range(0,np):
print(fmt.format(names[i], values[i], berman.cy_Potassium_Feldspar_berman_get_param_value(i), units[i]))
except AttributeError:
pass
Test the functions that allow modification of the array of parameter values
try:
values[1] = 100.0
berman.cy_Potassium_Feldspar_berman_set_param_values(values)
fmt = "{0:<10.10s} {1:13.6e} {2:13.6e} {3:<10.10s}"
for i in range(0,np):
print(fmt.format(names[i], values[i], berman.cy_Potassium_Feldspar_berman_get_param_value(i), units[i]))
except (AttributeError, NameError):
pass
Test the functions that allow modification of a particular parameter value
try:
berman.cy_Potassium_Feldspar_berman_set_param_value(1, 1.0)
fmt = "{0:<10.10s} {1:13.6e} {2:13.6e} {3:<10.10s}"
for i in range(0,np):
print(fmt.format(names[i], values[i], berman.cy_Potassium_Feldspar_berman_get_param_value(i), units[i]))
except AttributeError:
pass
Evaluate parameter derivatives …
try:
fmt = " {0:<10.10s} {1:13.6e}"
for i in range(0, np):
print ('Derivative with respect to parameter: ', names[i], ' of')
print (fmt.format('G', berman.cy_Potassium_Feldspar_berman_dparam_g(t, p, i)))
print (fmt.format('dGdT', berman.cy_Potassium_Feldspar_berman_dparam_dgdt(t, p, i)))
print (fmt.format('dGdP', berman.cy_Potassium_Feldspar_berman_dparam_dgdp(t, p, i)))
print (fmt.format('d2GdT2', berman.cy_Potassium_Feldspar_berman_dparam_d2gdt2(t, p, i)))
print (fmt.format('d2GdTdP', berman.cy_Potassium_Feldspar_berman_dparam_d2gdtdp(t, p, i)))
print (fmt.format('d2GdP2', berman.cy_Potassium_Feldspar_berman_dparam_d2gdp2(t, p, i)))
print (fmt.format('d3GdT3', berman.cy_Potassium_Feldspar_berman_dparam_d3gdt3(t, p, i)))
print (fmt.format('d3GdT2dP', berman.cy_Potassium_Feldspar_berman_dparam_d3gdt2dp(t, p, i)))
print (fmt.format('d3GdTdP2', berman.cy_Potassium_Feldspar_berman_dparam_d3gdtdp2(t, p, i)))
print (fmt.format('d3GdP3', berman.cy_Potassium_Feldspar_berman_dparam_d3gdp3(t, p, i)))
except (AttributeError, TypeError):
pass
try:
%timeit berman.cy_Potassium_Feldspar_berman_calib_g(t,p)
except AttributeError:
pass
try:
%timeit berman.cy_Potassium_Feldspar_berman_g(t,p)
except AttributeError:
pass
267 ns ± 5.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)