Using Sympy sympify on a black-box numerical function

Question

The overall problem that I am trying to solve is to develop code which accepts string equations from user input or files, parses the equations, and solves the equations given a valid set of known values for variables. The approach must allow the user to enter a thermophysical function (such as CoolProp's PropsSI or HAPropsSI) in equation(s), and ideally, any user-defined function or object. Based on initial work I thought Sympy was a way to go.

Therefore, I have been trying to understand how to sympify a numerical function for use in systems of equations in Sympy.

The function is HAPropsSI from the CoolProp library. The Coolprops functions are implemented in C++ and wrapped for use in Python. It is not built on numpy per se, but is vectorized to accept 1D numpy arrays in addition to ints, floats, and lists.

Here is an example of what I tried:

from CoolProp.HumidAirProp import HAPropsSI
from sympy import symbols, sympify 

# Example calculating enthalpy as a function of temp., pressure, % RH:
T = 298.15
P = 101325
RH = 0.5

h = HAPropsSI("H", "T", T, "P", P, "R", RH)
print(h) # returns the float value h = 50423.45

# Example using Sympy:
Temp, Press, RH = symbols('Temp Press RH')
sym_h = sympify('HAPropsSI("H", "T", Temp, "P", Press, "R", RH)', {'HAPropsSI':HAPropsSI}) 

Sympify tries to parse the expression and then use eval on the function with symbols which results in the following traceback:

ValueError                                Traceback (most recent call last)
ValueError: Error from parse_expr with transformed code: 'HAPropsSI ("H","T",Symbol (\'Temp\' ),"P",Symbol (\'Press\' ),"R",Symbol (\'RH\' ))'

The above exception was the direct cause of the following exception:

TypeError                                 Traceback (most recent call last)
C:\Users\JIMCAR~1\AppData\Local\Temp/ipykernel_3076/1321321868.py in <module>
     12 
     13 Temp, Press, RH = symbols('Temp Press RH')
---> 14 sym_h = sympify('HAPropsSI("H", "T", Temp, "P", Press, "R", RH)', {'HAPropsSI':HAPropsSI})
     15 
     16 '''

~\AppData\Roaming\Python\Python38\site-packages\sympy\core\sympify.py in sympify(a, locals, convert_xor, strict, rational, evaluate)
    470     try:
    471         a = a.replace('\n', '')
--> 472         expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate)
    473     except (TokenError, SyntaxError) as exc:
    474         raise SympifyError('could not parse %r' % a, exc)

~\AppData\Roaming\Python\Python38\site-packages\sympy\parsing\sympy_parser.py in parse_expr(s, local_dict, transformations, global_dict, evaluate)
   1024         for i in local_dict.pop(None, ()):
   1025             local_dict[i] = None
-> 1026         raise e from ValueError(f"Error from parse_expr with transformed code: {code!r}")
   1027 
   1028 

~\AppData\Roaming\Python\Python38\site-packages\sympy\parsing\sympy_parser.py in parse_expr(s, local_dict, transformations, global_dict, evaluate)
   1015 
   1016     try:
-> 1017         rv = eval_expr(code, local_dict, global_dict)
   1018         # restore neutral definitions for names
   1019         for i in local_dict.pop(None, ()):

~\AppData\Roaming\Python\Python38\site-packages\sympy\parsing\sympy_parser.py in eval_expr(code, local_dict, global_dict)
    909     Generally, ``parse_expr`` should be used.
    910     """
--> 911     expr = eval(
    912         code, global_dict, local_dict)  # take local objects in preference
    913     return expr

<string> in <module>

CoolProp\HumidAirProp.pyx in CoolProp.CoolProp.HAPropsSI()

CoolProp\HumidAirProp.pyx in CoolProp.CoolProp.HAPropsSI()

TypeError: Numerical inputs to HAPropsSI must be ints, floats, lists, or 1D numpy arrays.

An example application would be to create an equation and solve for an unknown (Press, Temp, or RH) given the value of h:

eqn = Eq(sym_h, 50423.45)
nsolve(eqn, Press, 1e5)

What I am trying to accomplish is not so different from:

Python: Using sympy.sympify to perform a safe eval() on mathematical functions

Though I admit I am unclear on the details of the subclassing.

Thanks for any insights.