当我求解方程组时发生TypeError

Question

from math import exp, log
from sympy import Symbol, symbols, solve, Eq
Z = 70;p_abs = 101.325*((1-2.25577*(10**-5)*Z)**5.2559);t_std = 15-0.0065*Z;RH = 0.5;t_db = 20
K_db = t_db + 273.15
C8 = -5.8002206e+03C9 = 1.3914993e+00;C10 = -4.8640239e-02;C11 = 4.1764768e-05;C12 = -1.4452093e-08;C13 = 6.5459673e+00
p_ws_db = exp(C8/K_db+C9+C10*K_db+C11*K_db**2+C12*K_db**3+C13*log(K_db))/1000
p_w_db = p_ws_db*RH # partial pressure of water vapor_db
W_s_db = 0.621945*p_ws_db/(p_abs-p_ws_db)
W_db = 0.621945*p_w_db/(p_abs-p_w_db)
p_w_wb = (W_db*p_abs)/(0.621945+W_db)
t_wb, K_wb, W_s_wb, p_ws_wb = symbols('t_wb K_wb W_s_wb p_ws_wb')
e1 = Eq(K_wb, t_wb + 273.15)
e2 = Eq(p_ws_wb, exp(C8/K_wb+C9+C10*K_wb+C11*K_wb**2+C12*K_wb**3+C13*log(K_wb))/1000)
e3 = Eq(W_s_wb, (W_db*((2501+1.86*t_db)-4.186*t_wb)+1.006*(t_db-t_wb))/(2501-2.326*t_wb))
e4 = Eq(p_ws_wb, (W_s_wb*p_abs)/(W_s_wb+0.621945))
print(fsolve([e1,e2,e3,e4], t_wb, p_ws_wb, K_wb, W_s_wb))

This is the code what have 4 equation and 4 unknowns. I am trying solving this equations by using sympy.solve. But it can't solve with an error;

TypeError: can't convert expression to float.

I guess exp or log create a problem.

Answer 1

print(fsolve([e1,e2,e3,e4], t_wb, p_ws_wb, K_wb, W_s_wb))

There is no fsolve in SymPy. There is fsolve in SciPy, a numeric solver. SciPy cannot work with SymPy objects, in particular it convert convert them to floats. Neither can exp and log that you imported from math .

Understand the difference between numeric computation and symbolic computation. If you want to compute exp(a) and a is a symbol, you need symbolic exp from SymPy, not a numeric exp from math or NumPy or somewhere else.

Correct import statements:

from sympy import symbols, Eq, exp, log
from scipy.optimize import fsolve

Correct execution of numerical solution:

eqns = lambdify([t_wb, p_ws_wb, K_wb, W_s_wb], [e.lhs - e.rhs for e in [e1, e2, e3, e4]])    
print(fsolve(lambda x: eqns(*x), [10, 10, 10, 10]))

Here, lambdify creates a function that SciPy can use, from the SymPy objects you have. It's a main tool for using SymPy objects in numeric modules. The created function takes four arguments, listed first, and returns four outputs, which are the difference between the left and right sides of each equation.

The initial vector [10, 10, 10, 10] is just a guess for solution, fsolve needs it as a starting point. The solution it finds is

[1.51295417e+03 7.10681717e+01 1.78610417e+03 1.50246122e+00]