Solving two non-linear equations in Octave

问题

I am trying to solve the following two equations using Octave:

eqn1 = (wp/Cwc)^(2*N) - (1/10^(0.1*Ap))-1 == 0;
eqn2 = (ws/Cwc)^(2*N) - (1/10^(0.1*As))-1 == 0;

I used the following code:

syms Cwc N
eqn1 = (wp/Cwc)^(2*N) - (1/10^(0.1*Ap))-1 == 0;
eqn2 = (ws/Cwc)^(2*N) - (1/10^(0.1*As))-1 == 0;
sol = solve(eqn1 ,eqn2, Cwc, N)

ws,wp,As, and Ap are given as 1.5708, 0.31416, 0.5, 45 respectively.

But I am getting the following error:

error: Python exception: NotImplementedError: could not solve
126491*(pi*(3*10**N*sqrt(314311)*pi**(-N)/1223)**(1/N)/2)**(2*N) - 126495
occurred at line 7 of the Python code block:
d = sp.solve(eqs, *symbols, dict=True)

What should I do to solve this?

---

Edit:

I modified the equations a little bit.

pkg load symbolic
clear all
syms Cwc N
wp = 0.31416
ws = 1.5708
As = 45
Ap = 0.5
eqn2 = N - log10(((1/(10^(0.05*As)))^2)-1)/2*log10(ws/Cwc) == 0;
eqn1 = N - log10(((1/(10^(0.05*Ap)))^2)-1)/2*log10(wp/Cwc) == 0;
sol = solve(eqn1,eqn2,Cwc,N)

And now I am getting this error:

error: Python exception: AttributeError: MutableDenseMatrix has no attribute is_Relational.
occurred at line 3 of the Python code block:
if arg.is_Relational:

回答1:

Looking at the equations, with unknowns in the base and exponent of the same term, highly suggests there is no symbolic solution to be found. I gave a simplified system (2/x)^y = 4, (3/x)^y = 5 to a couple of symbolic solvers, neither of which got anything from it. So, the only way to solve this is numerically (which makes sense because the four known parameters you have are some floating point numbers anyway). Octave's numeric solver for this purpose is fsolve. Example of usage:

function y = f(x)
  Cwc = x(1);
  N = x(2);
  ws = 1.5708;
  wp = 0.31416;
  As = 0.5;
  Ap = 45;
  y = [(wp/Cwc)^(2*N) - (1/10^(0.1*Ap))-1; (ws/Cwc)^(2*N) - (1/10^(0.1*As))-1];
endfunction

fsolve(@f, [1; 1])

(Here, [1; 1] is an initial guess.) The output is

0.31413
0.19796

来源：https://stackoverflow.com/questions/42802588/solving-two-non-linear-equations-in-octave