Solve always returns 0x1 sym results for a non linear system of equations, symbolic toolbox

Hi!

Can someone help me out with this please? I try to solve this nonlinear system of equations but solve always give me a 0x1 sym result for all the unknown parameters (A,I,V,alfa, gamma, fi)! I have also tried to use vpasolve but it gives me the same results!

I am using MATLAB R2017a!

Thanks in advance!

clear all
clc
n=1;
r=0.1;
A0=r^2*pi;
I0=(2*r)^4*pi/64;
ro=2700;
E=210*10^9;
w=100;
l=1;
syms x
V = sym('V', [1 n]);
I = sym('I', [1 n]);
A = sym('A', [1 n]);
fi= sym('fi', [1 n]);
gamma=sym('gamma', [1 n]);
alfa=sym('alfa', [1 n]);
for oszlop=1:n
    vvektor(oszlop)=V(oszlop)*exp(1j*oszlop*x/l+fi(oszlop));
    Ivektor(oszlop)=I(oszlop)*exp(1j*oszlop*x/l+gamma(oszlop));
    Avektor(oszlop)=A(oszlop)*exp(1j*oszlop*x/l+alfa(oszlop));
end
v=sum(vvektor);
i2=sum(Ivektor)+I0;
a=sum(Avektor)+A0;
clear vvektror Ivektor;
baloldal=i2*diff(v,x,4)-2*diff(i2,x,1)*diff(v,x,3)+diff(i2,x,2)*diff(v,x,2);
jobboldal=ro*a*w*w/E;
xvektor=linspace(0,l,6*n);
for k=1:numel(xvektor)
    baloldalvektor(k)=subs(baloldal,x,xvektor(k));
    jobboldalvektor(k)=subs(jobboldal,x,xvektor(k));    
end
for k=1:numel(xvektor)
    eqns(k)=baloldalvektor(k)-jobboldalvektor(k)==0;    
end
 S=solve(eqns,A,V,I,alfa,fi,gamma,'IgnoreAnalyticConstraints', true)

Answer 1

[Nicolas Schmit]

Solve always returns 0x1 because your equations are not compatible. To demonstrate if, solve the first and second equations with respect to A.

A1 = solve(eqns(1),A);
A2 = solve(eqns(2),A);

Take the difference, and simplify the results.

diffA = simplify(A1-A2);

If you look closely at the results, you see that diffA cannot be null for a finite value of alfa. Therefore, the equations are not compatible.

There is probably a problem somewhere in your equations.

[Mohammed Ouallal]

Hello Mr. Schmit,

I am facing the same problem. Could you be more specific about the statament that you have done about the proble in equation.

I had a non linear equation of the type (C*x^a*y^b*z^c*w^d*u^e*v^f). The variables here are (C,a,b,c,d,e,f).

I apply taylor expansion to the whole equation, I ended up with somehow a linear equation. I can assure you that there is no problem in the original equation.

here I attach my code to solve the equation "cost".

[John D'Errico]

@Mohammed Ouallal - this is apparently a completely different problem. that you got a non-answer is because you are trying to solve the problem the wrong way. You need to use nonlinear regression and estimation tools. And there is no need to even use symbolic tools in this. All that does is slow your code down here. So you get no answer, AND you get that slowly.

[Mohammed Ouallal]

That brings me back to gradient descent. The reason I tried to solve a system of equation is that my cost function does not decrease at all. I am sure that this is not the right place to discuss this. I have submitted a problem 2 or 3 days ago about Gradient descent, mini batch GD and stochastic GD. If you could look at it, I appreciate it.