How to solve a non-linear equation system as function handle with fsolve?

Hello. I have been trying for long while to use the function fsolve to solve a non-linear equation system without success. This nonlinear equation system is basically a huge symbolic 12x1 column vector named ec with 12 equations built with 6 symbolic variables: q1,q2,...,q6.

I converted this vector ec into a function handle to be able to insert it into fsolve. However, this solution keeps issuing errors, and I have reached a point in which I do not know what to do.

The examples on the internet always include an external function with the non-linear equation system typed directly on it. I just cannot do this, because I need to do previously some symbolic operations to build ec. The values of ec and q are:

ec =
 
                sin(q6)*(cos(q1)*cos(q2)*sin(q3)*sin(q4) - cos(q4)*sin(q1) + cos(q1)*cos(q3)*sin(q2)*sin(q4)) - cos(q6)*(cos(q2 + q3)*cos(q1)*sin(q5) + cos(q5)*sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*cos(q5)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*cos(q5)*sin(q2)) - 3097002709122497/18014398509481984
                cos(q6)*(cos(q1)*cos(q4) + cos(q2)*sin(q1)*sin(q3)*sin(q4) + cos(q3)*sin(q1)*sin(q2)*sin(q4)) + sin(q6)*(cos(q2 + q3)*sin(q1)*sin(q5) - cos(q1)*cos(q5)*sin(q4) + cos(q2)*cos(q4)*cos(q5)*sin(q1)*sin(q3) + cos(q3)*cos(q4)*cos(q5)*sin(q1)*sin(q2)) - 6124274932042799/36028797018963968
                                                                                                                                                                                                                  - sin(q2 + q3)*cos(q5) - cos(q2 + q3)*cos(q4)*sin(q5) - 139701203459709/140737488355328
 70*cos(q1) + 360*cos(q1)*sin(q2) - 65*sin(q1)*sin(q4)*sin(q5) + 380*cos(q1)*cos(q2)*cos(q3) - 380*cos(q1)*sin(q2)*sin(q3) + 65*cos(q1)*cos(q2)*cos(q3)*cos(q5) - 65*cos(q1)*cos(q5)*sin(q2)*sin(q3) - 65*cos(q1)*cos(q2)*cos(q4)*sin(q3)*sin(q5) - 65*cos(q1)*cos(q3)*cos(q4)*sin(q2)*sin(q5) + 19869/50
                 sin(q6)*(cos(q1)*cos(q4) + cos(q2)*sin(q1)*sin(q3)*sin(q4) + cos(q3)*sin(q1)*sin(q2)*sin(q4)) - cos(q6)*(cos(q2 + q3)*sin(q1)*sin(q5) - cos(q1)*cos(q5)*sin(q4) + cos(q2)*cos(q4)*cos(q5)*sin(q1)*sin(q3) + cos(q3)*cos(q4)*cos(q5)*sin(q1)*sin(q2)) + 2202239090516653/2251799813685248
                                                                                                                                                                       cos(q2 + q3)*cos(q6)*sin(q4) - sin(q6)*(sin(q2 + q3)*sin(q5) - cos(q2 + q3)*cos(q4)*cos(q5)) + 7591943296130745/288230376151711744
                                                                                                                                         cos(q2 + q3)*cos(q1)*cos(q5) - sin(q5)*(sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*sin(q2)) - 102014544375725/18014398509481984
  70*sin(q1) + 360*sin(q1)*sin(q2) - 380*sin(q1)*sin(q2)*sin(q3) + 380*cos(q2)*cos(q3)*sin(q1) + 65*cos(q1)*sin(q4)*sin(q5) + 65*cos(q2)*cos(q3)*cos(q5)*sin(q1) - 65*cos(q5)*sin(q1)*sin(q2)*sin(q3) - 65*cos(q2)*cos(q4)*sin(q1)*sin(q3)*sin(q5) - 65*cos(q3)*cos(q4)*sin(q1)*sin(q2)*sin(q5) - 1563/20
                                                                                                                                                                        cos(q6)*(sin(q2 + q3)*sin(q5) - cos(q2 + q3)*cos(q4)*cos(q5)) + cos(q2 + q3)*sin(q4)*sin(q6) - 2129854249224409/18014398509481984
                 cos(q6)*(cos(q1)*cos(q2)*sin(q3)*sin(q4) - cos(q4)*sin(q1) + cos(q1)*cos(q3)*sin(q2)*sin(q4)) + sin(q6)*(cos(q2 + q3)*cos(q1)*sin(q5) + cos(q5)*sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*cos(q5)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*cos(q5)*sin(q2)) - 8872946535830847/9007199254740992
                                                                                                                                        cos(q2 + q3)*cos(q5)*sin(q1) - sin(q5)*(cos(q2)*cos(q4)*sin(q1)*sin(q3) - cos(q1)*sin(q4) + cos(q3)*cos(q4)*sin(q1)*sin(q2)) - 8718732974408059/72057594037927936
                                                                                                  360*cos(q2) - 380*cos(q2)*sin(q3) - 380*cos(q3)*sin(q2) - 65*cos(q2)*cos(q5)*sin(q3) - 65*cos(q3)*cos(q5)*sin(q2) - 65*cos(q2)*cos(q3)*cos(q4)*sin(q5) + 65*cos(q4)*sin(q2)*sin(q3)*sin(q5) - 39571/100

q =
 
 q1
 q2
 q3
 q4
 q5
 q6

And here is the code.

funec = matlabFunction(ec);    % Converts the symbolic column vector into a function handle

qini = zeros(1,6);             % Initial guess
    
ci = fsolve(funec(q.'),qini);  % fsolve with the function handle, unknown variables and initial guess
                               % done many variations here, none of them worked

The main error shown by MATLAB is:

Not enough input arguments.

Error in
symengine>@(q1,q2,q3,q4,q5,q6)[sin(q6).*(-cos(q4).*sin(q1)+cos(q1).*cos(q2).*sin(q3).*sin(q4)+cos(q1).*cos(q3).*sin(q2).*sin(q4))-cos(q6).*(cos(q2+q3).*cos(q1).*sin(q5)+cos(q5).*sin(q1).*sin(q4)+cos(q1).*cos(q2).*cos(q4).*cos(q5).*sin(q3)+cos(q1).*cos(q3).*cos(q4).*cos(q5).*sin(q2))-1.719181857497141e-1;cos(q6).*(cos(q1).*cos(q4)+cos(q2).*sin(q1).*sin(q3).*sin(q4)+cos(q3).*sin(q1).*sin(q2).*sin(q4))+sin(q6).*(cos(q2+q3).*sin(q1).*sin(q5)-cos(q1).*cos(q5).*sin(q4)+cos(q2).*cos(q4).*cos(q5).*sin(q1).*sin(q3)+cos(q3).*cos(q4).*cos(q5).*sin(q1).*sin(q2))-1.699827759672145e-1;-sin(q2+q3).*cos(q5)-cos(q2+q3).*cos(q4).*sin(q5)-9.926367529524001e-1;cos(q1).*7.0e1+cos(q1).*sin(q2).*3.6e2-sin(q1).*sin(q4).*sin(q5).*6.5e1+cos(q1).*cos(q2).*cos(q3).*3.8e2-cos(q1).*sin(q2).*sin(q3).*3.8e2+cos(q1).*cos(q2).*cos(q3).*cos(q5).*6.5e1-cos(q1).*cos(q5).*sin(q2).*sin(q3).*6.5e1-cos(q1).*cos(q2).*cos(q4).*sin(q3).*sin(q5).*6.5e1-cos(q1).*cos(q3).*cos(q4).*sin(q2).*sin(q5).*6.5e1+3.9738e2;sin(q6).*(cos(q1).*cos(q4)+cos(q2).*sin(q1).*sin(q3).*sin(q4)+cos(q3).*sin(q1).*sin(q2).*sin(q4))-cos(q6).*(cos(q2+q3).*sin(q1).*sin(q5)-cos(q1).*cos(q5).*sin(q4)+cos(q2).*cos(q4).*cos(q5).*sin(q1).*sin(q3)+cos(q3).*cos(q4).*cos(q5).*sin(q1).*sin(q2))+9.77990617608461e-1;-sin(q6).*(sin(q2+q3).*sin(q5)-cos(q2+q3).*cos(q4).*cos(q5))+cos(q2+q3).*cos(q6).*sin(q4)+2.633984452816549e-2;-sin(q5).*(sin(q1).*sin(q4)+cos(q1).*cos(q2).*cos(q4).*sin(q3)+cos(q1).*cos(q3).*cos(q4).*sin(q2))+cos(q2+q3).*cos(q1).*cos(q5)-5.662944800628733e-3;sin(q1).*7.0e1+sin(q1).*sin(q2).*3.6e2-sin(q1).*sin(q2).*sin(q3).*3.8e2+cos(q2).*cos(q3).*sin(q1).*3.8e2+cos(q1).*sin(q4).*sin(q5).*6.5e1+cos(q2).*cos(q3).*cos(q5).*sin(q1).*6.5e1-cos(q5).*sin(q1).*sin(q2).*sin(q3).*6.5e1-cos(q2).*cos(q4).*sin(q1).*sin(q3).*sin(q5).*6.5e1-cos(q3).*cos(q4).*sin(q1).*sin(q2).*sin(q5).*6.5e1-7.815e1;cos(q6).*(sin(q2+q3).*sin(q5)-cos(q2+q3).*cos(q4).*cos(q5))+cos(q2+q3).*sin(q4).*sin(q6)-1.182306613292333e-1;cos(q6).*(-cos(q4).*sin(q1)+cos(q1).*cos(q2).*sin(q3).*sin(q4)+cos(q1).*cos(q3).*sin(q2).*sin(q4))+sin(q6).*(cos(q2+q3).*cos(q1).*sin(q5)+cos(q5).*sin(q1).*sin(q4)+cos(q1).*cos(q2).*cos(q4).*cos(q5).*sin(q3)+cos(q1).*cos(q3).*cos(q4).*cos(q5).*sin(q2))-9.850949540347428e-1;-sin(q5).*(-cos(q1).*sin(q4)+cos(q2).*cos(q4).*sin(q1).*sin(q3)+cos(q3).*cos(q4).*sin(q1).*sin(q2))+cos(q2+q3).*cos(q5).*sin(q1)-1.2099672617183e-1;cos(q2).*3.6e2-cos(q2).*sin(q3).*3.8e2-cos(q3).*sin(q2).*3.8e2-cos(q2).*cos(q5).*sin(q3).*6.5e1-cos(q3).*cos(q5).*sin(q2).*6.5e1-cos(q2).*cos(q3).*cos(q4).*sin(q5).*6.5e1+cos(q4).*sin(q2).*sin(q3).*sin(q5).*6.5e1-3.9571e2]

Error in fsolve (line 242)

I hope I have been clear enough. Thank you very much for your time.

• Jose

Answer 1

[madhan ravi]

qini = zeros(1,6);             % Initial guess
ci = fsolve(@funec,qini)       % fsolve with the function handle, unknown variables and initial guess
                               % done many variations here, none of them worked
function ec = funec(x);
q1 = x(1);
q2 = x(2);
q3 = x(3);
q4 = x(4);
q5 = x(5);
q6 = x(6);

ec =[...
    sin(q6)*(cos(q1)*cos(q2)*sin(q3)*sin(q4) - cos(q4)*sin(q1) + cos(q1)*cos(q3)*sin(q2)*sin(q4)) - cos(q6)*(cos(q2 + q3)*cos(q1)*sin(q5) + cos(q5)*sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*cos(q5)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*cos(q5)*sin(q2)) - 3097002709122497/18014398509481984
    cos(q6)*(cos(q1)*cos(q4) + cos(q2)*sin(q1)*sin(q3)*sin(q4) + cos(q3)*sin(q1)*sin(q2)*sin(q4)) + sin(q6)*(cos(q2 + q3)*sin(q1)*sin(q5) - cos(q1)*cos(q5)*sin(q4) + cos(q2)*cos(q4)*cos(q5)*sin(q1)*sin(q3) + cos(q3)*cos(q4)*cos(q5)*sin(q1)*sin(q2)) - 6124274932042799/36028797018963968
    - sin(q2 + q3)*cos(q5) - cos(q2 + q3)*cos(q4)*sin(q5) - 139701203459709/140737488355328
    70*cos(q1) + 360*cos(q1)*sin(q2) - 65*sin(q1)*sin(q4)*sin(q5) + 380*cos(q1)*cos(q2)*cos(q3) - 380*cos(q1)*sin(q2)*sin(q3) + 65*cos(q1)*cos(q2)*cos(q3)*cos(q5) - 65*cos(q1)*cos(q5)*sin(q2)*sin(q3) - 65*cos(q1)*cos(q2)*cos(q4)*sin(q3)*sin(q5) - 65*cos(q1)*cos(q3)*cos(q4)*sin(q2)*sin(q5) + 19869/50
    sin(q6)*(cos(q1)*cos(q4) + cos(q2)*sin(q1)*sin(q3)*sin(q4) + cos(q3)*sin(q1)*sin(q2)*sin(q4)) - cos(q6)*(cos(q2 + q3)*sin(q1)*sin(q5) - cos(q1)*cos(q5)*sin(q4) + cos(q2)*cos(q4)*cos(q5)*sin(q1)*sin(q3) + cos(q3)*cos(q4)*cos(q5)*sin(q1)*sin(q2)) + 2202239090516653/2251799813685248
    cos(q2 + q3)*cos(q6)*sin(q4) - sin(q6)*(sin(q2 + q3)*sin(q5) - cos(q2 + q3)*cos(q4)*cos(q5)) + 7591943296130745/288230376151711744
    cos(q2 + q3)*cos(q1)*cos(q5) - sin(q5)*(sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*sin(q2)) - 102014544375725/18014398509481984
    70*sin(q1) + 360*sin(q1)*sin(q2) - 380*sin(q1)*sin(q2)*sin(q3) + 380*cos(q2)*cos(q3)*sin(q1) + 65*cos(q1)*sin(q4)*sin(q5) + 65*cos(q2)*cos(q3)*cos(q5)*sin(q1) - 65*cos(q5)*sin(q1)*sin(q2)*sin(q3) - 65*cos(q2)*cos(q4)*sin(q1)*sin(q3)*sin(q5) - 65*cos(q3)*cos(q4)*sin(q1)*sin(q2)*sin(q5) - 1563/20
    cos(q6)*(sin(q2 + q3)*sin(q5) - cos(q2 + q3)*cos(q4)*cos(q5)) + cos(q2 + q3)*sin(q4)*sin(q6) - 2129854249224409/18014398509481984
    cos(q6)*(cos(q1)*cos(q2)*sin(q3)*sin(q4) - cos(q4)*sin(q1) + cos(q1)*cos(q3)*sin(q2)*sin(q4)) + sin(q6)*(cos(q2 + q3)*cos(q1)*sin(q5) + cos(q5)*sin(q1)*sin(q4) + cos(q1)*cos(q2)*cos(q4)*cos(q5)*sin(q3) + cos(q1)*cos(q3)*cos(q4)*cos(q5)*sin(q2)) - 8872946535830847/9007199254740992
    cos(q2 + q3)*cos(q5)*sin(q1) - sin(q5)*(cos(q2)*cos(q4)*sin(q1)*sin(q3) - cos(q1)*sin(q4) + cos(q3)*cos(q4)*sin(q1)*sin(q2)) - 8718732974408059/72057594037927936
    360*cos(q2) - 380*cos(q2)*sin(q3) - 380*cos(q3)*sin(q2) - 65*cos(q2)*cos(q5)*sin(q3) - 65*cos(q3)*cos(q5)*sin(q2) - 65*cos(q2)*cos(q3)*cos(q4)*sin(q5) + 65*cos(q4)*sin(q2)*sin(q3)*sin(q5) - 39571/100];
end

[Jose Antonio Aliaga]

Great idea there, thank you!

Edit: Sorry, I didn't realize that there is no calling to the vector ec from the function funec. The idea you posted would only require me to run the code for the generation of ec once and then just copypaste it on the function. That way it works, but it is not 100% functional.

[Matt J]

@Jose,

You should accept-click the answer, since it solved your problem.

[Jose Antonio Aliaga]

Hello @Matt, I actually accepted it because at first glance I thought it was correct. It worked, but it was more like a rig instead of a solution. As I said on the OP:

"The examples on the internet always include an external function with the non-linear equation system typed directly on it. I just cannot do this, because I need to do previously some symbolic operations to build ec. "

[madhan ravi]

Jose don‘t get over excited, What is your question?, it‘s not clear yet.

[Jose Antonio Aliaga]

@Madhan: The question is:

Is there a way not to have to copypaste the ec vector in the function funec? I would like to call it from the main script, where it is calculated.

Regards.

[madhan ravi]

Just pass ec to the function fine by parameterizing the function. https://in.mathworks.com/help/matlab/math/parameterizing-functions.html

[Jose Antonio Aliaga]

Thank you for your patience and time. I've accepted your answer.

Answer 2

[Alex Sha]

Multi-results:

1:

q1: 2.96669036114669

q2: 1.70487333682449

q3: 15.5136953998108

q4: 5.27144773940526

q5: 0.142189641996628

q6: 2.92624078062874

2:

q1: -0.174902292443192

q2: -1.65677974125393

q3: -0.222132574088401

q4: -2.7442677404906

q5: -0.315684317666849

q6: -4.74367456197212

3:

...

[Jose Antonio Aliaga]

How did you get those?