How to fixe this error with fsolve ?

Hello everyone.

I am having trouble to solve a system of two nonlinear equations of two variables with the fsolve command. Here is how I proceed:

• I define a function of 5 variables:

function y = eq2(Par,kl,kf,ml,okt,omt) % Par is structure that contains parameters (constants) of my function
    ... % lines of instructions
end

The function eq2 works well. For example:

eq2(Par,.5,1,0.1,0.3,0.5) 

% gives 
ans =
    0.0011   -0.9532

• Then I fixe the value of 3 variables and define the function of the two remaining variables:

    fun = @(kl,ml) eq2(Par,kl,1,ml,0.3,0.5);

The function fun works as well. For example:

    fun(0.5,0.1)
% gives
ans =
    0.0011   -0.9532

% same answer as before, as expected    

• Then I want to solve the equation fun(kl,ml)=(0,0):

x0 = [0.1,0.1];
solve(fun,x0)

which does not work. I get the error message:

Error using sym.getEqnsVars>checkVariables (line 92)

Second argument must be a vector of symbolic variables.

Error in sym.getEqnsVars (line 56)

checkVariables(vars);

Error in solve>getEqns (line 429)

[eqns, vars] = sym.getEqnsVars(argv{:});

Error in solve (line 226)

[eqns,vars,options] = getEqns(varargin{:});

I don't understand the error message, and I don't know what is wrong in my code. If the problem were only that solution does not exist the message should be different.

Can someone help me please ? Thank you in advance.

[Star Strider]

Idossou Marius Adom posted —

Sorry. I did not put the Par structure and the function because it is heavy. Here they are:

Parameters

% Par structure
    Par.alpha1           = 0.35/3; 
    Par.alpha2           = 0.35*2/3; 
    Par.alpha3           = 0.6; 
    Par.psik             = 1/2; 
    Par.Ak               = 1; 
    Par.Bk               = 1.1; 
    Par.sigmak           = 2;  
    Par.psim             = 1/2; 
    Par.Am               = 1; 
    Par.Bm               = 1.1; 
    Par.sigmam           = 2; 
    Par.rhok             = 1-1/Par.sigmak;   
    Par.rhom             = 1-1/Par.sigmam;   
    Par.delta            = 0.1/55;
    Par.R               = 1 + 0.055/52; 
    Par.beta            = 1/Par.R; 
    Par.theta           = 0.479179;
    Par.w               = 2;
    Par.Gamma           = (1-Par.alpha3)*(Par.alpha3/Par.w)^(Par.alpha3/(1-Par.alpha3));
    Par.alpha1t          = Par.alpha1/(1-Par.alpha3);
    Par.alpha2t          = Par.alpha2/(1-Par.alpha3);
    Par.alpha3t          = Par.alpha3/(1-Par.alpha3);

Function:

function y = eq2(Par,kl,kf,ml,okt,omt)
    %
    y(1) = -1 + Par.beta*(1-Par.delta) + Par.beta*Par.alpha1t*Par.Gamma*Par.psik*Par.Ak^Par.rhok*kl.^(Par.rhok-1).* ...
        ( ...
        Par.theta*(Par.psim*(Par.Am*ml).^Par.rhom + (1-Par.psim)*(Par.Bm*omt).^Par.rhom).^(Par.alpha2t/Par.rhom).*...
        (Par.psik*(Par.Ak*kl).^Par.rhok + (1-Par.psik)*(Par.Bk*(kf+okt)).^Par.rhok).^(Par.alpha1t/Par.rhok-1) + ...
        (1-Par.theta)*(Par.psim*(Par.Am*ml).^Par.rhom).^(Par.alpha2t/Par.rhom).*...
        (Par.psik*(Par.Ak*kl).^Par.rhok + (1-Par.psik)*(Par.Bk*kf).^Par.rhok).^(Par.alpha1t/Par.rhok-1)...
        );
    %
    y(2) = -1 + Par.beta*Par.alpha2t*Par.Gamma*Par.psim*Par.Am^Par.rhom*ml.^(Par.rhom-1).* ...
        ( ...
        Par.theta*(Par.psim*(Par.Am*ml).^Par.rhom + (1-Par.psim)*(Par.Bm*omt).^Par.rhom).^(Par.alpha2t/Par.rhom-1).*...
        (Par.psik*(Par.Ak*kl).^Par.rhok + (1-Par.psik)*(Par.Bk*(kf+okt)).^Par.rhok).^(Par.alpha1t/Par.rhok) + ...
        (1-Par.theta)*(Par.psim*(Par.Am*ml).^Par.rhom).^(Par.alpha2t/Par.rhom-1).*...
        (Par.psik*(Par.Ak*kl).^Par.rhok + (1-Par.psik)*(Par.Bk*kf).^Par.rhok).^(Par.alpha1t/Par.rhok)...
        );
    %    
end

Other lines of code:

eq2(Par,.5,1,0.1,0.3,0.5)

fun = @(kl,ml) eq2(Par,kl,1,ml,0.3,0.5);

fun(0.5,0.1)

x0 = [0.1,0.1];
solve(fun,x0)

Thank you.

[J. Alex Lee]

you are invoking "solve", rather than "fsolve"...

[VBBV]

Use fsolve as

 % if true
    % code
 % end
options = optimoptions('fsolve','Display','iter');
[x fval] = fsolve(fun,x0,options)

[Idossou Marius Adom]

Thank you very much J. Alex Lee and Vasishta Bhargava. It works now.