Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.

I am trying to obtain a numerical answer for a non linear system with 3 equations and 3 unknowns. When running the code, I receive:

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm
instead. 
> In fsolve (line 287)
  In RegimeTwo (line 60) 

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the selected value of the function tolerance, and
the problem appears regular as measured by the gradient.

<stopping criteria details>

Equation solved. The sum of squared function values, r = 1.832713e-25, is less
than sqrt(options.TolFun) = 1.000000e-03. The relative norm of the gradient of
r, 3.027138e-14, is less than 1e-4*options.TolFun = 1.000000e-10.

Optimization Metric                                        Options
relative norm(grad r) =   3.03e-14           1e-4*TolFun =   1e-10 (selected)
r =   1.83e-25                             sqrt(TolFun) =  1.0e-03 (selected)

My code:

opts    = optimset('fsolve');                   
opts    = optimset(opts,'Maxiter',700,'Tolx',1e-6,'tolfun',1e-6); 

xx      = [0 0 0];

nle     = fsolve(Switch,xx,opts, lambda,row, mu, mu_one, a, b, c, r, gamma, A, sigma_one, beta1,delta1);

OP      = nle(1,1); 
EC      = nle(1,2); 
OC      = nle(1,3);

My function:

function [m, VM, SP] = Switch(h,lambda,row, mu, mu_one, a, b, c, r, gamma, A, sigma_one, beta1,delta1) 

OP   = h(1); 
EC   = h(2); 
OC   = h(3); 

pi   = (lambda+row-mu)/((row+lambda-mu_one)*(row-mu));                                  
m    = -OC+((1/(r*b*gamma))*(pi*row*OP-c-r*a))^(1/(gamma-1)) ;                                
A_hat= (-lambda*A)/ (((sigma_one^2)/2)*beta1*(beta1-1)+(mu_one*beta1)-(row+lambda)) ;         

VM   = A_hat*(OP^beta1) + EC*(OP^delta1)- (pi*OC*OP)+((c*OC+r*(a*OC+b*(OC^gamma)))/row); 
SP   = beta1*A_hat*(OP^(beta1-1)) + delta1*EC*(OP^(delta1-1))- (pi*OC);

Any ideas where I am going wrong?

Answer 1

[Torsten]

function res = Switch(h,lambda,row, mu, mu_one, a, b, c, r, gamma, A, sigma_one, beta1,delta1)

OP = h(1); EC = h(2); OC = h(3);

pi = (lambda+row-mu)/((row+lambda-mu_one)*(row-mu)); 
m = -OC+((1/(r*b*gamma))*(pi*row*OP-c-r*a))^(1/(gamma-1)) ; 
A_hat= (-lambda*A)/ (((sigma_one^2)/2)*beta1*(beta1-1)+(mu_one*beta1)-(row+lambda)) ; 
VM = A_hat*(OP^beta1) + EC*(OP^delta1)- (pi*OC*OP)+((c*OC+r*(a*OC+b*(OC^gamma)))/row); 
SP = beta1*A_hat*(OP^(beta1-1)) + delta1*EC*(OP^(delta1-1))- (pi*OC);

res(1,1) = m;
res(2,1) = VM;
res(3,1) = SP;

Best wishes

Torsten.