Error using fsolve inside a parfor loop

I have a system of 5 non-linear equations I am trying to solve using fsolve. I am trying to solve this system for a bunch of different combinations of initial guesses for each of the 5 variables and then see which one produces the most accurate result. IG is a 1x11^4 cell array, where each entry is a 1x5 vector containing a set of initial guesses. I am trying to execute the following parfor loop:

s = size(IG);

Accuracies = zeros(s);

parfor (i = 1:s(2), 4)

[x,fval] = fsolve(@(x) max_Jemit(x, n0, kTe_eV, Vc), IG{i}, opts);

Accuracies(i) = fval(1)^2 + fval(2)^2 + fval(3)^2 + fval(4)^2 + fval(5)^2;

end

I obtain the following error:

Error using JemitSolver>max_Jemit (line 553)

Matrix dimensions must agree.

Error in parallel.internal.pool.deserialize>@(x)max_Jemit(x,n0,kTe_eV,Vc)

Error in fsolve (line 242)

fuser = feval(funfcn{3},x,varargin{:});

Error in JemitSolver (line 155)

parfor (i = 1:s(2), 4)

Caused by:

Failure in initial objective function evaluation. FSOLVE cannot continue.

Line 553 that it refers to is inside the function max_Jemit where I define my system of equations:

function F = max_Jemit(x, n0, kTe_eV, Vc)

global qe me epsilon0

kTe_J = kTe_eV*qe;

eta_s = (qe*x(5))/(kTe_J);

eta_0 = (qe*x(2))/(kTe_J);

jc = x(4)*qe*sqrt(kTe_J/me)*(2*eta_s)^(3/2);

nu_i = x(1)/x(4);

Jb = x(3)/jc; This is the line it does not like

lambda_D = sqrt((epsilon0*kTe_J)/(x(4)*qe^2));

Enorm = (qe*lambda_D)/(kTe_J);

F(1) = nu_i - 1 - 2*eta_s*Jb;

F(2) = eta_0 - (1/2)*(nu_i/(1-Jb));

F(3) = (2/Enorm^2)*(2*nu_i*eta_0*(sqrt(1 + eta_s/eta_0)-1) - Jb*(2*eta_s)^2 + exp(-eta_s) - 1);

F(4) = x(4) - n0*exp(-eta_0);

F(5) = Vc - x(5) - x(2);

end

I have no issues when doing this exact code in a normal for-loop. These errors only arise when I use parfor. Am I not able to use cell arrays with parfor loops?

Answer 1

[Walter Roberson]

global variables are not copied to workers in parfor.

You will need to use parfevalOnAll to set the global variables to their desired values.

[JONAH TAYLOR]

Thank you so much for the help, this worked!