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

My code has the following error:

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using

Levenberg-Marquardt algorithm instead.

> In fsolve (line 298)

In Design (line 16)

Error using levenbergMarquardt (line 16)

Objective function is returning undefined values at initial point. fsolve cannot continue.

Error in fsolve (line 397)

levenbergMarquardt(funfcn,x,verbosity,options,defaultopt,f,JAC,caller, ...

Error in Design (line 16)

neff=fsolve(TM,Nx(i));

Can anyone tell me what is wrong with my below code:

for n=0:1

lamda=1.55;

ko=2.*pi./lamda;

n1TE=1.5100;

n2TE=1.4900;

n4TE=1.4444;

Nx=1.4900:0.0001:1.5100; % as n2<refractive index<n1

b=((n.*pi+atan(sqrt(Nx.^2-n2TE.^2)./sqrt(n1TE.^2-Nx.^2))+atan(sqrt(Nx.^2-n4TE.^2)/sqrt(n1TE.^2-Nx.^2)))./(ko.*sqrt((n1TE.^2-Nx.^2))));

for m=0:1

a=b;

n3TM=1.4895;

n5TM=1.4895;

TM=@(neff) 2.*ko.*a.*sqrt(Nx.^2-neff.^2)-m.*pi-atan((sqrt(neff.^2-n3TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n3TM.^2))-atan((sqrt(neff.^2-n5TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n5TM.^2));

neff=fsolve(TM,Nx);

plot(b,neff)

end

end

Answer 1

[Stephan]

Hi,

add this line before you call fsolve:

opts = optimoptions(@fsolve,'Algorithm', 'levenberg-marquardt');

Then in your call of fsolve add the options:

neff = fsolve(TM,Nx,opts)

Best regards

Stephan

[Areez Khail Memon]

Hi Stephen,

Thank you for your answer. I have eidted it but again this error shows:

Error using levenbergMarquardt (line 16)

Objective function is returning undefined values at initial point. fsolve cannot continue.

Error in fsolve (line 397)

levenbergMarquardt(funfcn,x,verbosity,options,defaultopt,f,JAC,caller, ...

Error in Design (line 15)

neff = fsolve(TM,Nx,opts);

you can see a screen shot.

Regards,

Areez

[Stephan]

try:

Nx = 1.5;

Note that:

...fsolve uses the number of elements in and size of x0 to determine the number and size of variables that TM accepts...

[Stephan]

For me it works. try:

clear Nx

You have some more problems i guess - try:

n=[0 1];
lamda=1.55;
ko=2.*pi./lamda;
n1TE=1.5100;
n2TE=1.4900;
n4TE=1.4444;
Nx=1.5;     % as n2<refractive index<n1
b=((n.*pi+atan(sqrt(Nx.^2-n2TE.^2)./sqrt(n1TE.^2-Nx.^2))+atan(sqrt(Nx.^2-n4TE.^2)/sqrt(n1TE.^2-Nx.^2)))./(ko.*sqrt((n1TE.^2-Nx.^2))));
m = [0 1];
a=b;
n3TM=1.4895;
n5TM=1.4895;
TM=@(neff,m) 2.*ko.*a.*sqrt(Nx.^2-neff.^2)-m.*pi-atan((sqrt(neff.^2-n3TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n3TM.^2))-atan((sqrt(neff.^2-n5TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n5TM.^2));
neff = nan(1,numel(m));
for k = 1:numel(m)
    neff(k)=fsolve(@(neff)TM(neff,m(k)),Nx);
end
scatter(b,neff,'or')
hold on
plot(b,neff)
hold off

Answer 2

[Areez Khail Memon]

can not assign Nx value as it is defined as range. Is their any other way to get the value of neff from the above given equation?

Answer 3

[Ill ch]

Hi Areez,

i think there are problem with your function. Could you post here your mathematical function on which you want to fit your data? try even this one:

opts = optimoptions(@fsolve,'Algorithm', 'levenberg-marquardt');
clear Nx
n=[0 1];
lamda=1.55;
ko=2.*pi./lamda;
n1TE=1.5100;
n2TE=1.4900;
n4TE=1.4444;
Nx=1.5;     % as n2<refractive index<n1
b=((n.*pi+atan(sqrt(Nx.^2-n2TE.^2)./sqrt(n1TE.^2-Nx.^2))+atan(sqrt(Nx.^2-n4TE.^2)/sqrt(n1TE.^2-Nx.^2)))./(ko.*sqrt((n1TE.^2-Nx.^2))));
m = [0 1];
a=b;
n3TM=1.4895;
n5TM=1.4895;
TM=@(neff,m) 2.*ko.*a.*sqrt(Nx.^2-neff.^2)-m.*pi-atan((sqrt(neff.^2-n3TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n3TM.^2))-atan((sqrt(neff.^2-n5TM.^2)./sqrt(Nx.^2-neff.^2)).*(Nx.^2./n5TM.^2));
neff = nan(1,numel(m));
for k = 1:numel(m)
    neff(k)=fsolve(@(neff)TM(neff,m(k)),Nx,opts);
end