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

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Areez Khail Memon
回答： Ill ch 2019-10-2
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

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回答（3 个）

Stephan
Stephan 2019-3-7
编辑：Stephan 2019-3-7
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
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Stephan
Stephan 2019-3-7
编辑：Stephan 2019-3-7
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
Stephan 2019-3-7
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

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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?
Ill ch
Ill ch 2019-10-2
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

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