lsqcurvefit can't get to the right values

Hi

I'm trying to run my code but for some reason it's not trying to converge. the numbers don't change at all

What can be the cause of it? and how do i fix it?

clear
clc

x0 = [75,775 0 0 290 788];
lb = [0	750	-2 -2 280 780];
ub = [90 800 2 2 300 800];
needed_results = zeros(1,5);
harminics_positions_pix = [596, 548, 510, 480, 457];
x = lsqcurvefit(@simulation_grating, x0, harminics_positions_pix,needed_results,lb,ub)

epsilon_equation = 1x5

1.0e-03 * -0.663922364844540 -0.504252608292091 -0.386921645947969 -0.298242547108015 -0.495377384240422

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Warning: Trust-region-reflective algorithm requires at least as many equations as variables; using Levenberg-Marquardt algorithm instead.

epsilon_equation = 1x5

1.0e-03 * -0.663922432249899 -0.504252662749099 -0.386921690925949 -0.298242584926721 -0.495377436938948

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epsilon_equation = 1x5

1.0e-03 * -0.663922381844982 -0.504252621722722 -0.386921656843434 -0.298242556135210 -0.495377384240422

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epsilon_equation = 1x5

1.0e-03 * -0.663922365618754 -0.504252608893471 -0.386921646426198 -0.298242547495274 -0.495377384819959

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epsilon_equation = 1x5

1.0e-03 * -0.663922365262067 -0.504252608623340 -0.386921646222971 -0.298242547344451 -0.495377384554310

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epsilon_equation = 1x5

1.0e-03 * -0.663922364469610 -0.504252607754201 -0.386921645197090 -0.298242546143862 -0.495377383922764

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epsilon_equation = 1x5

1.0e-03 * -0.663922364083193 -0.504252608341175 -0.386921646815808 -0.298242548719612 -0.495377383765274

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epsilon_equation = 1x5

1.0e-03 * -0.663921043265454 -0.504251557941020 -0.386920789638927 -0.298241834660169 -0.495376371941583

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epsilon_equation = 1x5

1.0e-03 * -0.663921110670646 -0.504251612397876 -0.386920834616810 -0.298241872478751 -0.495376424639943

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epsilon_equation = 1x5

1.0e-03 * -0.663921060265869 -0.504251571371610 -0.386920800534378 -0.298241843687337 -0.495376371941583

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epsilon_equation = 1x5

1.0e-03 * -0.663921042491253 -0.504251557339612 -0.386920789160712 -0.298241834272896 -0.495376371362047

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epsilon_equation = 1x5

1.0e-03 * -0.663921042847940 -0.504251557609743 -0.386920789363967 -0.298241834423705 -0.495376371627696

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epsilon_equation = 1x5

1.0e-03 * -0.663921042890496 -0.504251557403130 -0.386920788888062 -0.298241833696044 -0.495376371623897

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epsilon_equation = 1x5

1.0e-03 * -0.663921042504107 -0.504251557990118 -0.386920790506780 -0.298241836271794 -0.495376371466449

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Local minimum possible.
lsqcurvefit stopped because the relative size of the current step is less than
the value of the step size tolerance.

x = 1x6

0.749999886362764 7.749999997838026 -0.000000094280308 -0.000000052120071 2.900000000290558 7.879999999991456

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function [epsilon_equation] = simulation_grating(x0,harminics_positions_pix)

format long
theta_i = x0(1);
lamda0 = x0(2)*1e-9;
diff_dist1 = x0(3)*1e-2;
diff_dist2 = x0(4)*1e-2;
pix_start = x0(5);
pix_end  = x0(6);
d= 1e-3/600;
dia_mcp = 27e-3;
pixels_dia = pix_end-pix_start+1;
pos_middle = (pix_end+pix_start)/2;
pix_size=dia_mcp/pixels_dia;
%theta_i = 75; %deg
const_sin_i = sind(theta_i);
%lamda0=775e-9; %nm
theta_out=asind(const_sin_i-lamda0/d);
harmonics = [13,15,17,19];
harmonics_position = (pos_middle-harminics_positions_pix).*pix_size;
theta_out = asind(const_sin_i-lamda0/d./harmonics);

I_p_helium = 24.6; %eV
lamda_Ip=1240*1e-9/I_p_helium;
pix_helium = 545;

theta_out = [theta_out asind(const_sin_i-lamda_Ip/d)];
harmonics_position = [harmonics_position (pos_middle-545).*pix_size];
dist1= 20e-2+diff_dist1;
dist2 = 10.5e-2+diff_dist2;
L_harmonic = sqrt(dist1^2+(dist2-harmonics_position).^2);
L_harmonic_13 = sqrt(dist1^2+(dist2-harmonics_position(1)).^2);
diff_from_13 = harmonics_position - harmonics_position(1);

L_harmonic = L_harmonic(2:end);
diff_from_13 = diff_from_13(2:end);


epsilon_equation = diff_from_13.^2 - (L_harmonic.^2 + L_harmonic_13.^2 - 2.*L_harmonic.*L_harmonic_13.*cosd(theta_out - theta_i))



end

[Sam Chak]

Use "comments" to annotate the equation number, variable names, type (vector or matrix) and generally what the code does.

Try avoiding using "long" variable names to improve the readability of the code, which normally speeds up the efficiency when troubleshooting the code.

Answer 1

[Torsten]

It seems that a variation of your parameters has almost no effect on epsilon_equation. This makes lsqcurvefit assume it cannot make progress from your initial values. Maybe you could use another unit for epsilon_equation that multiplies it's current values by 1e6 up to 1e9, e.g.

[Sam Chak]

Could this possibly explain why the parameters have almost no effect on the epsilon equation?

needed_results          = zeros(1,5);                   % xdata
harminics_positions_pix = [596, 548, 510, 480, 457];    % ydata
plot(harminics_positions_pix, needed_results, '-o'), grid on
xlabel('harminics positions pix'), ylabel('needed results'), title('Data')

[Eli]

what kind of other units? I assume you don't meand just multiplying the epsilon by 10^9 in the function result - > i tried it and it doesn't converge to where i expect it to.

Maybe you can take a look at the error message?

Warning: Trust-region-reflective algorithm requires at least as many

equations as variables; using Levenberg-Marquardt algorithm instead.

> In lsqncommon (line 94)

In lsqcurvefit (line 306)

In grating_spectrum (line 9)

Local minimum found.

Optimization completed because the size of the gradient is less than

1e-4 times the value of the function tolerance.

<stopping criteria details>

[Torsten]

It's not an error message - it tells you that lsqcurvefit succeeded.

But you should ask yourself whether it makes sense to fit 7 parameters if you only have 6 equations to fix them. Usually this means that you have one degree of freedom and that your problem has an infinite number of solutions. It means further that the parameters you get will most probably have no physical meaning - in accordance with your observation that " it doesn't converge to where i expect it to".