Overwriting the maximum function evaluation

Hi all, I have some data to be fitted with the function (please refer to my code). However, despite manually setting the maximumfunctionevaluation limit, the computer doesn't seem to take it and it says the solver stops prematurely. May I ask what have I done wrong?

%% Preparation 
clear;clc 

data = importdata("FCPIB-293K-2.5mW-400nm-Jan072021 -ibg -bg -chirp.csv"); % insert file path within parenthesis 



%% Preamble 

% Fundamental constants
h = 4.0135667696*10^-15; % units: eV/ Hz
c = 3*10^8; % SI units
kB = 8.617333268*10^-5; % units: eV/ K

% Clean up of data to select range of values 
wavelength = data(1:end, 1);
delay_t = data(1, 1:end); % conatains all of the delay times
E = (h*c)./(wavelength*10^-9); % contains all of the probe energies
Range_E = E>=1.5 & E<=2.2;
Range_T = delay_t>=0.5 & delay_t<=1000;

% for one delay time
T = find(Range_T);
T_min = min(T);
T_max = max(T);
t = 57; % choose an integer b/w T_min and T_max
delaytime = delay_t(1, t);
disp(delaytime)

% Initial parameter guess and bounds 
lb = [0, 293, -1]; ub = [Inf, 1200, 1];
y0 = [2*10^9, 1000, 0.5];


% Data for fitting 
E_p = E(Range_E); % selected probe energies
delta_Abs = -1*data(Range_E,t); 
delta_Abs_norm = delta_Abs./max(abs(delta_Abs)); % normalised delta_Abs
Range_Efit = E_p>=1.62 & E_p<=max(E_p);
E_fit = E_p(Range_Efit);
delta_Abs_norm_fit = delta_Abs_norm(Range_Efit);

% Fitting function
function F = MB(y, E_fit)
    F = y(1).*exp(-(E_fit./(8.617333268*10^-5.*y(2)))) + y(3);
end 


%% Curve fitting options 

% % Initial parameter guess and bounds 
% lb = [0, 293, -1]; ub = [Inf, 800, 1];
% y0 = [1.2*10^9, 700, 0.5];


% lsqcurvefit and choose between different algorithm that lsqcurvefit employs (3C1, comment those lines that are not choosen and uncomment the line that is choosen, if not, matlab will take the last line of "optim_lsq" by default)
optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'levenberg-marquardt', 'MaxFunctionEvaluations',10^10, 'MaxIterations', 10^10, 'FunctionTolerance',10^-10, 'StepTolerance', 10^-10);
% optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'trust-region-reflective', 'MaxFunctionEvaluations',10^10, 'MaxIterations',10^10, 'FunctionTolerance',10^-20, 'StepTolerance', 10^-20);
% optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'interior-point', 'MaxFunctionEvaluations',1000, 'MaxIterations', 1000, 'FunctionTolerance',10^-20, 'StepTolerance', 10^-20);

% Solver for lsqcurvefit
[y, residualnorm, residual, exitflag, output, lambda, jacobian] = lsqcurvefit(@MB, y0, E_fit, delta_Abs_norm_fit, lb, ub);



%% Plot command 

plot(E_p, delta_Abs_norm,'Black')
hold on 
plot(E_fit, MB(y, E_fit), 'LineWidth', 1.0, 'Color', 'red')
xlabel('Probe Photon Energy (eV)')
ylabel('Normalised \Delta A (a.u.)')
legend('Experimental Data', 'Fitted Curve')
disp(y(1,1))
disp(y(1,2))
disp(y(1,3))

Answer 1

[Star Strider]

The options structure to lsqcurvefit must be the argument to it, since (except for name-value pair arguments), arguments to MATLAB functions are positional.

So in your call to lsqcurvefit, use:

[y, residualnorm, residual, exitflag, output, lambda, jacobian] = lsqcurvefit(@MB, y0, E_fit, delta_Abs_norm_fit, lb, ub, [], [], [], [], [], optim_lsq);

I tested that and it worked. (I also added a ga call to get a better initial estimate of ‘y0’, and then let lsqcurvefit tweak it.)

%% Preparation 
clear;clc 

data = importdata("FCPIB-293K-2.5...bg -chirp.csv"); % insert file path within parenthesis 



%% Preamble 

% Fundamental constants
h = 4.0135667696*10^-15; % units: eV/ Hz
c = 3*10^8; % SI units
kB = 8.617333268*10^-5; % units: eV/ K

% Clean up of data to select range of values 
wavelength = data(1:end, 1);
delay_t = data(1, 1:end); % conatains all of the delay times
E = (h*c)./(wavelength*10^-9); % contains all of the probe energies
Range_E = E>=1.5 & E<=2.2;
Range_T = delay_t>=0.5 & delay_t<=1000;

% for one delay time
T = find(Range_T);
T_min = min(T);
T_max = max(T);
t = 57; % choose an integer b/w T_min and T_max
delaytime = delay_t(1, t);
disp(delaytime)

    0.5976

% Initial parameter guess and bounds 
lb = [0, 293, -1]; ub = [Inf, 1200, 1];
y0 = [2*10^9, 1000, 0.5];


% Data for fitting 
E_p = E(Range_E); % selected probe energies
delta_Abs = -1*data(Range_E,t); 
delta_Abs_norm = delta_Abs./max(abs(delta_Abs)); % normalised delta_Abs
Range_Efit = E_p>=1.62 & E_p<=max(E_p);
E_fit = E_p(Range_Efit);
delta_Abs_norm_fit = delta_Abs_norm(Range_Efit);

% Fitting function
function F = MB(y, E_fit)
    F = y(1).*exp(-(E_fit./(8.617333268*10^-5.*y(2)))) + y(3);
end 


%% Curve fitting options 

% % Initial parameter guess and bounds 
% lb = [0, 293, -1]; ub = [Inf, 800, 1];
% y0 = [1.2*10^9, 700, 0.5];


% lsqcurvefit and choose between different algorithm that lsqcurvefit employs (3C1, comment those lines that are not choosen and uncomment the line that is choosen, if not, matlab will take the last line of "optim_lsq" by default)
optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'levenberg-marquardt', 'MaxFunctionEvaluations',10^10, 'MaxIterations', 10^10, 'FunctionTolerance',10^-10, 'StepTolerance', 10^-10);
% optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'trust-region-reflective', 'MaxFunctionEvaluations',10^10, 'MaxIterations',10^10, 'FunctionTolerance',10^-20, 'StepTolerance', 10^-20);
% optim_lsq = optimoptions('lsqcurvefit', 'Algorithm', 'interior-point', 'MaxFunctionEvaluations',1000, 'MaxIterations', 1000, 'FunctionTolerance',10^-20, 'StepTolerance', 10^-20);

ftns = @(y) norm(delta_Abs_norm_fit - MB(y, E_fit));
y0 = ga(ftns, 3, [], [], [], [], lb, ub)

ga stopped because the average change in the fitness value is less than options.FunctionTolerance.

y0 = 1x3

1.0e+03 * 0.0334 1.1626 0.0000

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% Solver for lsqcurvefit
[y, residualnorm, residual, exitflag, output, lambda, jacobian] = lsqcurvefit(@MB, y0, E_fit, delta_Abs_norm_fit, lb, ub, [], [], [], [], [], optim_lsq);

Local minimum found.

Optimization completed because the size of the gradient is less than
1e-4 times the value of the function tolerance.

y

y = 1x3

1.0e+06 * 2.2743 0.0012 -0.0000

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%% Plot command 

plot(E_p, delta_Abs_norm,'Black')
hold on 
plot(E_fit, MB(y, E_fit), 'LineWidth', 1.0, 'Color', 'red')
xlabel('Probe Photon Energy (eV)')
ylabel('Normalised \Delta A (a.u.)')
legend('Experimental Data', 'Fitted Curve')

disp(y(1,1))

   2.2743e+06

disp(y(1,2))

        1200

disp(y(1,3))

   -0.0551

[Jack]

Thank you Star!

[Star Strider]

As always, my pleasure!

Answer 2

[Torsten]

You didn't include the structure "optim_lsq" in the call to lsqcurvefit.

[Jack]

May I ask where should I put the "optim_lsq" in the call to lsqcurvefit? Is there a specific position that "optim_lsq" has to take in the call of lsqcurvefit?

[Steven Lord]

Put it in the location of the options input argument in the arguments list shown on the lsqcurvefit documentation page.