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# Fitting procedure using MultiStart - doesn't recognize objective function

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Samuele Bolotta on 15 Mar 2021
Commented: Samuele Bolotta on 22 Mar 2021
I'm trying to fit a function to some data using MultiStart in order to find more reliably the global minimum.
This is the code:
[~,~,CPSC,t] = generate_current(80,15,0,-70,-30,0.44,15,0.73,3,120); % Generate current
% Initial values
gmc = 50;
gmg = 50;
tde = 1;
tdi = 1;
tre = 1;
tri = 1;
G_max_chl = 80;
G_max_glu = 15;
EGlu = -70;
EChl = 0;
Vm = -30;
tau_rise_In = 0.44;
tau_decay_In = 15;
tau_rise_Ex = 0.73;
tau_decay_Ex = 3;
y = awgn(CPSC,25,'measured'); % Add white noise
%% Perform fit
[xdata, ydata] = prepareCurveData(t, y);
lb = [-70 0 1 1 -30 0 0 0 0]; % Lower bound
ub = [-70 0 150 150 -30 20 20 5 5]; % Upper bound
p0 = [-70 0 gmc gmg -30 tde tdi tre tri]; % Starting values
% Set up fittype and options.
fitfcn = @(varargin) ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * (Vm - EChl)) + ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));
[xfitted,errorfitted] = lsqcurvefit(fitfcn,p0,xdata,ydata,lb,ub);
problem = createOptimProblem('lsqcurvefit','x0',p0,'objective',fitfcn,...
'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata);
ms = MultiStart('PlotFcns',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,50)
%% Plot fit with data
figure( 'Name', 'Fit' );
h = plot( fitresult1, xdata, ydata );
legend( h, 'CPSC at -30mV', 'Fit to CPSC', 'Location', 'NorthEast', 'Interpreter', 'none');
subtitle('Realistic values')
% Label axes
xlabel( 'time', 'Interpreter', 'none' );
ylabel( 'pA', 'Interpreter', 'none' );
grid on
And this is the function that I call at the beginning:
function [EPSC, IPSC, CPSC, t] = generate_current(G_max_chl, G_max_glu, EGlu, EChl, Vm, tau_rise_In, tau_decay_In, tau_rise_Ex, tau_decay_Ex,tmax)
dt = 0.1; % time step duration (ms)
t = 0:dt:tmax-dt;
% Compute compound current
IPSC = ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * (Vm - EChl));
EPSC = ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));
CPSC = IPSC + EPSC;
end
The error that I get is:
Error using lsqcurvefit (line 269)
Function value and YDATA sizes are not equal.
Error in global_m_fit (line 32)
[xfitted,errorfitted] = lsqcurvefit(fitfcn,p0,xdata,ydata,lb,ub);
I'm not sure why that is the case.
Thanks!
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Star Strider on 15 Mar 2021

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### Accepted Answer

Walter Roberson on 15 Mar 2021
fitfcn = @(varargin) ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * (Vm - EChl)) + ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));
That ignores the input trial parameters, returning a constant expression. However the curve fitting routines pass in trial coefficients of a smaller size in order to validate the function, and your routine is failing to return something of the same size as the trial coefficients.
It is not clear to me what the point is in using a fitting function that ignores its inputs.
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Samuele Bolotta on 22 Mar 2021
Ah yes, I was being naive. I fixed those things you're mentioning. I think the most interesting thing is that if we compare the mean of x (local solver) and the mean of xmulti (multistart, with 50 local solver runs) for 30 iterations, they are almost exactly the same. I'm sure the difference is not statistically significant.
So the problem seems to be related not to the starting points, but to the amount of noise (because with lower levels it works perfectly). I'll try Splitting the Linear and Nonlinear Problems (https://it.mathworks.com/help/optim/ug/nonlinear-data-fitting-problem-based-example.html).
Thanks again for your time!

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### More Answers (1)

Alan Weiss on 15 Mar 2021
I think that you need to have just one input variable, typically called x, and have each of your other named variables be a component of x. For example,
function y = objfun(x)
EGlu = x(1);
EChl = x(2);
G_max_chl = x(3);
G_max_glu = x(4);
Vm = x(5);
tau_rise_In = x(6);
tau_decay_In = x(7);
tau_rise_Ex = x(8);
tau_decay_Ex = x(9);
t = x(10);
y = ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * (Vm - EChl)) + ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));
end
For details, see Writing Scalar Objective Functions. But maybe I got it wrong, and you are using lsqnonlin. Make the appropriate modifications as in Writing Vector and Matrix Objective Functions.
Alan Weiss
MATLAB mathematical toolbox documentation
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