# Nonlinear fitting - No output function with MultiStart

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Samuele Bolotta on 15 Mar 2021
Commented: Samuele Bolotta on 16 Mar 2021
I'm fitting a function to some nonlinear data. However, the output that I get is:
MultiStart with properties:
UseParallel: 0
Display: 'final'
FunctionTolerance: 1.0000e-06
MaxTime: Inf
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'all'
XTolerance: 1.0000e-06
No plot and not output function.
This is the code:
% Parameters
p(1) = G_max_chl;
p(2) = G_max_glu;
p(3) = tau_rise_In;
p(4) = tau_decay_In;
p(5) = tau_rise_Ex;
p(6) = tau_decay_Ex;
% Create the objective function
fitfcn = @(p, Vm, EGlu, EChl, dt, tmax) ((p(1)) .* ((1 - exp(-(0:dt:tmax-dt) / p(3))) .* exp(-(0:dt:tmax-dt) / p(4))) * (Vm - EChl)) + ((p(2)) .* ((1 - exp(-(0:dt:tmax-dt) / p(5))) .* exp(-(0:dt:tmax-dt) / p(6))) * (Vm - EGlu));
% Create the training data
rng default % For reproducibility
N = 200; % Number of data points
preal = [80,15,0.44,0.73,15,3]; % Real coefficients
Vm = -30;
Eglu = 0;
EChl = -70;
dt = 0.1;
tmax = 120;
ydata = fitfcn(preal,xdata); % Response data with noise
ydata = awgn(ydata,35,'measured');
% Set bounds and initial point.
lb = [0,0,0,0,0,0];
ub = [150,150,5,5,20,20];
p0 = 5*ones(1,6); % Arbitrary initial points
% Find the best local fit
[xfitted,errorfitted] = lsqcurvefit(fitfcn,p0,xdata,ydata,lb,ub)
%Set up the problem for MultiStart.
problem = createOptimProblem('lsqcurvefit','x0',p0,'objective',fitfcn,...
'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata);
% Find a global solution.
ms = MultiStart('PlotFcns',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,200)
I am not sure what I'm doing wrong.
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### Accepted Answer

Star Strider on 15 Mar 2021
Unfortunately, this:
fitfcn = @(p, Vm, EGlu, EChl, dt, tmax) ((p(1)) .* ((1 - exp(-(0:dt:tmax-dt) / p(3))) .* exp(-(0:dt:tmax-dt) / p(4))) * (Vm - EChl)) + ((p(2)) .* ((1 - exp(-(0:dt:tmax-dt) / p(5))) .* exp(-(0:dt:tmax-dt) / p(6))) * (Vm - EGlu));
is not going to work with lsqcurvefit, or likely any other optimisation function.
The problems (that I can easily see) are:
fitfcn = @(p, Vm, EGlu, EChl, dt, tmax) ((p(1)) .* ((1 - exp(-(0:dt:tmax-dt) / p(3))) .* exp(-(0:dt:tmax-dt) / p(4))) * (Vm - EChl)) + ((p(2)) .* ((1 - exp(-(0:dt:tmax-dt) / p(5))) .* exp(-(0:dt:tmax-dt) / p(6))) * (Vm - EGlu));
↑ ← 't MUST BE AN INDEPENDENT VARIABLE ↑ ↑ ← ↑ ← EXTRA PARAMETERS ↑ ← t ↑← 't ↑ ← ↑ ← EXTRA PARAMETERS
So it should be:
fitfcn = @(p, t, Vm, EGlu, EChl) ((p(1)) .* ((1 - exp(-t / p(3))) .* exp(-t / p(4))) * (Vm - EChl)) + ((p(2)) .* ((1 - exp(-t / p(5))) .* exp(-t / p(6))) * (Vm - EGlu));
and the lsqcurvefit call:
B = lsqcurvefit(@(p,t)fitfcn(p, t, Vm, EGlu, EChl), B0, t, ydata)
with ‘Vm’, ‘EGlu’ and ‘EChl’ existing in the calling function workspace.
That should come close to working, although it may require some revision.
I cannot test it so I am posting it as UNTESTED CODE.
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Samuele Bolotta on 16 Mar 2021
Thanks for your explanation!
Unfortunately, even removing the 's' it still gives me the same error. Doing this, I can find a local but not the global minimum. I'll try with GA, but would like to understand what I'm doing wrong here first.
% Find the best local fit
[xfitted,errorfitted] = lsqcurvefit(@(p,t)fitfcn(p, t, Vm, EGlu, EChl), p0, xdata, ydata,lb,ub)
%Set up the problem for MultiStart.
problem = createOptimProblem('lsqcurvefit','x0',p0,'objective',fitfcn,...
'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata);
% Find a global solution
ms = MultiStart('PlotFcn',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,200)

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