TroubleShoot FMinSearch with subscript assignment mismatch

I keep getting the following error:

Subscripted assignment dimension mismatch.

Error in fminsearch (line 190)
fv(:,1) = funfcn(x,varargin{:})

when I try to run the following optimization

objective = @(p) log(besseli(0,(((p(1)*exp(-xData/p(2))).*yData)./Variance),1)) - (((p(1)*exp(-xData/p(2))).^2) ./ (2.*Variance));

% unconstrained nonlinear optimization
parEst = fminsearch(objective,p0);

p0 is [1,2]. Variance is a predefined scalar. xData and yData are both [1,8].

Please help me as I have tried reading the help documents for fminsearch and for anonymous functions, but can't figure it out.

Answer 1

[Torsten]

A scalar must be returned to fminsearch from "objective" ; you return a vector.

Best wishes

Torsten.

[Eric Diaz]

Oh, okay. Hmmm...well, that makes things difficult for me. I am very familiar with using lsqcurvefit, which does not seem to have any problem with taking vectors of data. Do you have any suggestions on how to fix the issue?

[Torsten]

You will have to supply the sum of squared differences of your model expression and your experimental data. But I must admit, since your function involves both xtata and ydata, I don't know what is yi_model and what is yi_experiment.

Best wishes

Torsten.

[Eric Diaz]

Initially, I tried to break down my objective function, however I ran into issues with not having my p (parameter vector) variable defined as Matlab executed the term1 definition. So, I just put my model straight into my objective function in my previous post.

This is how I would like to write my code, as it reads more clearly. Please note that I put the sum function around the objective function below. Is the correct way to do the sum? Also, do you know a way around not having the parameter vector defined?

signalModel = p(1)*exp(-xData/p(2));

term1 = (signalModel.*yData)./Variance;
term2 = (signalModel.^2) ./ (2.*Variance);

objective = @(p) sum(log(besseli(0,term1,1)) - term2);

Answer 2

[John D'Errico]

This happens over and over again. fminsearch is an OPTIMIZER. It does not do nonlinear regression. There is a difference.

An optimizer finds the minimum value of a general function of multiple parameters. So a SCALAR valued function of one or more variables.

A nonlinear regression can be turned into an optimization by forming the sum of squares of residuals, and minimizing that as an objective.

But if you just throw a vector into a tool like fminsearch, expect it to fail. fminsearch has no idea what you want to do. Computers cannot read your mind.

[Eric Diaz]

Thanks for your input John. I think what I need to do is just figure out the correct way to do that summation over the time points.