graphing norm of residuals

I used the fminseach to fit non linear equation , how I can graph the residuals . when I seached it I saw it in the graph tool box . how I can graph it if I'm not using the tool box?

[Bjorn Gustavsson]

Do you mean graph the residuals as fminsearch progresses? Or graph the different terms that goes into your non-linear equation? Or something else?

[MOH]

Graphing the residuals as fminsearch progresses

Answer 1

[Walter Roberson]

You can create an options structure that specifies PlotFcn https://www.mathworks.com/help/matlab/math/plot-functions.html

You can create a custom plot function; https://www.mathworks.com/help/optim/ug/output-function.html

The particular field you would want to plot is named fval

[Walter Roberson]

@optimplotfval plots the function value. fminsearch() is only defined for scalar real values, so the difference between plotting the norm and the function value is that the norm would never be negative. If the function value goes negative, it is not obvious to me that you would be wanting to plot its absolute value.

[Bjorn Gustavsson]

The way @MOH describes his wish in terms of "residuals" makes me think that it is some case of sum-of-squares that is being minimized. In that case it might be preferable to use lsqnonlin instead of fminsearch, and one would get another type of plot for the function-values during the optimization progress.

[MOH]

Thanks,what I did I fitted a plot of x, y (vectors) using fminsearch by minimizing the sum sqr error. @bojrn @walter . If I want to graph the norm of residual what should I do. As per my understanding the seq of error it is the same as the residual , is that correct?

[Walter Roberson]

I posted the link above to the structure needed for custom plot functions; you would create such a function (start by copying optimplotfval) and then you would specify it as a PlotFcn in your options.

The difference compared to the existing optimplotfval is that you would need to deliberately plot abs(fval) and so would have the odd situation where the plot would get worse as the fval got more negative.

If you are certain that the output of your function is strictly non-negative, then you can just specify @optimplotfval as your PlotFcn in your options, without having to do anything more. This would not strictly be norm(fval) but it would have the same output provided that the function is strictly >= 0

[Walter Roberson]

Perhaps you have structured your search along the lines of

[bestpara, bestresidue] = fminsearch(@(parameters) objective(parameters, xdata, ydata), x0);

function residue = objective(parameters, xdata, ydata)
   predictions = some function of parameters and xdata
   residue = norm(predictions - ydata);
end

If so then to plot the residues, add options to the fminsearch call with 'PlotFcn' of @optimplotfval .