Max value of a fit

How do I find the max value of a fit to data. I am using:

f=fit(x,y,'poly5')

I have tried

p=polyder(f)
roots(P)

But I get an error

Answer 1

[Torsten]

f=fit(x,y,'poly5');
c = coeffvalues(f);
cd = polyder(c);
roots(cd);

Best wishes

Torsten.

[Jason]

Thankyou, John and Torsten.

So I typically have more than one root of the derivative. Is there a better way to determine the max as shown by the graph below.

[Jason]

OK, I've worked out how:

for j=1:3000
  A(j,:)=f(j);   %Create a column array
end

B=max(A(:));
idx=find(A==B);

[Torsten]

At least an approximation of the maximum value ...

Best wishes

Torsten.

[Jason]

Yes, they represent a level on a 12bit DAC, so I only need unit granularity. Jason

[gwoo]

Just to simplify, that little bit of code can be:

A = f([1:3000]'); % Create a column array

[maxValue, maxIndex] = max(A); % Second output of max() is the index of the max value

This simplification works if A is a 1-column vector.

Answer 2

[John D'Errico]

So what error did you get? It helps if you are complete in your comments about an error so that others can help you.

I'll bet that since polyder is not designed to work with polynomials in the form that polyfit generates, that it did not understand how to work with the polynomial object returned from fit.

This should work though:

roots(polyder(coeffvalues(f)))

[John D'Errico]

To determine the maximum value, you evaluate the function at each (real) candidate. Thus at each root of the derivative, evaluate the original function, and take the maximum value over all candidate roots.

If a root was outside of the interval (the support of your data) then this would be extrapolation, so generally a bad idea to use extrapolated values for this, especially if the extrapolation was done from a polynomial.

In some circumstances, you might also compare the value of the function at the first and last data point, assuming you choose not to allow extrapolation. For the curve as shown in your figure, this is of course not necessary.