2nd order polynomial fitting with NaNs

Question

Nikos Makris 2011-1-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/334-2nd-order-polynomial-fitting-with-nans

I want to fit a 2nd order polynomial to my data

x=(1,256) y=(1,256)

Only 40 cells from each side of the y array include values, the rest are NaN. So far i have used the polyfit() function but it does not work when the y array contains NaNs. Another function is interp1() which works properly but the fitting methods are limited (no polynomial option).

Are you aware of any other function that is suitable for this problem?

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Answer 1

Egon Geerardyn 2011-1-24

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https://ww2.mathworks.cn/matlabcentral/answers/334-2nd-order-polynomial-fitting-with-nans#answer_455

Try indexing your data points to your non-NaN-points

Let's just work on an example:

%%just generating data
x = 1:10;
y = x.^2 + randn(size(x));
y(4) = NaN;     %I introducce a NaN in y
%%getting indices where y is valid (not NaN)
idxValid = ~isnan(y);
%%fitting
poly = polyfit(x(idxValid),y(idxValid),2);
%%plot
figure;
plot(x,y,'xr','DisplayName','Data points'); hold on;
plot(x,polyval(poly,x),'DisplayName','Fitted'); hold off;
legend('show')

As you will see: this fits only the non NaN data.

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Egon Geerardyn 2011-1-24

@Nikos: it is impossible to include NaN in fitting. NaN stands for not a number (this might mean 0/0 in some cases), it really is an unknown value, so it's impossible to perform any calculation on it. How do you see a fit working when you don't know the values?

What are you actually trying to do? Do you want your polynomial to return values even for x-values where the y-value was NaN? If so, that's exactly what the code above does. That is also the most sensible case for a fit. So I hope you misunderstood my last sentence.

If you want your model to return NaN where y was NaN, you can just put these values there:

yModel = polyval(poly,x);

yModel(~idxValid) = NaN;

Nikos Makris 2011-1-25