Can I get the mathematical expression of an interpolation?
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Jaime De La Mota Sanchis
am 8 Okt. 2021
Kommentiert: Steven Lord
am 9 Okt. 2021
Hello everyone. I am working with interpolated data.
I want to obtain the mathematical expression of the interpollating polynomial. I have written
sfX1 = fit([positions(:,1), positions(:,2)],windX_in_the_node_vector,'poly34')
And the output returns the linear model poly which is what I am looking for, f(x,y)=a*x^3+b*y^3+...
However, I would be interested in using other kinds of interpolations. I have tried linear, lowess, linearinterp, cubicinterp and nearest and instead of poly34. Unfortunately, instead of a polynomial such as the one in poly34, the code returns
Linear interpolant:
sfX2(x,y) = piecewise linear surface computed from p
Coefficients:
p = coefficient structure
and so on. Is there a way for me to obtain the mathematical expressions as the ones in poly34?
Best regards.
Jaime.
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Walter Roberson
am 8 Okt. 2021
For piecewise fits, the mathematical expressions would have to be written in terms of heaviside() or similar functions. Would that even be useful to you?
At the moment I am not aware of any function to convert piecewise fits to heaviside, but I believe it would be possible to write such a function... but is it worth doing?
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Steven Lord
am 8 Okt. 2021
Bearbeitet: Steven Lord
am 8 Okt. 2021
Are you looking for a mathematical expression for the fitted model or do you just want to be able to evaluate the fitted model at new points? In the former case, how were you hoping to use such an expression? If the latter case, that's easy.
load census
f = fit(cdate, pop, 'linear', 'Normalize', 'on')
plot(cdate, pop, 'r-+', 1977, f(1977), 'ko') % Evaluate f in 1977
Looks like a pretty good match.
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