Can I get the mathematical expression of an interpolation?

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.

[Walter Roberson]

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?

[Jaime De La Mota Sanchis]

Hello. I think that would be very useful to me, as I feared, it seems like even if it can be done, a lot of work should be put in it.

Answer 1

[Steven Lord]

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')

f = 
     Linear interpolant:
       f(x) = piecewise polynomial computed from p
       where x is normalized by mean 1890 and std 62.05
     Coefficients:
       p = coefficient structure

plot(cdate, pop, 'r-+', 1977, f(1977), 'ko') % Evaluate f in 1977

Looks like a pretty good match.

[Jaime De La Mota Sanchis]

I was hoping for the former, since I need to send that expression to a coworker who uses a different software. However, I will study this and see if I can implement my model in matlab. Thanks.

[Walter Roberson]

What input format would your coworker need?

'linearinterp' creates a TriangleSurfaceInterpolant object that only supports an evaluation public method. It has a hidden property which is a TriScatteredInterp object -- which only stores the points and does not store any decomposed information. Internally, TriScatteredInterp uses delaunay triangulation which in turn is based upon creating voroni diagrams and then converting coordinates to barycenter coordinates in order to do interpolation.

[Jaime De La Mota Sanchis]

I want to send it to another computer where pyomo, an optimizator made in python is used. I have sent the coefficients to said optimizator, but the result is numerically unfeasible.

[Steven Lord]

The MATLAB Engine API for Python may be of interest to you.