Surface fitting tool. What does center and scale do?

Hi everybody,

As the title says, I'm playing with surface fitting tool to create my surface using linear method. Can someone please explain to me what the option center and scale is doing to my graph. I have tried to do same thing with griddata function and I get the same result for my surface as I get using fitting tool but only when center and scale box is unchecked.

Thanks in advance.

Answer 1

[Tom Lane]

If you have the Statistics Toolbox, the following commands will reproduce the sftool results:

[X,Y,Z] = peaks;
x2fx([X(:) Y(:)],'q')\Z(:)  % without centering/scaling
x2fx(zscore([X(:) Y(:)]),'q')\Z(:)  % with centering scaling

The idea is that the x variable is replaced by (x-mean(x))/std(x) and the y variable is replace similarly. This is done before any polynomial terms are computed. The transformation won't change the fit theoretically, but it will make the results better conditioned on a computer with finite precision.

[Imo]

Thank you Tom Lane for your respond. If you could just check this image that I made first without center and scale and with on second. You will notice how graph is not smooth at the verticals where my real data points for the z are(7.5, 10, 12,5, 15, 22.5, 25, 27.5). (don't mind colors of the contours).

I actually need to calculate the area inside each contour so my worries are that I'm not going to get the same results.

http://img703.imageshack.us/img703/2573/usporedbay.jpg

[Tom Lane]

Can you tell me what type of fit you used? You mentioned linear in your original question. I assume that is linear interpolation?

Unfortunately we have stepped out of my area of expertise. I think this interpolant is based on a Delauney triangulation, and I would expect that to be affected by different scaling of the X and Y data. I don't know enough about the method or your data to have any intuition about whether one ought to be smoother or better than the other.

[Imo]

Yes linear interpolation, It be so. I'm acquiring Statistic toolbox in near future. Thanks Tom for the explanation, this is not my area of expertise either:)