Using cubic splines to fit data
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Hi, I have a quite involved code for fitting cubic splines to data. I have noticed something odd and wondered if anyone had experience with this. For horizontal data, the spline fits extremely well, however for data within a small x range and large y, i.e. a series of vertical points, the spline is very odd! I have attached two images, first the data set and next the resulting fits.. Any help would be appreciated.
John D'Errico on 18 Oct 2016
First of all, why are you writing cubic spline codes to fit data, if you don't really understand cubic splines, and the issues involved with them?
I'm not sure why I made this an answer, since you say nothing concrete about what EXACTLY you are doing. There are lots of ways you can fit a spline to data, and the data that you have is nothing I would ever decide that a spline would be a good choice for. Do you presume noise in the fit? Is this an interpolating spline? (Why would you do that, EVER? But people do.)
Are you fitting the horizontal lines as separate functions, thus y as function of x for each horizontal set of points? Are the vertical lines fit as x as a function of y? If not, then why not? If you are trying to fit a spline through essentially vertical data in the form of y(x), you should realize that is an insane thing to do. (Sorry but it is.) Or are you somehow trying to fit all of these points at once? (How can I guess what you're doing wrong, when you say nothing?)
The fact is, there are spline codes out there. You would do far better to learn to use an appropriate spline code before trying to write your own. As it is, I'm not at all sure why you are trying to use splines on that data at all.