Interpolate non monotonic and repetitive sperimental data

Hi, I have a matrix of experimental points like this

360,795727281504  361,650330617608  361,650330617608  362,642755698073  363,288968788277  364,054221131940  364,054221131940  364,054221131940  364,054221131940  364,054221131940  364,054221131940  365,288499105590  366,191936918042  366,676715118651  366,676715118651
0,588235294117647  0,584313725490196  0,584313725490196  0,580392156862745  0,584313725490196  0,584313725490196  0,584313725490196  0,584313725490196  0,588235294117647  0,588235294117647  0,588235294117647  0,596078431372549  0,592156862745098  0,588235294117647  0,588235294117647

X value --> 1st row | Y value --> 2nd row

I'd like to interpolate this points, note that sometime X or Y value could repeat.

Thanks !

[Image Analyst]

Do you have a question? Maybe something like "Here is my code for interp1(). Can you tell me why it's not working?"

Tip read this link

[Francesco Panico]

Yes, do you know any matlab function that can interpolate data like this? Intep1 or Spline don't work, because point aren't monotone and matlab says "Index exceed matrix dimension". Polyfit don't give me a good approximation of the whole function

Thanks

[Image Analyst]

You can make your data monotonic by doing

[sortedx, sortorder] = sort(x, 'ascend');
sortedy = y(sortorder);

If you have a model for the function, you can use fitglm. See attached examples. If you just want to smooth, you can use sgolayfilt().

Attach your x and y data if you want more help. And be sure to read the link I gave you. If you had, I'd be working on your problem right now, but unfortunately you didn't and now I have to head out for dinner for a few hours.

[Francesco Panico]

Hi, thanks for your help . I attached my data here. And I'm reading the links right now.

Answer 1

[John D'Errico]

This is not a question about interpolation. Why not?

What is interpolation? It involves finding a curve that passes EXACTLY through the data points.

You clearly don't want to do that. But you are trying to use tools for interpolation, thus spline, interp1, etc.

You want to do smoothing and approximation. Since you have no model for this process, at best, you need to use a tool for spline smoothing of some sort. Polynomial curve fitting is a really BAD idea here, because you would need a really high order polynomial for the fit.

A good tool for this purpose would be my SLM Toolbox. There are many options. But given this very small set of rather noisy data, I tried this:

spl = slmengine(x,y,'plot','on','reg','cross');

which seems to be as much as it is worth.

You can download it from the File Exchange.

24443-slm-shape-language-modeling

Now that you have uploaded your data,

mdl = slmengine(x,y,'plot','on','knots',100,'maxvalue',1);

If I now look more carefully at just the first section that seems fairly linear, there are a couple of things I see.

First, the curve seems to have a periodic behavior, that the spline wanted to follow. You can either smooth that out, treating it as noise, or you can chase it as I allowed the spline to do here.

Next, I see that your data appears to be quantized. So rather than random noise, you have a process that takes on only discrete levels. I'm not sure this really matters too much in context though.

[Francesco Panico]

Thanks John D'Errico it's a very powerful tool and It's able to solve my problem !