MATLAB: How to construct cubic splines

plotting

Hello, I am trying to implement the following code in Matlab but it dose not work.

x = 2*pi*[0 1 .1:.2:.9];
y = cos(x);
csp = csape( x, y, 'periodic' );
hold on
fnplt(csp,'g')
hold off

Best Answer

Do you have the curve fitting toolbox? CSAPE is part of that TB. (It used to be in the splines TB but that got merged into the curve fitting TB some years ago.)

My SLM toolbox (found on the file exchange) does allow periodic boundary conditions.

x = 2*pi*[0:.1:1];
y = cos(x);
SLM = slmengine(x,y,'knots',x,'endcond','periodic','regul',0,'result','pp','plot','on');

So a purely interpolating cubic spline, with periodic boundary conditions.

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MATLAB: Interpolate non monotonic and repetitive sperimental data

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.

MATLAB: Import data to splinetool create spline with function

I understand that you have created a spline using 'cftool' and would like to use the same in 'splinetool'. You can do so by taking a function handle and use it in 'splinetool' An example follows: You can construct a cubic spline interpolant that matches the cosine function at the following sites x, using the csapi command.

 x = 2*pi*[0 1 .1:.2:.9];
 y = cos(x);
 cs = csapi(x,y);

You can then view the interpolating spline by using fnplt and get its handle-

h = fnplt(cs,2);

Now, you can use 'h' in 'splinetool' when it prompts you to import your own data.

Hope this helps!

Best Answer

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MATLAB: Interpolate non monotonic and repetitive sperimental data

MATLAB: Import data to splinetool create spline with function

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