Cubic spline interpolation with slope at left end equal to zero?

Hi, all,

I am doing a cubic spline interpolation with some data points. I want the slope at the left end to be zero and don't do anything to the slope at the right end(In the online example, both slope at both ends are forced to be zero). Does anyone know how to do this? Thank you.

Here is my data points:

if true
  x = [0,0.152789493879,0.305539702586,0.458371723707,...
  0.59356259,0.728929965449,0.864429595769,1];
  y = [0,0.013083199999528,0.155041100006201,0.209241100004874,...
       0.178395800001454,0.093888600007631,-0.033515100003569,-0.196524899991346];
end

[John D'Errico]

Why do you think you need the (if true) conditional wrapped around it?

[Qingjie]

Physically, the left point is a energy minimum point, which means the slope should be zero. But due to the limited number of data points, I guess spline interpolation cannot produce a zero slope at the left point.

Answer 1

[John D'Errico]

My SLM tool box will let you create an interpolating spline with the properties you desire.

pp = slmengine(x,y,'knots',x,'leftslope',0,'result','pp');

There are many other things it can do, but this is a simple one. You can get the result in a pp form as I show, or in my own SLM format.

[Qingjie]

Thank you John. I haven't used such tool box before, should I put it in the toolbox directory of MATLAB after I download it?

[John D'Errico]

No. Never put downloaded files in the MATLAB toolbox directories. This will cause problems. Instead, put the downloaded (unzipped) directory some place on your drive, then add that directory to your MATLAB search path. (Use pathtool for this, saving the new search path afterwards.)

[Qingjie]

Thank you very much John. It works really well. Also thank you for a very wonderful comment on my previous question on nonlinear fitting.