| SPLINE function [message #79230] |
Fri, 10 February 2012 07:48 |
jen
Messages: 1
Registered: February 2012
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Junior Member |
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Just wondering what type of spline the built in IDL SPLINE function
actually solves?
In the help it just says 'cubic spline interpolation', however there
are a lot of different types of spline that are based on a cubic
spline or reduce to a cubic spline depending on the parameters chosen.
I'd kind of assumed it was a standard cubic spline with natural
boundary conditions, however I don't think this is right because:
a) There is a tension parameter, which does not exist for a cubic
spline. According to the IDL help, this gives a cubic spline if the
tension is set to 0, but the default is 1 - i.e. NOT a cubic spline.
I've read that rational splines have a tension parameter, but I'm not
sure if there are any other types of spline which have this?
b) I wrote my own simple cubic spline routine (so that I could try
different boundary conditions), and it produces slightly different
results to the built in SPLINE function even when I set it to natural
boundary conditions.
c) I took a look at the code, and although I don't fully understand
what it does, I can see some things which are definitely not part of
the solution to a basic cubic spline. E.g it takes the hyperbolic sine
& cosine of a function involving the tension parameter & the gradient
between each pair of nodes, and seems to use this to determine the
elements of the tridiagonal matrix which is solved to find the spline
coefficients. I don't know what type of spline would be solved in this
way?
If anyone can offer any insight on this, I'd really appreciate it.
Thanks.
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