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jen  
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 More options Feb 10, 10:48 am
Newsgroups: comp.lang.idl-pvwave
From: jen <jenhers...@gmail.com>
Date: Fri, 10 Feb 2012 07:48:25 -0800 (PST)
Local: Fri, Feb 10 2012 10:48 am
Subject: SPLINE function
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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Craig Markwardt  
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 More options Feb 11, 9:41 am
Newsgroups: comp.lang.idl-pvwave
From: Craig Markwardt <craig.markwa...@gmail.com>
Date: Sat, 11 Feb 2012 06:41:36 -0800 (PST)
Local: Sat, Feb 11 2012 9:41 am
Subject: Re: SPLINE function
On Feb 10, 10:48 am, jen <jenhers...@gmail.com> wrote:

I don't have a lot of insight into how SPLINE works, but I do remember
that early on, SPLINE didn't work well for me and I abandoned it.  ( I
think it was a robustness thing. )

I've used SPL_INIT and SPL_INTERP ever since and they've worked fine.
And more to your point, they use Numerical Recipes spline routines
which are a cubic spline with natural boundary conditions.

Craig


 
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