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Petipace
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 2:24 am

You could take a look at http://www.netlib.org/dierckx/.

concur.f implements the clamped smoothing spline.

Disclaimer: I haven’t used this library myself, but Dierckx’s book is quite good.
 
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Alan
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 5:28 am

You could take a look at http://www.netlib.org/dierckx/.

concur.f implements the clamped smoothing spline.

Disclaimer: I haven’t used this library myself, but Dierckx’s book is quite good.

Thank you -- it looks like Dierckx's book may indeed have what I am searching for -- ordered a decently priced used copy.
 
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Cuchulainn
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 12:55 pm

 
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FaridMoussaoui
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 5:13 pm

That's package was removed from CRAN repos. Orphaned and archived on 2014.
It was mainly a call to the fortran librairies.
 
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Cuchulainn
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 7:30 pm

That's package was removed from CRAN repos. Orphaned and archived on 2014.
It was mainly a call to the fortran librairies.
All that work for nothing?
 
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FaridMoussaoui
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Re: Smoothing splines (clamped spline)

July 22nd, 2019, 9:13 pm

It means it is not actively maintained but it is still there. I even installed it for a test and it's working (you need a fortran compiler).
 
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Cuchulainn
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Re: Smoothing splines (clamped spline)

September 13th, 2019, 1:08 pm

This might be useful; in particular, estimation of the smoothing parameter [$]\lambda[$].

 
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Cuchulainn
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Re: Smoothing splines (clamped spline)

September 13th, 2019, 1:39 pm

Hi Daniel,

Thank you for the code. I haven't opened it yet. Let me know if I will find the solution to the following problem, which will answer your question.

I want to find the piecewise cubic polynomial [$]g(t)[$] that solves the following problem:

(*) minimize [$] \left( \sum_{i=1}^n \{ y_i - g(t_i) \}^2 + \lambda \int_a^b \{ g''(u) \}^2 \, du \right)[$], 

subject to 
(A) given values for [$]g'(a)[$] and [$]g'(b)[$], where [$] a < t_1 < t_2 < \cdots < t_n < b[$], 
(B) given data [$]\{t_i,y_i\}[$] and
(C) given [$]\lambda > 0[$], the 'smoothing' parameter.

Without (A), this is the standard smoothing spline problem, solved by Reinsch (1967) (fulltext here) and with many subsequent treatments. 

BTW, I've got your 2018 book. Correct me if I'm wrong, but it looks like the cubic splines discussed there are just *interpolating* splines; i.e., the solution to (*) when [$]\lambda=0[$]?
.
Alan,
Don't suppose you have a numeric example for this?
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