[Scilab-users] Cubic spline

[Rafael Guerra]

Hi Claus,

To try understand the significance of the differences between Scilab and the Fortran code, you could provide a small sample dataset (<10 points) that illustrates your point and tell us what you do not like.
Say, you could provide:  [xi,yi] the spline input, [x,yf] the Fortran results and [x,ys] the Scilab results.

According to interp1 documentation it seems that there is no option to pass any spline arguments such as 'natural'. There are many more options available when using the dedicated splin and interp functions, as in the example I have provided.

Regarding the quality of the linear algebra methods used in Scilab, this is beyond my knowledge.
It seems that BLAS/LAPACK are used but not always.
See discussion on: https://wiki.scilab.org/LackOfUseOfBLAS-LAPACK and also the references provided.

Regards,
Rafael


From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Claus Futtrup
Sent: Tuesday, September 20, 2016 9:25 PM
To: users at lists.scilab.org
Subject: Re: [Scilab-users] Cubic spline

Hi Rafael Guerra, et al.

Thank you for clarifying this to me - that interp1 uses not-a-knot as default. IMHO Scilab documentation should be clear about this.

>What do you mean by your result is "OK, but it's not perfect, compared to a Fortran script"?

I can try to make a snapshot ... what kind do you need? Like a difference in the resulting vector, a piece of source code ... or maybe a graph plot illustrating the difference?

Since the default acc. to your script is not-a-knot ... returning to my original question, is it true I can alter this to 'natural' cubic spline by writing:

a(:,1) = interp1(log(f3),a1,log(f),'spline','natural');

?

... The documentation for interp1 spline isn't clear whether 'natural' is an option for the extrapolation. The documentation in Scilab ( https://help.scilab.org/docs/6.0.0/en_US/interp1.html ) only says:



The extrapolation parameter sets the evaluation rule for extrapolation, i.e for xp(i)not in [x1,xn] interval
"extrap"

the extrapolation is performed by the defined method. yp=interp1(x,y,xp,method,"extrap")

... And the documentation provides no examples of adding this "extrap" parameter to the spline fitting (or any other fitting).


???

Anyway, the Fortran code uses 'natural' cubic spline and (as mentioned) DGTTRF and DGTTRS - are there any Scilab equivalent functions? ... I might wish to try to code (exactly) the same spline functionality, just to eliminate a potential error here.

DGTTRF computes an LU factorization of a real tridiagonal matrix A
* using elimination with partial pivoting and row interchanges.

DGTTRS solves one of the systems of equations
* A*X = B or A'*X = B,
* with a tridiagonal matrix A using the LU factorization computed
* by DGTTRF.

( Source: https://www.gfd-dennou.org/arch/ruby/products/ruby-lapack/doc/dgt.html )

P.S. Sorry for the not-so-fast response time, 1) I'm thinking a lot about it, 2) I shall try not to make too many false statements ... but it's a bit difficult because I don't understand why I get the differences that I observe - and I feel a bit like I'm searching for the reason (the solution) while being blind-folded.

Best regards,
Claus

On 11-09-2016 18:48, Rafael Guerra wrote:
Hi,

The code line using interp1 and the spline method seems to perform "not_a_knot" cubic spline interpolation, as demonstrated by the simple test here below:


x0 = [0 1 2 3 4];

y0 = [0 -1 0 2 1];

x = 0:0.05:4;

y1 = interp1(x0,y0,x,'spline');

d = splin(x0, y0,"not_a_knot");

e = splin(x0, y0,"natural");

y2 = interp(x, x0, y0, d);

y3 = interp(x, x0, y0, e);

clf();

plot(x,y1,'blue',x,y2,'--green',x,y3,'red',x0,y0,'Xblack')


What do you mean by your result is "OK, but it's not perfect, compared to a Fortran script"?
Could you provide a snapshot?

Regards,
Rafae;

From: Claus Futtrup
Sent: Friday, September 09, 2016 8:34 PM
To: International users mailing list for Scilab. <users at lists.scilab.org><mailto:users at lists.scilab.org>
Subject: [Scilab-users] Cubic spline

Hi there

In Scilab I've used interp1 to calculate a cubic spline interpolation, like this:

a(:,1) = interp1(log(f3),a1,log(f),'spline');

a = amplitude (magnitude). f3 is a frequency (27000 linear spaced data), a1 is the original data, f is the resampled 1200 frequencies (log-spaced), where I need the spline to interpolate some data for me.

Above should work OK, but it's not perfect, compared to a Fortran script. The fortran script calculates with its own cubic spline routine, utilizing LAPACK (DGTTRF and DGTTRS) to solve for polynomial coefficients.

The question is - above code line with the interp1 spline, which kind of spline is it?

Digging into interp, I see multiple options. Digging into splin, I also see multiple options.

I looks like the interp1 is using "natural" spline - is this correct?

It's strange because the splin help documentation doesn't recommend this. It says: Don't use the natural type unless the underlying function have zero second end points derivatives.

This might be my problem.

The Scilab help for interp1 doesn't give any examples, but does mention I can add an "extrap" method. Could this be any of the suggestions in the splin documentation. For example, could I write:

a(:,1) = interp1(log(f3),a1,log(f),'spline','not-a-knot');

?

P.S. Since not-a-knot is mentioned as the default for the splin function, I think it should also be made the default for interp1 ... just my two cents.

/Claus




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