Subject: ratinterpol does not reproduce rational function
From: andre maute
Date: Fri, 28 Dec 2012 02:24:44 +0100
On 12/28/2012 02:23 AM, andre maute wrote:
> On 12/27/2012 11:53 AM, Mario Rodriguez wrote:
>> El jue, 27-12-2012 a las 02:23 +0100, andre maute escribi?:
>>> Hi list,
>>>
>>> I have the following test case
>>>
>>> --- ratinterpol.mac ------------
>>> display2d : false;
>>> load(interpol);
>>> h : makelist( [k,-2*(k+1)*(2*k+1)/(k*(k+2))], k,1,12);
>>> ratinterpol(h,2);
>>> --- ratinterpol.mac ------------
>>>
>>> I get this unexpected behavior
>>>
>>> --- output -------------
>>> $ maxima -b ratinterpol.mac
>>> Maxima 5.27.0 http://maxima.sourceforge.net
>>> using Lisp SBCL 1.0.57-1.fc17
>>> Distributed under the GNU Public License. See the file COPYING.
>>> Dedicated to the memory of William Schelter.
>>> The function bug_report() provides bug reporting information.
>>> STYLE-WARNING: redefining MAXIMA::$FILE_TYPE in DEFUN
>>> (%i1) batch(ratinterpol.mac)
>>>
>>> read and interpret file: /home/user/ratinterpol.mac
>>> (%i2) display2d : false
>>> (%o2) false
>>> (%i3) load(interpol)
>>> (%o3)
>>> "/home/user/opt/maxima/share/maxima/5.27.0/share/numeric/interpol.mac"
>>> (%i4) h:makelist([k,(-2*(1+k)*(1+2*k))/(k*(2+k))],k,1,12)
>>> (%o4)
>>> [[1,-4],[2,-15/4],[3,-56/15],[4,-15/4],[5,-132/35],[6,-91/24],[7,-80/21],[8,-153/40],[9,-380/99],[10,-77/20],[11,-552/143],[12,-325/84]]
>>>
>>> (%i5) ratinterpol(h,2)
>>> Unable to compute the LU factorization
>>> #0:
>>> ratinterpol(tab=[[1,-4],[2,-15/4],[3,-56/15],[4,-15/4],[5,-132/35],[6,-91/24],[7,-80/21],[8,-153/40],[9,-380/99],[10...,r=2,select=[])(linearalgebra.mac
>>>
>>> line 310)
>>> -- an error. To debug this try: debugmode(true);
>>> (%o5) "/home/user/ratinterpol.mac"
>>> --- output -------------
>>
>> Hello,
>>
>> ratinterpol calls linsolve_by_lu to solve a linear system that gives the
>> values of the coefficients of the two polynomials in the rational
>> function.
>>
>> In your example, the linear system built by ratinterpol is not
>> compatible. Maybe there is not any rational function with degree 2 in
>> the numerator such that it passes thru all the sample points. The degree
>> of the denominator is automatically calculated so that the there are as
>> many unknowns as equations.
> This is clearly a rational function in k with numerator and
> denominator degree 2
>
> (%i4) h:makelist([k,(-2*(1+k)*(1+2*k))/(k*(2+k))],k,1,12)
>
>
> Regards
> Andre
>