[Scilab-users] Fwd: Re: ?= =?utf-8?q? Re : problem with matrix of polynomials

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[Scilab-users] Fwd: Re: ?= =?utf-8?q? Re : problem with matrix of polynomials


I'll keep thinking about it, but in the meantime, I noticed that when displaying

a = A*inv(A)

we get the customary list of columns as the total width exceeds the available horizontal space. However, we get one "column 1" header and three "column 2" headers instead of "column 1", ..., "column 4". Seemingly it is not only the header which is repeated, but aldo the columns, i.e., column 2 appears three times.

This seems to be a display bug. 

Regards,

Federico Miyara

 

Back to the possible reason of causing this issue when u substitute a value into the %s  into A*inv(A)

Assume a = A*inv(A), a(1,1) which suppose to be ~ 1 is : 

--> a(1,1)
ans  =

                                                                   
   1.630D-38 + 1.586D-40s + 4.110D-43s^2 + 1.120D-46s^3 + 1.998D-50s^4 + 3.586D-55s^5 
   --------------------------------------------------------------------------- 
                                                                          
                      1.630D-38 + 4.283D-42s + 7.960D-46s^2

the coefficients in numerator and denominator are very small value and with complex number involve, there might be come kind of limitation in the numerical software. 

this could be shown if you subs with smaller number: 

--> horner(A*inv(A), %i*2*%pi*1)
ans  =

   0.9991047 + 0.0595012i   0.0000225 - 5.350D-08i   0.0000132 - 5.350D-08i   0.0000132 - 5.350D-08i
   0.0000552 - 0.1037974i   0.9990938 + 0.0595013i  -0.0008828 - 2.194D-09i  -0.0008828 - 2.194D-09i
   0.0000229 - 7.699D-10i   0.0008778 - 1.540D-09i   1.0008549 + 0.0595013i   0.0008789 - 1.549D-09i
  -0.0000645 + 0.1025666i  -0.0008778 + 1.540D-09i  -0.0008789 + 1.549D-09i   0.9990971 + 0.0595013i

you get the correct answer

This is so far I could go, further details such as how the a double precision real or complex number handled in numerical software are beyond my knowledge.
thanks.

Regards,
Chin Luh




---- On Mon, 09 Mar 2020 22:20:38 +0800 Antoine Monmayrant [hidden email] wrote ----

Hello,

It seems that this value is below %eps==2.2e-16, so I though that once encoded in double the difference between 2e-20 and 0 is too small to be properly taken into account.
Am I missing something?

Antoine


Le Lundi, Mars 09, 2020 15:11 CET, Chin Luh Tan <[hidden email]> a écrit:
 
 
initially I thought could it be possible the number is too small (or too large) to be handled  by double? 
 
after trying scaling down the problem, I notice that in Scilab 6.0.2 onwards:
 
--> 2e-20*%i
ans  =
 
   0. 
 
in Scilab 5.5.2
 
-->2e-20*%i
ans  =
 
    2.000D-20i 
 
 
Could this be the issue?
 
thanks.
 
rgds,
CL
 
---- On Mon, 09 Mar 2020 21:04:12 +0800 Stéphane Mottelet <[hidden email]> wrote ----
 
Maybe an inversion made in state-space could me more reliable ?

S.

Le 09/03/2020 à 13:36, [hidden email] a écrit :
> Hello Federico,
>
> cond() and rcond() do not accept rationals, but the determinant of A is very close to 0:
> --> det(A)
> ans =
>
> 3.573D-10
> ------------------------
> 0.0000027s² +7.433D-10s³
>
> This likely explains that the inversion is not reliable.
>
> Regards
> Samuel
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--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

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Re: Fwd: Re: ?= =?utf-8?q? Re : problem with matrix of polynomials

Le 10/03/2020 à 00:40, Federico Miyara a écrit :

>
> I'll keep thinking about it, but in the meantime, I noticed that when
> displaying
>
> a = A*inv(A)
>
> we get the customary list of columns as the total width exceeds the
> available horizontal space. However, we get one "column 1" header and
> three "column 2" headers instead of "column 1", ..., "column 4".
> Seemingly it is not only the header which is repeated, but aldo the
> columns, i.e., column 2 appears three times.
>
> This seems to be a display bug.


Please upgrade to 6.1.0, where this is fixed.


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