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

[Chin Luh Tan]

Hi, 



sorry for this misleading finding, infact I've second message to turn it down.





******************

ignore the previous finding, turn out to be it seems like just a display issue. 



However, I think my initial thought of the precision might be the issue? some number are too small (first case) and giving error during computation?

******************



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 <amonmayr at laas.fr> 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 <mailto:chinluh.tan at bytecode-asia.com> 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 <mailto:stephane.mottelet at utc.fr> wrote ----

 

Maybe an inversion made in state-space could me more reliable ?

S.

Le 09/03/2020 à 13:36, mailto:sgougeon at free.fr 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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