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

[Federico Miyara]

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. [Smile]
> 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
>     <chinluh.tan at bytecode-asia.com
>     <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
>     <stephane.mottelet at utc.fr <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, sgougeon at free.fr
>         <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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