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
<[email protected]>* 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
<[email protected]
<mailto:[email protected]>> 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
<[email protected] <mailto:[email protected]>>*
wrote ----
Maybe an inversion made in state-space could me more reliable ?
S.
Le 09/03/2020 à 13:36, [email protected]
<mailto:[email protected]> 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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