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<div class="moz-forward-container">I'll keep thinking about it, but
in the meantime, I noticed that when displaying <br>
<br>
a = A*inv(A)<br>
<br>
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.<br>
<br>
This seems to be a display bug. <br>
<br>
Regards, <br>
<br>
Federico Miyara<br>
<br>
<br>
<br>
<blockquote type="cite"
cite="mid:170bffc2b46.d855246737750.4965631307156628552@bytecode-asia.com">
<div style="font-family: Verdana, Arial, Helvetica, sans-serif;
font-size: 10pt;">
<div>Back to the possible reason of causing this issue when u
substitute a value into the %s into A*inv(A)<br>
</div>
<div><br>
</div>
<div>Assume a = A*inv(A), a(1,1) which suppose to be ~ 1 is : <br>
</div>
<div><br>
</div>
<div>--> a(1,1) <br>
</div>
<div>ans =<br>
</div>
<div><br>
</div>
<div>
<br>
</div>
<div> 1.630D-38 + 1.586D-40s + 4.110D-43s^2 + 1.120D-46s^3 +
1.998D-50s^4 + 3.586D-55s^5 <br>
</div>
<div>
--------------------------------------------------------------------------- <br>
</div>
<div>
<br>
</div>
<div> 1.630D-38 + 4.283D-42s +
7.960D-46s^2<br>
</div>
<div><br>
</div>
<div>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. <br>
</div>
<div><br>
</div>
<div>this could be shown if you subs with smaller number: <br>
</div>
<div><br>
</div>
<div>--> horner(A*inv(A), %i*2*%pi*1) <br>
</div>
<div>ans =<br>
</div>
<div><br>
</div>
<div> 0.9991047 + 0.0595012i 0.0000225 - 5.350D-08i
0.0000132 - 5.350D-08i 0.0000132 - 5.350D-08i<br>
</div>
<div> 0.0000552 - 0.1037974i 0.9990938 + 0.0595013i
-0.0008828 - 2.194D-09i -0.0008828 - 2.194D-09i<br>
</div>
<div> 0.0000229 - 7.699D-10i 0.0008778 - 1.540D-09i
1.0008549 + 0.0595013i 0.0008789 - 1.549D-09i<br>
</div>
<div> -0.0000645 + 0.1025666i -0.0008778 + 1.540D-09i
-0.0008789 + 1.549D-09i 0.9990971 + 0.0595013i<br>
</div>
<div><br>
</div>
<div>you get the correct answer<br>
</div>
<div><br>
</div>
<div>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. <img
ref="image"
src="cid:part1.ED4381C2.42E874EC@fceia.unr.edu.ar"
data-attr="smiley" title="Smile" style="vertical-align:
middle; width: 24px; height: 24px;" class=""><br>
</div>
<div>thanks.<br>
</div>
<div><br>
</div>
<div>Regards,<br>
</div>
<div>Chin Luh</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div class="zmail_extra" style=""
data-zbluepencil-ignore="true">
<div><br>
</div>
<div id="Zm-_Id_-Sgn1">---- On Mon, 09 Mar 2020 22:20:38
+0800 <b>Antoine Monmayrant <a
class="moz-txt-link-rfc2396E"
href="mailto:amonmayr@laas.fr" moz-do-not-send="true"><amonmayr@laas.fr></a></b>
wrote ----<br>
</div>
<div><br>
</div>
<blockquote style="border-left: 1px solid rgb(204, 204,
204); padding-left: 6px; margin: 0px 0px 0px 5px;">
<div>
<div>Hello,<br>
</div>
<div><br>
</div>
<div>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.<br>
</div>
<div>Am I missing something?<br>
</div>
<div><br>
</div>
<div>Antoine<br>
</div>
<div><br>
</div>
<div><br>
</div>
<div>Le Lundi, Mars 09, 2020 15:11 CET, Chin Luh Tan
<<a href="mailto:chinluh.tan@bytecode-asia.com"
target="_blank" moz-do-not-send="true">chinluh.tan@bytecode-asia.com</a>>
a écrit:<br>
</div>
<div> <br>
</div>
<blockquote> <br>
</blockquote>
<div style="font-family: Verdana, Arial, Helvetica,
sans-serif;font-size: 10.0pt;">
<div>initially I thought could it be possible the
number is too small (or too large) to be handled by
double? <br>
</div>
<div> <br>
</div>
<div>after trying scaling down the problem, I notice
that in Scilab 6.0.2 onwards:<br>
</div>
<div> <br>
</div>
<div>--> 2e-20*%i<br>
</div>
<div>ans =<br>
</div>
<div> <br>
</div>
<div> 0. <br>
</div>
<div> <br>
</div>
<div>in Scilab 5.5.2<br>
</div>
<div> <br>
</div>
<div>-->2e-20*%i<br>
</div>
<div>ans =<br>
</div>
<div> <br>
</div>
<div> 2.000D-20i <br>
</div>
<div> <br>
</div>
<div> <br>
</div>
<div>Could this be the issue?<br>
</div>
<div> <br>
</div>
<div>thanks.<br>
</div>
<div> <br>
</div>
<div>rgds,<br>
</div>
<div>CL<br>
</div>
<div class="x_-1527920102zmail_extra">
<div> <br>
</div>
<div>---- On Mon, 09 Mar 2020 21:04:12 +0800 <b>Stéphane
Mottelet <<a
href="mailto:stephane.mottelet@utc.fr"
target="_blank" moz-do-not-send="true">stephane.mottelet@utc.fr</a>></b>
wrote ----<br>
</div>
<div> <br>
</div>
<blockquote style="border-left: 1.0px solid
rgb(204,204,204);padding-left: 6.0px;margin: 0.0px
0.0px 0.0px 5.0px;">
<div>Maybe an inversion made in state-space could
me more reliable ?<br>
<br>
S.<br>
<br>
Le 09/03/2020 à 13:36, <a target="_blank"
href="mailto:sgougeon@free.fr"
moz-do-not-send="true">sgougeon@free.fr</a> a
écrit :<br>
> Hello Federico,<br>
><br>
> cond() and rcond() do not accept rationals,
but the determinant of A is very close to 0:<br>
> --> det(A)<br>
> ans =<br>
><br>
> 3.573D-10<br>
> ------------------------<br>
> 0.0000027s² +7.433D-10s³<br>
><br>
> This likely explains that the inversion is
not reliable.<br>
><br>
> Regards<br>
> Samuel<br>
>
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<br>
--<br>
Stéphane Mottelet<br>
Ingénieur de recherche<br>
EA 4297 Transformations Intégrées de la Matière
Renouvelable<br>
Département Génie des Procédés Industriels<br>
Sorbonne Universités - Université de Technologie
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