<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head><meta content="text/html;charset=UTF-8" http-equiv="Content-Type"></head><body ><div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10pt;"><div>Hi, <br></div><div><br></div><div>sorry for this misleading finding, infact I've second message to turn it down.<br></div><div><br></div><div><br></div><div>******************<br></div><div>ignore the previous finding, turn out to be it seems like just a display issue. <br></div><div><br></div><div>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?<br></div><div>******************<br></div><div><br></div><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:0.28869236100.2456978353450750704.170bffc2b47__smiley__img__src" data-attr="smiley" title="Smile" style="vertical-align: middle; width: 24px; height: 24px;"><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 <amonmayr@laas.fr></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">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">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">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>> _______________________________________________<br>> users mailing list<br>> <a target="_blank" href="mailto:users@lists.scilab.org">users@lists.scilab.org</a><br>> <a target="_blank" href="https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users">https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users</a><br><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 de Compiègne<br>CS 60319, 60203 Compiègne cedex<br>Tel : +33(0)344234688<br><a target="_blank" href="http://www.utc.fr/~mottelet">http://www.utc.fr/~mottelet</a><br><br>_______________________________________________<br>users mailing list<br><a target="_blank" href="mailto:users@lists.scilab.org">users@lists.scilab.org</a><br><a target="_blank" href="http://lists.scilab.org/mailman/listinfo/users">http://lists.scilab.org/mailman/listinfo/users</a></div></blockquote></div><div> <br></div></div><div><br></div><div>
_______________________________________________ <br></div><div>users mailing list <br></div><div><a href="mailto:users@lists.scilab.org" target="_blank">users@lists.scilab.org</a> <br></div><div><a href="http://lists.scilab.org/mailman/listinfo/users" target="_blank">http://lists.scilab.org/mailman/listinfo/users</a> <br></div></div></blockquote></div><div><br></div></div><br></body></html>