<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p><br>
</p>
<div class="moz-cite-prefix">Le 29/01/2019 à 23:10, Federico Miyara
a écrit :<br>
</div>
<blockquote type="cite" cite="mid:5C50CF4F.4040302@fceia.unr.edu.ar">
<meta content="text/html; charset=windows-1252"
http-equiv="Content-Type">
<br>
<font face="Courier New, Courier, monospace">Stephane,<br>
</font><br>
<blockquote cite="mid:916859f7-6573-cf33-a2ee-452c30f08120@utc.fr"
type="cite">
<blockquote type="cite"
cite="mid:5C50AE20.1000004@fceia.unr.edu.ar">However, I must
say that acos(1-%eps) gives on my Scilab 6.0.1 (Windows 7, i7
processor) a result of <br>
</blockquote>
Federico, you have to try 1+%eps or -1-%eps !<br>
</blockquote>
<br>
acos(x) with x > 1 is indeed imaginary, so there is no
unexpected result.<br>
<br>
However, I see now that it hadn't been said that in-domain
arguments yielded complex results but -1 - %eps was the culprit.<br>
<br>
But, for instance, <br>
<br>
min([-1-%eps, -1-%eps*2/3, -1, -1+ %eps, -0.9]) >= -1 <br>
<br>
is false (on my system), so the test performed by Paul Carrico
would not succeed if there were a -1-%eps among the values of the
vector.<br>
<br>
Only when alpha*%eps with alpha < 0.5 is the minimum the test
is successful, but in such case acos() yields a value close to
%pi, not a complex value<br>
<br>
--> acos(-1 - 0.499*%eps)<br>
ans =<br>
<br>
3.141592653589793100000<br>
</blockquote>
<p>logical, since</p>
<p>--> -1 - 0.499*%eps == -1<br>
ans =<br>
<br>
T<br>
</p>
<p>--> acos(-1 - 0.499*%eps)==%pi<br>
ans =<br>
<br>
T<br>
<br>
</p>
<p>S.<br>
</p>
<blockquote type="cite" cite="mid:5C50CF4F.4040302@fceia.unr.edu.ar">
<br>
When alpha > 0.5 the test is not successful nor is the acos()
real:<br>
<br>
--> acos(-1 - 0.50000001*%eps)<br>
ans =<br>
<br>
3.141592653589793100000 - 0.000000021073424255447i<br>
<br>
(this is a binary rounding situation since %eps is 2^-52)<br>
<br>
I think the original question is not completely solved. Why a
number that is not smaller to -1 (asuming the min test is
successful) yields a complex acos?<br>
<br>
An why it does in some systems and not in others? (Assuming Paul's
report is accurate) <br>
<br>
There is another situation where this happens, when an fft is
performed on a real signal, then filtered in the frequency domain
and then the ifft is applied. The result should be real, but
sometimes there are small imaginary parts. <br>
<br>
In this case there is a reason, complex exponentials are used in
the algorithm so arithmetioc errors may not completely cancel out
because of arithmetic and precision issues.<br>
<br>
Federico Miyara<br>
<div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2">
<br>
<br>
<hr style="border:none; color:#909090; background-color:#B0B0B0;
height: 1px; width: 99%;">
<table style="border-collapse:collapse;border:none;">
<tbody>
<tr>
<td style="border:none;padding:0px 15px 0px 8px"> <a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/www.avast.com/antivirus"
moz-do-not-send="true"> <img
src="http://static.avast.com/emails/avast-mail-stamp.png"
alt="Avast logo" moz-do-not-send="true" border="0">
</a> </td>
<td>
<p style="color:#3d4d5a;
font-family:"Calibri","Verdana","Arial","Helvetica";
font-size:12pt;"> El software de antivirus Avast ha
analizado este correo electrónico en busca de virus. <br>
<a
href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/www.avast.com/antivirus"
moz-do-not-send="true">www.avast.com</a> </p>
</td>
</tr>
</tbody>
</table>
<br>
<a href="#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" width="1"
height="1" moz-do-not-send="true"> </a></div>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
users mailing list
<a class="moz-txt-link-abbreviated" href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>
<a class="moz-txt-link-freetext" 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>
</pre>
</blockquote>
</body>
</html>