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<font face="Courier New, Courier, monospace">This is an improved
version of the acos function with input argument check:<br>
<br>
</font>
<pre style="font-family:Monospaced;font-style:normal;font-size:14.0;"><span style="color:rgb(176,24,19);">function</span> <span style="color:rgb(131,67,16);font-weight:bold;">y</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);text-decoration:underline;">acos1</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">x</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(75,149,50);font-weight:bold;font-style:italic;">// Check if components are real</span>
<span style="color:rgb(0,0,0);">is_real</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">imag</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">x</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">==</span><span style="color:rgb(188,143,143);">0</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(75,149,50);font-weight:bold;font-style:italic;">// Leave real-only components</span>
<span style="color:rgb(0,0,0);">x1</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">is_real</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(131,67,16);font-weight:bold;">x</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(75,149,50);font-weight:bold;font-style:italic;">// Check if components are real and belong to [-1, 1]</span>
<span style="color:rgb(0,0,0);">in_domain</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">is_real</span> <span style="color:rgb(92,92,92);">&</span> <span style="color:rgb(74,85,219);">(</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(92,92,92);"><=</span><span style="color:rgb(0,0,0);">x1</span> <span style="color:rgb(92,92,92);">&</span> <span style="color:rgb(0,0,0);">x1</span><span style="color:rgb(92,92,92);"><=</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(75,149,50);font-weight:bold;font-style:italic;">// Imaginary part of acos(x) is accepted only if </span>
<span style="color:rgb(75,149,50);font-weight:bold;font-style:italic;">// x does not belong to [-1, 1] </span>
<span style="color:rgb(131,67,16);font-weight:bold;">y</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(0,0,0);">in_domain</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">real</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(50,185,185);">acos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">x</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(92,92,92);">+</span> <span style="color:rgb(74,85,219);">(</span><span style="color:rgb(92,92,92);">~</span><span style="color:rgb(0,0,0);">in_domain</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">acos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">x</span><span style="color:rgb(74,85,219)!
;">)</sp
an><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(176,24,19);">endfunction</span></pre>
<br>
This works on vectors and arrays as well. Unfortunately i couldn't
find a component-wise isreal() function, otherwise it would have
been simpler!<br>
<br>
<div class="moz-cite-prefix">Federico Miyara<br>
<br>
<br>
On 29/01/2019 12:58, Stéphane Mottelet wrote:<br>
</div>
<blockquote cite="mid:dd8de4d8-e037-5065-eb80-b3402670bb6f@utc.fr"
type="cite">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<div class="moz-cite-prefix">It is the same if x is slightly >
1:</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">--> x=1+%eps<br>
x = <br>
<br>
1.<br>
<br>
<br>
--> acos(x)<br>
ans =<br>
<br>
2.107D-08i <br>
</div>
<div class="moz-cite-prefix"><br>
</div>
--> format(25); x <br>
x = <br>
<br>
1.0000000000000002220446
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Le 29/01/2019 à 16:55, Carrico, Paul
a écrit :<br>
</div>
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<div class="WordSection1">
<p class="MsoNormal"><span
style="font-size:12.0pt;color:#1F497D" lang="EN-US">When I
scroll to the list, the lowest (positive) value is 8.4<sup>E</sup>-08
(works fine) and no %eps .<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:12.0pt;color:#1F497D" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:12.0pt;color:#1F497D" lang="EN-US">How
Can I check if %eps is in?<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:12.0pt;color:#1F497D" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #B5C4DF
1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><a name="_____replyseparator"
moz-do-not-send="true"></a><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext;mso-fareast-language:FR">De :</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext;mso-fareast-language:FR">
users [<a moz-do-not-send="true"
class="moz-txt-link-freetext"
href="mailto:users-bounces@lists.scilab.org">mailto:users-bounces@lists.scilab.org</a>]
<b>De la part de</b> Stéphane Mottelet<br>
<b>Envoyé :</b> mardi 29 janvier 2019 16:50<br>
<b>À :</b> <a moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:users@lists.scilab.org">users@lists.scilab.org</a><br>
<b>Objet :</b> [EXTERNAL] Re: [Scilab-users] acos
leads to complex values<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal">Le 29/01/2019 à 16:45, Carrico, Paul a
écrit :<o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<p class="MsoNormal"><span lang="EN-US">Dear All</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">I spent some time in
looking for a mistake in my code ; finally Ive found
that the ACOS of a real vector leads to some complex
values (???)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<pre><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#32B9B9" lang="ES">acos</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="ES">(</span><span style="font-size:12.0pt;font-family:"Monospaced","serif"" lang="ES">Scar_P</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="ES">(</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#FFAA00" lang="ES">:</span><span style="font-size:12.0pt;font-family:"Monospaced","serif"" lang="ES">,</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="ES">1</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="ES">)</span><span style="font-size:12.0pt;font-family:"Monospaced&!
;quo!
t;,"
;serif"" lang="ES"> </span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#5C5C5C" lang="ES">./</span><span style="font-size:12.0pt;font-family:"Monospaced","serif"" lang="ES"> CM_x_CN</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="ES">(</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#FFAA00" lang="ES">:</span><span style="font-size:12.0pt;font-family:"Monospaced","serif"" lang="ES">,</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:rosybrown" lang="ES">1</span><span style="font-size:12.0pt;font-family:"Monospaced","serif";color:#4A55DB" lang="ES">))</span><o:p></o:p></pre>
</blockquote>
<p>Are your really sure, because we may have<o:p></o:p></p>
<p>--> x=-1-%eps <br>
x = <br>
<br>
-1.<br>
<br>
<br>
--> acos(x)<br>
ans =<br>
<br>
3.1415927 - 2.107D-08i<o:p></o:p></p>
<p>S.<o:p></o:p></p>
<p><o:p> </o:p></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<pre><span style="font-size:12.0pt;font-family:"Monospaced","serif"" lang="ES"> </span><o:p></o:p></pre>
<p class="MsoNormal"><span lang="EN-US">(the formula worked
so far)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">I checked that the
input values are correct:</span><o:p></o:p></p>
<p class="MsoListParagraph"
style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><!--[if !supportLists]--><span
style="mso-list:Ignore">-<span style="font:7.0pt
"Times New Roman""> </span></span><!--[endif]--><span
lang="EN-US">Comprised between [-1; 1] using MIN and MAX</span><o:p></o:p></p>
<p class="MsoListParagraph"
style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><!--[if !supportLists]--><span
style="mso-list:Ignore">-<span style="font:7.0pt
"Times New Roman""> </span></span><!--[endif]--><span
lang="EN-US">Composed only of real values using ISREAL
(all the vectors are correct)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">Thus I do not
understand why complex values appear ?</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">May it come from the
vectorization ?</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">Paul</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:12.0pt;font-family:"Times New
Roman","serif";mso-fareast-language:FR"><br>
<br>
<o:p></o:p></span></p>
<pre>_______________________________________________<o:p></o:p></pre>
<pre>users mailing list<o:p></o:p></pre>
<pre><a href="mailto:users@lists.scilab.org" moz-do-not-send="true">users@lists.scilab.org</a><o:p></o:p></pre>
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</blockquote>
<p><o:p> </o:p></p>
<pre>-- <o:p></o:p></pre>
<pre>Stéphane Mottelet<o:p></o:p></pre>
<pre>Ingénieur de recherche<o:p></o:p></pre>
<pre>EA 4297 Transformations Intégrées de la Matière Renouvelable<o:p></o:p></pre>
<pre>Département Génie des Procédés Industriels<o:p></o:p></pre>
<pre>Sorbonne Universités - Université de Technologie de Compiègne<o:p></o:p></pre>
<pre>CS 60319, 60203 Compiègne cedex<o:p></o:p></pre>
<pre>Tel : +33(0)344234688<o:p></o:p></pre>
<pre><a href="https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/urldefense.proofpoint.com/v2/url?u=http-3A__www.utc.fr_-7Emottelet&d=DwMG-g&c=0hKVUfnuoBozYN8UvxPA-w&r=4TCz--8bXfJhZZvIxJAemAJyz7Vfx78XvgYu3LN7eLo&m=rN8DsnGalih7CBHModSb9evOi3rmZRFFYcBFHTC71gU&s=34gC0H3RYWxwcKp7fr4bR5XFfy1acxO72YI9AYJJFhA&e=" moz-do-not-send="true">http://www.utc.fr/~mottelet</a><o:p></o:p></pre>
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<p><br>
</p>
<pre class="moz-signature" cols="72">--
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
<a moz-do-not-send="true" class="moz-txt-link-freetext" href="http://www.utc.fr/%7Emottelet">http://www.utc.fr/~mottelet</a></pre>
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<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://www.avast.com/antivirus">www.avast.com</a>
</p>
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