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<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">Hi,<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">For huge matrices of strings like your variable “b”,
<span class="SpellE">eval</span>() <span style="mso-spacerun:yes"> </span>or <span class="SpellE">
evstr</span>() do not seem to work efficiently in Scilab 5.5.2.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">However, if you have a fast hard disk (<span class="SpellE">SSD</span>), it will be comparatively lightning fast to do the conversion via I/O functions
such as:<o:p></o:p></span></font></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">csvWrite</span></font></span><font color="black"><span style="color:black">(<span class="SpellE">b,"outb.csv</span>");<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">c=<span class="SpellE">csvRead</span>("outb.csv");<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">Then use c in your code, which has now type of ‘constant’, with nor further need for
<span class="SpellE">eval</span>/<span class="SpellE">evstr</span>.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">Rgds</span></font></span><font color="black"><span style="color:black">,<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black">Rafael<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;color:black"><o:p> </o:p></span></font></p>
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<p class="MsoNormal"><b><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt;mso-fareast-font-family:"Times New Roman";color:windowtext;font-weight:bold">From:</span></font></b><font color="black"><span style="mso-fareast-font-family:"Times New Roman";color:windowtext">
users [mailto:users-bounces@lists.scilab.org] <b><span style="font-weight:bold">On Behalf Of
</span></b><span class="SpellE">Carrico</span>, Paul<br>
<b><span style="font-weight:bold">Sent:</span></b> Friday, June 30, 2017 12:46 PM<br>
<b><span style="font-weight:bold">To:</span></b> Users mailing list for Scilab <users@lists.scilab.org><br>
<b><span style="font-weight:bold">Subject:</span></b> Re: [Scilab-users] [EXTERNAL] Re: my loop faster than vectorization (???)<o:p></o:p></span></font></p>
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</div>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">Hi<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">Interesting feedback, but different of mine
</span></font><font color="#1f497d" face="Wingdings"><span style="font-family:Wingdings;color:#1F497D">J</span></font><font color="#1f497d"><span style="color:#1F497D"><o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">With n=100000 with my working station under Windows 7.0 with Scilab 5.5.2<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">(from memory I noticed the same behavior on my old laptop under Ubuntu 16.04
<span class="SpellE">LTS</span>)<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">duration1 =<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> 93.057
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> duration2 =<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> 108.325
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> duration3 =<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><b><font size="2" color="red" face="Calibri"><span style="font-size:11.0pt;color:red;font-weight:bold"> 1.279
<o:p></o:p></span></font></b></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> duration3 =<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> 135.178
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><span class="SpellE"><i><u><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D;font-style:italic">Nota</span></font></u></i></span><font color="#1f497d"><span style="color:#1F497D">: nevertheless for
huge asci files containing millions of lines (not in the same format of course) , I finally decided to “outsource” this work<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D">Paul<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></p>
<p><b><i><font size="2" color="gray" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;color:gray;mso-ansi-language:FR;font-weight:bold;font-style:italic">EXPORT CONTROL :
<br>
</span></font></i></b><b><font size="2" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;mso-ansi-language:FR;font-weight:bold">Cet email ne contient pas de données techniques<br>
This email <span class="SpellE">does</span> not <span class="SpellE">contain</span>
<span class="SpellE">technical</span> data</span></font></b><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"><o:p> </o:p></span></font></p>
<div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="mso-outline-level:1"><a name="_____replyseparator"></a><b><font size="2" color="black" face="Tahoma"><span lang="FR" style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:windowtext;mso-ansi-language:FR;mso-fareast-language:FR;font-weight:bold">De :</span></font></b><font size="2" color="black" face="Tahoma"><span lang="FR" style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:windowtext;mso-ansi-language:FR;mso-fareast-language:FR">
users [<a href="mailto:users-bounces@lists.scilab.org">mailto:users-bounces@lists.scilab.org</a>]
<b><span style="font-weight:bold">De la part de</span></b> Alexis Cros<br>
<b><span style="font-weight:bold">Envoyé :</span></b> vendredi 30 juin 2017 12:33<br>
<b><span style="font-weight:bold">À :</span></b> Users mailing list for Scilab<br>
<b><span style="font-weight:bold">Objet :</span></b> [<span class="SpellE">EXTERNAL</span>]
<span class="SpellE">Re</span>: [Scilab-users] <span class="SpellE">my</span> <span class="SpellE">
loop</span> <span class="SpellE">faster</span> <span class="SpellE">than</span> <span class="SpellE">
vectorization</span> (???)<o:p></o:p></span></font></p>
</div>
</div>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR">Hi,<o:p></o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR">On
<span class="SpellE">my</span> computer came, in <span class="SpellE">order</span> of
<span class="SpellE">rapidity</span>, 1st case, 2nd, 4th <span class="SpellE">then</span> 3rd<o:p></o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR"> duration1 =
<br>
<br>
0.1907777<o:p></o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR"> duration2 =
<br>
<br>
0.2304603<o:p></o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR"> duration3 =
<br>
<br>
23.275328 wow!<o:p></o:p></span></font></p>
<p><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR"> duration4 =
<br>
<br>
0.2531153<o:p></o:p></span></font></p>
<p><span class="SpellE"><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;mso-ansi-language:FR">We</span></font></span><span lang="FR" style="mso-ansi-language:FR">
<span class="SpellE">may</span> compare <span class="SpellE">who</span> has the best computer ^^<o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></p>
<div>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR">Le 29/06/2017 à 09:56,
<span class="SpellE">Carrico</span>, Paul a écrit :<o:p></o:p></span></font></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">Here is the correct code – loop faster here (68 time faster with n = 100 000)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR">I’m</span></font></span><span lang="FR" style="mso-ansi-language:FR"> confuse<o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"> <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR">Paul<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR">#############################################################<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="#32b9b9" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;color:#32B9B9;mso-ansi-language:FR;mso-fareast-language:FR">mode</span></font><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">(</span></font><font color="rosybrown" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:rosybrown;mso-ansi-language:FR;mso-fareast-language:FR">0</span></font><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="#32b9b9" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;color:#32B9B9;mso-ansi-language:FR;mso-fareast-language:FR">clear</span></font></span><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">n
</span></font><font color="#5c5c5c" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#5C5C5C;mso-ansi-language:FR;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:rosybrown;mso-ansi-language:FR;mso-fareast-language:FR">10000</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">0.1</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">*</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">0.6</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">*</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">a
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">rand</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">b
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">a</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 1 :
<span class="SpellE">eval</span> on each row</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<pre><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0">tic</span></font></u><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">()</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></pre>
<pre><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">i</span></font></span><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">=</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#ffaa00" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#FFAA00">:</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">(</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">upper_bound</span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">-</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">lower_bound</span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">+</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">)</span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">'</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">c</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">(</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">i,</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">)</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced"> </span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">=</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced"> </span></font><font size="2" color="#32b9b9" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#32B9B9">zeros</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">((</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">upper_bound</span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">-</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">lower_bound</span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">+</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">)</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">,</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">)</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">c</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">(</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">i,</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">)</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced"> </span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">=</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced"> </span></font><span class="SpellE"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0">eval</span></font></u></span><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">(</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">b</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">(</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">lower_bound</span></font><font size="2" color="#ffaa00" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#FFAA00">:</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">upper_bound,</span></font><font size="2" color="rosybrown" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:rosybrown">1</span></font><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">))</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></pre>
<pre><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced">duration1 </span></font><font size="2" color="#5c5c5c" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#5C5C5C">=</span></font><font size="2" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced"> </span></font><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0">toc</span></font></u><font size="2" color="#4a55db" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#4A55DB">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></pre>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 2 :
<span class="SpellE">eval</span> on the complete matrix</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">d</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR"> b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#5C5C5C;mso-ansi-language:FR;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#AE5CB0;mso-ansi-language:FR;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">d</span></font><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">duration2
</span></font><font color="#5c5c5c" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#5C5C5C;mso-ansi-language:FR;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#AE5CB0;mso-ansi-language:FR;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 3 :with an
<span class="SpellE">uggly</span> loop</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">e
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">for</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">i</span> </span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR"> lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> e</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">))</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">end</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">duration3
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 4 :with an
<span class="SpellE">uggly</span> loop (<span class="SpellE">eval</span> on the complete matrix)</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">for</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">i</span> </span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">lower_bound</span></span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR"> b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">end</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">duration3
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#1f497d" face="Calibri"><span style="font-size:11.0pt;color:#1F497D"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p><b><i><font size="2" color="gray" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;color:gray;mso-ansi-language:FR;font-weight:bold;font-style:italic">EXPORT CONTROL :
<br>
</span></font></i></b><b><font size="2" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;mso-ansi-language:FR;font-weight:bold">Cet email ne contient pas de données techniques<br>
This email <span class="SpellE">does</span> not <span class="SpellE">contain</span>
<span class="SpellE">technical</span> data</span></font></b><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="mso-outline-level:1"><b><font size="2" color="black" face="Tahoma"><span lang="FR" style="font-size:10.0pt;font-family:"Tahoma",sans-serif;mso-ansi-language:FR;mso-fareast-language:FR;font-weight:bold">De :</span></font></b><font size="2" face="Tahoma"><span lang="FR" style="font-size:10.0pt;font-family:"Tahoma",sans-serif;mso-ansi-language:FR;mso-fareast-language:FR">
users [<a href="mailto:users-bounces@lists.scilab.org">mailto:users-bounces@lists.scilab.org</a>]
<b><span style="font-weight:bold">De la part de</span></b> <span class="SpellE">Carrico</span>, Paul<br>
<b><span style="font-weight:bold">Envoyé :</span></b> jeudi 29 juin 2017 09:29<br>
<b><span style="font-weight:bold">À :</span></b> International users mailing list for Scilab. (<a href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>)<br>
<b><span style="font-weight:bold">Objet :</span></b> [<span class="SpellE">EXTERNAL</span>] [Scilab-users]
<span class="SpellE">my</span> <span class="SpellE">loop</span> <span class="SpellE">
faster</span> <span class="SpellE">than</span> <span class="SpellE">vectorization</span> (???)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"> <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR">Hi all<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span lang="FR" style="font-size:11.0pt;mso-ansi-language:FR"> <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">I’m facing a case where a loop is faster than vectorization (at least I hope I’m using vectorization) ... I’m necessarily doing something wrong but I don’t see what</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">Hope somebody will point out my mistake</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">Thanks for your time</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">Paul</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt">################################################</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#32b9b9" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">mode</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">0</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#32b9b9" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">clear</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">n
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">10000</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">0.1</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">*</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">0.6</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">*</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">a
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">rand</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">n,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">b
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">a</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 1 :
<span class="SpellE">eval</span> on each row</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">c
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">c</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">))</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">duration1
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 2 :
<span class="SpellE">eval</span> on the complete matrix</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">d</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR"> b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">([</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)]</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">d
</span></font><font color="#5c5c5c" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#5C5C5C;mso-ansi-language:FR;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#AE5CB0;mso-ansi-language:FR;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">d</span></font><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">duration2
</span></font><font color="#5c5c5c" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#5C5C5C;mso-ansi-language:FR;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span lang="FR" style="font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#AE5CB0;mso-ansi-language:FR;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span lang="FR" style="font-family:Monospaced;color:#4A55DB;mso-ansi-language:FR;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span lang="FR" style="font-size:11.0pt;font-family:Monospaced;mso-ansi-language:FR;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 3 :with an
<span class="SpellE">uggly</span> loop</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">e
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">for</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">i</span> </span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">lower_bound</span></span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> e</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">))</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">end</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">duration3
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><i><font size="2" color="#64ae64" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:FR;font-style:italic">// case 4 :with an
<span class="SpellE">uggly</span> loop (<span class="SpellE">eval</span> on the complete matrix)</span></font></i><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><u><font size="2" color="#ae5cb0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">tic</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">zeros</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">((</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#32b9b9" face="Monospaced"><span style="font-family:Monospaced;color:#32B9B9;mso-fareast-language:FR">string</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">for</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">i</span> </span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#ffaa00" face="Monospaced"><span style="font-family:Monospaced;color:#FFAA00;mso-fareast-language:FR">:</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><span class="SpellE"><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">upper_bound</span></font></span><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
<span class="SpellE">lower_bound</span></span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR"> f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR"> b</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">i</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">+</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">lower_bound</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">-</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">,</span></font><font color="rosybrown" face="Monospaced"><span style="font-family:Monospaced;color:rosybrown;mso-fareast-language:FR">1</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="#a020f0" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;color:#A020F0;mso-fareast-language:FR">end</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">f
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><span class="SpellE"><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">eval</span></font></u></span><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">(</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">f</span></font><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">)</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">;</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Monospaced"><span style="font-size:11.0pt;font-family:Monospaced;mso-fareast-language:FR">duration3
</span></font><font color="#5c5c5c" face="Monospaced"><span style="font-family:Monospaced;color:#5C5C5C;mso-fareast-language:FR">=</span></font><font face="Monospaced"><span style="font-family:Monospaced;mso-fareast-language:FR">
</span></font><u><font color="#ae5cb0" face="Monospaced"><span style="font-family:Monospaced;color:#AE5CB0;mso-fareast-language:FR">toc</span></font></u><font color="#4a55db" face="Monospaced"><span style="font-family:Monospaced;color:#4A55DB;mso-fareast-language:FR">()</span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p><b><i><font size="2" color="gray" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;color:gray;mso-ansi-language:FR;font-weight:bold;font-style:italic">EXPORT CONTROL :
<br>
</span></font></i></b><b><font size="2" face="Arial"><span lang="FR" style="font-size:10.0pt;font-family:"Arial",sans-serif;mso-ansi-language:FR;font-weight:bold">Cet email ne contient pas de données techniques<br>
This email <span class="SpellE">does</span> not <span class="SpellE">contain</span>
<span class="SpellE">technical</span> data</span></font></b><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><font size="2" color="black" face="Calibri"><span style="font-size:11.0pt"> </span></font><span lang="FR" style="mso-ansi-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;font-family:"Times New Roman",serif;mso-ansi-language:FR;mso-fareast-language:FR"><br style="mso-special-character:line-break">
<![if !supportLineBreakNewLine]><br style="mso-special-character:line-break">
<![endif]><o:p></o:p></span></font></p>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR">_______________________________________________<o:p></o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR">users mailing list<o:p></o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR"><a href="mailto:users@lists.scilab.org">users@lists.scilab.org</a><o:p></o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR"><o:p> </o:p></span></font></pre>
<pre><font size="2" color="black" face="Courier New"><span lang="FR" style="font-size:10.0pt;mso-ansi-language:FR"><a href="https://urldefense.proofpoint.com/v2/url?u=http-3A__lists.scilab.org_mailman_listinfo_users&d=DwMG-g&c=0hKVUfnuoBozYN8UvxPA-w&r=4TCz--8bXfJhZZvIxJAemAJyz7Vfx78XvgYu3LN7eLo&m=lqXcavC4NeUi3iMQNIGQmPIeyYDToYymAQN6OVKhmdY&s=ucgWvT1-1CKXk_NCyJrgfIFxEQ2fKSqX6I1yKKkMZDE&e=">http://lists.scilab.org/mailman/listinfo/users</a><o:p></o:p></span></font></pre>
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</blockquote>
<p class="MsoNormal"><font size="3" color="black" face="Times New Roman"><span lang="FR" style="font-size:12.0pt;font-family:"Times New Roman",serif;mso-ansi-language:FR;mso-fareast-language:FR"><o:p> </o:p></span></font></p>
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