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Hi,<br>
<br>
I guess that you are expecting too much from the solver. The exact
mathematical result of the integral is 0. Now, the mathematical sin
function is approximated by a floating point implementation, which
is so that :<br>
<br>
-->sin(2*%pi)<br>
ans =<br>
- 2.449D-16 <br>
<br>
See the script :<br>
<br>
for atol = [1.e-1 1.e-2 1.e-4 1.e-8 1.e-10 1.e-12 1.e-14]<br>
instr = "I = integrate(""sin(x)"",""x"",0,2*%pi,atol);";<br>
ierr = execstr(instr,"errcatch");<br>
if ( ierr == 0 ) then<br>
mprintf("atol=%e, I=%.17e\n",atol,I)<br>
else<br>
mprintf("atol=%e, I=XXX\n",atol)<br>
end<br>
end<br>
<br>
This produces :<br>
<br>
atol=1.000000e-001, I=2.26062574420357380e-016<br>
atol=1.000000e-002, I=2.26062574420357380e-016<br>
atol=1.000000e-004, I=2.26062574420357380e-016<br>
atol=1.000000e-008, I=2.26062574420357380e-016<br>
atol=1.000000e-010, I=2.26062574420357380e-016<br>
atol=1.000000e-012, I=2.26062574420357380e-016<br>
atol=1.000000e-014, I=XXX<br>
<br>
Hence, it suffices to reduce the request for the absolute error to
get an answer.<br>
<br>
Best regards,<br>
<br>
Michaël Baudin<br>
<br>
PS-1<br>
I admit that there might not be enough informations provided by
Scilab in the gateway.<br>
The various output of the solvers are described in the ier variable
of :<br>
<br>
<a href="http://www.netlib.org/quadpack/dqags.f">http://www.netlib.org/quadpack/dqags.f</a><br>
<br>
There are 6 different causes of failures, all of them being
represented by the single "Convergence problem".<br>
<br>
PS-2<br>
A similar problem was discussed at :<br>
<br>
<a href="http://bugzilla.scilab.org/show_bug.cgi?id=5728">http://bugzilla.scilab.org/show_bug.cgi?id=5728</a><br>
<br>
PS-3<br>
There are issues with the integrate function, with the management of
default input arguments:<br>
<br>
<a href="http://bugzilla.scilab.org/show_bug.cgi?id=8351">http://bugzilla.scilab.org/show_bug.cgi?id=8351</a><br>
<br>
Le 18/10/2010 16:25, José Luis Volta Grau a écrit :
<blockquote
cite="mid:3777DD50587E4370999184E3BEE4DF26@usera1d930417d"
type="cite">
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<meta name="GENERATOR" content="MSHTML 8.00.6001.18975">
<style></style>
<div><font face="Arial" size="2">Hi Jean:</font></div>
<div> </div>
<div><font face="Arial" size="2">Change the tolerance and you will
get the result of integrate('sin(x)','x',0,2*%pi,1e-5)</font></div>
<div> </div>
<div><font face="Arial" size="2">-->integrate('sin(x)','x',0,2*%pi,1e-5)<br>
ans =<br>
<br>
2.222D-16 </font></div>
<div> </div>
<div><font face="Arial" size="2">which is almost zero.</font></div>
<div> </div>
<div><font face="Arial" size="2">J.L.</font></div>
<blockquote style="border-left: 2px solid rgb(0, 0, 0);
padding-left: 5px; padding-right: 0px; margin-left: 5px;
margin-right: 0px;">
<div style="font: 10pt arial;">----- Original Message ----- </div>
<div style="font: 10pt arial; background: none repeat scroll 0%
0% rgb(228, 228, 228);"><b>From:</b> <a
moz-do-not-send="true" title="jean.podlecki@sfr.fr"
href="mailto:jean.podlecki@sfr.fr">jean podlecki</a> </div>
<div style="font: 10pt arial;"><b>To:</b> <a
moz-do-not-send="true" title="users@lists.scilab.org"
href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>
</div>
<div style="font: 10pt arial;"><b>Sent:</b> Monday, October 18,
2010 9:22 AM</div>
<div style="font: 10pt arial;"><b>Subject:</b> [scilab-Users]
Convergence problem</div>
<div><br>
</div>
<span style="font-family: Helvetica; font-size: medium;"
class="Apple-style-span">God afternoon,</span>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">Here's
my problem.</div>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">-------------------------------------------------</div>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">
<div>-->integrate('sin(x)','x',0,2*%pi)</div>
<div> !--error 24 </div>
<div>Problème de convergence ...</div>
<div><br>
</div>
<div>at line 70 of function integrate called by : </div>
<div>integrate('sin(x)','x',0,2*%pi)</div>
</div>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">-------------------------------------------------</div>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">Is it
right ? How can I get the correct answer ?</div>
<div style="font-family: Helvetica; font-size: medium;"><br>
</div>
<div style="font-family: Helvetica; font-size: medium;">Jean.</div>
<br>
</blockquote>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Michaël Baudin
Ingénieur de développement
<a class="moz-txt-link-abbreviated" href="mailto:michael.baudin@scilab.org">michael.baudin@scilab.org</a>
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
</pre>
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