<div dir="ltr">Hello Samuel,<div><br></div><div>Thanks for the solution. As pointed out it is best to show the equation being assessed (from <a href="http://www.bernoulli.org">www.bernoulli.org</a>). The one I looked at was the following:</div><div><br></div><div><img src="cid:ii_kxso5vh60" alt="Explicit_formula.PNG" width="468" height="101"><br></div><div><br></div><div>Using nchoosek in the original code gives the same issue. </div><div><br></div><div>Lester</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, 29 Dec 2021 at 22:46, Samuel Gougeon <<a href="mailto:sgougeon@free.fr">sgougeon@free.fr</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<div>Hello Lester,</div>
<div><br>
<br>
</div>
<div>Le 29/12/2021 à 09:00, Lester Anderson
a écrit :<br>
</div>
<blockquote type="cite">
<div dir="ltr">Hello,
<div><br>
</div>
<div>A quick query. Have adapted existing Matlab code for Scilan
to calculate Bernoulli numbers using an explicit formula (<a href="http://www.bernoulli.org" target="_blank">www.bernoulli.org</a>).
</div>
</div>
</blockquote>
<br>
Not so explicit. Could you please provide the formula, before
implementing it in Scilab language?<br>
The following is a "vectorized" version of your code, likely with
the same mistake:<br>
<pre style="font-family:Monospaced;font-style:normal"><span style="color:rgb(0,0,0)">B</span><span style="color:rgb(92,92,92)">=</span><span style="color:rgb(74,85,219)">[</span><span style="color:rgb(74,85,219)">]</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">for</span> <span style="color:rgb(0,0,0)">m</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">0</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(188,143,143)">20</span>
<span style="color:rgb(0,0,0)">Sum</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">0</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">for</span> <span style="color:rgb(0,0,0)">k</span><span style="color:rgb(92,92,92)">=</span><span style="color:rgb(188,143,143)">0</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(0,0,0)">m</span>
<span style="color:rgb(0,0,0)">v</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">0</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(0,0,0)">k</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(0,0,0)">Sum</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(0,0,0)">Sum</span> <span style="color:rgb(92,92,92)">+</span> <span style="color:rgb(50,185,185)">sum</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(0,0,0)">v</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(0,0,0)">nchoosek</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">k</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(0,0,0)">v</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">v</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">/</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">k</span><span style="color:rgb(92,92,92)">+</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span>
<span style="color:rgb(0,0,0)">B</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(92,92,92)">+</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(0,0,0)">Sum</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span></pre>
<p>A working implementation based on the recurrent formula
<u></u><u></u><u></u><u></u><u></u><u></u><font face="monospace"><u></u><u></u><u></u><u></u><u></u>
B<u></u><u></u>m<u></u><u></u><u></u>=<u></u><u></u><u></u><u></u>−<u></u><u></u>1<u></u><u></u><u></u><u></u>m<u></u><u></u>+<u></u><u></u>1<u></u><u></u><u></u><u></u><u></u>∑<u></u><u></u><u></u>k<u></u><u></u>=<u></u><u></u>0<u></u><u></u><u></u><u></u>m<u></u><u></u>−<u></u><u></u>1<u></u><u></u><u></u><u></u><u></u>(<u></u><u></u><u></u><u></u>m<u></u><u></u>+<u></u><u></u>1<u></u><u></u><u></u>k<u></u><u></u><u></u>)<u></u><u></u><u></u><u></u>B<u></u><u></u>k<u></u><u></u><u></u><u></u><u></u></font><br>
</p>
<p>could be:</p>
<pre style="font-family:Monospaced;font-style:normal"><span style="color:rgb(0,0,0)">mMax</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">20</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(0,0,0)">B</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(50,185,185)">zeros</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(0,0,0)">mMax</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(0,0,0)">B</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(188,143,143)">2</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(188,143,143)">1</span> <span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(92,92,92)">/</span><span style="color:rgb(188,143,143)">2</span><span style="color:rgb(74,85,219)">]</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">for</span> <span style="color:rgb(0,0,0)">m</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">2</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(188,143,143)">2</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(0,0,0)">mMax</span>
<span style="color:rgb(0,0,0)">B</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(92,92,92)">+</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(92,92,92)">-</span><span style="color:rgb(50,185,185)">sum</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">nchoosek</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(92,92,92)">+</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(188,143,143)">0</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(0,0,0)">B</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">/</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">m</span><span style="color:rgb(92,92,92)">+</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span><font face="monospace">
--> B</font><font face="monospace">
ans =</font><font face="monospace">
column 1 to 13</font><font face="monospace">
1. -0.5 0.1666667 0. -0.0333333 0. 0.0238095 0. -0.0333333 0. 0.0757576 0. -0.2531136</font>
</pre>
<font face="monospace"><br>
column 14 to 21<br>
0. 1.1666667 0. -7.0921569 0. 54.971178 0.
-529.12424<br>
</font><br>
<p>To fasten the loop, the call to nchoosek() could be replaced with
the 3 last rows of Pascal's triangle.<br>
<br>
Regards<br>
Samuel<br>
</p>
</div>
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</blockquote></div>