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<div class="moz-cite-prefix">Hi Arvid<br>
<br>
Thanks for the tip. I'll investigate the precision I have in
Fortran.<br>
<br>
/Claus<br>
<br>
On 22-08-2016 12:54, Arvid Rosén wrote:<br>
</div>
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cite="mid:DB5PR02MB1720A4AE6655A053A7B35851A1E80@DB5PR02MB1720.eurprd02.prod.outlook.com"
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<div>One thing to watch out for in cases like this is the old
extended precision 80-bit floating point format. Scilab 5
doesn't use it, but the Fortan program might do I guess. Scilab
4 used it too, and when I switched from version 4 to 5 some
numerical results related to resonant filters changed in my
setup.</div>
<div><br>
</div>
<div>Cheers,</div>
<div>Arvid<br>
<br>
<div class="acompli_signature">Get <a moz-do-not-send="true"
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt"
face="Calibri, sans-serif" color="#000000"><b>From:</b> users
<a class="moz-txt-link-rfc2396E" href="mailto:users-bounces@lists.scilab.org"><users-bounces@lists.scilab.org></a> on behalf of Paul
Bignier <a class="moz-txt-link-rfc2396E" href="mailto:paul.bignier@scilab-enterprises.com"><paul.bignier@scilab-enterprises.com></a><br>
<b>Sent:</b> Monday, August 22, 2016 9:06:50 AM<br>
<b>To:</b> Users mailing list for Scilab<br>
<b>Subject:</b> Re: [Scilab-users] Numerical precision</font>
<div> </div>
</div>
<div>
<p><br>
</p>
<p>Hello Claus,</p>
<p>If I get this right, after finding discrepancies between
Scilab & Fortran, you identified the origin of the
problem: the input was different.</p>
<p>So you fed Scilab the same input you had in Fortran and got
equal results, so no problem so far.</p>
<p>Have you tried feeding Fortran the Scilab input? See if it
gives the same results as Scilab.</p>
<p>As for the input/output variation, it's not that surprising
to me if your system is poorly conditioned, especially at some
points of interest (near the resonance frequency).</p>
<p>Best regards,</p>
<p>Paul<br>
</p>
<br>
<div class="moz-cite-prefix">On 08/21/2016 06:51 PM, Claus
Futtrup wrote:<br>
</div>
<blockquote type="cite">
<div class="moz-cite-prefix">Hi there<br>
<br>
OK, so I went ahead and took some Fortran input ... yes, I
do get the same output as Fortran, so it seems there's no
calculation error per se in Scilab. It's just tiny
differences in the input which generate large differences in
output. It's scary.<br>
<br>
If you compare the input (dz1 in scilab vs. dz1 in fortran,
you get differences of around :<br>
<br>
1->dz1s./dz1f<br>
ans =<br>
<br>
0.9998331 + 0.0000339i <br>
0.9998132 + 0.0000391i <br>
0.9998197 + 0.0000391i <br>
<br>
<br>
And if you compare input for dz2, you get similar tiny
differences :<br>
<br>
-1->dz2s./dz2f<br>
ans =<br>
<br>
0.9999629 + 0.0000126i <br>
0.9999600 + 0.0000145i <br>
0.9999635 + 0.0000145i <br>
<br>
The difference in magnitude is on the scale of less than
0.02%.<br>
<br>
Here's a complete script, including comments which shows the
results and explains. I only include the three datapoints
around fs, which are of interest:<br>
<br>
<pre style="font-family:Monospaced; font-style:normal; font-size:12.0"><span style="color:rgb(100,174,100); font-style:italic">// dz_test.sce</span>
<span style="color:rgb(100,174,100); font-style:italic">// Scilab input/output for zm_star:</span>
<span style="color:rgb(0,0,0)">dz1s</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.503483777422459</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.5757953650438843</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.5114164682962974</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.5883274915921053</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.5189524114871444</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.6013228498050527</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span><span style="color:rgb(74,85,219)">]</span>
<span style="color:rgb(0,0,0)">dz2s</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.9956247120533783</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.1585555511721832</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.019729681961281</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.1864195137402458</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.0436439978573127</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.2149095747738672</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span><span style="color:rgb(74,85,219)">]</span>
<span style="color:rgb(0,0,0)">mu</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">1.997015667744342</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(0,0,0)">zm_star</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(0,0,0)">mu</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">*</span> <span style="color:rgb(0,0,0)">dz1s</span> <span style="color:rgb(92,92,92)">.*</span> <span style="color:rgb(0,0,0)">dz2s</span> <span style="color:rgb(92,92,92)">./</span> <span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">dz2s</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(0,0,0)">mu</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(0,0,0)">dz1s</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(100,174,100); font-style:italic">// =</span>
<span style="color:rgb(100,174,100); font-style:italic">// 67.582546 - 57.549843i </span>
<span style="color:rgb(100,174,100); font-style:italic">// 104.56363 + 0.9610187i </span>
<span style="color:rgb(100,174,100); font-style:italic">// 64.846465 + 47.016802i</span>
<span style="color:rgb(100,174,100); font-style:italic">// Fortran input:</span>
<span style="color:rgb(0,0,0)">dz1f</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.50358736782056468</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.57587442109900699</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.51153502148422891</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.58841744553307240</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.51906952093260994</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.60141095056474114</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span><span style="color:rgb(74,85,219)">]</span>
<span style="color:rgb(0,0,0)">dz2f</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.99567617243878548</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.1585859673221321</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.0197876382178386</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.1864521484345998</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span>
<span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.0436997434456954</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1.2149387979780446</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(218,112,214)">%i</span><span style="color:rgb(74,85,219)">]</span>
<span style="color:rgb(0,0,0)">zm_star</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(0,0,0)">mu</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">*</span> <span style="color:rgb(0,0,0)">dz1f</span> <span style="color:rgb(92,92,92)">.*</span> <span style="color:rgb(0,0,0)">dz2f</span> <span style="color:rgb(92,92,92)">./</span> <span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">dz2f</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(0,0,0)">mu</span><span style="color:rgb(92,92,92)">*</span><span style="color:rgb(0,0,0)">dz1f</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(100,174,100); font-style:italic">// Scilab output:</span>
<span style="color:rgb(100,174,100); font-style:italic">// =</span>
<span style="color:rgb(100,174,100); font-style:italic">// 66.547108 - 58.427427i </span>
<span style="color:rgb(100,174,100); font-style:italic">// 105.67638 - 0.8443203i </span>
<span style="color:rgb(100,174,100); font-style:italic">// 66.018415 + 47.279403i </span>
<span style="color:rgb(100,174,100); font-style:italic">// Fortran output:</span>
<span style="color:rgb(100,174,100); font-style:italic">// ( 66.547108467527437 , -58.427426595183157 )</span>
<span style="color:rgb(100,174,100); font-style:italic">// ( 105.67638116311093 ,-0.84432029182632362 )</span>
<span style="color:rgb(100,174,100); font-style:italic">// ( 66.018415098214774 , 47.279402998470466 )</span></pre>
<br>
As can be seen. Scilab gives the same output as Fortran,
when the input is the same.<br>
<br>
I'm just totally surprised how such small differences in
input can generate such large differences in output.<br>
<br>
Best regards,<br>
Claus<br>
<br>
On 21-08-2016 16:11, Claus Futtrup wrote:<br>
</div>
<blockquote type="cite">
<p>Dear Scilab Users</p>
<p>I have a script, which imitates a Fortran script. I can
see there's a difference in calculation of about 1%, which
is very strange to me. Input parameters (dz1 and dz2
vectors, length 1200) to the equation seem to agree within
0,1% ... so right now my theory is that the precision
slips away when I do the following calculation:</p>
<p>Scilab: <span style="color:rgb(0,0,0)">zm_star</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(0,0,0)">mu</span><span
style="color:rgb(74,85,219)">)</span><span
style="color:rgb(92,92,92)">*</span>
<span style="color:rgb(0,0,0)">dz1</span> <span
style="color:rgb(92,92,92)">.*</span>
<span style="color:rgb(0,0,0)">dz2</span> <span
style="color:rgb(92,92,92)">./</span>
<span style="color:rgb(74,85,219)">(</span><span
style="color:rgb(0,0,0)">dz2</span><span
style="color:rgb(92,92,92)">-</span><span
style="color:rgb(0,0,0)">mu</span><span
style="color:rgb(92,92,92)">*</span><span
style="color:rgb(0,0,0)">dz1</span><span
style="color:rgb(74,85,219)">)</span><span
style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(100,174,100); font-style:italic">//
model free mech. impedance</span></p>
<p>Fortran: zm_star = (1-mu)*dz1*dz2/(dz2-mu*dz1)<br>
</p>
<p>Do you see anything in the Scilab formulation, which
should worry me / which would give me such a high error?</p>
<p>P.S. mu is a mass-ratio = 1.9970156677443420... and it's
exactly the same value in both Scilab and Fortran.<br>
</p>
<p>Most of the calculations in the output vector are OK, but
in particular around the resonance frequency, I can list
the following three datapoints (zm_star(47:49)), to show
what is worrying me:</p>
<p>In Fortran, data no. 47-48-49 (near fs):<br>
<br>
( 66.547108467527437 , -58.427426595183157 )<br>
( 105.67638116311093 ,-0.84432029182632362 )<br>
( 66.018415098214774 , 47.279402998470466 )<br>
<br>
Whereas in Scilab I get:<br>
<br>
67.58254632254881 - 57.549843258298814*%i<br>
104.56362768103634 + 0.9610187273575014*%i<br>
64.84646498264745 + 47.01680213507681*%i</p>
<p>In particular the imaginary part is different at the
middle data point (near fs) where from Fortran the value
is negative, whereas in Scilab the value is positive. It
seems that the calculation of zm_star involves some math
operations that could be critical to the precision.</p>
<p>If you study the impedance magnitude (pythagoras...), the
results from Fortran are about 1% higher in value - IMHO
that's non-negligible.</p>
<p>Studying the Nyquist circle plot of the data, it seems to
me that in general the Fortran calculation is more
correct.</p>
<p>What is going wrong with the Scilab equation? Please let
me know if you have any ideas how to increase the
precision of the calculation. Thanks.</p>
<p>P.S. I'm using Scilab 5.5.0 (64 bit, Windows 10). Could
it be the Intel Math Kernel that's doing this wrong?<br>
</p>
<p>/Claus<br>
</p>
</blockquote>
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