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<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
cite="mid:b90b7f68-668f-e995-d5d7-19620d56975c@gmail.com"
type="cite">
<meta content="text/html; charset=windows-1252"
http-equiv="Content-Type">
<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
cite="mid:bf13cc67-1b88-d6fc-71ae-bc3b40ea4bd1@gmail.com"
type="cite">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
<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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