[Scilab-users] Numerical precision
Claus Futtrup
cfuttrup at gmail.com
Mon Aug 22 20:54:02 CEST 2016
Hi Arvid
Thanks for the tip. I'll investigate the precision I have in Fortran.
/Claus
On 22-08-2016 12:54, Arvid Rosén wrote:
> 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.
>
> Cheers,
> Arvid
>
> Get Outlook for iOS <https://aka.ms/o0ukef>
>
> ------------------------------------------------------------------------
> *From:* users <users-bounces at lists.scilab.org> on behalf of Paul
> Bignier <paul.bignier at scilab-enterprises.com>
> *Sent:* Monday, August 22, 2016 9:06:50 AM
> *To:* Users mailing list for Scilab
> *Subject:* Re: [Scilab-users] Numerical precision
>
>
> Hello Claus,
>
> If I get this right, after finding discrepancies between Scilab &
> Fortran, you identified the origin of the problem: the input was
> different.
>
> So you fed Scilab the same input you had in Fortran and got equal
> results, so no problem so far.
>
> Have you tried feeding Fortran the Scilab input? See if it gives the
> same results as Scilab.
>
> 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).
>
> Best regards,
>
> Paul
>
>
> On 08/21/2016 06:51 PM, Claus Futtrup wrote:
>> Hi there
>>
>> 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.
>>
>> If you compare the input (dz1 in scilab vs. dz1 in fortran, you get
>> differences of around :
>>
>> 1->dz1s./dz1f
>> ans =
>>
>> 0.9998331 + 0.0000339i
>> 0.9998132 + 0.0000391i
>> 0.9998197 + 0.0000391i
>>
>>
>> And if you compare input for dz2, you get similar tiny differences :
>>
>> -1->dz2s./dz2f
>> ans =
>>
>> 0.9999629 + 0.0000126i
>> 0.9999600 + 0.0000145i
>> 0.9999635 + 0.0000145i
>>
>> The difference in magnitude is on the scale of less than 0.02%.
>>
>> 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:
>>
>> // dz_test.sce
>>
>> // Scilab input/output for zm_star:
>>
>> dz1s = [-0.503483777422459-0.5757953650438843*%i
>> -0.5114164682962974-0.5883274915921053*%i
>> -0.5189524114871444-0.6013228498050527*%i]
>>
>> dz2s = [-0.9956247120533783-1.1585555511721832*%i
>> -1.019729681961281-1.1864195137402458*%i
>> -1.0436439978573127-1.2149095747738672*%i]
>>
>> mu = 1.997015667744342;
>>
>> zm_star = (1-mu)* dz1s .* dz2s ./ (dz2s-mu*dz1s);
>>
>> // =
>> // 67.582546 - 57.549843i
>> // 104.56363 + 0.9610187i
>> // 64.846465 + 47.016802i
>>
>> // Fortran input:
>>
>> dz1f = [-0.50358736782056468-0.57587442109900699*%i
>> -0.51153502148422891-0.58841744553307240*%i
>> -0.51906952093260994-0.60141095056474114*%i]
>>
>> dz2f = [-0.99567617243878548-1.1585859673221321*%i
>> -1.0197876382178386-1.1864521484345998*%i
>> -1.0436997434456954-1.2149387979780446*%i]
>>
>> zm_star = (1-mu)* dz1f .* dz2f ./ (dz2f-mu*dz1f);
>>
>> // Scilab output:
>>
>> // =
>> // 66.547108 - 58.427427i
>> // 105.67638 - 0.8443203i
>> // 66.018415 + 47.279403i
>>
>> // Fortran output:
>> // ( 66.547108467527437 , -58.427426595183157 )
>> // ( 105.67638116311093 ,-0.84432029182632362 )
>> // ( 66.018415098214774 , 47.279402998470466 )
>>
>> As can be seen. Scilab gives the same output as Fortran, when the
>> input is the same.
>>
>> I'm just totally surprised how such small differences in input can
>> generate such large differences in output.
>>
>> Best regards,
>> Claus
>>
>> On 21-08-2016 16:11, Claus Futtrup wrote:
>>>
>>> Dear Scilab Users
>>>
>>> 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:
>>>
>>> Scilab: zm_star = (1-mu)* dz1 .* dz2 ./ (dz2-mu*dz1); // model free
>>> mech. impedance
>>>
>>> Fortran: zm_star = (1-mu)*dz1*dz2/(dz2-mu*dz1)
>>>
>>> Do you see anything in the Scilab formulation, which should worry me
>>> / which would give me such a high error?
>>>
>>> P.S. mu is a mass-ratio = 1.9970156677443420... and it's exactly the
>>> same value in both Scilab and Fortran.
>>>
>>> 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:
>>>
>>> In Fortran, data no. 47-48-49 (near fs):
>>>
>>> ( 66.547108467527437 , -58.427426595183157 )
>>> ( 105.67638116311093 ,-0.84432029182632362 )
>>> ( 66.018415098214774 , 47.279402998470466 )
>>>
>>> Whereas in Scilab I get:
>>>
>>> 67.58254632254881 - 57.549843258298814*%i
>>> 104.56362768103634 + 0.9610187273575014*%i
>>> 64.84646498264745 + 47.01680213507681*%i
>>>
>>> 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.
>>>
>>> If you study the impedance magnitude (pythagoras...), the results
>>> from Fortran are about 1% higher in value - IMHO that's non-negligible.
>>>
>>> Studying the Nyquist circle plot of the data, it seems to me that in
>>> general the Fortran calculation is more correct.
>>>
>>> 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.S. I'm using Scilab 5.5.0 (64 bit, Windows 10). Could it be the
>>> Intel Math Kernel that's doing this wrong?
>>>
>>> /Claus
>>>
>>
>>
>>
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>
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