[Scilab-users] Strange behaviour of prod on rationals

[Federico Miyara]

Pierre,

Thanks for your answer.

However, I believe no involved computatins are required to get the 
correct result. The multiplication of the two polynomials from the 
denominators is straightforward, no need to solve any system, no risk of 
ill-conditioned or badly-scaled matrices.

This must be another kind of problem.

Regards,

Federico Miyara

On 17/03/2020 06:48, Perrichon wrote:
>
> Hello Federico
>
> I have met few months or years ago this problem when i was developping 
> my  « OPTSIM Solution » software to fix parameters of a PID for 
> turbines (30 mw to 2 gw) in Nyquist and Bode Plans with hydraulic 
> parameters site
>
> So I’ve seen instability of the denominator, witch damage calculus.
>
> I don ‘t remember what I’ve done to get a cool solution, but it  has 
> been a hard and severe problem with syslin, tf2ss and ss2tf instructions
>
> Sincerely
>
> Pierre P.
>
> *De :*users <users-bounces at lists.scilab.org> *De la part de* Federico 
> Miyara
> *Envoyé :* mardi 17 mars 2020 10:31
> *À :* Users mailing list for Scilab <users at lists.scilab.org>
> *Objet :* [Scilab-users] Strange behaviour of prod on rationals
>
>
> Dear all,
>
> Look at this code (the coefficients are actually the result of pevious 
> calculations):
>
> NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
> 5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
> DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
>        8.336136 + 7.0282601*%s + %s^2]
> q = NUM./DEN
>
> Running it yields
>
>    5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s²
>    ---------------------------------- ----------------------------------
>        0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²
>
> This is, correctly, a two-component rational vector with the expected 
> numerators and denominators.
>
> Now let's evaluate
>
> q = prod(NUM./DEN)
>
> The prod documantation sys that the argument may be "an array of 
> reals, complex, booleans, polynomials or rational fractions". It 
> should provide the rational obtained by multiplying the twonumrators 
> and the two denominators. However, we get
>
>    3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
> ------------------------------------------------------------
> 1
>
> The numeratoris right, but the expected denominator has been just 
> replaced by 1
>
> However, rewriting the command as
>
> prod(NUM)/prod(DEN)
>
> we get the expected result:
>
>    3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
> ------------------------------------------------------------
>        1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴
>
> This is quite strange!
>
> Now we repeat with simpler polynomials:
>
> NUM = [1-%s 2-%s]
> DEN = [1+%s 2+%s]
> q = NUM./DEN
>
> We get
>
>    1 -s  2 -s
>    ----  ----
>    1 +s  2 +s
>
> Now evaluate
>
> prod(NUM./DEN)
>
> The result is the expected one!
>
>    2 -3s +s²
>    ---------
>    2 +3s +s²
>
> The behavior seems to depend on the type of polynomials.
>
> Is this a bug or there is something I'm not interpreting correctly?
>
> Regards,
>
> Federico Miyara
>
>
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