[Scilab-users] [EXTERNAL] Re: acos leads to complex values

[Stéphane Mottelet]

Le 29/01/2019 à 20:48, Federico Miyara a écrit :
>
> I think it would be interesting to include an input argument check in 
> some functions prone to give complex results in limiting cases (such 
> as acos or asin) so that if inside the domain (to within 1 %eps) where 
> the output argument should be real the imaginary part is canceled. 
> Something like this for scalars:
>
> function  y=acos1(x)
> if   isreal(x)
>      if  -1<=x  &  x<=1
>          y  =  real(acos(x))
>      else
>          y  =  acos(x)
>      end
> end
> endfunction
>
> However, I must say that acos(1-%eps) gives on my Scilab 6.0.1 
> (Windows 7, i7 processor) a result of
Federico, you have to try 1+%eps or -1-%eps !
>
> 0.000000021073424255447,
>
> being %eps
>
> 0.0000000000000002220446
>
> I get no imaginary part. I guess there must be some dependency on the 
> arithmetic engine.
>
>
> Federico Miyara
>
>
> On 29/01/2019 12:58, Stéphane Mottelet wrote:
>> It is the same if x is slightly > 1:
>>
>> --> x=1+%eps
>>  x  =
>>
>>    1.
>>
>>
>> --> acos(x)
>>  ans  =
>>
>>    2.107D-08i
>>
>> --> format(25); x
>>  x  =
>>
>>    1.0000000000000002220446
>>
>> Le 29/01/2019 à 16:55, Carrico, Paul a écrit :
>>>
>>> When I scroll to the list, the lowest (positive) value is 8.4^E -08 
>>> (works fine) and no %eps .
>>>
>>> How Can I check if %eps is in?
>>>
>>> *De :*users [mailto:users-bounces at lists.scilab.org] *De la part de* 
>>> Stéphane Mottelet
>>> *Envoyé :* mardi 29 janvier 2019 16:50
>>> *À :* users at lists.scilab.org
>>> *Objet :* [EXTERNAL] Re: [Scilab-users] acos leads to complex values
>>>
>>> Le 29/01/2019 à 16:45, Carrico, Paul a écrit :
>>>
>>>     Dear All
>>>
>>>     I spent some time in looking for a mistake in my code ; finally
>>>     I’ve found that the ACOS of a real vector leads to some complex
>>>     values (???)
>>>
>>>     acos(Scar_P(:,1)./CM_x_CN(:,1))
>>>
>>> Are your really sure, because we may have
>>>
>>> --> x=-1-%eps
>>>  x  =
>>>
>>>   -1.
>>>
>>>
>>> --> acos(x)
>>>  ans  =
>>>
>>>    3.1415927 - 2.107D-08i
>>>
>>> S.
>>>
>>>     (the formula worked so far)
>>>
>>>     I checked that the input values are correct:
>>>
>>>     -Comprised between [-1; 1] using MIN and MAX
>>>
>>>     -Composed only of real values using ISREAL (all the vectors are
>>>     correct)
>>>
>>>     Thus I do not understand why complex values appear ?
>>>
>>>     May it come from the vectorization ?
>>>
>>>     Paul
>>>
>>>
>>>
>>>     _______________________________________________
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>>> -- 
>>> Stéphane Mottelet
>>> Ingénieur de recherche
>>> EA 4297 Transformations Intégrées de la Matière Renouvelable
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>>
>> -- 
>> Stéphane Mottelet
>> Ingénieur de recherche
>> EA 4297 Transformations Intégrées de la Matière Renouvelable
>> Département Génie des Procédés Industriels
>> Sorbonne Universités - Université de Technologie de Compiègne
>> CS 60319, 60203 Compiègne cedex
>> Tel : +33(0)344234688
>> http://www.utc.fr/~mottelet
>>
>>
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