I prefer the display after applying
https://codereview.scilab.org/#/c/20981/:
--> x0=%pi/4;h=%eps/2
h =
1.110D-16
--> cos(x0+%i*h)
ans =
0.7071068 - 7.850D-17i
However, we could discuss if the arbitrary switch to "e" mode is
desirable or not, but since Scilab 6.0 we have got used to this display
mixing "v" and "e" mode...
BTW, this patch also fixes the more general problem of ambiguous display
of quantities like (below is the display after the patch)
--> 1+%eps
ans =
1.0000000
Currently Scilab makes users believe that a complex/non real number is
real by hiding small non-zero real parts, and makes users believe that a
non-integer number is integer by hiding zeros in the fractional part.
Each year I have to warn my students, and I am really getting upset
about this. The aforementionned patch also fixes that.
S.
Le 12/09/2019 à 11:59, Stéphane Mottelet a écrit :
Le 12/09/2019 à 11:55, Antoine ELIAS a écrit :
Hello Stéphane,
In Scilab 6.0.2 without format("e", 24)
--> h = %eps/128, x0=%pi/4
h =
1.735D-18
x0 =
0.7853982
--> (cos(x0+h)-cos(x0-h))/2/h
ans =
0.
--> cos(x0+%i*h)
ans =
0.7071068
--> imag(cos(x0+%i*h))/h
ans =
-0.7071068
--> -sin(x0)
ans =
-0.7071068
It seems to be close of Matlab's outputs, no ?
No, Scilab display is singularly different:
--> cos(x0+%i*h)
ans =
0.7071068
the above has an imaginary part, which is quite small, but essential
in the computation. Matlab is quite explicit here:
>> cos(x0+i*h)
ans =
0.7071 - 0.0000i
I probably not understand your problem ...
Antoine
Le 12/09/2019 à 10:26, Stéphane Mottelet a écrit :
Hello all,
The subject has been already discussed a lot but I would like it to
be discussed again because I now have a real rationale to promote a
change in the way complex numbers with small imaginary part are
displayed.
I don't know if some of you were aware of the clever technique of
complex-step derivative approximation, but until yesterday I was not
(see e.g.
https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/mdolab.engin.umich.edu/sites/default/files/Martins2003CSD.pdf).
Roughly speaking, using the extension of a real function x->f(x) to
the complex plane allows to compute an approximation of the
derivative f'(x0) at a real x0 without using a substraction, like in
the central difference formula (f(x0+h)-f(x0-h))/2/h which is
subject to substractive cancelation when h is small. In Scilab most
operators and elementary functions are already complex-aware so this
is easy to illustrate the technique. For example let us approximate
the derivative of x->cos(x) at x=%pi/4, first with the central
difference formula, then with the complex step technique:
--> format("e",24)
--> h=%eps/128, x0=%pi/4
h =
1.73472347597680709D-18
x0 =
7.85398163397448279D-01
--> (cos(x0+h)-cos(x0-h))/2/h
ans =
0.00000000000000000D+00
--> imag(cos(x0+%i*h))/h
ans =
-7.07106781186547462D-01
--> -sin(x0)
ans =
-7.07106781186547462D-01
You can see the pathological approximation with central difference
formula and the perfect (up to relative machine precision)
approximation of complex-step formula.
However, the following is a pity:
--> cos(x0+%i*h)
ans =
7.07106781186547573D-01
We cannot see the imaginary part although seeing the latter is
fundamental in the complex-step technique. We have to force the
display like this, and frankly I don't like having to do that with
my students:
--> imag(cos(x0+%i*h))
ans =
-1.22663473334669916D-18
I hope that you will find that this example is a good rationale to
change the default display of Scilab. To feed the discussion, here
is how Matlab displays things, without having to change the default
settings:
>> h=eps/128, x0=pi/4
h =
1.7347e-18
x0 =
0.7854
>> (cos(x0+h)-cos(x0-h))/2/h
ans =
0
>> cos(x0+i*h)
ans =
0.7071 - 0.0000i
>> imag(cos(x0+i*h))/h
ans =
-0.7071
>> -sin(x0)
ans =
-0.7071
_______________________________________________
users mailing list
users@lists.scilab.org
https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
--
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
_______________________________________________
users mailing list
users@lists.scilab.org
http://lists.scilab.org/mailman/listinfo/users
