Stéphane,
--> x=1:0.1:2
x =
1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7000000 1.8 1.9 2.
However I get this:
> x=1:0.1:2
x =
1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.
But it is true that x(7) - 1.7 yields 2.220D-16. Here there are two
problems, an arithmetic one and a display one. Formatting to a
sufficiently large number of digits the arithmetic problem (or
limitation, probably unsurmountable, originated in the incompatibility
of binary and decimal systems) is evident:
> format(20)
> x=1:0.1:2
x =
column 1 to 6
1. 1.10000000000000009 1.19999999999999996 1.30000000000000004
1.39999999999999991 1.5
column 7 to 11
1.60000000000000009 1.70000000000000018 1.8 1.89999999999999991 2.
Why this triggers showing several zeros I don't understand, probably a
bug, but it can be seen that it happens when the numeric error affects
te 16th decimal digit.
Regards,
Federico Miyara
--> x(7)
ans =
1.6
--> x(7)-1.6
ans =
0.
--> x(8)
ans =
1.7000000
--> x(8)-1.7
ans =
2.220D-16
I think that we do agree about the fact that the actual Scilab display
--> x=1:0.1:2
x =
1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.
--> x(7)
ans =
1.6
--> x(7)-1.6
ans =
0.
--> x(8)
ans =
1.7
--> x(8)-1.7
ans =
2.220D-16
is pretty but not correct/homogeneous/honest. The display that is
obtained with the patch (first lines of this email) is correct+honest
but not homogeneous. A pretty + mathematically correct display would be:
--> x=1:0.1:2
x =
1.0000000 1.1000000 1.2000000 1.3000000 1.4000000
1.0000005 1.6000000 1.7000000 1.8000000 1.9000000 2.0000000
--> x(7)
ans =
1.6
--> x(8)
ans =
1.7000000
--> x(8)-1.7
ans =
2.220D-16
i.e. when the matrix to display is not a scalar, add always trailing
zeros for homogeneity, BUT when it is a scalar, add trailing zeros
only when the actual stored value is different from the displayed value.
The first thing that you can see is that the default format(10) would
be very verbose, but this is tunable. A value of 7 would be ok, but
quite low for format("e").
S.
Le 13/09/2019 à 13:37, Stéphane Mottelet a écrit :
Le 13/09/2019 à 13:07, Samuel Gougeon a écrit :
Le 12/09/2019 à 18:55, Stéphane Mottelet a écrit :
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...
... and IMO it's very suitable. The only rule should be that, */for
a given format's width/*, */the more the number of significant
displayed figures the better./* When the exponent format is used, it
takes 4 or 5 digits (D+12, D+123). As a consequence, in v mode,
small (absolute) values should be displayed in normal mode down to 4
non-significant 0 (e.g. 0.000012), and switched to "e" mode beyond.
In v mode, forcing the display of 0.0123456 in "e" mode on the
(bad) reason that some other huge or tiny numbers in the matrix are
displayed in this mode, would print 1.234D-02, and so make invisible
2 significant figures.
I do not see any reason that would impose the display mode to be
homogeneous over all elements of a matrix, possibly canceling the
display of significant figures in the given format's width.
I agree Samuel.
Regards
Samuel
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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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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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