Re: Uniform partition of an interval

[J.C. Gonzalez]

Dirk Laurie wrote:
> 
> On Wed, 17 May 2000, John W. Eaton wrote:
> 
> > On 17-May-2000, address@hidden <address@hidden> wrote:
> >
> > | Hello!
> > |
> > | What is the MAIN reason that 1.8:0.05:1.9 produces [1.8000 1.8500]
> > | and not [1.8000 1.8500 1.9000]?
> > | I am using 2.0.14 version of Octave.
> > | Thank you for your answer.
> > | Best regards,
> > | Emil Zagar
> >
> > I'd guess that the MAIN reason is that there is a bug in the way
> > Octave is trying (very hard) to compute the correct number of elements
> > for ranges.  If you're in a debugging mood, the code to look at is in
> > the Range::nelem_internal and related functions in liboctave/Range.cc.
> >
> > jwe
> 
> It is obscene to write code that intimately explores the delicate secrets
> of floating-point arithmetic on a particular implementation.  The decent
> programmer uses the colon range operator only on integers, or in cases
> where the total range is not close to a multiple of the step size.
> I.e. '1.8+(0:2)*0.05' or '1.8:0.05:1.91'.
> 

Obscene? Decent?

> But we live in an age where seemliness is not part of the popular ethos,
> and people will write things like 'y=1.8:0.05:1.9'.  We should agree what
> that should do.  Intuitively one feels that a:h:b with h>0 should be
> equivalent to:
>   y=[]; x=a;
>   while x<=b, y=[y x]; x += h; end
> And indeed, if I run the above in Octave on my i686 machine, I get
> [1.8000 1.8500].  Yet it is unsatisfactory, because with pencil and
> paper, or on a decimal machine, or on some binary machines, I would have
> got [1.8000 1.8500 1.9000].
> 
> One can get round the problem by saying it should be equivalent to:
>   r=(b-a)/h; n=round(r);
>   if h*abs(n-r)>max(a,b)*eps, n=floor(r); end
>   y=a+h*(0:n);
> 
> But doing so would treat one case of a pervasive problem: the
> non-intuitiveness of floating-point comparison.  A good cure should work
> in other places too.
> 
> I think Octave should borrow an idea from the grandfather of interactive
> matrix languages, namely APL.  This language has a built-in variable which
> in Octave we would call 'comparison_tolerance'.  Then we could write:
> 

I agree, but ... shouldn't we use better "linspace" ?
BTW, this is what I get in my case (same result
in GNU Octave, version 2.0.16 @ i686-pc-linux-gnu, and
version 2.0.13 @ alpha-dec-osf4.0d.

octave:1> linspace(1.8,1.9,3)
ans =
  1.8000  1.8500  1.9000

octave:2> 1.8:.05:1.9
ans =
  1.8000  1.8500

Cheers,

J C
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