[Numpy-discussion] step paramter for linspace
Sebastian Berg
sebastian at sipsolutions.net
Fri Mar 1 09:53:53 EST 2013
On Fri, 2013-03-01 at 13:34 +0000, Nathaniel Smith wrote:
> On Fri, Mar 1, 2013 at 12:33 PM, Henry Gomersall <heng at cantab.net> wrote:
> > On Fri, 2013-03-01 at 13:25 +0100, Sebastian Berg wrote:
> >> there has been a request on the issue tracker for a step parameter to
> >> linspace. This is of course tricky with the imprecision of floating
> >> point numbers.
> >
> > How is that different to arange? Either you specify the number of points
> > with linspace, or you specify the step with arange. Is there a third
> > option?
>
> arange is designed for ints and gives you a half-open interval,
> linspace is designed for floats and gives you a closed interval. This
> means that when arange is used on floats, it does weird things that
> linspace doesn't:
>
> In [11]: eps = np.finfo(float).eps
>
> In [12]: np.arange(0, 1, step=0.2)
> Out[12]: array([ 0. , 0.2, 0.4, 0.6, 0.8])
>
> In [13]: np.arange(0, 1 + eps, step=0.2)
> Out[13]: array([ 0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>
> In [14]: np.linspace(0, 1, 6)
> Out[14]: array([ 0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>
> In [15]: np.linspace(0, 1 + eps, 6)
> Out[15]: array([ 0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>
> The half-open/closed thing also has effects on what kind of api is
> reasonable. arange(0, 1, step=0.8) makes perfect sense (it acts like
> python range(0, 10, step=8)). linspace(0, 1, step=0.8) is just
> incoherent, though, because linspace guarantees that both the start
> and end points are included.
>
> > My usual hack to deal with the numerical bounds issue is to add/subtract
> > half the step.
>
> Right. Which is exactly the sort of annoying, content-free code that a
> library is supposed to handle for you, so you can save mental energy
> for more important things :-).
>
> The problem is to figure out exactly how strict we should be. Like,
> presumably linspace(0, 1, step=0.8) should fail, rather than round 0.8
> to 0.5 or 1. That would clearly violate "in the face of ambiguity,
> refuse the temptation to guess".
>
> OTOH, as Sebastian points out, requiring that the step be *exactly* a
> divisor of the value (stop - start), within 1 ULP, is probably
> obnoxious.
>
> Would anything bad happen if we just required that, say, (stop -
> start)/step had to be within "np.allclose" of an integer, i.e., to
> some reasonable relative and absolute precision, and then rounded the
> number of steps to match that integer exactly?
I was a bit worried about what happens for huge a number of steps. Have
to rethink a bit about it, but I guess one should be able to relax it...
or maybe someone here has a nice idea on how to relax it.
It seems to me that there is a bit of a trade off if you get into the
millions of steps range, because absolute errors that make sense for few
steps are suddenly in the range integers.
>
> -n
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