[Numpy-discussion] Weird numpy.arange behavoir
Robert Kern
robert.kern at gmail.com
Wed Jun 6 23:09:01 EDT 2007
Luke wrote:
> I am integrating some equations and need to generate rank 1 time
> arrays to pass to my integrator. I need them to have the same
> interval between each entry and have the same number of elements. In
> matlab this is trivial, and it is in numpy as well, except I'm getting
> some weird behavoir:
>
> import numpy as N
> T = 0.1
> dt = 0.01
>
> k=0
> t = N.arange(k*T,(k+1)*T+h,h)
>
> Output:
> array([ 0. , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08,
> 0.09, 0.1 ])
>
> So far so good.
>
> Here is where the problem arises:
>
> k=1
> t = N.arange(k*T,(k+1)*T+h,h)
> array([ 0.1 , 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18,
> 0.19, 0.2 , 0.21])
>
> Note that this time array has more entries, and in fact, the last
> entry is greater than (k+1)*T = (1+1)*0.01 = 2*0.01 = 0.2
>
> Now if it was consistent for all k>0, then it would be fine. However,
> this is not the case:
>
> k=3
> t = N.arange(k*T,(k+1)*T+h,h)
>
> Output:
> array([ 0.3 , 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38,
> 0.39, 0.4 ])
>
> Now, this one has the same number of entries as the case where k=0.
>
> Can anybody:
> 1) Offer a solution to this?
Use linspace() instead.
> 2) Explain this behavoir would occur and ever be desirable?
It's not that it's desirable; it's just unavoidable.
> I read the numpy.arange docstring and it says that this may occur, but
> I don't understand why you would ever want this to occur. Apparently,
> the length of the returned array is:
>
> ceil((stop-start)/step)
>
> The weird thing is that in this simple example, (stop-start)/step is
> always exactly 11, since ((k+1)*T + h - k*T)/(h) = (T+h)/h =
> (0.1+0.01)/(0.01) = 11.0. In this, there shouldn't be any roundoff
> error.
Yes, there is. Neither 0.1 nor 0.01 are exactly representable in binary floating
point. There is roundoff error before you ever get to the actual operations.
> So in this simple example that was harmlessly constructed
> (i.e., my period time was an exact integer multiple of my step time),
> arange behaves undesirably (at least I think it does).
>
> After a few tests, I found that if instead of ceil, round was used,
> then it eliminated my problem, but I don't know if this would have
> other undesirable effects in other situations.
That just moves the problem elsewhere and is inconsistent with the integer behavior.
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco
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