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To: python-list@python.org
From: Robert Kern <robert.kern@gmail.com>
Subject: Re: Strange output from arange()
Date: Mon, 25 Jul 2011 14:45:00 -0500
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On 7/25/11 2:20 PM, Christopher Barrington-Leigh wrote:
> The following code:
>
>      from pylab import arange
>      nSegments=5.0
>      print arange(0,1.0+1.0/nSegments,1.0/nSegments)
>      nSegments=6.0
>      print arange(0,1.0+1.0/nSegments,1.0/nSegments)
>      nSegments=8.0
>      print arange(0,1.0+1.0/nSegments,1.0/nSegments)
>      nSegments=10.0
>      print arange(0,1.0+1.0/nSegments,1.0/nSegments)
>
> gives an output of:
>
> [ 0.   0.2  0.4  0.6  0.8  1. ]
> [ 0.          0.16666667  0.33333333  0.5         0.66666667
> 0.83333333  1.          1.16666667]
> [ 0.     0.125  0.25   0.375  0.5    0.625  0.75   0.875  1.   ]
> [ 0.   0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1. ]
>
> These arrays have lengths, 6, 8, 9, and 11, in stead of 6, 7, 9, and
> 11.
> What is going on for the case of n=6?

Floating point computations are not always accurate, and when one tries to 
compute "the same thing" two different ways, one may get inconsistent results. 
This is what is happening with n=6. 1+1./6 happens to be slightly greater than 
7*(1./6) while 1+1./5 happens to be slightly less than 6*(1./5), etc. The trick 
of using 1.0+1.0/nSegments/2 tends to work better.

Nonetheless, if you want to get exactly nSegments segments with exact endpoints, 
you should use numpy.linspace(0.0, 1.0, nSegments+1). That's a much better API 
for what you want.

Also, you will want to ask numpy questions on the numpy-discussion mailing list, 
not here.

   http://www.scipy.org/Mailing_Lists

-- 
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