________________________________
From: Charles R Harris <charlesr.har...@gmail.com>
To: Discussion of Numerical Python <numpy-discussion@scipy.org>
Sent: Fri, November 12, 2010 10:34:58 AM
Subject: Re: [Numpy-discussion] Change in Python/Numpy numerics with Py version
2.6 ?
On Fri, Nov 12, 2010 at 8:02 AM, Lou Pecora <lou_boog2...@yahoo.com> wrote:
I ran across what seems to be a change in how numerics are handled in Python 2.6
>or Numpy 1.3.0 or both, I'm not sure. I've recently switched from using Python
>2.4 and Numpy 1.0.3 to using the Python 2.6 and Numpy 1.3.0 that comes with
SAGE
>which is a large mathematical package. But the issue seems to be a Python one,
>not a SAGE one.
>
>Here is a short example of code that gives the new behavior:
>
># ---- Return the angle between two vectors ------------
>def get_angle(v1,v2):
> '''v1 and v2 are 1 dimensional numpy arrays'''
> # Make unit vectors out of v1 and v2
> v1norm=sqrt(dot(v1,v1))
> v2norm=sqrt(dot(v2,v2))
> v1unit=v1/v1norm
> v2unit=v2/v2norm
> ang=acos(dot(v1unit,v2unit))
> return ang
>
>When using Python 2.6 with Numpy 1.3.0 and v1 and v2 are parallel the dot
>product of v1unit and v2unit sometimes gives 1.0+epsilon where epsilon is the
>smallest step in the floating point numbers around 1.0 as given in the sys
>module. This causes acos to throw a Domain Exception. This does not happen when
>I use Python 2.4 with Numpy 1.0.3.
>
>
Probably an accident or slight difference in compiler optimization. Are you
running on a 32 bit system by any chance?
Yes, I am running on a 32 bit system. Mac OS X 10.4.11.
>I have put in a check for the exception situation and the code works fine
>again. I am wondering if there are other changes that I should be aware of.
>Does anyone know the origin of the change above or other differences in the
>handling of numerics between the two versions?
>Thanks for any insight.
>
The check should have been there in the first place, the straight forward
method
is subject to roundoff error. It isn't very accurate for almost identical
vectors either, you would do better to work with the difference vector in that
case: 2*arcsin(||v1 - v2||/2) when v1 and v2 are normalized, or you could try
2*arctan2(||v1 - v2||, ||v1 + v2||). It is also useful to see how the
Householder reflection deals with the problem.
I left the exception catch in place. You're right. I hadn't thought about the
Householder reflection. Good point.
Thanks.
-- Lou Pecora, my views are my own.
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