On Fri, Nov 12, 2010 at 8:02 AM, Lou Pecora <lou_boog2000@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?
 

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.

Chuck