[SciPy-user] floating point pedagogical problem

[Robert Kern]

Ryan Krauss wrote:
> I have  a floating point issue that is forcing me to teach my students
> more python/computer science than I want to:
> 
> In [36]: temp
> Out[36]: NumPy array, format: long
> [-1.         -0.83045267 -0.64773663 -0.45185185 -0.24279835 -0.02057613
>   0.21481481  0.46337449  0.72510288  1.        ]
> 
> In [37]: arccos(temp)
> Out[37]: NumPy array, format: long
> [                  nan            2.55071609            2.27540616
>             2.03963643            1.81604581            1.59137391
>             1.35429411            1.08899693            0.75961255
>                    nan]
> 
> 
> We are doing a robotics problem involving inverse kinematics where
> they need to take the arccos and arcsin of some vectors.  The problem
> is that
> In [38]: eps=1e-15
> 
> In [39]: -1-eps < temp[0] < -1+eps
> Out[39]: True
> 
> So, my current solution is to check for theta +/- 1 +/- eps problems like this:
> 
> tempout = []
> for item in temp:
> 	if -1-eps<item<-1+eps:
> 		tempout.append(-1.0)
> 	elif 1-eps<item<1+eps:
> 		tempout.append(1.0)
> 	else:
> 		tempout.append(item)
> tempout = array(tempout)
> 
> Is there a better way? 

clip(temp, -1.0, 1.0)

That will silently allow obviously bogus values like 1.5, but you may not care
overmuch for the problem.

> Is making arccos and arcsin check for +/-1 +/-
> eps reasonable? 

I don't think so. eps may not be the appropriate fuzz-factor for the problem.

> Or should I give a lecture on floating point evils?

Are they using floating point? If so, then yes, they need to know about the
little buggers.

For domain issues like this, though, it's simple enough to say that floating
point introduces inaccuracies and sometimes functions that have restricted
domains require some extra care to clip inputs to the domain.

-- 
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