Since you are mentioning some improvements (I have confirmed them!) I would
like to ask what code are you using for benchmarking numpy.

I wanted to know what code was faster:

sum(|x|)/N or sqrt(sum(x**2))/sqrt(N)

I wrote a timeit test and discovered that using the function dot(x,x) to
compute sum(x**2) gives the best result and is one order of magnitude faster
than sum(|x|).
I found that sum and absolute are approx. 5 times slower than dot. I also
noticed that the std function is slightly slower than a python
implementation code.

These are the results for some operations in a randn vector of size 1000:


      48.9+-22.6us: np.dot(v,v)
     628.8+-87.3us: np.sum(np.absolute(v))
     518.3+-65.9us: np.sum(v*v)
     118.0+-1.4us: v*v
     234.4+-56.5us: np.absolute(v)
     234.3+-56.2us: v.sum()
    1175.2+-58.6us: v.std()
     969.6+-77.4us: vv=np.mean(v)-v;(np.sqrt(np.dot(vv,vv)/(len(v)-1)))


The code for timming the numpy operations:

#################

import timeit
import numpy as np

p= """
import numpy as np
vsize=1000
v=np.randn(vsize)
"""

vs=[
'np.dot(v,v)',
'np.sum(np.absolute(v))',
'np.sum(v*v)',
'v*v',
'np.absolute(v)',
'v.sum()',
'v.std()',
'vv=np.mean(v)-v;(np.sqrt(np.dot(vv,vv)/(len(v)-1)))']

ntests=1000
tries=5


for s in vs:
    t = timeit.Timer(s,p)
    r=(np.array(t.repeat(tries,ntests))/ntests) * 10.0e6
    print ("%10.1f+-%3.1fus: %s " % (np.mean(r), np.std(r) ,s))

#################

If some one have a complete benchmarking set of functions I would like to
use them.

Thanks.

Hugo Gamboa