[Numpy-discussion] ufunc for sum of squared difference

[Matthew Harrigan]

I was reading this
<http://notes-on-cython.readthedocs.io/en/latest/std_dev.html> and got
thinking about if a ufunc could compute the sum of squared differences in a
single pass without a temporary array.  The python code below demonstrates
a possible approach.

import numpy as np
x = np.arange(10)
c = 1.0
def add_square_diff(x1, x2):
    return x1 + (x2-c)**2
ufunc = np.frompyfunc(add_square_diff, 2, 1)
print(ufunc.reduce(x) - x[0] + (x[0]-c)**2)
print(np.sum(np.square(x-c)))

I have (at least) 4 questions:
1. Is it possible to pass run time constants to a ufunc written in C for
use in its inner loop, and if so how?
2. Is it possible to pass an initial value to reduce to avoid the clean up
required for the first element?
3. Does that ufunc work, or are there special cases which cause it to fall
apart?
4. Would a very specialized ufunc such as this be considered for
incorporating in numpy since it would help reduce time and memory of
functions already in numpy?

Thank you,
Matt
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