[Numpy-discussion] ufunc for sum of squared difference

[Sebastian Berg]

On Fr, 2016-11-04 at 13:11 -0400, Matthew Harrigan wrote:
> I was reading this 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?

I don't think its anticipated, since a ufunc could in most cases use a
third argument, but a 3 arg ufunc can't be reduced. Not sure if there
might be some trickery possible.

> 2. Is it possible to pass an initial value to reduce to avoid the
> clean up required for the first element?

This is the identity normally. But the identity can only be 0, 1 or -1
right now I think. The identity is what the output array gets
initialized with (which effectively makes it the first value passed
into the inner loop).

> 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?
> 

Might be mixing up things, however, IIRC the single pass approach has a
bad numerical accuracy, so that I doubt that it is a good default
algorithm.

- Sebastian


> Thank you,
> Matt
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