[Numpy-discussion] ufunc for sum of squared difference

[Matthew Harrigan]

I didn't notice identity before.  Seems like frompyfunc always sets it to
None.  If it were zero maybe it would work as desired here.

In the writing your own ufunc doc, I was wondering if the pointer to data
could be used to get a constant at runtime.  If not, what could that be
used for?

static void double_logit(char **args, npy_intp *dimensions,
                            npy_intp* steps, void* data)

Why would the numerical accuracy be any different?  The subtraction and
square operations look identical and I thought np.sum just calls
np.add.reduce, so the reduction step uses the same code and would therefore
have the same accuracy.

Thanks

On Fri, Nov 4, 2016 at 1:56 PM, Sebastian Berg <sebastian at sipsolutions.net>
wrote:

> 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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