[SciPy-Dev] Pull request 9190 - Support specifying axes for fftconvolve

[Todd]

Allowing specifying the axes for convolve and fftconvolve was discussed in
issue #3525 [1]. I have implemented this feature for fftconvolve [2].  It
allows the user the specify one or more axes as the axes over which the
convolution will be carried.  Other axes will be broadcast together,
although both arrays must have the same number of dimensions (it will not
automatically add implicit length-1 dimensions to make the number of
dimensions match).

As I side-effect of this, I also implemented a new pair of helper functions
for n-dimensional transforms that calculates the shape and axes arguments.
This is shared between fftn, ifftn, dctn, idctn, dstn, idstn, and
fftconvolve.  It also adds some additional benefits.  These functions now
support any integer array-like as their shape and axes arguments instead of
just tuples.  The functions now consistently interpret individual ints as
length-1 arrays of ints.  They also support negative values in the shape
argument, which is interpreted as just using the length of that particular
dimension from the original array.

I have also implemented unit tests for everything, and updated the relevant
function signatures.

This feature is a prerequisite for implementing the overlap-add method [2]
for convolution, which has enormous performance benefits for two arrays of
very different sizes (one is larger by a factor of more than a few times)
where both arrays are large (both are more than a few hundred samples long).

[1] https://github.com/scipy/scipy/issues/3525
[2] https://github.com/scipy/scipy/pull/9190
[3] https://en.wikipedia.org/wiki/Overlap%E2%80%93add_method
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