[AstroPy] Convolution of NumPy arrays of arbitrary dimension

Mon Aug 13 11:30:06 EDT 2018

Foad,
It sounds like you maybe are looking for a correlation rather than a
convolution?

>>> from scipy.ndimage import correlate
>>> correlate(A, B)

array([[36, 28, 14,  4,  2],
       [20, 24, 24, 14,  9],
       [16, 26, 28, 23, 23],
       [24, 21, 19, 27, 25]])

 Jake VanderPlas
 Senior Data Science Fellow
 Director of Open Software
 University of Washington eScience Institute

On Mon, Aug 13, 2018 at 1:31 AM, Foad Sojoodi Farimani <
f.s.farimani at gmail.com> wrote:

> Dear Jake,
>
> Thanks alot for your reply.
> I just tried the scipy.ndimage.convolve and it doesn't seem to be what I'm
> looking for. I use the term convolution as used in the context of the Cauchy
> product <https://en.wikipedia.org/wiki/Cauchy_product> of multivariate
> power series (polynomials). for example
>
>     from scipy.ndimage import convolve
>     import numpy as np
>
>     D1=np.array([4,5])
>     D2=np.array([2,3])
>     A=np.random.randint(10,size=D1)
>     B=np.random.randint(10,size=D2)
>
>     print(A)
>     print(B)
>
> results:
>
> [[9 5 2 0 1]
>  [1 9 8 4 4]
>  [7 9 2 9 6]
>  [5 0 8 8 2]]
> [[4 6 9]
>  [9 0 8]]
>
> I expect the first element of the conve(A,B) to be 36 but
> the print(convolve(A, B)) results in:
>
> [[168 185 185 137  85]
>  [230 205 237 196 209]
>  [212 151 233 198 218]
>  [115 189 152 210 174]]
>
> Also the conve(A,B) should be of the shape A.shape+B.shape-1
> while scipy.ndimage.convolve result is of the A.shape. the conv I'm looking
> for is commutative as the Cauchy product of two polynomial is.
>
> Best,
> Foad
>
>
>
> On Sat, Aug 11, 2018 at 10:11 PM Jacob Vanderplas <
> jakevdp at cs.washington.edu> wrote:
>
>> Hi Foad
>>
>>
>>> Thanks a lot for the reply. I have indeed seen scipy.ndimage.convolve
>>> and have mentioned it in the OP
>>> <https://stackoverflow.com/questions/51794274/convolution-of-numpy-arrays-of-arbitrary-dimension-for-cauchy-product-of-multiva>.
>>> but some questions:
>>>
>>
>> I saw that, but you seemed to imply there that it was limited to 1 and 2
>> dimensions, when it works for arbitrary dimensions.
>>
>>
>>>
>>>
>>>    1. although there is nothing about the dimension limit of the
>>>    ndarrays in its official page
>>>    <https://docs.scipy.org/doc/scipy-0.16.1/reference/generated/scipy.ndimage.filters.convolve.html>,
>>>    but I haven't seen any examples showing it works with higher dimensions.
>>>
>>> I showed an example of a simple four-dimensional convolution in my
>> original response.
>>
>>
>>>
>>>    1. what is the difference between astropy.convolve_fft and
>>>    scipy.signal.convolve? It seems to me they are for function analysis
>>>    <https://en.wikipedia.org/wiki/Convolution> not array arithmetics.
>>>
>>> By design, scipy.signal.convolve and scipy.signal.fftconvolve produce
>> the same results. The difference is that the latter uses an FFT to compute
>> the results, which is generally faster than direct convolution for large
>> inputs. astropy.convolve_fft is similar to scipy.signal.fftconvolve, with a
>> few differences listed in the documentation
>> <http://docs.astropy.org/en/stable/api/astropy.convolution.convolve_fft.html>
>> .
>>
>>>
>>>    1. As I can see the term convolution, even for array arithmetics is
>>>    used for different purposes. For example there is
>>>    also scipy.ndimage.filters.convolve which apparently calculates
>>>    different things. My final goal is to do finite multivariate formal power
>>>    series multiplication (Cauchy product). I think I have figured the formula
>>>    out here
>>>    <https://math.stackexchange.com/questions/2877478/cauchy-product-of-multivariate-formal-power-series>,
>>>    but I'm not sure if it is correct completely. questions are:
>>>       1. is my formula correct?
>>>          - if not what is the correct one?
>>>          2. if yes has this been done before?
>>>       - if yes where? does any of the above functions do the job?
>>>          3. regardless of the correctness of the formula and existence
>>>       of other implementations, is my implementation correct so far?
>>>       4. how to finish the final step to populate the ndarray using the
>>>       conv function?
>>>
>>> At a glance, I'm not certain if your formula or implementation is
>> correct, and I don't have the time to dig-in at the moment.
>>
>> Perhaps someone else can help with that part.
>>
>> Best of luck,
>>    Jake
>>
>>
>>> Thanks a gain and looking forwards to hearing back.
>>>
>>> Best,
>>> Foad
>>>
>>> On Sat, Aug 11, 2018 at 1:56 AM Adam Ginsburg <adam.g.ginsburg at gmail.com>
>>> wrote:
>>>
>>>>
>>>>
>>>> On Fri, Aug 10, 2018 at 5:51 PM, Jacob Vanderplas <
>>>> jakevdp at cs.washington.edu> wrote:
>>>>
>>>>> Hi Foad,
>>>>> I'm sorry if I'm misunderstanding something, but does
>>>>> scipy.ndimage.convolve not address your use case? It implements
>>>>> N-dimensional convolution:
>>>>>
>>>>> from scipy.ndimage import convolveimport numpy as np
>>>>>
>>>>> x = np.random.rand(10, 10, 10, 10)
>>>>> w = np.ones((3, 3, 3, 3))
>>>>>
>>>>> result = convolve(x, w)
>>>>>
>>>>> For completeness, astropy's convolve_fft supports this same operation
>>>> since it's doing an nd fft under the hood, but the direct convolution
>>>> (astropy.convolution.convolve) does not, since we had to hard-code the
>>>> direct convolution operations in each dimension and so far there has been
>>>> no demand for an n-dimensional convolution with n>3.
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