[SciPy-User] [SciPy-user] 2d convolution with 'full' in one dimension and 'valid' in another

[Tom K.]

Paul-405 wrote:
> 
> I have a n x m matrix A and n x k matrix B where k >> m. I would like to
> compute
> the 'full' convolution of A and B along 2nd dimension and get a result
> that is n
> x (m + k - 1).
> 
> If I select mode='full' in scipy.signal.convolve, I get a result that is
> 'full'
> in both dimensions and a result that is (n + n - 1) x (m + k - 1).
> Currently, I
> do this:
> 
> C = np.array([sp.signal.correlate(A[i], B[i], mode='full') for i in
> range(n)])
> 
> I do this a lot with fixed A and varying B. I was wondering if there is a
> faster
> way. Perhaps I should be using fft's instead.
> 

Paul, What you describe does not sound to me like a 'valid' convolution in
the other dimension - it sounds like no convolution at all.  You want a 1D
convolution along only one dimension of 2 ND arrays, not an ND convolution
of 2 ND arrays, right?

One thing that may be faster is pre-allocating the output array and
assigning it in a loop:
def convolve1(x, y):
    n1 = x.shape[-1]
    n2 = y.shape[-1]
    z = np.empty((x.shape[0], n1+n2-1), dtype=x.dtype)
    for i in xrange(x.shape[0]):
        z[i] = np.convolve(x[i], y[i])
    return z

This was about 2.5x faster than the one-liner that you provided for a simple
example (n=1000, m=100, k=1000).

Anyone else have thoughts about fast ways to do 1D convolution along only
one dimension of 2 ND arrays?

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