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  1. PO
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    <p>Have you tried using <a href="https://github.com/numba/numba" rel="nofollow">Numba</a>? It's a package that allows you to wrap Python code that is usually slow with a JIT compiler. I took a quick stab at your problem using Numba and got a significant speed up. Using IPython's magic <code>timeit</code> magic function, the <code>custom_convolution</code> function took ~18 s, while Numba's optimized function took 10.4 ms. That's a <strong>speed up of more than 1700</strong>.</p> <p>Here's how Numba is implemented. </p> <pre><code>import numpy as np from numba import jit, double s = 15 array_a = np.random.rand(s ** 3).reshape(s, s, s) array_b = np.random.rand(s ** 3).reshape(s, s, s) # Original code def custom_convolution(A, B): dimA = A.shape[0] dimB = B.shape[0] dimC = dimA + dimB C = np.zeros((dimC, dimC, dimC)) for x1 in range(dimA): for x2 in range(dimB): for y1 in range(dimA): for y2 in range(dimB): for z1 in range(dimA): for z2 in range(dimB): x = x1 + x2 y = y1 + y2 z = z1 + z2 C[x, y, z] += A[x1, y1, z1] * B[x2, y2, z2] return C # Numba'ing the function with the JIT compiler fast_convolution = jit(double[:, :, :](double[:, :, :], double[:, :, :]))(custom_convolution) </code></pre> <p>If you compute the residual between the results of both functions you will get zeros. This means that the JIT implementation is working without any problems. </p> <pre><code>slow_result = custom_convolution(array_a, array_b) fast_result = fast_convolution(array_a, array_b) print np.max(np.abs(slow_result - fast_result)) </code></pre> <p>The output I get for this is <code>0.0</code>. </p> <p>You can either install Numba into your current Python setup or try it quickly with the <a href="http://continuum.io/downloads.html" rel="nofollow">AnacondaCE</a> package from continuum.io. </p> <p>Last but not least, Numba's function is faster than the <code>scipy.signal.fftconvolve</code> function by a factor of a few. </p> <p>Note: I'm using Anaconda and not AnacondaCE. There are some differences between the two packages for Numba's performance, but I don't think it will differ too much. </p>
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    1. POConvolution of two three dimensional arrays with padding on one side too slow
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    1. COThat's a nice package.
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      1. USCris Stringfellow
 

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