1. Write a Python function using for loops to calculate the pairwise distance matrix given two sets of vectors. The function signature should look like this:
np.ndarray <- cdist(xs, ys, dist)where xs and ys are collections of vectors, and dist is some function for a distance metric. Write a function for the Euclidean distance metric with the signature:
float <- euclidean_distance(x, y)Example of usage:
coords = [(35.0456, -85.2672),
(35.1174, -89.9711),
(35.9728, -83.9422),
(36.1667, -86.7833)]
cdist(coords, coords, euclidean_distance)where coords is interpreted as 4 row vectors of dimension 2 each. The result should be
Euclidean metric
array([[ 0. , 4.70444794, 1.6171966 , 1.88558331],
[ 4.70444794, 0. , 6.0892811 , 3.35605413],
[ 1.6171966 , 6.0892811 , 0. , 2.84770898],
[ 1.88558331, 3.35605413, 2.84770898, 0. ]])Time the performance of your function for Euclidean distance metric using %timeit for the given data sets XA and XB.
Use the library function scipy.spatial.distance.cdist to see how much speed-up is achievable.
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import numpy as np
np.random.seed(123)
n1 = 50
n2 = 100
p = 10
XA = np.random.normal(0, 1, (n1, p))
XB = np.random.normal(0, 1, (n2, p))
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2. Write a version cdist_numpy to speed up calculations using vectorization and broadcasting. Check that it gives the correct answers on coords and compare timings.
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3. Write a verison cdist_numba using numba JIT. Check that it gives the correct answers on coords and compare timings.
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4. Write a verison cdist_cython using Cython AIT. Check that it gives the correct answers on coords and compare timings.
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