Calculate Euclidean Distance With Numpy

I have a point set which I have stored its coordinates in three different arrays (xa, ya, za). Now, I want to calculate the euclidean distance between each point of this point set

Solution 1:

A different solution would be to use the spatial module from scipy, the KDTree in particular.

This class learn from a set of data and can be interrogated given a new dataset:

from scipy.spatial import KDTree
# create some fake data
x = arange(20)
y = rand(20)
z = x**2
# put them togheter, should have a form [n_points, n_dimension]
data = np.vstack([x, y, z]).T
# create the KDTree
kd = KDTree(data)

now if you have a point you can ask the distance and the index of the closet point (or the N closest points) simply by doing:

kd.query([1, 2, 3])
# (1.8650720813822905, 2)# your may differs

or, given an array of positions:

#bogus position
x2 = rand(20)*20
y2 = rand(20)*20
z2 = rand(20)*20
# join them togheter as the input
data2 = np.vstack([x2, y2, z2]).T
#query them
kd.query(data2)

#(array([ 14.96118553,   9.15924813,  16.08269197,  21.50037074,#    18.14665096,  13.81840533,  17.464429  ,  13.29368755,#    20.22427196,   9.95286671,   5.326888  ,  17.00112683,#     3.66931946,  20.370496  ,  13.4808055 ,  11.92078034,#     5.58668204,  20.20004206,   5.41354322,   4.25145521]),#array([4, 3, 2, 4, 2, 2, 4, 2, 3, 3, 2, 3, 4, 4, 3, 3, 3, 4, 4, 4]))

Solution 2:

You can calculate the difference from each xa to each xb with np.subtract.outer(xa, xb). The distance to the nearest xb is given by

np.min(np.abs(np.subtract.outer(xa, xb)), axis=1)

To extend this to 3D,

distances = np.sqrt(np.subtract.outer(xa, xb)**2 + \
    np.subtract.outer(ya, yb)**2 + np.subtract.outer(za, zb)**2)
distance_to_nearest = np.min(distances, axis=1)

If you actually want to know which of the b points is the nearest, you use argmin in place of min.

index_of_nearest = np.argmin(distances, axis=1)

Solution 3:

There is more than one way of doing this. Most importantly, there's a trade-off between memory-usage and speed. Here's the wasteful method:

s = (1, -1)
d = min((xa.reshape(s)-xb.reshape(s).T)**2
     + (ya.reshape(s)-yb.reshape(s).T)**2
     + (za.reshape(s)-zb.reshape(s).T)**2), axis=0)

The other method would be to iterate over the point set in b to avoid the expansion to the full blown matrix.