If you just want the distances between each pair of points, then you don't need to calculate a full distance matrix.
Instead, calculate it directly:
import numpy as np
x = np.array([[[1,2,3,4,5],
[5,6,7,8,5],
[5,6,7,8,5]],
[[11,22,23,24,5],
[25,26,27,28,5],
[5,6,7,8,5]]])
y = np.array([[[31,32,33,34,5],
[35,36,37,38,5],
[5,6,7,8,5]],
[[41,42,43,44,5],
[45,46,47,48,5],
[5,6,7,8,5]]])
xx = x.reshape(2, -1)
yy = y.reshape(2, -1)
dist = np.hypot(*(xx - yy))
print dist
To explain a bit more about what's going on, first we reshape the arrays such that they have a 2xN shape (-1
is a placeholder that tells numpy to calculate the correct size along that axis automatically):
In [2]: x.reshape(2, -1)
Out[2]:
array([[ 1, 2, 3, 4, 5, 5, 6, 7, 8, 5, 5, 6, 7, 8, 5],
[11, 22, 23, 24, 5, 25, 26, 27, 28, 5, 5, 6, 7, 8, 5]])
Therefore, when we subtract xx
and yy
, we'll get a 2xN array:
In [3]: xx - yy
Out[3]:
array([[-30, -30, -30, -30, 0, -30, -30, -30, -30, 0, 0, 0, 0,
0, 0],
[-30, -20, -20, -20, 0, -20, -20, -20, -20, 0, 0, 0, 0,
0, 0]])
We can then unpack this in to dx
and dy
components:
In [4]: dx, dy = xx - yy
In [5]: dx
Out[5]:
array([-30, -30, -30, -30, 0, -30, -30, -30, -30, 0, 0, 0, 0,
0, 0])
In [6]: dy
Out[6]:
array([-30, -20, -20, -20, 0, -20, -20, -20, -20, 0, 0, 0, 0,
0, 0])
And calculate the distance (np.hypot
is equivalent to np.sqrt(dx**2 + dy**2)
):
In [7]: np.hypot(dx, dy)
Out[7]:
array([ 42.42640687, 36.05551275, 36.05551275, 36.05551275,
0. , 36.05551275, 36.05551275, 36.05551275,
36.05551275, 0. , 0. , 0. ,
0. , 0. , 0. ])
Or we can have the unpacking done automatically and do it all in one step:
In [8]: np.hypot(*(xx - yy))
Out[8]:
array([ 42.42640687, 36.05551275, 36.05551275, 36.05551275,
0. , 36.05551275, 36.05551275, 36.05551275,
36.05551275, 0. , 0. , 0. ,
0. , 0. , 0. ])
If you want to calculate other types of distances, just change np.hypot
to the function you'd like to use. For example, for Manhattan/city-block distances:
In [9]: dist = np.sum(np.abs(xx - yy), axis=0)
In [10]: dist
Out[10]: array([60, 50, 50, 50, 0, 50, 50, 50, 50, 0, 0, 0, 0, 0, 0])