Calculate Euclidian Distance in two numpy arrays

Question

I have two numpy arrays as following.

X = np.array([-0.34095692,-0.34044722,-0.27155318,-0.21320583,-0.44657865,-0.19587836, -0.29414279, -0.3948753 ,-0.21655774 , -0.34857087])
Y = np.array([0.16305762,0.38554548, 0.10412536, -0.57981103, 0.17927523, -0.22612216, -0.34569697, 0.30463137,0.01301744,-0.42661108])

These are x and y coordination of 10 users. I need to find similarity between each user. For eg :

x1 = -0.34095692
y1 = 0.16305762
x2 = -0.34044722
y2 = 0.38554548

Euclidean distance = (|x1-y1|^2 + |x2-y2|^2)^1/2

So ultimately I want to get a matrix like following: Help me on achieving this.

Answer 1

Short snippet that does the job :

A = (X-Y)**2
p, q = np.meshgrid(np.arange(10), np.arange(10))
np.sqrt(A[p]-A[q])

Edit : Explanations

1. A is just a precomputed vector with all squared differences.
2. The magic is in np.meshgrid : The purpose of this function is to generate all pairs of values in tow different arrays. This is not the best solution because you will get the whole matrix but it's not a big deal for the number of samples you have. Values generated will correspond to the indices of A .
3. The indexation part A[p] is some kind of magic too. Try it yourself to understand its behaviour.
4. Here the matrix is full of nan but that's what you ask for. The true euclidean distance is + , not - .

p & q :

 array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])

array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
   [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
   [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],
   [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
   [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],
   [6, 6, 6, 6, 6, 6, 6, 6, 6, 6],
   [7, 7, 7, 7, 7, 7, 7, 7, 7, 7],
   [8, 8, 8, 8, 8, 8, 8, 8, 8, 8],
   [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]) 

Answer 2

Use zip(X, Y) to get the coordinate pairs, and if you wanna get the euclidian distance between points, it should be (|x1-x2|^2+|y1-y2|^2)^0.5 ， not (|x1-y1|^2 - |x2-y2|^2)^1/2 :

In [125]: coords=zip(X, Y)

In [126]: from scipy import spatial
     ...: dists=spatial.distance.cdist(coords, coords)

In [127]: dists
Out[127]: 
array([[ 0.        ,  0.22248844,  0.09104884,  0.75377329,  0.10685954,
         0.41534165,  0.5109039 ,  0.15149362,  0.19490308,  0.58971785],
       [ 0.22248844,  0.        ,  0.28973034,  0.9737061 ,  0.23197262,
         0.62852005,  0.73270705,  0.09751671,  0.39258852,  0.81219719],
       [ 0.09104884,  0.28973034,  0.        ,  0.68642072,  0.19047682,
         0.33880688,  0.45038919,  0.23539542,  0.1064197 ,  0.53629553],
       [ 0.75377329,  0.9737061 ,  0.68642072,  0.        ,  0.79415038,
         0.35411306,  0.24770988,  0.90290761,  0.59283795,  0.20443561],
       [ 0.10685954,  0.23197262,  0.19047682,  0.79415038,  0.        ,
         0.47665258,  0.54665574,  0.13560014,  0.28381556,  0.61376196],
       [ 0.41534165,  0.62852005,  0.33880688,  0.35411306,  0.47665258,
         0.        ,  0.15477091,  0.56683251,  0.24003205,  0.25201351],
       [ 0.5109039 ,  0.73270705,  0.45038919,  0.24770988,  0.54665574,
         0.15477091,  0.        ,  0.65808357,  0.36700881,  0.09751671],
       [ 0.15149362,  0.09751671,  0.23539542,  0.90290761,  0.13560014,
         0.56683251,  0.65808357,  0.        ,  0.34181257,  0.73270705],
       [ 0.19490308,  0.39258852,  0.1064197 ,  0.59283795,  0.28381556,
         0.24003205,  0.36700881,  0.34181257,  0.        ,  0.45902146],
       [ 0.58971785,  0.81219719,  0.53629553,  0.20443561,  0.61376196,
         0.25201351,  0.09751671,  0.73270705,  0.45902146,  0.        ]])

To get the upper triangle of this array, use numpy.triu :

In [128]: np.triu(dists)
Out[128]: 
array([[ 0.        ,  0.22248844,  0.09104884,  0.75377329,  0.10685954,
         0.41534165,  0.5109039 ,  0.15149362,  0.19490308,  0.58971785],
       [ 0.        ,  0.        ,  0.28973034,  0.9737061 ,  0.23197262,
         0.62852005,  0.73270705,  0.09751671,  0.39258852,  0.81219719],
       [ 0.        ,  0.        ,  0.        ,  0.68642072,  0.19047682,
         0.33880688,  0.45038919,  0.23539542,  0.1064197 ,  0.53629553],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.79415038,
         0.35411306,  0.24770988,  0.90290761,  0.59283795,  0.20443561],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.47665258,  0.54665574,  0.13560014,  0.28381556,  0.61376196],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.15477091,  0.56683251,  0.24003205,  0.25201351],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.65808357,  0.36700881,  0.09751671],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.        ,  0.34181257,  0.73270705],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.        ,  0.        ,  0.45902146],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.        ,  0.        ,  0.        ]])