distance matrix between points

04-12-2017 06:25 AM
New Contributor III

Hello all!


I cannot find the way how to create a distance matrix from a point layer. If I use the point distance tool from the proximity toolbox I just get a table with the distances between each point within the layer but I need a 1:1 data matrix (rows and columns as points, values as distances and the diagonal with 0 values). There must be certainly a way how to create this…

I need the distance matrix for other calculations.

I am using ArcGIS 10.3.1 for Desktop (Advanced Licence).

Do you have any ideas?


Thanks for four support.

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7 Replies
MVP Esteemed Contributor

I have posted in my blog a number of times on distance calculations.  You can use scipy.distance.cdist to produce a squareform matrix, however, I prefer to use a pure numpy based solution using einsum which does the same trick.

Here is the def from a larger module I maintain.

def e_dist(a, b, metric='euclidean'):
    """Distance calculation for 1D, 2D and 3D points using einsum
    : a, b   - list, tuple, array in 1,2 or 3D form
    : metric - euclidean ('e','eu'...), sqeuclidean ('s','sq'...), 
    a = np.asarray(a)
    b = np.atleast_2d(b)
    a_dim = a.ndim
    b_dim = b.ndim
    if a_dim == 1:
        a = a.reshape(1, 1, a.shape[0])
    if a_dim >= 2:
        a = a.reshape(np.prod(a.shape[:-1]), 1, a.shape[-1])
    if b_dim > 2:
        b = b.reshape(np.prod(b.shape[:-1]), b.shape[-1])
    diff = a - b
    dist_arr = np.einsum('ijk,ijk->ij', diff, diff)
    if metric[:1] == 'e':
        dist_arr = np.sqrt(dist_arr)
    dist_arr = np.squeeze(dist_arr)
    return dist_arr

and here is simple set of data points so you can see how it works

a = np.arange(10).reshape(5,2)
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7],
       [8, 9]])

array([[ 0.000,  2.828,  5.657,  8.485,  11.314],
       [ 2.828,  0.000,  2.828,  5.657,  8.485],
       [ 5.657,  2.828,  0.000,  2.828,  5.657],
       [ 8.485,  5.657,  2.828,  0.000,  2.828],
       [ 11.314,  8.485,  5.657,  2.828,  0.000]])

give it a shot.  3D distance can also be determine using einsum notation

You can also use an upper of lower matrix format if you want to make it easier to read

np.triu(e_dist(a, a))

array([[ 0.000,  2.828,  5.657,  8.485,  11.314],
       [ 0.000,  0.000,  2.828,  5.657,  8.485],
       [ 0.000,  0.000,  0.000,  2.828,  5.657],
       [ 0.000,  0.000,  0.000,  0.000,  2.828],
       [ 0.000,  0.000,  0.000,  0.000,  0.000]])
New Contributor III

Hello Dan,

I just thought after using the “Point Distance” tool there will be another tool where I can simply convert the table with the distances into a data matrix.

But thanks for your help.

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MVP Esteemed Contributor

Not with your requirements, you might be able to cobble an OD matrix from excel but everything else in Arc* is a linear table format

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Regular Contributor II

Did you try Generate Near Table tool without check Find only closest feature?

MVP Esteemed Contributor

except it doesn't return a matrix with 0's on the diagonal

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Regular Contributor II

Yes, You are right ,Dan

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New Contributor III

Hi Abdullah,

yeah I have already tried that but the result is the same as by using the “Point distance” tool with the only difference that there is a new column in the attribute table with the ranks of the distances but it remains a table…So I have to use the solution from Dan.

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