Finding Distant Pairs in Python taking advantage of pandas

Question

I have this file:

This can be read as:

data = np.loadtxt('test_2_stack_overflow.csv', delimiter=',')

or

dfr = pd.read_csv('test_2_stack_overflow.csv',header=None)

The column index represent the x coordinate and the row the y coordinate of a pixel whose value is reported in the file.

I would like to select all the pairs that have the same distance (+-a tollerance). The easiest way could be to apply two loops but I would like to take advantage of the numpy or pandas.

I am thinking to apply a sort of

diff = dfr.apply(lambda col: ((col.name - col.index)**2 + (col.name - col.index)**2)**0.5) 

This however seems not feasible. I am also thinking to follow another path. I could create a two dimensional vector of coordinates, this could be also be more general.

I could create a vector for the coordinates:

xx = np.arange(4)
yy = np.arange(4)

coord = np.array(np.meshgrid(xx,yy)).T.reshape(-1,2)

After that I could compute the distances between each pair:

ref = pd.DataFrame.from_records(coord, columns=('x', 'y'))

diff2 = dfr.apply(
    lambda col: np.sqrt(
        abs(ref.iloc[col.name]['x'] - ref.iloc[col.index]['x']) ** 2 +
        abs(ref.iloc[col.name]['y'] - ref.iloc[col.index]['y']) ** 2
    )
)

However, I get the following:

As you can notice, the values are all integer and that is not possible. For example, the points with coordinates (0,2) and (3,1) should have a distance of (sqrt(10))

What do you think? Should I choose a better strategy ans/or is there any error?

Thanks

Answer 1

Maybe, you are looking for cdist:

from scipy.spatial.distance import cdist

xx = np.arange(4)
yy = np.arange(4)

grid = np.array(np.meshgrid(xx, yy)).T.reshape(-1, 2)
dist = cdist(grid, grid)

Output:

>>> dist
array([[0.        , 1.        , 2.        , 3.        , 1.        ,
        1.41421356, 2.23606798, 3.16227766, 2.        , 2.23606798,
        2.82842712, 3.60555128, 3.        , 3.16227766, 3.60555128,
        4.24264069],
       [1.        , 0.        , 1.        , 2.        , 1.41421356,
        1.        , 1.41421356, 2.23606798, 2.23606798, 2.        ,
        2.23606798, 2.82842712, 3.16227766, 3.        , 3.16227766,
        3.60555128],
       [2.        , 1.        , 0.        , 1.        , 2.23606798,
        1.41421356, 1.        , 1.41421356, 2.82842712, 2.23606798,
        2.        , 2.23606798, 3.60555128, 3.16227766, 3.        ,
        3.16227766],
       [3.        , 2.        , 1.        , 0.        , 3.16227766,
        2.23606798, 1.41421356, 1.        , 3.60555128, 2.82842712,
        2.23606798, 2.        , 4.24264069, 3.60555128, 3.16227766,
        3.        ],
       [1.        , 1.41421356, 2.23606798, 3.16227766, 0.        ,
        1.        , 2.        , 3.        , 1.        , 1.41421356,
        2.23606798, 3.16227766, 2.        , 2.23606798, 2.82842712,
        3.60555128],
       [1.41421356, 1.        , 1.41421356, 2.23606798, 1.        ,
        0.        , 1.        , 2.        , 1.41421356, 1.        ,
        1.41421356, 2.23606798, 2.23606798, 2.        , 2.23606798,
        2.82842712],
       [2.23606798, 1.41421356, 1.        , 1.41421356, 2.        ,
        1.        , 0.        , 1.        , 2.23606798, 1.41421356,
        1.        , 1.41421356, 2.82842712, 2.23606798, 2.        ,
        2.23606798],
       [3.16227766, 2.23606798, 1.41421356, 1.        , 3.        ,
        2.        , 1.        , 0.        , 3.16227766, 2.23606798,
        1.41421356, 1.        , 3.60555128, 2.82842712, 2.23606798,
        2.        ],
       [2.        , 2.23606798, 2.82842712, 3.60555128, 1.        ,
        1.41421356, 2.23606798, 3.16227766, 0.        , 1.        ,
        2.        , 3.        , 1.        , 1.41421356, 2.23606798,
        3.16227766],
       [2.23606798, 2.        , 2.23606798, 2.82842712, 1.41421356,
        1.        , 1.41421356, 2.23606798, 1.        , 0.        ,
        1.        , 2.        , 1.41421356, 1.        , 1.41421356,
        2.23606798],
       [2.82842712, 2.23606798, 2.        , 2.23606798, 2.23606798,
        1.41421356, 1.        , 1.41421356, 2.        , 1.        ,
        0.        , 1.        , 2.23606798, 1.41421356, 1.        ,
        1.41421356],
       [3.60555128, 2.82842712, 2.23606798, 2.        , 3.16227766,
        2.23606798, 1.41421356, 1.        , 3.        , 2.        ,
        1.        , 0.        , 3.16227766, 2.23606798, 1.41421356,
        1.        ],
       [3.        , 3.16227766, 3.60555128, 4.24264069, 2.        ,
        2.23606798, 2.82842712, 3.60555128, 1.        , 1.41421356,
        2.23606798, 3.16227766, 0.        , 1.        , 2.        ,
        3.        ],
       [3.16227766, 3.        , 3.16227766, 3.60555128, 2.23606798,
        2.        , 2.23606798, 2.82842712, 1.41421356, 1.        ,
        1.41421356, 2.23606798, 1.        , 0.        , 1.        ,
        2.        ],
       [3.60555128, 3.16227766, 3.        , 3.16227766, 2.82842712,
        2.23606798, 2.        , 2.23606798, 2.23606798, 1.41421356,
        1.        , 1.41421356, 2.        , 1.        , 0.        ,
        1.        ],
       [4.24264069, 3.60555128, 3.16227766, 3.        , 3.60555128,
        2.82842712, 2.23606798, 2.        , 3.16227766, 2.23606798,
        1.41421356, 1.        , 3.        , 2.        , 1.        ,
        0.        ]])