How to sort a numpy array based on the both arrays and also conditions

Question

I have a numpy array with three columns and hundres of rows. I want to sort it based on two columns and in cases also regard the third column in my sorting. This is my input (they are x , y and z coordinates):

my_point=np.array([[1., 2., 90.9],
                   [1., 0., 100.1],
                   [1.8, 0., 2.8],
                   [1.8, 2., 3.1],
                   [1.8, 1., 2.7],
                   [3., 0., 3.],
                   [3., 2., 2.9],
                   [2., 1., 100.],
                   [2., 0., 100.]])

Firstly, I want to sort it based on the first ( x ) and second column ( y ) and secondly modify this sort based on the third column ( z ). The key issue is that I must sort my data based on x and y and cannot change it to x and z or y and z , because then it changes the order of all the points. This is my sorting code:

result_array=my_point[np.lexsort((my_point[:,1],my_point[:,0]))]

It gives me:

array([[1., 0., 100.1],
       [1., 2., 90.9],
       [1.8, 0., 2.8],
       [1.8, 1., 2.7],
       [1.8, 2., 3.1],
       [2., 0., 100.],
       [2., 1., 100.],
       [3., 0., 3. ],
       [3., 2., 2.9]])

It is correct but I want to modify my sort based on the third column. I want to consider the values of this column, when it is highly different from the adjacent rows. As result_array shows, third column of its second, third and fourth rows ( [1.8, 0., 2.8] , [1.8, 1., 2.7] and [1.8, 2., 3.1] ) have very low values compared to the next two rows. The x value of these rows is just a little bit higher than next ones and in such cases I want to neglect it and give priority to z values:

array([[1., 0., 100.1],
       [1., 2., 90.9],
       [2., 0., 100.],
       [2., 1., 100.],
       [1.8, 0., 2.8],
       [1.8, 1., 2.7],
       [1.8, 2., 3.1],
       [3., 0., 3. ],
       [3., 2., 2.9]])

For more clarity, I have uploaded a fig showing my desired order of points in 3d space. I think It can be done maybe through defining a function for sorting but I have no idea on how to do it. In advance, I do appreciate any help.

Answer 1

You could define a sort function like

sortfunc = my_point[:, 0] * 100 + my_point[:, 1] * 10 - my_point[:, 2]

idx = np.argsort(sortfunc)
my_point[idx]
# array([[  1. ,   0. , 100.1],
#        [  1. ,   2. ,  90.9],
#        [  2. ,   0. , 100. ],
#        [  2. ,   1. , 100. ],
#        [  1.8,   0. ,   2.8],
#        [  1.8,   1. ,   2.7],
#        [  1.8,   2. ,   3.1],
#        [  3. ,   0. ,   3. ],
#        [  3. ,   2. ,   2.9]])

Of course the coefficients 100 , 10 , and -1 are then a matter of tuning.