Sort numpy string array using positional data

Question

I have a numpy array of strings

names = array([
    'p00x00', 'p01x00', 'p02x00', 'p03x00', 'p04x00', 'p05x00',
    'p00x01', 'p01x01', 'p02x01', 'p03x01', 'p04x01', 'p05x01',
    'p00x02', 'p01x02', 'p02x02', 'p03x02', 'p04x02', 'p05x02',
    'p00x03', 'p01x03', 'p02x03', 'p03x03', 'p04x03', 'p05x03',
    'p00x04', 'p01x04', 'p02x04', 'p03x04', 'p04x04', 'p05x04',
    'p00x05', 'p01x05', 'p02x05', 'p03x05', 'p04x05', 'p05x05'])

And corresponding position data

X = array([2.102235, 2.094113, 2.086038, 2.077963, 2.069849, 2.061699])
Y = array([-7.788431, -7.780364, -7.772306, -7.764247, -7.756188, -7.748114])

How can I sort names using X and Y such that I get out a sorted grid of names with shape (6, 6)? Note that there are essentially 6 unique X and Y positions -- I'm not just arbitrarily choosing 6x6.

names = array([
    ['p00x00', 'p01x00', 'p02x00', 'p03x00', 'p04x00', 'p05x00'],
    ['p00x01', 'p01x01', 'p02x01', 'p03x01', 'p04x01', 'p05x01'],
    ['p00x02', 'p01x02', 'p02x02', 'p03x02', 'p04x02', 'p05x02'],
    ['p00x03', 'p01x03', 'p02x03', 'p03x03', 'p04x03', 'p05x03'],
    ['p00x04', 'p01x04', 'p02x04', 'p03x04', 'p04x04', 'p05x04'],
    ['p00x05', 'p01x05', 'p02x05', 'p03x05', 'p04x05', 'p05x05']])

I realize in this case that I could simply reshape the array, but in general the data will not work out this neatly.

To me it looks like there are 36 different x values and 36 different y values. I'm afraid that this question is not quite clear enough to be answered. — Thomas Kühn
– Thomas Kühn, Commented Feb 2, 2018 at 13:47
Nevertheless, I think np.argsort might be your solution here. — Thomas Kühn
– Thomas Kühn, Commented Feb 2, 2018 at 13:48
@ThomasKühn agreed that strictly speaking there are 36 unique values in x and y, but 6 values differ by ~0.01 while the others differ by ~0.0001. — lanery
– lanery, Commented Feb 2, 2018 at 13:52
@ThomasKühn I noticed that and maybe should have clarified, but I just reversed ([::-1]) x_ordered and took the transpose of the output to get the correct order. Thanks! — lanery
– lanery, Commented Feb 2, 2018 at 14:22

Thomas Kühn · Accepted Answer · 2018-02-02 14:06:50Z

You can use numpy.argsort to get the indexes of the elements of an array after it's sorted. These indices you can then use to sort your names array.

import numpy as np

names = np.array([
    'p00x00', 'p01x00', 'p02x00', 'p03x00', 'p04x00', 'p05x00',
    'p00x01', 'p01x01', 'p02x01', 'p03x01', 'p04x01', 'p05x01',
    'p00x02', 'p01x02', 'p02x02', 'p03x02', 'p04x02', 'p05x02',
    'p00x03', 'p01x03', 'p02x03', 'p03x03', 'p04x03', 'p05x03',
    'p00x04', 'p01x04', 'p02x04', 'p03x04', 'p04x04', 'p05x04',
    'p00x05', 'p01x05', 'p02x05', 'p03x05', 'p04x05', 'p05x05'])

X = np.array([2.102235, 2.094113, 2.086038, 2.077963, 2.069849, 2.061699])
Y = np.array([-7.788431, -7.780364, -7.772306, -7.764247, -7.756188, -7.748114])

x_order = np.argsort(X)
y_order = np.argsort(Y)

names_ordered = names.reshape(6,6)[np.meshgrid(x_order,y_order)]

print(names_ordered)

gives the following output:

[['p00x05' 'p00x04' 'p00x03' 'p00x02' 'p00x01' 'p00x00']
 ['p01x05' 'p01x04' 'p01x03' 'p01x02' 'p01x01' 'p01x00']
 ['p02x05' 'p02x04' 'p02x03' 'p02x02' 'p02x01' 'p02x00']
 ['p03x05' 'p03x04' 'p03x03' 'p03x02' 'p03x01' 'p03x00']
 ['p04x05' 'p04x04' 'p04x03' 'p04x02' 'p04x01' 'p04x00']
 ['p05x05' 'p05x04' 'p05x03' 'p05x02' 'p05x01' 'p05x00']]

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