Radius search in list of coordinates
Question:
I’m using python 2.7 and numpy (import numpy as np).
I have a list of x-y coordinates in the following shape:
coords = np.zeros((100, 2), dtype=np.int)
I have a list of values corresponding to these coordinates:
values = np.zeros(100, dtype=np.int)
My program is populating these arrays.
Now, for each coordinate, I want to find neighbours within radius r that have a non-zero value. What’s the most efficient way to do that?
Answers:
Demo:
import pandas as pd
from scipy.spatial.distance import pdist, squareform
In [101]: np.random.seed(123)
In [102]: coords = np.random.rand(20, 2)
In [103]: r = 0.3
In [104]: d = pd.DataFrame(squareform(pdist(coords)))
In [105]: d
Out[105]:
0 1 2 3 4 5 6 7 8 9 10 11 12
0 0.000000 0.539313 0.138885 0.489671 0.240183 0.566555 0.343214 0.541508 0.525761 0.295906 0.566702 0.326087 0.045059
1 0.539313 0.000000 0.509028 0.765644 0.299834 0.212418 0.535287 0.253292 0.378472 0.305322 0.504946 0.501173 0.545672
2 0.138885 0.509028 0.000000 0.369830 0.240542 0.484970 0.459329 0.449965 0.591335 0.217102 0.434730 0.187983 0.100192
3 0.489671 0.765644 0.369830 0.000000 0.579235 0.639118 0.827519 0.585140 0.946945 0.474554 0.383486 0.266724 0.444612
4 0.240183 0.299834 0.240542 0.579235 0.000000 0.364005 0.335128 0.355671 0.368796 0.148598 0.482379 0.327450 0.251218
5 0.566555 0.212418 0.484970 0.639118 0.364005 0.000000 0.676135 0.055591 0.576447 0.272729 0.315123 0.399127 0.555655
6 0.343214 0.535287 0.459329 0.827519 0.335128 0.676135 0.000000 0.679527 0.281035 0.481218 0.813671 0.621056 0.387169
7 0.541508 0.253292 0.449965 0.585140 0.355671 0.055591 0.679527 0.000000 0.602427 0.245620 0.261309 0.350237 0.526773
8 0.525761 0.378472 0.591335 0.946945 0.368796 0.576447 0.281035 0.602427 0.000000 0.498845 0.811462 0.695304 0.559738
9 0.295906 0.305322 0.217102 0.474554 0.148598 0.272729 0.481218 0.245620 0.498845 0.000000 0.333842 0.208528 0.282959
10 0.566702 0.504946 0.434730 0.383486 0.482379 0.315123 0.813671 0.261309 0.811462 0.333842 0.000000 0.254850 0.533784
11 0.326087 0.501173 0.187983 0.266724 0.327450 0.399127 0.621056 0.350237 0.695304 0.208528 0.254850 0.000000 0.288072
12 0.045059 0.545672 0.100192 0.444612 0.251218 0.555655 0.387169 0.526773 0.559738 0.282959 0.533784 0.288072 0.000000
13 0.339648 0.350100 0.407307 0.769145 0.202592 0.501132 0.185248 0.511020 0.186913 0.347808 0.678357 0.527288 0.372879
14 0.530211 0.104003 0.473790 0.689158 0.303486 0.109841 0.589377 0.149459 0.468906 0.257676 0.404710 0.431203 0.527905
15 0.622118 0.178856 0.627453 0.923461 0.391044 0.387645 0.509836 0.431502 0.273610 0.450269 0.683313 0.656742 0.639993
16 0.337079 0.211995 0.297111 0.582175 0.113238 0.251168 0.434076 0.246505 0.403684 0.107671 0.409858 0.316172 0.337886
17 0.271897 0.311029 0.313864 0.668400 0.097022 0.424905 0.252905 0.426640 0.279160 0.243693 0.576241 0.422417 0.296806
18 0.664617 0.395999 0.554151 0.592343 0.504234 0.184188 0.833801 0.157951 0.758223 0.376555 0.212643 0.410605 0.642698
19 0.328445 0.719013 0.238085 0.186618 0.476045 0.642499 0.671657 0.594990 0.828653 0.413697 0.465589 0.245340 0.284878
13 14 15 16 17 18 19
0 0.339648 0.530211 0.622118 0.337079 0.271897 0.664617 0.328445
1 0.350100 0.104003 0.178856 0.211995 0.311029 0.395999 0.719013
2 0.407307 0.473790 0.627453 0.297111 0.313864 0.554151 0.238085
3 0.769145 0.689158 0.923461 0.582175 0.668400 0.592343 0.186618
4 0.202592 0.303486 0.391044 0.113238 0.097022 0.504234 0.476045
5 0.501132 0.109841 0.387645 0.251168 0.424905 0.184188 0.642499
6 0.185248 0.589377 0.509836 0.434076 0.252905 0.833801 0.671657
7 0.511020 0.149459 0.431502 0.246505 0.426640 0.157951 0.594990
8 0.186913 0.468906 0.273610 0.403684 0.279160 0.758223 0.828653
9 0.347808 0.257676 0.450269 0.107671 0.243693 0.376555 0.413697
10 0.678357 0.404710 0.683313 0.409858 0.576241 0.212643 0.465589
11 0.527288 0.431203 0.656742 0.316172 0.422417 0.410605 0.245340
12 0.372879 0.527905 0.639993 0.337886 0.296806 0.642698 0.284878
13 0.000000 0.408426 0.339019 0.274263 0.105627 0.668252 0.643427
14 0.408426 0.000000 0.282070 0.194058 0.345013 0.294029 0.663142
15 0.339019 0.282070 0.000000 0.344028 0.355134 0.568361 0.854775
16 0.274263 0.194058 0.344028 0.000000 0.181494 0.399730 0.513362
17 0.105627 0.345013 0.355134 0.181494 0.000000 0.581128 0.551910
18 0.668252 0.294029 0.568361 0.399730 0.581128 0.000000 0.649183
19 0.643427 0.663142 0.854775 0.513362 0.551910 0.649183 0.000000
result:
In [107]: d[(0 < d) & (d < r)].apply(lambda x: x.dropna().index.tolist())
Out[107]:
0 [2, 4, 9, 12, 17]
1 [4, 5, 7, 14, 15, 16]
2 [0, 4, 9, 11, 12, 16, 19]
3 [11, 19]
4 [0, 1, 2, 9, 12, 13, 16, 17]
5 [1, 7, 9, 14, 16, 18]
6 [8, 13, 17]
7 [1, 5, 9, 10, 14, 16, 18]
8 [6, 13, 15, 17]
9 [0, 2, 4, 5, 7, 11, 12, 14, 16, 17]
10 [7, 11, 18]
11 [2, 3, 9, 10, 12, 19]
12 [0, 2, 4, 9, 11, 17, 19]
13 [4, 6, 8, 16, 17]
14 [1, 5, 7, 9, 15, 16, 18]
15 [1, 8, 14]
16 [1, 2, 4, 5, 7, 9, 13, 14, 17]
17 [0, 4, 6, 8, 9, 12, 13, 16]
18 [5, 7, 10, 14]
19 [2, 3, 11, 12]
dtype: object
You can also do this only in numpy and scipy, I find it faster.
from scipy.spatial.distance import pdist, squareform
import numpy
SIZE=512
N_PARTICLE=100
RADIUS = 15
VALUE_THRESHOLD = 0
coords = numpy.random.randint(0, SIZE, size=(N_PARTICLE, 2))
values = numpy.random.randint(0, 2, (N_PARTICLE))
square_dist = squareform(pdist(coords, metric='euclidean'))
condlist = []
for i, row in enumerate(square_dist[:]):
condlist.append(numpy.where((values>VALUE_THRESHOLD) & (row < RADIUS) & (row > 0))[0].tolist())
It must be a better way to do it thoughtfully.
I’m using python 2.7 and numpy (import numpy as np).
I have a list of x-y coordinates in the following shape:
coords = np.zeros((100, 2), dtype=np.int)
I have a list of values corresponding to these coordinates:
values = np.zeros(100, dtype=np.int)
My program is populating these arrays.
Now, for each coordinate, I want to find neighbours within radius r that have a non-zero value. What’s the most efficient way to do that?
Demo:
import pandas as pd
from scipy.spatial.distance import pdist, squareform
In [101]: np.random.seed(123)
In [102]: coords = np.random.rand(20, 2)
In [103]: r = 0.3
In [104]: d = pd.DataFrame(squareform(pdist(coords)))
In [105]: d
Out[105]:
0 1 2 3 4 5 6 7 8 9 10 11 12
0 0.000000 0.539313 0.138885 0.489671 0.240183 0.566555 0.343214 0.541508 0.525761 0.295906 0.566702 0.326087 0.045059
1 0.539313 0.000000 0.509028 0.765644 0.299834 0.212418 0.535287 0.253292 0.378472 0.305322 0.504946 0.501173 0.545672
2 0.138885 0.509028 0.000000 0.369830 0.240542 0.484970 0.459329 0.449965 0.591335 0.217102 0.434730 0.187983 0.100192
3 0.489671 0.765644 0.369830 0.000000 0.579235 0.639118 0.827519 0.585140 0.946945 0.474554 0.383486 0.266724 0.444612
4 0.240183 0.299834 0.240542 0.579235 0.000000 0.364005 0.335128 0.355671 0.368796 0.148598 0.482379 0.327450 0.251218
5 0.566555 0.212418 0.484970 0.639118 0.364005 0.000000 0.676135 0.055591 0.576447 0.272729 0.315123 0.399127 0.555655
6 0.343214 0.535287 0.459329 0.827519 0.335128 0.676135 0.000000 0.679527 0.281035 0.481218 0.813671 0.621056 0.387169
7 0.541508 0.253292 0.449965 0.585140 0.355671 0.055591 0.679527 0.000000 0.602427 0.245620 0.261309 0.350237 0.526773
8 0.525761 0.378472 0.591335 0.946945 0.368796 0.576447 0.281035 0.602427 0.000000 0.498845 0.811462 0.695304 0.559738
9 0.295906 0.305322 0.217102 0.474554 0.148598 0.272729 0.481218 0.245620 0.498845 0.000000 0.333842 0.208528 0.282959
10 0.566702 0.504946 0.434730 0.383486 0.482379 0.315123 0.813671 0.261309 0.811462 0.333842 0.000000 0.254850 0.533784
11 0.326087 0.501173 0.187983 0.266724 0.327450 0.399127 0.621056 0.350237 0.695304 0.208528 0.254850 0.000000 0.288072
12 0.045059 0.545672 0.100192 0.444612 0.251218 0.555655 0.387169 0.526773 0.559738 0.282959 0.533784 0.288072 0.000000
13 0.339648 0.350100 0.407307 0.769145 0.202592 0.501132 0.185248 0.511020 0.186913 0.347808 0.678357 0.527288 0.372879
14 0.530211 0.104003 0.473790 0.689158 0.303486 0.109841 0.589377 0.149459 0.468906 0.257676 0.404710 0.431203 0.527905
15 0.622118 0.178856 0.627453 0.923461 0.391044 0.387645 0.509836 0.431502 0.273610 0.450269 0.683313 0.656742 0.639993
16 0.337079 0.211995 0.297111 0.582175 0.113238 0.251168 0.434076 0.246505 0.403684 0.107671 0.409858 0.316172 0.337886
17 0.271897 0.311029 0.313864 0.668400 0.097022 0.424905 0.252905 0.426640 0.279160 0.243693 0.576241 0.422417 0.296806
18 0.664617 0.395999 0.554151 0.592343 0.504234 0.184188 0.833801 0.157951 0.758223 0.376555 0.212643 0.410605 0.642698
19 0.328445 0.719013 0.238085 0.186618 0.476045 0.642499 0.671657 0.594990 0.828653 0.413697 0.465589 0.245340 0.284878
13 14 15 16 17 18 19
0 0.339648 0.530211 0.622118 0.337079 0.271897 0.664617 0.328445
1 0.350100 0.104003 0.178856 0.211995 0.311029 0.395999 0.719013
2 0.407307 0.473790 0.627453 0.297111 0.313864 0.554151 0.238085
3 0.769145 0.689158 0.923461 0.582175 0.668400 0.592343 0.186618
4 0.202592 0.303486 0.391044 0.113238 0.097022 0.504234 0.476045
5 0.501132 0.109841 0.387645 0.251168 0.424905 0.184188 0.642499
6 0.185248 0.589377 0.509836 0.434076 0.252905 0.833801 0.671657
7 0.511020 0.149459 0.431502 0.246505 0.426640 0.157951 0.594990
8 0.186913 0.468906 0.273610 0.403684 0.279160 0.758223 0.828653
9 0.347808 0.257676 0.450269 0.107671 0.243693 0.376555 0.413697
10 0.678357 0.404710 0.683313 0.409858 0.576241 0.212643 0.465589
11 0.527288 0.431203 0.656742 0.316172 0.422417 0.410605 0.245340
12 0.372879 0.527905 0.639993 0.337886 0.296806 0.642698 0.284878
13 0.000000 0.408426 0.339019 0.274263 0.105627 0.668252 0.643427
14 0.408426 0.000000 0.282070 0.194058 0.345013 0.294029 0.663142
15 0.339019 0.282070 0.000000 0.344028 0.355134 0.568361 0.854775
16 0.274263 0.194058 0.344028 0.000000 0.181494 0.399730 0.513362
17 0.105627 0.345013 0.355134 0.181494 0.000000 0.581128 0.551910
18 0.668252 0.294029 0.568361 0.399730 0.581128 0.000000 0.649183
19 0.643427 0.663142 0.854775 0.513362 0.551910 0.649183 0.000000
result:
In [107]: d[(0 < d) & (d < r)].apply(lambda x: x.dropna().index.tolist())
Out[107]:
0 [2, 4, 9, 12, 17]
1 [4, 5, 7, 14, 15, 16]
2 [0, 4, 9, 11, 12, 16, 19]
3 [11, 19]
4 [0, 1, 2, 9, 12, 13, 16, 17]
5 [1, 7, 9, 14, 16, 18]
6 [8, 13, 17]
7 [1, 5, 9, 10, 14, 16, 18]
8 [6, 13, 15, 17]
9 [0, 2, 4, 5, 7, 11, 12, 14, 16, 17]
10 [7, 11, 18]
11 [2, 3, 9, 10, 12, 19]
12 [0, 2, 4, 9, 11, 17, 19]
13 [4, 6, 8, 16, 17]
14 [1, 5, 7, 9, 15, 16, 18]
15 [1, 8, 14]
16 [1, 2, 4, 5, 7, 9, 13, 14, 17]
17 [0, 4, 6, 8, 9, 12, 13, 16]
18 [5, 7, 10, 14]
19 [2, 3, 11, 12]
dtype: object
You can also do this only in numpy and scipy, I find it faster.
from scipy.spatial.distance import pdist, squareform
import numpy
SIZE=512
N_PARTICLE=100
RADIUS = 15
VALUE_THRESHOLD = 0
coords = numpy.random.randint(0, SIZE, size=(N_PARTICLE, 2))
values = numpy.random.randint(0, 2, (N_PARTICLE))
square_dist = squareform(pdist(coords, metric='euclidean'))
condlist = []
for i, row in enumerate(square_dist[:]):
condlist.append(numpy.where((values>VALUE_THRESHOLD) & (row < RADIUS) & (row > 0))[0].tolist())
It must be a better way to do it thoughtfully.