I have an input of 36,742 points which means if I wanted to calculate the lower triangle of a distance matrix (using the vincenty approximation) I would need to generate 36,742*36,741*0.5 = 1,349,974,563 distances.
I want to keep the pair combinations which are within 50km of each other. My current set-up is as follows
shops= [[id,lat,lon]...]
def lower_triangle_mat(points):
for i in range(len(shops)-1):
for j in range(i+1,len(shops)):
yield [shops[i],shops[j]]
def return_stores_cutoff(points,cutoff_km=0):
below_cut = []
counter = 0
for x in lower_triangle_mat(points):
dist_km = vincenty(x[0][1:3],x[1][1:3]).km
counter += 1
if counter % 1000000 == 0:
print("%d out of %d" % (counter,(len(shops)*len(shops)-1*0.5)))
if dist_km <= cutoff_km:
below_cut.append([x[0][0],x[1][0],dist_km])
return below_cut
start = time.clock()
stores = return_stores_cutoff(points=shops,cutoff_km=50)
print(time.clock() - start)
This will obviously take hours and hours. Some possibilities I was thinking of:
- Use numpy to vectorise these calculations rather than looping through
- Use some kind of hashing to get a quick rough-cut off (all stores within 100km) and then only calculate accurate distances between those stores
- Instead of storing the points in a list use something like a quad-tree but I think that only helps with the ranking of close points rather than actual distance -> so I guess some kind of geodatabase
- I can obviously try the haversine or project and use euclidean distances, however I am interested in using the most accurate measure possible
- Make use of parallel processing (however I was having a bit of difficulty coming up how to cut the list to still get all the relevant pairs).
Edit: I think geohashing is definitely needed here - an example from:
from geoindex import GeoGridIndex, GeoPoint
geo_index = GeoGridIndex()
for _ in range(10000):
lat = random.random()*180 - 90
lng = random.random()*360 - 180
index.add_point(GeoPoint(lat, lng))
center_point = GeoPoint(37.7772448, -122.3955118)
for distance, point in index.get_nearest_points(center_point, 10, 'km'):
print("We found {0} in {1} km".format(point, distance))
However, I would also like to vectorise (instead of loop) the distance calculations for the stores returned by the geo-hash.
Edit2: Pouria Hadjibagheri - I tried using lambda and map:
# [B]: Mapping approach
lwr_tr_mat = ((shops[i],shops[j]) for i in range(len(shops)-1) for j in range(i+1,len(shops)))
func = lambda x: (x[0][0],x[1][0],vincenty(x[0],x[1]).km)
# Trying to see if conditional statements slow this down
func_cond = lambda x: (x[0][0],x[1][0],vincenty(x[0],x[1]).km) if vincenty(x[0],x[1]).km <= 50 else None
start = time.clock()
out_dist = list(map(func,lwr_tr_mat))
print(time.clock() - start)
start = time.clock()
out_dist = list(map(func_cond,lwr_tr_mat))
print(time.clock() - start)
And they were all around 61 seconds (I restricted number of stores to 2000 from 32,000). Perhaps I used map incorrectly?