使用scipy.KDTree进行快速最近邻搜索。我正在使用KDTree.query_ball_point(pnt, r=some_distance)进行搜索。
由于我的点是lat，所以搜索（some_distance）的半径值必须是十进制度（我相信）。如果我想让用户可以访问它，我希望以公里，米，英里等方式给出距离。
使用python库将公里的距离转换为十进制度值的最佳方法是什么？我正在使用numpy，scipy和PySAL玩了一下。
帮助表示感谢， 路易斯
答案 0 :(得分：3)
来自here的经典计算：
距离
这使用'hasrsine'公式来计算两点之间的大圆距离 - 即地球表面上的最短距离 - 给出点之间的“如蝇蝇”距离（忽略任何一点）山，当然！）。
半正矢 公式：
a = sin²(Δφ/2) + cos(φ1).cos(φ2).sin²(Δλ/2)
c = 2.atan2(√a, √(1−a))
d = R.c
其中φ是纬度，λ是经度，R是地球半径（平均半径= 6,371km） 请注意，角度需要以弧度为单位才能传递给trig函数！
你当然可以从航海里程和公里的定义做一个非常粗略和准备好的近似：
海里（符号M，NM或nmi）是沿着任何子午线（海平面）测量的纬度弧长约一分钟的长度单位，或赤道的经度弧长约一分钟。根据国际协议，它的确定为1,852米（约6,076英尺）。
答案 1 :(得分：0)
这可能不是直接的解决方案，而是更多的参考。我之前尝试过使用hasrsine公式，但是使用它来计算最接近的n个邻居的集合，当用于数千个点时变得无法忍受。
所以我创建了一个哈希类（或映射？），可以放入二叉树中以便快速搜索。它不适用于距离而是角度（纬度，长度）。
find函数的工作原理是找到树中最近的点，然后向上走回树，直到找到n个节点。
geocode.py：
units = [(31-q, 180.0/(2 ** q)) for q in range(32)]
def bit_sum(bits):
return sum([2**bit for bit in bits])
class gpshash(object):
def __init__(self, longitude = None, latitude = None, **kwargs):
if(kwargs):
if(kwargs.has_key("longitude ") and kwargs.has_key("latitude ")):
self.longitude = geohash(degrees=kwargs["degrees"])
self.latitude = geohash(degrees=kwargs["hash"])
else:
if(longitude == None or latitude == None):
self.longitude = geohash(degrees=0)
self.latitude = geohash(degrees=0)
else:
self.longitude = geohash(degrees=longitude)
self.latitude = geohash(degrees=latitude)
long_hash = self.longitude.bin_hash
lat_hash = self.latitude.bin_hash
hash_str = ""
if(len(long_hash) == len(lat_hash)):
for i in range(len(long_hash)):
hash_str += (long_hash[i]+lat_hash[i])
self.bin_hash = hash_str
def __str__(self):
return "%s, %s" % (str(self.longitude.hash), str(self.latitude.hash))
def __repr__(self):
return str("<gpshash long: %f lat: %f>" % (self.longitude.degrees, self.latitude.degrees))
def __eq__(self, other):
if(isinstance(self, gpshash) and isinstance(other, gpshash)):
return (((self.longitude._hash ^ other.longitude._hash) == 0) and ((self.latitude._hash ^ other.latitude._hash) == 0))
else:
return False
class geohash(object):
def __init__(self, degrees = 0, **kwargs):
if(kwargs):
if(kwargs.has_key("degrees")):
self.degrees = kwargs["degrees"] % 360
self._hash = self.encode()
elif(kwargs.has_key("hash")):
self._hash = kwargs["hash"] % ((2 << 31) - 1)
self.degrees = self.decode()
else:
self.degrees = degrees % 360
self._hash = self.encode()
def __str__(self):
return str(self.hash)
def __repr__(self):
return str("<geohash degrees: %f hash: %s>" % (self.degrees, self.hash))
def __add__(self, other):
return geohash(hash=(self._hash + other._hash))
def __sub__(self, other):
return geohash(hash=(self._hash - other._hash))
def __xor__(self, other):
return geohash(hash=(self._hash ^ other._hash))
def __eq__(self, other):
if(isinstance(self, geohash) and isinstance(other, geohash)):
return ((self._hash ^ other._hash) == 0)
else:
return False
def encode(self):
lesser = filter(lambda (bit, angle): self.degrees >= angle, units)
combined = reduce(lambda (bits, angles), (bit, angle): (bits+[bit], angles + angle) if((angles + angle) <= self.degrees) else (bits, angles), lesser, ([], 0))
return bit_sum(combined[0])
def decode(self):
lesser = filter(lambda (bit, angle): self._hash>= (2 ** bit), units)
combined = reduce(lambda (bits, angles), (bit, angle): (bits+[bit], angles + angle) if((bit_sum(bits+[bit])) <= self._hash) else (bits, angles), lesser, ([], 0))
return combined[1]
@property
def hash(self):
self._hash = self.encode()
return "%08x" % self._hash
@property
def inv_hash(self):
self._inv_hash = self.decode()
return self._inv_hash
@property
def bin_hash(self):
self._bin_hash = bin(self._hash)[2:].zfill(32)
return self._bin_hash
class gdict(object):
'''
Base Geo Dictionary
Critical Components taken from Python26\Lib\UserDict.py
'''
__slots__ = ["parent", "left", "right", "hash_type"]
hash_type = None
def __init__(self, ihash=None, iparent=None):
def set_helper(iparent, cur_hex, hex_list):
ret_bin_tree = self.__class__(None, iparent)
if(hex_list):
ret_bin_tree.set_child(cur_hex, set_helper(ret_bin_tree, hex_list[0], hex_list[1:]))
return ret_bin_tree
elif(cur_hex):
ret_bin_tree.set_child(cur_hex, ihash)
return ret_bin_tree
self.parent = self
self.left = None
self.right = None
if(iparent != None):
self.parent = iparent
if(isinstance(ihash, self.hash_type)):
ilist = list(ihash.bin_hash)
if(len(ilist) > 1):
ret_bin_tree = set_helper(self, ilist[1], ilist[2:])
if(ret_bin_tree):
self.set_child(ilist[0], ret_bin_tree)
def set_child(self, istr, ichild):
if(istr == "0"):
self.left = ichild
elif(istr == "1"):
self.right = ichild
def get_child(self, istr):
if(istr == "0"):
return self.left
elif(istr == "1"):
return self.right
else:
return ""
def __repr__(self):
def repr_print_helper(ibin_tree, fmt_str = "", depth = 1):
if(not isinstance(ibin_tree, self.__class__)):
fmt_str += "\n"
fmt_str += ("%%%ds" % (depth)) % ""
fmt_str += ibin_tree.__repr__()
else:
if((ibin_tree.left != None and ibin_tree.right == None) or (ibin_tree.left == None and ibin_tree.right != None)):
if(ibin_tree.left != None):
fmt_str += "0"
fmt_str = repr_print_helper(ibin_tree.left, fmt_str, depth + 1)
elif(ibin_tree.right != None):
fmt_str += "1"
fmt_str = repr_print_helper(ibin_tree.right, fmt_str, depth + 1)
else:
if(ibin_tree.left != None):
fmt_str += "\n"
fmt_str += ("%%%ds" % (depth - 1)) % ""
fmt_str += "0"
fmt_str = repr_print_helper(ibin_tree.left, fmt_str, depth + 1)
if(ibin_tree.right != None):
fmt_str += "\n"
fmt_str += ("%%%ds" % (depth - 1)) % ""
fmt_str += "1"
fmt_str = repr_print_helper(ibin_tree.right, fmt_str, depth + 1)
return fmt_str
return repr_print_helper(self)
def find(self, ihash, itarget = 1):
class flat(list):
pass
def find_helper_base(iparent, ibin_tree, ihash):
ret_find = None
if(isinstance(ibin_tree, self.hash_type)):
ret_find = iparent
elif(len(ihash) > 0):
if(ibin_tree.get_child(ihash[0])):
ret_find = find_helper_base(ibin_tree, ibin_tree.get_child(ihash[0]), ihash[1:])
else:
ret_find = ibin_tree
return ret_find
def up_find(iflat, iparent, ibin_tree, ibias = "0"):
if((ibin_tree != iparent) and (len(iflat) < itarget)):
if(iparent.left):
if(len(iflat) >= itarget):
return
if(iparent.left != ibin_tree):
down_find(iflat, iparent.left, ibias)
if(iparent.right):
if(len(iflat) >= itarget):
return
if(iparent.right != ibin_tree):
down_find(iflat, iparent.right, ibias)
up_find(iflat, ibin_tree.parent.parent, ibin_tree.parent, ibias)
def down_find(iflat, ibin_tree, ibias = "0"):
if(len(iflat) >= itarget):
return
elif(isinstance(ibin_tree, self.hash_type)):
iflat += [ibin_tree]
else:
if(ibias == "1"):
if(ibin_tree.left):
down_find(iflat, ibin_tree.left, ibias)
if(ibin_tree.right):
down_find(iflat, ibin_tree.right, ibias)
else:
if(ibin_tree.right):
down_find(iflat, ibin_tree.right, ibias)
if(ibin_tree.left):
down_find(iflat, ibin_tree.left, ibias)
if(isinstance(ihash, self.hash_type)):
flatter = flat()
hasher = ihash.bin_hash
base = find_helper_base(self, self.get_child(hasher[0]), hasher[1:])
if(base):
down_find(flatter, base)
bias = flatter[0].bin_hash[0]
up_find(flatter, base.parent, base, bias)
return list(flatter)
def merge(self, from_bin_tree):
def merge_helper(to_bin_tree, from_bin_tree):
if(isinstance(from_bin_tree, self.__class__)):
if(from_bin_tree.left != None):
if(to_bin_tree.left != None):
merge_helper(to_bin_tree.left, from_bin_tree.left)
else:
from_bin_tree.left.parent = to_bin_tree
to_bin_tree.left = from_bin_tree.left
elif(from_bin_tree.right != None):
if(to_bin_tree.right != None):
merge_helper(to_bin_tree.right, from_bin_tree.right)
else:
from_bin_tree.right.parent = to_bin_tree
to_bin_tree.right = from_bin_tree.right
merge_helper(self, from_bin_tree)
class geodict(gdict):
'''
Geo Dictionary
'''
hash_type = geohash
def __init__(self, ihash=None, iparent=None):
gdict.__init__(self, ihash, iparent)
class gpsdict(gdict):
'''
GPS Dictionary
'''
hash_type = gpshash
def __init__(self, ihash=None, iparent=None):
gdict.__init__(self, ihash, iparent)
if(__name__ == "__main__"):
gpses = \
[
gpshash(90, 90),
gpshash(68, 24),
gpshash(144, 60),
gpshash(48, 91),
gpshash(32, 105),
gpshash(32, 150),
gpshash(167, 20),
gpshash(49, 116),
gpshash(81, 82),
gpshash(63, 79),
gpshash(129, 76)
]
base_dict = gpsdict()
for cur_hash in gpses:
base_dict.merge(gpsdict(cur_hash ))
print "All locations added:"
print base_dict
print ""
print "Trying to find 3 nearest points to:"
to_find = gpshash(60, 20)
print to_find.__repr__()
found = base_dict.find(to_find, 3)
print ""
print "Found the following:"
for x in found:
print x.__repr__()