Gabriel-p
1/22/2013 - 11:26 PM
Match two sets of on-sky coordinates to each other. I.e., find nearest neighbor of one that's in the other. Similar in purpose to IDL's
Match two sets of on-sky coordinates to each other. I.e., find nearest neighbor of one that's in the other.
Similar in purpose to IDL's spherematch, but totally different implementation.
Requires numpy and scipy.
"""
Match two sets of on-sky coordinates to each other.
I.e., find nearest neighbor of one that's in the other.
Similar in purpose to IDL's spherematch, but totally different implementation.
Requires numpy and scipy.
"""
from __future__ import division
import numpy as np
try:
from scipy.spatial import cKDTree as KDT
except ImportError:
from scipy.spatial import KDTree as KDT
def spherematch(ra1, dec1, ra2, dec2, tol=None, nnearest=1):
"""
Finds matches in one catalog to another.
Parameters
ra1 : array-like
Right Ascension in degrees of the first catalog
dec1 : array-like
Declination in degrees of the first catalog (shape of array must match `ra1`)
ra2 : array-like
Right Ascension in degrees of the second catalog
dec2 : array-like
Declination in degrees of the second catalog (shape of array must match `ra2`)
tol : float or None, optional
How close (in degrees) a match has to be to count as a match. If None,
all nearest neighbors for the first catalog will be returned.
nnearest : int, optional
The nth neighbor to find. E.g., 1 for the nearest nearby, 2 for the
second nearest neighbor, etc. Particularly useful if you want to get
the nearest *non-self* neighbor of a catalog. To do this, use:
``spherematch(ra, dec, ra, dec, nnearest=2)``
Returns
-------
idx1 : int array
Indecies into the first catalog of the matches. Will never be
larger than `ra1`/`dec1`.
idx2 : int array
Indecies into the second catalog of the matches. Will never be
larger than `ra1`/`dec1`.
ds : float array
Distance (in degrees) between the matches
"""
ra1 = np.array(ra1, copy=False)
dec1 = np.array(dec1, copy=False)
ra2 = np.array(ra2, copy=False)
dec2 = np.array(dec2, copy=False)
if ra1.shape != dec1.shape:
raise ValueError('ra1 and dec1 do not match!')
if ra2.shape != dec2.shape:
raise ValueError('ra2 and dec2 do not match!')
x1, y1, z1 = _spherical_to_cartesian(ra1.ravel(), dec1.ravel())
# this is equivalent to, but faster than just doing np.array([x1, y1, z1])
coords1 = np.empty((x1.size, 3))
coords1[:, 0] = x1
coords1[:, 1] = y1
coords1[:, 2] = z1
x2, y2, z2 = _spherical_to_cartesian(ra2.ravel(), dec2.ravel())
# this is equivalent to, but faster than just doing np.array([x1, y1, z1])
coords2 = np.empty((x2.size, 3))
coords2[:, 0] = x2
coords2[:, 1] = y2
coords2[:, 2] = z2
kdt = KDT(coords2)
if nnearest == 1:
idxs2 = kdt.query(coords1)[1]
elif nnearest > 1:
idxs2 = kdt.query(coords1, nnearest)[1][:, -1]
else:
raise ValueError('invalid nnearest ' + str(nnearest))
ds = _great_circle_distance(ra1, dec1, ra2[idxs2], dec2[idxs2])
idxs1 = np.arange(ra1.size)
if tol is not None:
msk = ds < tol
idxs1 = idxs1[msk]
idxs2 = idxs2[msk]
ds = ds[msk]
return idxs1, idxs2, ds
def _spherical_to_cartesian(ra, dec):
"""
(Private internal function)
Inputs in degrees. Outputs x,y,z
"""
rar = np.radians(ra)
decr = np.radians(dec)
x = np.cos(rar) * np.cos(decr)
y = np.sin(rar) * np.cos(decr)
z = np.sin(decr)
return x, y, z
def _great_circle_distance(ra1, dec1, ra2, dec2):
"""
(Private internal function)
Returns great circle distance. Inputs in degrees.
Uses vicenty distance formula - a bit slower than others, but
numerically stable.
"""
from numpy import radians, degrees, sin, cos, arctan2, hypot
# terminology from the Vicenty formula - lambda and phi and
# "standpoint" and "forepoint"
lambs = radians(ra1)
phis = radians(dec1)
lambf = radians(ra2)
phif = radians(dec2)
dlamb = lambf - lambs
numera = cos(phif) * sin(dlamb)
numerb = cos(phis) * sin(phif) - sin(phis) * cos(phif) * cos(dlamb)
numer = hypot(numera, numerb)
denom = sin(phis) * sin(phif) + cos(phis) * cos(phif) * cos(dlamb)
return degrees(arctan2(numer, denom))