""" Functions calculating the radial distance and radial velocity of satellites
with respect to their centrals
"""
import numpy as np
__all__ = ('radial_distance', 'radial_distance_and_velocity')
def _signed_dx(xs, xc, xperiod):
""" Calculate the 1-d distance between xs and xc,
accounting for periodic boundary conditions.
The returned result is positive when xs > xc, except when PBCs are applied,
in which case there is a sign flip.
"""
dx_uncorrected = xs - xc
abs_dx_uncorrected = np.abs(dx_uncorrected)
pbc_flip_mask = abs_dx_uncorrected > xperiod/2.
pbc_flip_sign = np.where(pbc_flip_mask, -1, 1)
original_sign = np.sign(dx_uncorrected)
abs_dx = np.where(pbc_flip_mask, np.abs(abs_dx_uncorrected - xperiod), abs_dx_uncorrected)
result = pbc_flip_sign*original_sign*abs_dx
return np.atleast_1d(result)
[docs]
def radial_distance(xs, ys, zs, xc, yc, zc, period, return_signed_1d_results=False):
""" Calculate the radial distance between the positions of a set of satellites
and their centrals, accounting for periodic boundary conditions.
If the coordinates ``xc, yc, zc`` of each satellite's central are not known in advance,
these can be computed by knowing the ``halo_hostid`` of the satellites, as shown in the Examples.
Parameters
----------
xs, ys, zs : ndarrays
Arrays of length (ngals, ) storing the xyz-coordinates of the satellites
xc, yc, zc : ndarrays
Arrays of length (ngals, ) storing the xyz-coordinates of the centrals
period : float or 3-element sequence
Length of the periodic box in each Cartesian direction.
If a single float is given, the box will be assumed to be a periodic cube.
If the points are not in a periodic box, set ``period`` to np.inf.
return_signed_1d_results : bool, optional
If set to True, the signed distances in each dimension will be returned
in addition to the radial distance. Default is False, in which case
only the radial distance will be returned
Returns
-------
drad : ndarray
Array of shape (ngals, ) storing the radial distances
Examples
--------
For demonstration purposes we will use a fake halo catalog and compute the radial distances
between all the satellites and their host halos.
>>> from halotools.sim_manager import FakeSim
>>> halocat = FakeSim()
>>> satmask = halocat.halo_table['halo_upid'] != -1
>>> satellites = halocat.halo_table[satmask]
Since Halotools catalogs do not come with the host halo position pre-computed,
we will need to calculate this information from knowledge of the ``halo_hostid`` of each satellite.
>>> from halotools.utils import crossmatch
>>> idxA, idxB = crossmatch(satellites['halo_hostid'], halocat.halo_table['halo_id'])
>>> satellites['halo_x_host_halo'] = np.nan
>>> satellites['halo_y_host_halo'] = np.nan
>>> satellites['halo_z_host_halo'] = np.nan
>>> satellites['halo_x_host_halo'][idxA] = halocat.halo_table['halo_x'][idxB]
>>> satellites['halo_y_host_halo'][idxA] = halocat.halo_table['halo_y'][idxB]
>>> satellites['halo_z_host_halo'][idxA] = halocat.halo_table['halo_z'][idxB]
>>> xs, ys, zs = satellites['halo_x'], satellites['halo_y'], satellites['halo_z']
>>> xc, yc, zc = satellites['halo_x_host_halo'], satellites['halo_y_host_halo'], satellites['halo_z_host_halo']
>>> satellites['radial_distance'] = radial_distance(xs, ys, zs, xc, yc, zc, halocat.Lbox)
"""
try:
xperiod, yperiod, zperiod = period
except TypeError:
xperiod, yperiod, zperiod = period, period, period
dx = _signed_dx(xs, xc, xperiod)
dy = _signed_dx(ys, yc, yperiod)
dz = _signed_dx(zs, zc, zperiod)
drad = np.sqrt(dx**2 + dy**2 + dz**2)
if return_signed_1d_results:
return drad, dx, dy, dz
else:
return drad
[docs]
def radial_distance_and_velocity(xs, ys, zs, vxs, vys, vzs, xc, yc, zc, vxc, vyc, vzc, period):
""" Calculate the radial distance between the positions of a set of satellites
and their centrals, accounting for periodic boundary conditions.
If the positions ``xc, yc, zc`` and velocities ``vxc, vyc, vzc``
of each satellite's central are not known in advance,
these can be computed by knowing the ``halo_hostid`` of the satellites,
as shown in the Examples.
Parameters
----------
xs, ys, zs : ndarrays
Arrays of length (ngals, ) storing the xyz-coordinates of the satellites
vxs, vys, vzs : ndarrays
Arrays of length (ngals, ) storing the xyz-velocities of the satellites
xc, yc, zc : ndarrays
Arrays of length (ngals, ) storing the xyz-coordinates of the centrals
vxc, vyc, vzc : ndarrays
Arrays of length (ngals, ) storing the xyz-velocities of the centrals
period : float or 3-element sequence
Length of the periodic box in each Cartesian direction.
If a single float is given, the box will be assumed to be a periodic cube.
If the points are not in a periodic box, set ``period`` to np.inf.
Returns
-------
drad : ndarray
Array of shape (ngals, ) storing the radial distances
vrad : ndarray
Array of shape (ngals, ) storing the radial velocities
Examples
--------
For demonstration purposes we will use a fake halo catalog and compute the radial distances
between all the satellites and their host halos.
>>> from halotools.sim_manager import FakeSim
>>> halocat = FakeSim()
>>> satmask = halocat.halo_table['halo_upid'] != -1
>>> satellites = halocat.halo_table[satmask]
Since Halotools catalogs do not come with the host halo position pre-computed,
we will need to calculate this information from knowledge of the ``halo_hostid`` of each satellite.
>>> from halotools.utils import crossmatch
>>> idxA, idxB = crossmatch(satellites['halo_hostid'], halocat.halo_table['halo_id'])
>>> satellites['halo_x_host_halo'] = np.nan
>>> satellites['halo_y_host_halo'] = np.nan
>>> satellites['halo_z_host_halo'] = np.nan
>>> satellites['halo_vx_host_halo'] = np.nan
>>> satellites['halo_vy_host_halo'] = np.nan
>>> satellites['halo_vz_host_halo'] = np.nan
>>> satellites['halo_x_host_halo'][idxA] = halocat.halo_table['halo_x'][idxB]
>>> satellites['halo_y_host_halo'][idxA] = halocat.halo_table['halo_y'][idxB]
>>> satellites['halo_z_host_halo'][idxA] = halocat.halo_table['halo_z'][idxB]
>>> satellites['halo_vx_host_halo'][idxA] = halocat.halo_table['halo_vx'][idxB]
>>> satellites['halo_vy_host_halo'][idxA] = halocat.halo_table['halo_vy'][idxB]
>>> satellites['halo_vz_host_halo'][idxA] = halocat.halo_table['halo_vz'][idxB]
>>> xs, ys, zs = satellites['halo_x'], satellites['halo_y'], satellites['halo_z']
>>> vxs, vys, vzs = satellites['halo_vx'], satellites['halo_vy'], satellites['halo_vz']
>>> xc, yc, zc = satellites['halo_x_host_halo'], satellites['halo_y_host_halo'], satellites['halo_z_host_halo']
>>> vxc, vyc, vzc = satellites['halo_vx_host_halo'], satellites['halo_vy_host_halo'], satellites['halo_vz_host_halo']
>>> drad, vrad = radial_distance_and_velocity(xs, ys, zs, vxs, vys, vzs, xc, yc, zc, vxc, vyc, vzc, halocat.Lbox)
"""
npts = len(np.atleast_1d(xs))
dvx = np.atleast_1d(vxs - vxc)
dvy = np.atleast_1d(vys - vyc)
dvz = np.atleast_1d(vzs - vzc)
drad, dx, dy, dz = radial_distance(xs, ys, zs, xc, yc, zc, period, return_signed_1d_results=True)
idx_nonzero_distance = drad > 0
num_nonzero_distance = np.count_nonzero(idx_nonzero_distance)
num_zero_distance = npts - num_nonzero_distance
vrad = np.zeros(npts)
if num_zero_distance > 0:
term1a = dvx[~idx_nonzero_distance]**2
term2a = dvy[~idx_nonzero_distance]**2
term3a = dvz[~idx_nonzero_distance]**2
vrad[~idx_nonzero_distance] = np.sqrt(term1a + term2a + term3a)
if num_nonzero_distance > 0:
term1b = dx[idx_nonzero_distance]*dvx[idx_nonzero_distance]
term2b = dy[idx_nonzero_distance]*dvy[idx_nonzero_distance]
term3b = dz[idx_nonzero_distance]*dvz[idx_nonzero_distance]
numerator = term1b + term2b + term3b
denominator = drad[idx_nonzero_distance]
vrad[idx_nonzero_distance] = numerator/denominator
return drad, vrad