relative_positions_and_velocities

halotools.mock_observables.relative_positions_and_velocities(x1, x2, period=None, **kwargs)

Return the vector pointing from x2 towards x1, that is, x1 - x2, accounting for periodic boundary conditions.

If keyword arguments v1 and v2 are passed in, additionally return the velocity v1 with respect to v2, with sign convention such that positive (negative) values correspond to receding (approaching) points.

Parameters:

x1array

1-d array of length Npts. If period is not None, all values must be contained in [0, Lbox)

x2array

1-d array of length Npts. If period is not None, all values must be contained in [0, Lbox)

periodfloat, optional

Size of the periodic box. Default is None for non-periodic case.

Returns:

xrelarray

1-d array of length Npts storing x1 - x2. If x1 > x2 and abs(x1 - x2) > period/2, the sign of d will be negative.

vrelarray, optional

1-d array of length Npts storing v1 relative to v2. Only returned if v1 and v2 are passed in.

Examples

>>> Lbox = 250.0
>>> x1 = 1.
>>> x2 = 249.
>>> result = relative_positions_and_velocities(x1, x2, period=Lbox)
>>> assert np.isclose(result, 2)

>>> result = relative_positions_and_velocities(x1, x2, period=None)
>>> assert np.isclose(result, -248)

>>> npts = 100
>>> x1 = np.random.uniform(0, Lbox, npts)
>>> x2 = np.random.uniform(0, Lbox, npts)
>>> result = relative_positions_and_velocities(x1, x2, period=Lbox)

Now let’s frame this result in terms of a physically motivated example. Suppose we have a central galaxy with position xc and velocity vc, and a satellite galaxy with position xs and velocity vs. We can calculate the vector pointing from the central to the satellite, as well as the satellites’s host-centric velocity:

>>> xcen, vcen = 249.9, 100
>>> xsat, vsat = 0.1, -300
>>> xrel, vrel = relative_positions_and_velocities(xsat, xcen, v1=vsat, v2=vcen, period=Lbox)
>>> assert np.isclose(xrel, +0.2)
>>> assert np.isclose(vrel, -400)

>>> xcen, vcen = 0.1, 100
>>> xsat, vsat = 249.9, -300
>>> xrel, vrel = relative_positions_and_velocities(xsat, xcen, v1=vsat, v2=vcen, period=Lbox)
>>> assert np.isclose(xrel, -0.2)
>>> assert np.isclose(vrel, +400)