def pecZ(x, y, z, vx, vy, vz, z_hubb, obs=np.zeros(3)):
'''
This function calculates peculiar z_hubbs for n-body simulation objects, given
their comoving position and velocity, and returns some other useful products of the calculation.
:param x: x-position for each object, in form [x1, x2,... xn]
:param y: y-position for each object, in form of param x
:param z: z-position for each object, in form of param x
:param vx: x-velocity for each object, in form [vx1, vx2,... vxn]
:param vy: y-velocity for each object, in form of param vx
:param vz: z-velocity for each object, in form of param vx
:param z_hubb: cosmological redshifts for each object, in form [z1, z2,... zn]
:param obs: The coordinates of the observer, in form [x, y, z]
:return: - the peculair z_hubb in each object in form of param redshift
- the total observed z_hubb (cosmological+peculiar)
- the peculiar velocity of each object, in the form of param vx, where negative
velocities are toward the observer, in comoving km/s
- the line-of-sight velocity, in proper km/s (peculiar velocity * a)
- distance from observer to object in comoving Mpc
- distance from observer to object in kpc proper (comoving dist * a)
- distorted distance from observer to object in Mpc proper
'''
# get relative position (r vector) of and position unit vector toward each object
r_rel = np.array([x, y, z]).T - obs
r_rel_mag = np.linalg.norm(r_rel, axis=1)
r_rel_hat = np.divide(r_rel, np.array([r_rel_mag]).T)
# dot velocity vectors with relative position unit vector to get peculiar velocity
v = np.array([vx, vy, vz]).T
v_mag = np.linalg.norm(v, axis=1)
v_pec = npm.inner1d(v, r_rel_hat)
# find total and peculiar z_hubb (full relativistic expression)
c = const.c.value / 1000
z_pec = np.sqrt((1 + v_pec / c) / (1 - v_pec / c)) - 1
z_tot = (1 + z_hubb) * (1 + z_pec) - 1
# find the distorted distance from appliying Hubble's law using the new z_tot z_hubbs
a = 1 / (1 + z_hubb)
r_dist = r_rel_mag + v_pec / 100. / cosmo.efunc(z_hubb) / a
#pdb.set_trace()
return z_pec, z_tot, v_pec, v_pec * a, r_rel_mag, r_rel_mag * a, r_dist
