def axes_correlated_with_input_vector(input_vectors, p=0., seed=None):
r"""
Calculate a list of 3d unit-vectors whose orientation is correlated
with the orientation of `input_vectors`.
Parameters
----------
input_vectors : ndarray
Numpy array of shape (npts, 3) storing a list of 3d vectors defining the
preferred orientation with which the returned vectors will be correlated.
Note that the normalization of `input_vectors` will be ignored.
p : ndarray, optional
Numpy array with shape (npts, ) defining the strength of the correlation
between the orientation of the returned vectors and the z-axis.
Default is zero, for no correlation.
Positive (negative) values of `p` produce galaxy principal axes
that are statistically aligned with the positive (negative) z-axis;
the strength of this alignment increases with the magnitude of p.
When p = 0, galaxy axes are randomly oriented.
seed : int, optional
Random number seed used to choose a random orthogonal direction
Returns
-------
unit_vectors : ndarray
Numpy array of shape (npts, 3)
"""
input_unit_vectors = normalized_vectors(input_vectors)
assert input_unit_vectors.shape[1] == 3
npts = input_unit_vectors.shape[0]
z_correlated_axes = axes_correlated_with_z(p, seed)
z_axes = np.tile((0, 0, 1), npts).reshape((npts, 3))
angles = angles_between_list_of_vectors(z_axes, input_unit_vectors)
rotation_axes = vectors_normal_to_planes(z_axes, input_unit_vectors)
matrices = rotation_matrices_from_angles(angles, rotation_axes)
return rotate_vector_collection(matrices, z_correlated_axes)
def mc_unit_sphere(self, Npts, **kwargs):
r"""
Returns Npts anisotropically distributed points on the unit sphere.
Parameters
----------
Npts : int
Number of 3d points to generate
seed : int, optional
Random number seed used in the Monte Carlo realization.
Default is None, which will produce stochastic results.
Returns
-------
x, y, z : array_like
Length-Npts arrays of the coordinate positions.
"""
seed = kwargs.get('seed', None)
if 'table' in kwargs:
table = kwargs['table']
try:
b_to_a = table['halo_b_to_a']
except KeyError:
b_to_a = 1.0
try:
c_to_a = table['halo_c_to_a']
except KeyError:
c_to_a = 1.0
try:
halo_axisA_x = table['halo_axisA_x']
halo_axisA_y = table['halo_axisA_y']
halo_axisA_z = table['halo_axisA_z']
except KeyError:
with NumpyRNGContext(seed):
v = random_unit_vectors_3d(len(table))
halo_axisA_x = v[:,0]
halo_axisA_y = v[:,1]
halo_axisA_z = v[:,2]
try:
halo_axisC_x = table['halo_axisC_x']
halo_axisC_y = table['halo_axisC_y']
halo_axisC_z = table['halo_axisC_z']
except KeyError:
with NumpyRNGContext(seed):
v = random_unit_vectors_3d(len(table))
halo_axisC_x = v[:,0]
halo_axisC_y = v[:,1]
halo_axisC_z = v[:,2]
else:
try:
b_to_a = np.atleast_1d(kwargs['b_to_a'])
except KeyError:
b_to_a = 1.0
try:
c_to_a = np.atleast_1d(kwargs['c_to_a'])
except KeyError:
c_to_a = 1.0
try:
halo_axisA_x = np.atleast_1d(kwargs['halo_axisA_x'])
halo_axisA_y = np.atleast_1d(kwargs['halo_axisA_y'])
halo_axisA_z = np.atleast_1d(kwargs['halo_axisA_z'])
except KeyError:
with NumpyRNGContext(seed):
v = random_unit_vectors_3d(1)
halo_axisC_x = v[:,0]
halo_axisC_y = v[:,1]
halo_axisC_z = v[:,2]
try:
halo_axisC_x = np.atleast_1d(kwargs['halo_axisC_x'])
halo_axisC_y = np.atleast_1d(kwargs['halo_axisC_y'])
halo_axisC_z = np.atleast_1d(kwargs['halo_axisC_z'])
except KeyError:
with NumpyRNGContext(seed):
v = random_unit_vectors_3d(len(halo_axisA_x))
halo_axisC_x = v[:,0]
halo_axisC_y = v[:,1]
halo_axisC_z = v[:,2]
v1 = np.vstack((halo_axisA_x, halo_axisA_y, halo_axisA_z)).T
v3 = np.vstack((halo_axisC_x, halo_axisC_y, halo_axisC_z)).T
v2 = np.cross(v1,v3)
with NumpyRNGContext(seed):
phi = np.random.uniform(0, 2*np.pi, Npts)
uran = np.random.rand(Npts)*2 - 1
cos_t = uran
sin_t = np.sqrt((1.-cos_t*cos_t))
b_to_a, c_to_a = self.anisotropy_bias_response(b_to_a, c_to_a)
c_to_b = c_to_a/b_to_a
# temporarily use x-axis as the major axis
x = 1.0/c_to_a*sin_t * np.cos(phi)
y = 1.0/c_to_b*sin_t * np.sin(phi)
z = cos_t
x_correlated_axes = np.vstack((x, y, z)).T
x_axes = np.tile((1, 0, 0), Npts).reshape((Npts, 3))
major_axes = v1
matrices = rotation_matrices_from_basis(v1,v2,v3)
# rotate x-axis into the major axis
#angles = angles_between_list_of_vectors(x_axes, major_axes)
#rotation_axes = vectors_normal_to_planes(x_axes, major_axes)
#matrices = rotation_matrices_from_angles(angles, rotation_axes)
correlated_axes = rotate_vector_collection(matrices, x_correlated_axes)
#correlated_axes = x_correlated_axes
return correlated_axes[:, 0], correlated_axes[:, 1], correlated_axes[:, 2]
def assign_positions(self, **kwargs):
"""
assign satellite positions based on subhalo radial positions and random angular positions.
"""
if 'table' in kwargs.keys():
table = kwargs['table']
halo_x = table['halo_x']
halo_y = table['halo_y']
halo_z = table['halo_z']
halo_hostid = table['halo_hostid']
halo_id = table['halo_id']
b_to_a = table['halo_b_to_a']
c_to_a = table['halo_c_to_a']
halo_axisA_x = table['halo_axisA_x']
halo_axisA_y = table['halo_axisA_y']
halo_axisA_z = table['halo_axisA_z']
halo_axisC_x = table['halo_axisC_x']
halo_axisC_y = table['halo_axisC_y']
halo_axisC_z = table['halo_axisC_z']
concentration = table['halo_nfw_conc']
rvir = table['halo_rvir']
try:
Lbox = kwargs['Lbox']
except KeyError:
Lbox = self._Lbox
else:
halo_x = kwargs['halo_x']
halo_y = kwargs['halo_y']
halo_z = kwargs['halo_z']
halo_hostid = kwargs['halo_hostid']
halo_id = kwargs['halo_id']
b_to_a = kwargs['halo_b_to_a']
c_to_a = kwargs['halo_c_to_a']
halo_axisA_x = kwargs['halo_axisA_x']
halo_axisA_y = kwargs['halo_axisA_y']
halo_axisA_z = kwargs['halo_axisA_z']
halo_axisC_x = kwargs['halo_axisC_x']
halo_axisC_y = kwargs['halo_axisC_y']
halo_axisC_z = kwargs['halo_axisC_z']
concentration = kwargs['halo_nfw_conc']
rvir = tabel['halo_rvir']
try:
Lbox = kwargs['Lbox']
except KeyError:
Lbox = self._Lbox
Npts = len(halo_x)
# get host halo properties
inds1, inds2 = crossmatch(halo_hostid, halo_id)
# some sub-haloes point to a host that does not exist
no_host = ~np.in1d(halo_hostid, halo_id)
if np.sum(no_host) > 0:
msg = ("There are {0} sub-haloes with no host halo.".format(
np.sum(no_host)))
warn(msg)
host_halo_concentration = np.zeros(Npts)
host_halo_concentration[inds1] = concentration[inds2]
host_halo_rvir = np.zeros(Npts)
host_halo_rvir[inds1] = rvir[inds2]
host_b_to_a = np.zeros(Npts)
host_b_to_a[inds1] = b_to_a[inds2]
host_c_to_a = np.zeros(Npts)
host_c_to_a[inds1] = c_to_a[inds2]
major_axis = np.vstack((halo_axisA_x, halo_axisA_y, halo_axisA_z)).T
minor_axis = np.vstack((halo_axisC_x, halo_axisC_y, halo_axisC_z)).T
inter_axis = np.cross(major_axis, minor_axis)
host_major_axis = np.zeros((Npts, 3))
host_inter_axis = np.zeros((Npts, 3))
host_minor_axis = np.zeros((Npts, 3))
host_major_axis[inds1] = major_axis[inds2]
host_inter_axis[inds1] = inter_axis[inds2]
host_minor_axis[inds1] = minor_axis[inds2]
# host x,y,z-position
halo_x[inds1] = halo_x[inds2]
halo_y[inds1] = halo_y[inds2]
halo_z[inds1] = halo_z[inds2]
# host halo centric positions
phi = np.random.uniform(0, 2 * np.pi, Npts)
uran = np.random.rand(Npts) * 2 - 1
cos_t = uran
sin_t = np.sqrt((1. - cos_t * cos_t))
b_to_a, c_to_a = self.anisotropy_bias_response(host_b_to_a,
host_c_to_a)
c_to_b = c_to_a / b_to_a
# temporarily use x-axis as the major axis
x = 1.0 / c_to_a * sin_t * np.cos(phi)
y = 1.0 / c_to_b * sin_t * np.sin(phi)
z = cos_t
x_correlated_axes = np.vstack((x, y, z)).T
x_axes = np.tile((1, 0, 0), Npts).reshape((Npts, 3))
matrices = rotation_matrices_from_basis(host_major_axis,
host_inter_axis,
host_minor_axis)
# rotate x-axis into the major axis
#angles = angles_between_list_of_vectors(x_axes, major_axes)
#rotation_axes = vectors_normal_to_planes(x_axes, major_axes)
#matrices = rotation_matrices_from_angles(angles, rotation_axes)
correlated_axes = rotate_vector_collection(matrices, x_correlated_axes)
x, y, z = correlated_axes[:, 0], correlated_axes[:,
1], correlated_axes[:,
2]
nfw = NFWPhaseSpace(conc_mass_model='direct_from_halo_catalog', )
dimensionless_radial_distance = nfw._mc_dimensionless_radial_distance(
host_halo_concentration)
x *= dimensionless_radial_distance
y *= dimensionless_radial_distance
z *= dimensionless_radial_distance
x *= host_halo_rvir
y *= host_halo_rvir
z *= host_halo_rvir
a = 1
b = b_to_a * a
c = c_to_a * a
T = (c**2 - b**2) / (c**2 - a**2)
q = b / a
s = c / a
x *= np.sqrt(q * s)
y *= np.sqrt(q * s)
z *= np.sqrt(q * s)
# host-halo centric radial distance
r = np.sqrt(x * x + y * y + z * z)
# move back into original cordinate system
xx = halo_x + x
yy = halo_y + y
zz = halo_z + z
xx[no_host] = halo_x[no_host]
yy[no_host] = halo_y[no_host]
zz[no_host] = halo_z[no_host]
# account for PBCs
xx, yy, zz = wrap_coordinates(xx, yy, zz, Lbox)
if 'table' in kwargs.keys():
# assign satellite galaxy positions
try:
mask = (table['gal_type'] == 'satellites')
except KeyError:
mask = np.array([True] * len(table))
msg = (
"`gal_type` not indicated in `table`.",
"The orientation is being assigned for all galaxies in the `table`."
)
print(msg)
table['x'] = halo_x * 1.0
table['y'] = halo_y * 1.0
table['z'] = halo_z * 1.0
table['x'][mask] = xx[mask]
table['y'][mask] = yy[mask]
table['z'][mask] = zz[mask]
table['r'] = 0.0
table['r'][mask] = r[mask]
table['halo_x'][mask] = halo_x[mask]
table['halo_y'][mask] = halo_y[mask]
table['halo_z'][mask] = halo_z[mask]
return table
else:
x = xx
y = yy
z = zz
return np.vstack((x, y, z)).T
def assign_positions(self, **kwargs):
"""
assign satellite positions based on subhalo radial positions and random angular positions.
"""
if 'table' in kwargs.keys():
table = kwargs['table']
halo_x = table['halo_x']
halo_y = table['halo_y']
halo_z = table['halo_z']
halo_axisA_x = table['halo_axisA_x']
halo_axisA_y = table['halo_axisA_y']
halo_axisA_z = table['halo_axisA_z']
halo_hostid = table['halo_hostid']
halo_id = table['halo_id']
try:
Lbox = kwargs['Lbox']
except KeyError:
Lbox = self._Lbox
else:
halo_x = kwargs['halo_x']
halo_y = kwargs['halo_y']
halo_z = kwargs['halo_z']
halo_hostid = kwargs['halo_hostid']
halo_id = kwargs['halo_id']
try:
Lbox = kwargs['Lbox']
except KeyError:
Lbox = self._Lbox
# get subhalo positions
x = halo_x * 1.0
y = halo_y * 1.0
z = halo_z * 1.0
# get host halo positions
inds1, inds2 = crossmatch(halo_hostid, halo_id)
# x-position
halo_x[inds1] = halo_x[inds2]
# y-position
halo_y[inds1] = halo_y[inds2]
# z-position
halo_z[inds1] = halo_z[inds2]
# get host halo orientation
host_halo_axisA_x = halo_axisA_x
host_halo_axisA_x[inds1] = halo_axisA_x[inds2]
host_halo_axisA_y = halo_axisA_y
host_halo_axisA_y[inds1] = halo_axisA_y[inds2]
host_halo_axisA_z = halo_axisA_z
host_halo_axisA_z[inds1] = halo_axisA_z[inds2]
host_halo_mjor_axes = np.vstack(
(halo_axisA_x, halo_axisA_y, halo_axisA_z)).T
# calculate radial positions
vec_r, r = radial_distance(x, y, z, halo_x, halo_y, halo_z, Lbox)
# rotate radial vectors arond halo major axis
N = len(x)
rot_angles = np.random.uniform(0.0, 2 * np.pi, N)
rot_axes = host_halo_mjor_axes
rot_m = rotation_matrices_from_angles(rot_angles, rot_axes)
new_vec_r = rotate_vector_collection(rot_m, vec_r)
xx = new_vec_r[:, 0]
yy = new_vec_r[:, 1]
zz = new_vec_r[:, 2]
# move back into original cordinate system
xx = halo_x + xx
yy = halo_y + yy
zz = halo_z + zz
# account for PBCs
mask = (xx < 0.0)
xx[mask] = xx[mask] + Lbox[0]
mask = (xx > Lbox[0])
xx[mask] = xx[mask] - Lbox[0]
mask = (yy < 0.0)
yy[mask] = yy[mask] + Lbox[1]
mask = (yy > Lbox[1])
yy[mask] = yy[mask] - Lbox[1]
mask = (zz < 0.0)
zz[mask] = zz[mask] + Lbox[2]
mask = (zz > Lbox[2])
zz[mask] = zz[mask] - Lbox[2]
if 'table' in kwargs.keys():
# assign satellite galaxy positions
try:
mask = (table['gal_type'] == 'satellites')
except KeyError:
mask = np.array([True] * len(table))
msg = (
"`gal_type` not indicated in `table`.",
"The orientation is being assigned for all galaxies in the `table`."
)
print(msg)
table['x'] = halo_x * 1.0
table['y'] = halo_y * 1.0
table['z'] = halo_z * 1.0
table['x'][mask] = xx[mask]
table['y'][mask] = yy[mask]
table['z'][mask] = zz[mask]
table['halo_x'][mask] = halo_x[mask]
table['halo_y'][mask] = halo_y[mask]
table['halo_z'][mask] = halo_z[mask]
return table
else:
x = xx
y = yy
z = zz
return np.vstack((x, y, z)).T
def vectors_between_list_of_vectors(x, y, p):
r"""
Starting from two input lists of vectors, return a list of unit-vectors
that lie in the same plane as the corresponding input vectors,
and where the input `p` controls the angle between
the returned vs. input vectors.
Parameters
----------
x : ndarray
Numpy array of shape (npts, 3) storing a collection of 3d vectors
Note that the normalization of `x` will be ignored.
y : ndarray
Numpy array of shape (npts, 3) storing a collection of 3d vectors
Note that the normalization of `y` will be ignored.
p : ndarray
Numpy array of shape (npts, ) storing values in the closed interval [0, 1].
For values of `p` equal to zero, the returned vectors will be
exactly aligned with the input `x`; when `p` equals unity, the returned
vectors will be aligned with `y`.
Returns
-------
v : ndarray
Numpy array of shape (npts, 3) storing a collection of 3d unit-vectors
lying in the plane spanned by `x` and `y`. The angle between `v` and `x`
will be equal to :math:`p*\theta_{\rm xy}`.
Examples
--------
Create two set of 3D vectors
>>> npts = int(1e4)
>>> x = np.random.random((npts, 3))
>>> y = np.random.random((npts, 3))
Define the parameter `p` fpr each pair of vectors
>>> p = np.random.uniform(0, 1, npts)
Find a set of vectors between the two sets
>>> v = vectors_between_list_of_vectors(x, y, p)
Note that `p` determines how close the new vector is to
the corresponding vectors in the original sets.
>>> angles_xy = angles_between_list_of_vectors(x, y)
>>> angles_xp = angles_between_list_of_vectors(x, v)
>>> assert np.allclose(angles_xy*p, angles_xp)
"""
assert np.all(p >= 0), "All values of p must be non-negative"
assert np.all(p <= 1), "No value of p can exceed unity"
z = vectors_normal_to_planes(x, y)
theta = angles_between_list_of_vectors(x, y)
angles = p * theta
rotation_matrices = rotation_matrices_from_angles(angles, z)
return normalized_vectors(rotate_vector_collection(rotation_matrices, x))
