FoFGroups¶

class
halotools.mock_observables.
FoFGroups
(positions, b_perp, b_para, period=None, Lbox=None, num_threads=1)[source] [edit on github]¶ Bases:
object
Friendsoffriends (FoF) groups class.
Build FoF groups in redshift space assuming the distant observer approximation.
The first two dimensions (x, y) define the plane for perpendicular distances. The third dimension (z) is used for lineofsight distances.
See the Formatting your xyz coordinates for Mock Observables calculations documentation page for instructions on how to transform your coordinate position arrays into the format accepted by the
positions
argument.See also Galaxy Catalog Analysis Example: Galaxy group identification.
Parameters: positions : array_like
Npts x 3 numpy array containing 3D positions of galaxies. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.
b_perp : float
Maximum linking length in the perpendicular direction, normalized to the mean separation between galaxies.
b_para : float
Maximum linking length in the parallel direction, normalized to the mean separation between galaxies.
period : array_like, optional
Length3 sequence defining the periodic boundary conditions in each dimension. If you instead provide a single scalar, Lbox, period is assumed to be the same in all Cartesian directions. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.
Lbox : array_like, optional
length 3 array defining boundaries of the simulation box.
num_threads : int, optional
Number of threads to use in calculation, where parallelization is performed using the python
multiprocessing
module. Default is 1 for a purely serial calculation, in which case a multiprocessing Pool object will never be instantiated. A string ‘max’ may be used to indicate that the pair counters should use all available cores on the machine.Examples
In this example we will populate the
FakeSim
with an HODstyle model to demonstrate how to use the groupfinder.>>> from halotools.sim_manager import FakeSim >>> halocat = FakeSim()
>>> from halotools.empirical_models import PrebuiltHodModelFactory >>> model = PrebuiltHodModelFactory('zheng07', threshold = 22) >>> model.populate_mock(halocat)
Now that we have a mock galaxy catalog, we will extract the 3d coordinates of the galaxy positions and place this information into the shape of the multid array expected by the
positions
argument ofFoFGroups
using thereturn_xyz_formatted_array
function.>>> from halotools.mock_observables import return_xyz_formatted_array
Note that
FoFGroups
is based on 2+1 dimensional positions, with the zdimension having a separate linking length from the xyplane. To make our example more realistic, we will apply the redshiftspace distortions to the zcoordinate when constructing thepositions
array.>>> x = model.mock.galaxy_table['x'] >>> y = model.mock.galaxy_table['y'] >>> z = model.mock.galaxy_table['z'] >>> vz = model.mock.galaxy_table['vz']
>>> positions = return_xyz_formatted_array(x, y, z, velocity = vz, velocity_distortion_dimension = 'z', period=halocat.Lbox)
The
b_perp
andb_para
arguments ofFoFGroups
control the linking lengths for the groupfinding. The values passed for these variables are assumed to be in units of the mean number density of the input points, so that if you want your FoF linking length to be, say, 0.15 times the mean number density, then you should setb_perp
to 0.15. Here we adopt the convention given in Berlind et al. (2006) and setb_perp
to 0.14 andb_para
to 0.75.>>> b_perp, b_para = (0.14,0.75) >>> groups = FoFGroups(positions, b_perp, b_para, period=halocat.Lbox)
Now that groups have been identified, we can create a new column of our
galaxy_table
storing the group ID that each galaxy belongs to.>>> model.mock.galaxy_table['fof_group_ID'] = groups.group_ids
At this point, we are now in a position to calculate a large variety of group aggregation statistics with the
fof_group_ID
as our grouping key. Thegroup_member_generator
is designed for exactly such calculations. See Galaxy Catalog Analysis Example: Galaxy group identification for a tutorial showing how to use this generator to analyze galaxy groups.Attributes Summary
group_ids
Determine integer IDs for groups. n_groups
Calculate the total number of groups, including 1member groups Methods Summary
create_graph
()Create graph from FoF sparse matrix (requires igraph package). get_betweenness
()Calculate the ‘betweenness’ of each galaxy vertex (requires igraph package). get_degree
()Calculate the ‘degree’ of each galaxy vertex (requires igraph package). get_edge_lengths
()Return the length of all edges (requires igraph package). get_edges
()Return all edges of the graph (requires igraph package). get_multiplicity
()Return the multiplicity of galaxies’ group (requires igraph package). Attributes Documentation

group_ids
¶ Determine integer IDs for groups.
Each member of a group is assigned a unique integer ID that it shares with all connected group members.
Returns: group_ids : np.array
array of group IDs for each galaxy

n_groups
¶ Calculate the total number of groups, including 1member groups
Returns: N_groups: int
number of distinct groups
Methods Documentation

create_graph
()[source] [edit on github]¶ Create graph from FoF sparse matrix (requires igraph package).

get_betweenness
()[source] [edit on github]¶ Calculate the ‘betweenness’ of each galaxy vertex (requires igraph package).
Returns: betweeness : np.array
the ‘betweenness’ of galaxies in groups

get_degree
()[source] [edit on github]¶ Calculate the ‘degree’ of each galaxy vertex (requires igraph package).
Returns: degree : np.array
the ‘degree’ of galaxies in groups

get_edge_lengths
()[source] [edit on github]¶ Return the length of all edges (requires igraph package).
Returns: lengths: np.array
The length of an ‘edge’ econnnecting galaxies, i.e. distance between galaxies.
Notes
The length is caclulated as:
\[L_{\rm edge} = \sqrt{r_{\perp}^2 + r_{\parallel}^2},\]where \(r_{\perp}\) and \(r_{\parallel}\) are the perendicular and parallel distance between galaixes.

get_edges
()[source] [edit on github]¶ Return all edges of the graph (requires igraph package).
Returns: edges: np.ndarray
N_edges x 2 array of vertices that are connected by an edge. The vertices are indicated by their index.

get_multiplicity
()[source] [edit on github]¶ Return the multiplicity of galaxies’ group (requires igraph package).
