GetMST

class GetMST([x=None, y=None, z=None, phi=None, theta=None, ra=None, dec=None, r=None, units='degree', do_prints=False])

A class for constructing and analysing the minimum spanning tree (MST). Input the node positions of a given data set to initiate the class.

Parameters:

• x (array) – Cartesian coordinates.

• y (array) – Cartesian coordinates.

• z (array) – Cartesian coordinates.

• phi (array) – Longitude coordinates.

• theta (array) – Latitude coordinates.

• ra (array) – Celestial longitude coordinates.

• dec (array) – Celestial latitude coordinates.

• r (array) – Radial distance.

• units (str) – ‘degree’ or ‘radians’ - the units of the celestial coordinates.

• do_prints (bool) – Tells the functions whether it is okay for it to print out statements.

Note

The default of all of the input parameters are set to None such that an internal parameter _mode of the MST can be set based on the input parameters. Supply:

• x and y - for 2D cartesian coordinate. _mode='2D'

• x, y and z - for 3D cartesian coordinates. _mode='3D'

• phi and theta - for tomographic coordinates. _mode='tomographic'

• phi, theta and r - for spherical polar coordinates. _mode='spherical polar'

• ra and dec - for celestial coordinates. _mode='tomographic celestial'

• ra, dec and r - for spherical celestial polar coordinates. _mode='spherical polar celestial'

define_k_neighbours(k_neighbours)

Sets the k_neighbours value. This is automatically set to 20 if this is not called.

Parameters:

k_neighbours (int) – The number of nearest neighbours to consider when creating the k-nearest neighbour graph.

scale_cut(scale_cut_length)

Defines the scale cut parameters if a scaling cut is required.

Parameters:

scale_cut_length (float) – The minimum allowed length in the k_nearest_neighbour_graph.

construct_mst()

Constructs the minimum spanning tree from the input data set.

get_degree()

Find the degree of each node in the constructed MST.

get_mean_degree_for_edges()

Finds the mean degree for each edge.

get_degree_for_edges()

Gets the degree at either end of an edge.

get_branches([box_size=None, sub_divisions=1])

Find the branches of a MST.

Parameters:

• box_size (float) – The size of the ‘2D’ or ‘3D’ box. Of course, this is only applicable if the data was constructed inside a box.

• sub_divisions (int) – The number of divisions used to divide the data set in each axis. Used for speeding up the branch finding algorithm when using many points (> 100000).

get_branch_edge_count()

Finds the number of edges included in each branch.

get_branch_shape()

Finds the shape of all branches. This is simply the straight line distance, between the two ends, divided by the branch length.

get_stats_vs_density(dx, box_size)

Computes the relation between the density contrast and the MST statistics.

Parameters:

• dx (float) – The length of the individual cells, that the full box will be divided into, across one dimension.

• box_size (float) – The length of the 2D or 3D box across one axis.

Returns:

a tuple of the following evaluated in each cell:

• density (array)

• mean_degree (array)

• mean_edge_length (array)

• mean_branch_length (array)

• mean_branch_shape (array)

To do:

Add support for data sets given in ‘tomographic’ and ‘spherical polar’ coordinates.

output_stats([include_index=False])

Outputs the MST statistics.

Parameters:

include_index (bool) – If True will output the indexes of the nodes for each edge and the indexes of edges in each branch.

Returns:

A tuple of the following:

• degree (array) – The degree of each node in the MST.

• edge_length (array) – The length of each edge in the MST.

• branch_length (array) – The length of branches in the MST.

• branch_shape (array) – The shape of branches in the MST.

• edge_index (array) – [Optional] A 2 dimensional array, where the first nested array shows the indexes for the nodes on one end of the edge and the second shows the other node.

• branch_index (array) – [Optional] A list of branches, where each branch is given as a list of the indexes of the member edges.

get_stats([include_index=False, sub_divisions=1, k_neighbours=None, scale_cut_length=0., partitions=1])

Computes the MST and outputs the statistics.

Parameters:

• include_index (bool) – If True will output the indexes of the nodes for each edge and the indexes of edges in each branch.

• sub_divisions (int) – The number of divisions used to divide the data set in each axis. Used for speeding up the branch finding algorithm when using many points (> 100000).

• k_neighbours (int) – The number of nearest neighbours to consider when creating the k-nearest neighbour graph.

• scale_cut_length (float) – The minimum allowed length in the k_nearest_neighbour_graph.

• partitions (int) – Number of partitions to divide the data set into.

Returns:

A tuple of the following:

• degree (array) – The degree of each node in the MST.

• edge_length (array) – The length of each edge in the MST.

• branch_length (array) – The length of branches in the MST.

• branch_shape (array) – The shape of branches in the MST.

• edge_index (array) – [Optional] A 2 dimensional array, where the first nested array shows the indexes for the nodes on one end of the edge and the second shows the other node.

• branch_index (array) – [Optional] A list of branches, where each branch is given as a list of the indexes of the member edges.

• groups (array) – [Optional] The assigned groups for each point in the data set (only outputted if include_index=True). Indexes here are indexes of the elements in each group.

Note

This will calculate all the MST statistics by putting the data set through the following functions:

1. k_neighbours (if k_neighbours is specified)

2. construct_mst

3. get_degree

4. get_degree_for_edges

5. get_branches

6. get_branch_shape

7. output_stats