all3DImbalIndices {treeDbalance}

Calculation of integral-based distance- and angle-based 3D imbalance indices

Description

all3DImbalIndices - This serves as a wrapper function to calculate a 3D imbalance index value of a 3D tree in phylo3D format according to the specified imbalance measurement and weighting scheme.
If problems occur with the estimation of the integrals, try to increase the optional parameters
rel.tolerance and max.subdiv.

A_Index - Calculates the 3D imbalance index "weighted integral-based centroid angle" of a 3D tree in phylo3D format using either the edge weights or the edge lengths as weights.
If problems occur with the estimation of the integrals, try to increase the optional parameters
rel.tolerance and max.subdiv.

alpha_Index - Calculates the 3D imbalance index "weighted integral-based minimal centroid angle" of a 3D tree in phylo3D format using either the edge weights or the edge lengths as weights.
If problems occur with the estimation of the integrals, try to increase the optional parameters
rel.tolerance and max.subdiv.

M_Index - Calculates the 3D imbalance index "weighted integral-based expanded relative centroid distance" of a 3D tree in phylo3D format using either the edge weights or the edge lengths as weights.
If problems occur with the estimation of the integrals, try to increase the optional parameters
rel.tolerance and max.subdiv.

mu_Int - Calculates the 3D imbalance index "weighted integral-based relative centroid distance" of a 3D tree in phylo3D format using either the edge weights or the edge lengths as weights.
If problems occur with the estimation of the integrals, try to increase the optional parameters
rel.tolerance and max.subdiv.

imbalInt_e - Calculates the integral of the node imbalance values over all possible subdividing nodes on an edge.

imbalProfile_e - Calculates the node imbalance values for a given set of subdivisions of an edge.

Usage

all3DImbalIndices(
  tree,
  imbal_type,
  weight = "edge_weight",
  rel.tolerance = 1e-10,
  max.subdiv = 200L
)

A_Index(tree, weight = "edge_weight", rel.tolerance = 1e-10, max.subdiv = 200L)

alpha_Index(
  tree,
  weight = "edge_weight",
  rel.tolerance = 1e-10,
  max.subdiv = 200L
)

M_Index(tree, weight = "edge_weight", rel.tolerance = 1e-10, max.subdiv = 200L)

mu_Index(
  tree,
  weight = "edge_weight",
  rel.tolerance = 1e-10,
  max.subdiv = 200L
)

imbalInt_e(
  p,
  v,
  centr_v,
  centr_v_weight,
  edge_weight,
  imbal_type,
  rel.tolerance = 1e-08,
  max.subdiv = 200L
)

imbalProfile_e(xs, p, v, centr_v, centr_v_weight, edge_weight, imbal_type)

Arguments

tree

A rooted tree in phylo3D format (no special node enumeration required, except that nodes are numbered from 1 to |V| = the total number of nodes). There must be at least 2 nodes, i.e., one edge. The attributes 'node.coord' and 'edge.weight' are strictly required.

imbal_type

Specifies which node imbalance measurement should be used. Available are:
"A" - centroid angle
"alpha" - minimal centroid angle
"M" - expanded relative centroid distance
"mu" - relative centroid distance

weight

Specifies how the node imbalance values should be weighted. Available weighting methods are:
"edge_weight" (default) -> Imbalance with regards to the total edge weight.
"edge_length" -> Imbalance with regards to the total edge length.

rel.tolerance

(Optional) Numeric value which specifies the relative tolerance which should be used for estimating the integral using stats::integrate. Set to 1e-10 by default (the stats::integrate default value is approx 3e-16).

max.subdiv

(Optional) Integer value which specifies the maximal number of interval subdivisions for estimating the integral using stats::integrate. Set to 200 by default (stats::integrate default value 100).

p

Numeric vector of size 3 (3D coordinates of parent node p).

v

Numeric vector of size 3 (3D coordinates of node v).

centr_v

Numeric vector of size 3 (3D coordinates of the centroid of the pending subtree of node v).

centr_v_weight

Numeric value >=0 (weight of the pending subtree of node v).

edge_weight

Numeric value >=0 (weight of the edge (p,v)).

xs

Numeric vector with values between 0 (included) and 1 (excluded). Set of edge subdivisions.

Value

all3DImbalIndices Numeric value indicating the internal 3D imbalance according to the chosen method.

A_Index Numeric value in the interval between 0 (included) and \pi (excluded). A value near \pi indicates a higher degree and near 0 a lower degree of asymmetry.

alpha_Index Numeric value in the interval between 0 (included) and \pi/2 (excluded). A value near \pi/2 indicates a higher degree and near 0 a lower degree of asymmetry.

M_Index Numeric value in the interval between 0 (included) and 1 (excluded). A value near 1 indicates a higher degree and near 0 a lower degree of asymmetry.

mu_Index Numeric value in the interval between 0 (included) and 1 (excluded). A value near 1 indicates a higher degree and near 0 a lower degree of asymmetry.

imbalInt_e Numeric value (0 minimal value, higher values indicate a higher degree of asymmetry).

imbalProfile_e Numeric vector of imbalance values (0 minimal value, higher values indicate a higher degree of asymmetry) for the edge subdivisions indicated by input xs.

Author(s)

Sophie Kersting

Examples

tree <- treeDbalance::extendPhylo(treeDbalance::example3Dtrees$bean09)
all3DImbalIndices(tree, imbal_type = "A", weight="edge_length")
A_Index(tree, weight="edge_weight")
alpha_Index(tree)
M_Index(tree, weight="edge_length")
mu_Index(tree, weight="edge_length")
imbalInt_e(p=c(0,0,1),v=c(0,0,0),centr_v=c(0.5,0,0),
    centr_v_weight=1,edge_weight=1,imbal_type="mu")
imbalProfile_e(xs=c(0,0.2,0.4),p=c(1,1,0),v=c(0,0,0),centr_v=c(0.5,0,0),
    centr_v_weight=1,edge_weight=1,imbal_type="A")