PyH {TDApplied}

Fast persistent homology calculations with python.

Description

This function is a wrapper of the python wrapper of the ripser engine for persistent cohomology, but is still faster than using the R package TDAstats (see the TDApplied package vignette for details).

Usage

PyH(
  X,
  maxdim = 1,
  thresh,
  distance_mat = FALSE,
  ripser,
  ignore_infinite_cluster = TRUE,
  calculate_representatives = FALSE
)

Arguments

X

either a matrix or dataframe, representing either point cloud data or a distance matrix. In either case there must be at least two rows and 1 column.

maxdim

the non-negative integer maximum dimension for persistent homology, default 1.

thresh

the non-negative numeric radius threshold for the Vietoris-Rips filtration.

distance_mat

a boolean representing whether the input X is a distance matrix or not, default FALSE.

ripser

the ripser python module.

ignore_infinite_cluster

a boolean representing whether to remove clusters (0 dimensional cycles) which die at the threshold value. Default is TRUE as this is the default for TDAstats homology calculations, but can be set to FALSE which is the default for python ripser.

calculate_representatives

a boolean representing whether to return a list of representative cocycles for the topological features found in the persistence diagram, default FALSE.

Details

If 'distance_mat' is 'TRUE' then 'X' must be a square matrix. The 'ripser' parameter should be the result of an 'import_ripser' function call, but since that function is slow the ripser object should be explicitly created before a PyH function call (see examples). Cohomology is computed over Z2, as is the case for the TDAstats function calculate_homology (this is also the default for ripser in c++). If representative cocycles are returned, then they are stored in a list with one element for each point in the persistence diagram, ignoring dimension 0 points. Each representative of a dimension d cocycle (1 for loops, 2 for voids, etc.) is a kxd dimension matrix/array containing the row number-labelled edges, triangles etc. in the cocycle.

Value

Either a dataframe containing the persistence diagram if 'calculate_representatives' is 'FALSE' (the default), otherwise a list with two elements: diagram of class diagram, containing the persistence diagram, and representatives, a list containing the edges, triangles etc. contained in each representative cocycle.

Author(s)

Shael Brown - [e-mail]

Examples

## Not run: 
# create sample data
df <- data.frame(x = 1:10,y = 1:10)

# import the ripser module
ripser <- import_ripser()

# calculate persistence diagram up to dimension 1 with a maximum
# radius of 5
phom <- PyH(X = df,thresh = 5,ripser = ripser)

## End(Not run)