funFiltration: Filtration from function values

In TDA: Statistical Tools for Topological Data Analysis

Filtration from function values

Description

The function funFiltration computes the filtration from the complex and the function values.

Usage

funFiltration(FUNvalues, cmplx, sublevel = TRUE)

Arguments

FUNvalues	The function values on the vertices of the complex.
cmplx	the complex.
sublevel	a logical variable indicating if the Persistence Diagram should be computed for sublevel sets (TRUE) or superlevel sets (FALSE) of the function. The default value is TRUE.

Details

See references.

Value

The function funFiltration returns a list with the following elements:

cmplx	a list representing the complex. Its i-th element represents the vertices of i-th simplex.
values	a vector representing the filtration values. Its i-th element represents the filtration value of i-th simplex.
increasing	a logical variable indicating if the filtration values are in increasing order (TRUE) or in decreasing order (FALSE).

Author(s)

Jisu Kim

References

Edelsbrunner H, Harer J (2010). "Computational topology: an introduction." American Mathematical Society.

See Also

filtrationDiag

Examples

n <- 5
X <- cbind(cos(2*pi*seq_len(n)/n), sin(2*pi*seq_len(n)/n))
maxdimension <- 1
maxscale <- 1.5
dist <- "euclidean"
library <- "Dionysus"

FltRips <- ripsFiltration(X = X, maxdimension = maxdimension,
               maxscale = maxscale, dist = "euclidean", library = "Dionysus",
               printProgress = TRUE)

FUNvalues <- X[, 1] + X[, 2]

FltFun <- funFiltration(FUNvalues = FUNvalues, cmplx = FltRips[["cmplx"]])

TDA documentation built on Feb. 16, 2023, 6:35 p.m.