funFiltration: Filtration from function values

Description

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

Usage

funFiltration(FUNvalues, cmplx, sublevel = TRUE)

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).

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.

Author

Jisu Kim

Details

See references.

References

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

Examples

Run this code

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"]])

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