View source: R/gridFiltration.R
gridFiltration | R Documentation |
The function gridFiltration
computes the Persistence Diagram of a filtration of sublevel sets (or superlevel sets) of a function evaluated over a grid of points in arbitrary dimension d
.
gridFiltration(
X = NULL, FUN = NULL, lim = NULL, by = NULL, FUNvalues = NULL,
maxdimension = max(NCOL(X), length(dim(FUNvalues))) - 1,
sublevel = TRUE, printProgress = FALSE, ...)
X |
an |
FUN |
a function whose inputs are 1) an |
lim |
a |
by |
either a number or a vector of length |
FUNvalues |
an |
maxdimension |
a number that indicates the maximum dimension of the homological features to compute: |
sublevel |
a logical variable indicating if the Persistence Diagram should be computed for sublevel sets ( |
printProgress |
if |
... |
additional parameters for the function |
If the values of X
, FUN
are set, then FUNvalues
should be NULL
. In this case, gridFiltration
evaluates the function FUN
over a grid. If the value of FUNvalues
is set, then X
, FUN
should be NULL
. In this case, FUNvalues
is used as function values over the grid.
Once function values are either computed or given, gridFiltration
constructs a filtration by triangulating the grid and considering the simplices determined by the values of the function of dimension up to maxdimension+1
.
The function gridFiltration
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 ( |
coordinates |
only if both |
The user can decide to use either the C++ library GUDHI, Dionysus, or PHAT. See references.
Since dimension of simplicial complex from grid points in R^d
is up to d
, homology of dimension \ge d
is trivial. Hence setting maxdimension
with values \ge d
is equivalent to maxdimension=d-1
.
Brittany T. Fasy, Jisu Kim, and Fabrizio Lecci
Fasy B, Lecci F, Rinaldo A, Wasserman L, Balakrishnan S, Singh A (2013). "Statistical Inference For Persistent Homology." (arXiv:1303.7117). Annals of Statistics.
Morozov D (2007). "Dionysus, a C++ library for computing persistent homology." https://www.mrzv.org/software/dionysus/
Bauer U, Kerber M, Reininghaus J (2012). "PHAT, a software library for persistent homology." https://bitbucket.org/phat-code/phat/
summary.diagram
, plot.diagram
,
distFct
, kde
, kernelDist
, dtm
,
alphaComplexDiag
, alphaComplexDiag
, ripsDiag
# input data
n <- 10
XX <- circleUnif(n)
## Ranges of the grid
Xlim <- c(-1, 1)
Ylim <- c(-1, 1)
lim <- cbind(Xlim, Ylim)
by <- 1
#Distance Function Diagram of the sublevel sets
FltGrid <- gridFiltration(
XX, distFct, lim = lim, by = by, sublevel = TRUE, printProgress = TRUE)
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