ripserr ports the Ripser and Cubical Ripser persistent homology calculation engines from C++ via Rcpp. It can be used as a convenient and rapid calculation tool in topological data analysis pipelines.
# install development version
devtools::install_github("rrrlw/ripserr")
# install from CRAN
install.packages("ripserr")Ripser (Vietoris-Rips complex) can be used as follows for data with dimension greater than or equal to 2.
# load ripserr
library("ripserr")
set.seed(42)
SIZE <- 100
# 2-dimensional example
dataset2 <- rnorm(SIZE * 2)
dim(dataset2) <- c(SIZE, 2)
vr_phom2 <- vietoris_rips(dataset2)
head(vr_phom2)
#> dimension birth death
#> 1 0 0 0.01004861
#> 2 0 0 0.02923702
#> 3 0 0 0.04550504
#> 4 0 0 0.06829826
#> 5 0 0 0.06853393
#> 6 0 0 0.07187663
tail(vr_phom2)
#> dimension birth death
#> 112 1 0.3916344 0.4239412
#> 113 1 0.3906770 0.5577989
#> 114 1 0.3880186 0.4029842
#> 115 1 0.3703398 0.5007012
#> 116 1 0.3330234 0.3416054
#> 117 1 0.2418318 0.2504820
# 3-dimensional example
dataset3 <- rnorm(SIZE * 3)
dim(dataset3) <- c(SIZE, 3)
vr_phom3 <- vietoris_rips(dataset3, max_dim = 2) # default: max_dim = 1
head(vr_phom3)
#> dimension birth death
#> 1 0 0 0.1282935
#> 2 0 0 0.1421812
#> 3 0 0 0.1516424
#> 4 0 0 0.1819928
#> 5 0 0 0.1858051
#> 6 0 0 0.2114116
tail(vr_phom3)
#> dimension birth death
#> 132 1 0.5212961 0.5233529
#> 133 2 1.1829207 1.1999911
#> 134 2 1.1194325 1.3245908
#> 135 2 1.0707410 1.0914850
#> 136 2 0.9433034 0.9867254
#> 137 2 0.6882204 0.6913078Cubical Ripser (cubical complex) can be used as follows for data with dimension equal to 2, 3, or 4.
# load ripserr
library("ripserr")
set.seed(42)
SIZE <- 10
# 2-dimensional example
dataset2 <- rnorm(SIZE ^ 2)
dim(dataset2) <- rep(SIZE, 2)
cub_phom2 <- cubical(dataset2)
head(cub_phom2)
#> dimension birth death
#> 1 0 -1.1943289 -0.8607926
#> 2 0 -2.4142076 -0.8509076
#> 3 0 -0.8113932 -0.7844590
#> 4 0 -1.7170087 -0.7844590
#> 5 0 -0.7272921 -0.5428288
#> 6 0 -0.9535234 -0.5428288
tail(cub_phom2)
#> dimension birth death
#> 22 1 0.8217731 0.9333463
#> 23 1 0.7681787 1.0385061
#> 24 1 0.7581632 1.5757275
#> 25 1 0.7208782 1.3025426
#> 26 1 0.6792888 1.4441013
#> 27 1 0.6359504 1.8951935
# 3-dimensional example
dataset3 <- rnorm(SIZE ^ 3)
dim(dataset3) <- rep(SIZE, 3)
cub_phom3 <- cubical(dataset3)
head(cub_phom3)
#> dimension birth death
#> 1 0 -1.926167 -1.737728
#> 2 0 -1.737297 -1.439229
#> 3 0 -1.924950 -1.439229
#> 4 0 -1.500221 -1.354600
#> 5 0 -2.277778 -1.354600
#> 6 0 -1.682481 -1.306676
tail(cub_phom3)
#> dimension birth death
#> 324 2 1.2488637 1.258482
#> 325 2 1.2009654 2.036972
#> 326 2 1.0452759 1.199978
#> 327 2 0.9885968 1.809382
#> 328 2 0.9310749 1.179696
#> 329 2 0.8447922 1.709689
# 4-dimensional example
dataset4 <- rnorm(SIZE ^ 4)
dim(dataset4) <- rep(SIZE, 4)
cub_phom4 <- cubical(dataset4)
head(cub_phom4)
#> dimension birth death
#> 1 0 -1.986299 -1.923519
#> 2 0 -1.822606 -1.816506
#> 3 0 -1.776392 -1.710786
#> 4 0 -1.833663 -1.710387
#> 5 0 -1.947054 -1.704791
#> 6 0 -1.701462 -1.639160
tail(cub_phom4)
#> dimension birth death
#> 4329 3 1.676609 2.019277
#> 4330 3 1.675766 1.932152
#> 4331 3 1.669449 2.149646
#> 4332 3 1.662486 1.863734
#> 4333 3 1.535361 1.963609
#> 4334 3 1.349235 2.263581- Calculation of persistent homology of Vietoris-Rips complexes using
Ripser (function named
vietoris_rips). - Calculation of persistent homology of cubical complexes using
Cubical Ripser (function named
cubical).
If you use the ripserr package in your work, please consider citing the following (based on use):
- General use of ripserr: Wadhwa RR, Piekenbrock M, Scott JG. ripserr: Calculate Persistent Homology with Ripser-based Engines; version 0.1.0. URL https://github.com/rrrlw/ripserr.
- Calculation using Vietoris-Rips complex: Bauer U. Ripser: Efficient computation of Vietoris-Rips persistence barcodes. 2019; arXiv: 1908.02518.
- Calculation using cubical complex: Kaji S, Sudo T, Ahara K. Cubical Ripser: Software for computing persistent homology of image and volume data. 2020; arXiv: 2005.12692.
To contribute to ripserr, you can create issues for any bugs/suggestions on the issues page. You can also fork the ripserr repository and create pull requests to add useful features.