arithmetic.RdCalculate sums, scalar multiples, absolute values, means, inner products, extrema, and moments of persistent landscapes. These operations arise from the Hilbert space structure on persistence landscapes (Bubenik, 2015).
pl_add(pl1, pl2)
pl_sum(pl_list)
pl_scale(pl, mult)
pl_abs(pl)
pl_diff(pl_list)
pl_mean(pl_list)
pl_var(pl_list, p = 2)
pl_sd(pl_list, p = 2)
pl_inner(pl1, pl2)
pl_min(pl, level = 1L)
pl_max(pl, level = 1L)
pl_range(pl, level = 1L)
pl_vmin(pl, level = pl_num_levels(pl))
pl_vmax(pl, level = pl_num_levels(pl))
pl_vrange(pl, level = pl_num_levels(pl))
pl_moment(pl, p = 1L, center = 0, level = 1L)
pl_vmoment(pl, p = 1L, center = 0, level = pl_num_levels(pl))Persistence landscapes.
A list of persistence landscapes.
Persistence landscapes.
Double; a real-valued scale factor.
Positive integer or infinity; the power used to compute a norm or moment.
Positive integer; the level of the persistence landscape (up to)
whose moment to calculate. This value is internally decreased by 1L to
prevent off-by-one errors when passing to C++ code.
Double; where to center the moment.
A persistence landscape (an object of S4 class 'Rcpp_PersistenceLandscape'), a list of persistence landscapes, a real number, or a vector of real numbers.
These functions are prefixed pl_*() to help users access them via
tab-completion. Some take their names from the underlying S4 class methods
and are only provided to enable composition via pipes: add, scale,
abs, inner, min (minimum), max (maximum), and moment; range
combines min and max. Others mimic classic R functions to handle lists
of persistence landscapes: sum, diff, mean, var, and sd. Finally,
some are vectorizations of the preceding: vmin, vmax, vrange, and
vmoment.
Rcpp_PersistenceLandscape-methods for prefix and infix syntax.
# scale a landscape
x <- tdaunif::sample_torus_tube(40, 2.5)
pd <- ripserr::vietoris_rips(x, dim = 1L, threshold = 2)
#> Warning: `dim` parameter has been deprecated; use `max_dim` instead.
pl <- landscape(pd, degree = 1, exact = FALSE, xmax = 2.5, xby = 0.1)
print(pl$getInternal()[2, , ])
#> [,1] [,2]
#> [1,] 0.0 0.00000000
#> [2,] 0.1 0.00000000
#> [3,] 0.2 0.00000000
#> [4,] 0.3 0.00000000
#> [5,] 0.4 0.00000000
#> [6,] 0.5 0.00000000
#> [7,] 0.6 0.00000000
#> [8,] 0.7 0.05167421
#> [9,] 0.8 0.04113183
#> [10,] 0.9 0.00000000
#> [11,] 1.0 0.00000000
#> [12,] 1.1 0.00000000
#> [13,] 1.2 0.00000000
#> [14,] 1.3 0.00000000
#> [15,] 1.4 0.00000000
#> [16,] 1.5 0.00000000
#> [17,] 1.6 0.00000000
#> [18,] 1.7 0.00000000
#> [19,] 1.8 0.00000000
#> [20,] 1.9 0.00000000
#> [21,] 2.0 0.00000000
#> [22,] 2.1 0.00000000
#> [23,] 2.2 0.00000000
#> [24,] 2.3 0.00000000
#> [25,] 2.4 0.00000000
#> [26,] 2.5 0.00000000
print(pl$scale(0.5)$getInternal()[2, , ])
#> [,1] [,2]
#> [1,] 0.0 0.00000000
#> [2,] 0.1 0.00000000
#> [3,] 0.2 0.00000000
#> [4,] 0.3 0.00000000
#> [5,] 0.4 0.00000000
#> [6,] 0.5 0.00000000
#> [7,] 0.6 0.00000000
#> [8,] 0.7 0.02583710
#> [9,] 0.8 0.02056591
#> [10,] 0.9 0.00000000
#> [11,] 1.0 0.00000000
#> [12,] 1.1 0.00000000
#> [13,] 1.2 0.00000000
#> [14,] 1.3 0.00000000
#> [15,] 1.4 0.00000000
#> [16,] 1.5 0.00000000
#> [17,] 1.6 0.00000000
#> [18,] 1.7 0.00000000
#> [19,] 1.8 0.00000000
#> [20,] 1.9 0.00000000
#> [21,] 2.0 0.00000000
#> [22,] 2.1 0.00000000
#> [23,] 2.2 0.00000000
#> [24,] 2.3 0.00000000
#> [25,] 2.4 0.00000000
#> [26,] 2.5 0.00000000
# create two landscapes from the same sampling distribution
x <- tdaunif::sample_torus_tube(40, 2.5)
y <- tdaunif::sample_torus_tube(40, 2.5)
x_pd <- ripserr::vietoris_rips(x, dim = 1, threshold = 2)
#> Warning: `dim` parameter has been deprecated; use `max_dim` instead.
y_pd <- ripserr::vietoris_rips(y, dim = 1, threshold = 2)
#> Warning: `dim` parameter has been deprecated; use `max_dim` instead.
x_pl <- landscape(x_pd, degree = 1, exact = FALSE, xmax = 2.5, xby = 0.1)
y_pl <- landscape(y_pd, degree = 1, exact = FALSE, xmax = 2.5, xby = 0.1)
# compare landscapes and calculate mean landscape
print(x_pl$getInternal())
#> , , 1
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [2,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [3,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [4,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [5,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [6,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [7,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [8,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [2,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [3,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [4,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [5,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [6,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [7,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [8,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0 0 0 0 0 0 0.050136363 0.1415052864 0.04424601
#> [2,] 0 0 0 0 0 0 0.009642749 0.0016243337 0.04150529
#> [3,] 0 0 0 0 0 0 0.000000000 0.0005088148 0.04056985
#> [4,] 0 0 0 0 0 0 0.000000000 0.0000000000 0.00000000
#> [5,] 0 0 0 0 0 0 0.000000000 0.0000000000 0.00000000
#> [6,] 0 0 0 0 0 0 0.000000000 0.0000000000 0.00000000
#> [7,] 0 0 0 0 0 0 0.000000000 0.0000000000 0.00000000
#> [8,] 0 0 0 0 0 0 0.000000000 0.0000000000 0.00000000
#> [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] 0.02227656 0 0 0.05048058 0 0 0 0 0 0
#> [2,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [3,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [4,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [5,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [6,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [7,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [8,] 0.00000000 0 0 0.00000000 0 0 0 0 0 0
#> [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0
#>
print(y_pl$getInternal())
#> , , 1
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [2,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [3,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [4,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [5,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [6,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [7,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [2,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [3,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [4,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [5,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [6,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [7,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0 0 0 0 0 0.03722113 0.137221129 0.095184528 0.004993068
#> [2,] 0 0 0 0 0 0.00000000 0.013504139 0.080211838 0.000000000
#> [3,] 0 0 0 0 0 0.00000000 0.004595203 0.039436042 0.000000000
#> [4,] 0 0 0 0 0 0.00000000 0.000000000 0.032114568 0.000000000
#> [5,] 0 0 0 0 0 0.00000000 0.000000000 0.008034788 0.000000000
#> [6,] 0 0 0 0 0 0.00000000 0.000000000 0.000000000 0.000000000
#> [7,] 0 0 0 0 0 0.00000000 0.000000000 0.000000000 0.000000000
#> [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18]
#> [1,] 0 0.07482755 0.1748276 0.185926 0.08592595 0 0 0 0
#> [2,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [3,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [4,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [5,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [6,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [7,] 0 0.00000000 0.0000000 0.000000 0.00000000 0 0 0 0
#> [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 0 0
#>
print(pl_mean(list(x_pl, y_pl))$getInternal())
#> , , 1
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [2,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [3,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [4,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [5,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [6,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [7,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [8,] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [2,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [3,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [4,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [5,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [6,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [7,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#> [8,] 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0 0 0 0 0 0.01861056 0.093678746 0.118344907 0.02461954
#> [2,] 0 0 0 0 0 0.00000000 0.011573444 0.040918086 0.02075264
#> [3,] 0 0 0 0 0 0.00000000 0.002297601 0.019972428 0.02028493
#> [4,] 0 0 0 0 0 0.00000000 0.000000000 0.016057284 0.00000000
#> [5,] 0 0 0 0 0 0.00000000 0.000000000 0.004017394 0.00000000
#> [6,] 0 0 0 0 0 0.00000000 0.000000000 0.000000000 0.00000000
#> [7,] 0 0 0 0 0 0.00000000 0.000000000 0.000000000 0.00000000
#> [8,] 0 0 0 0 0 0.00000000 0.000000000 0.000000000 0.00000000
#> [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17]
#> [1,] 0.01113828 0.03741378 0.08741378 0.1182033 0.04296298 0 0 0
#> [2,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [3,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [4,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [5,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [6,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [7,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [8,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 0 0 0
#> [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0 0 0
#>
if (FALSE) {
set.seed(492869L)
# compute landscape for a large sample
pt <- tdaunif::sample_torus_tube(1000, 5)
pd <- ripserr::vietoris_rips(pt, dim = 2, threshold = 2)
pl <- landscape(pd, degree = 1, exact = FALSE, xby = 0.1, xmin = 0, xmax = 2)
# compute landscapes for a large sample of small samples
pl_list <- c()
for (i in seq(100)) {
pti <- tdaunif::sample_torus_tube(100, 5)
pdi <- ripserr::vietoris_rips(pti, dim = 2, threshold = 2)
pli <- landscape(pdi, degree = 1, exact = FALSE, xby = 0.1, xmin = 0, xmax = 2)
pl_list <- c(pl_list, pli)
}
# compute the mean landscape
pl_avg <- pl_mean(pl_list)
# compute the distance between the landscapes
pl_diff <- pl$add(pl_avg$scale(-1))
print(pl_inner(pl_diff, pl_diff))
}