find_box  R Documentation 
Finding the numbers of boxes that given (multivariate) points fall
into (the default is similar to findInterval()
but
other methods are provided, too).
find_box(x, endpoints = NULL,
method = c("per.dim", "lexicographic", "nested", "diagonal"),
rightmost.closed = TRUE, left.open = TRUE, ...)
x 

endpoints 

method 

rightmost.closed 
see 
left.open 
see 
... 
additional arguments passed to the underlying

The box numbers can be used, for example, to color points; see the examples below.
"per.dim"
(n,d)
matrix of box numbers per
dimension.
"lexicographic"
, "nested"
, "diagonal"
n
vector with box numbers.
Note that, as findInterval()
, 0
means ‘in no box’.
Marius Hofert
## Example data
n < 1000
d < 2
set.seed(271)
U < matrix(runif(n * d), ncol = d) # (n, d)matrix of data (here: in [0,1]^d)
### 1 Basic example calls ######################################################
## Define endpoints and evaluate for different methods
epts < seq(0, 1, by = 1/5) # 5 boxes per dimension
find_box(U, endpoints = epts)[1:10,] # default "per.dim" (first 10 points only)
boxes.lexi < find_box(U, endpoints = epts, method = "lexicographic")
boxes.nest < find_box(U, endpoints = epts, method = "nested")
boxes.diag < find_box(U, endpoints = epts, method = "diagonal")
## Special cases
## First row of U (n = 1)
U[1,] # ~= (0.25, 0.14)
stopifnot(find_box(U[1, 1:2], endpoints = epts) == c(2, 1))
stopifnot(find_box(U[1, 1:2], endpoints = epts, method = "lexicographic") == 1)
## Note concerning the last line: It's 1 because all other boxes are empty
stopifnot(find_box(U[1, 1:2], endpoints = epts, method = "nested") == 2)
stopifnot(find_box(U[1, 1:2], endpoints = epts, method = "diagonal") == 0)
## Single number U[1,1] (d = 1)
U[1,1] # ~= 0.25
stopifnot(find_box(U[1,1], endpoints = epts) == 2)
stopifnot(find_box(U[1,1], endpoints = epts, method = "lexicographic") == 1)
stopifnot(find_box(U[1,1], endpoints = epts, method = "nested") == 2)
stopifnot(find_box(U[1,1], endpoints = epts, method = "diagonal") == 2)
### 2 Coloring points in lexicographic ordering ################################
## Define color palette
library(RColorBrewer)
basecols < c("#000000", brewer.pal(8, name = "Dark2")[c(8,7,3,1,5,4,2,6)])
mypal < function(n) rep_len(basecols, length.out = n)
## Colors
ncols < diff(range(boxes.lexi)) + 1 # maximal number of colors needed
palette(mypal(ncols)) # set palette according to maximum number of colors needed
## Boxes of equal size
boxes.lexi < find_box(U, endpoints = epts, method = "lexicographic")
cols < if(min(boxes.lexi) == 0) boxes.lexi + 1 else boxes.lexi
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts, h = epts, col = "gray50") # guides
## Boxes of different sizes and numbers
epts. < list(seq(0.2, 1, by = 1/5), seq(1/3, 1, by = 1/3))
boxes.lexi < find_box(U, endpoints = epts., method = "lexicographic")
cols < if(min(boxes.lexi) == 0) boxes.lexi + 1 else boxes.lexi
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts.[[1]], h = epts.[[2]], col = "gray50")
### 3 Coloring points along the diagonal in a nested way #######################
## Boxes of equal size (with 'middle' part)
boxes.nest < find_box(U, endpoints = epts, method = "nested")
cols < if(min(boxes.nest) == 0) boxes.nest + 1 else boxes.nest # color numbers
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts, h = epts, col = "gray50") # guides
## Boxes of different sizes (without 'middle' part; have to be the same number of
## boxes per dimension, otherwise there is no obvious 'diagonal')
epts. < lapply(1:d, function(j) c(0, 0.1, 0.3, 0.6, 1)) # 4 boxes per dimension
boxes.nest < find_box(U, endpoints = epts., method = "nested")
cols < if(min(boxes.nest) == 0) boxes.nest + 1 else boxes.nest # color numbers
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts.[[1]], h = epts.[[2]], col = "gray50") # guides
### 4 Coloring points along the diagonal #######################################
## Boxes of equal size
boxes.diag < find_box(U, endpoints = epts, method = "diagonal")
cols < if(min(boxes.diag) == 0) boxes.diag + 1 else boxes.diag # color numbers
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts, h = epts, col = "gray50") # guides
## Boxes of different sizes (have to be the same number of
## boxes per dimension, otherwise there is no obvious 'diagonal')
epts. < lapply(1:d, function(j) c(0, 0.05, 0.1, 0.3, 0.6, 1))
boxes.diag < find_box(U, endpoints = epts., method = "diagonal")
cols < if(min(boxes.diag) == 0) boxes.diag + 1 else boxes.diag # color numbers
plot(U, pch = 20, xlab = expression(U[1]), ylab = expression(U[2]), col = cols)
abline(v = epts.[[1]], h = epts.[[2]], col = "gray50") # guides
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