intrval: Relational Operators for Intervals

Evaluating if values of vectors are within different open/closed intervals (x %[]% c(a, b)), or if two closed intervals overlap (c(a1, b1) %[o]% c(a2, b2)). Operators for negation and directional relations also implemented.

Value-to-interval relations

Values of x are compared to interval endpoints a and b (a <= b). Endpoints can be defined as a vector with two values (c(a, b)): these values will be compared as a single interval with each value in x. If endpoints are stored in a matrix-like object or a list, comparisons are made element-wise.

x <- rep(4, 5)
a <- 1:5
b <- 3:7
cbind(x=x, a=a, b=b)
x %[]% cbind(a, b) # matrix
x %[]% data.frame(a=a, b=b) # data.frame
x %[]% list(a, b) # list

If lengths do not match, shorter objects are recycled. Return values are logicals. Note: interval endpoints are sorted internally thus ensuring the condition a <= b is not necessary.

These value-to-interval operators work for numeric (integer, real) and ordered vectors, and object types which are measured at least on ordinal scale (e.g. dates).

Closed and open intervals

The following special operators are used to indicate closed ([, ]) or open ((, )) interval endpoints:

Operator	Expression	Condition
%[]%	x %[]% c(a, b)	x >= a & x <= b
%[)%	x %[)% c(a, b)	x >= a & x < b
%(]%	x %(]% c(a, b)	x > a & x <= b
%()%	x %()% c(a, b)	x > a & x < b

Negation and directional relations

Equal	Not equal	Less than	Greater than
%[]%	%)(%	%[<]%	%[>]%
%[)%	%)[%	%[<)%	%[>)%
%(]%	%](%	%(<]%	%(>]%
%()%	%][%	%(<)%	%(>)%

Interval-to-interval relations

The overlap of two closed intervals, [a1, b1] and [a2, b2], is evaluated by the %[o]% operator (a1 <= b1, a2 <= b2). Endpoints can be defined as a vector with two values (c(a1, b1))or can be stored in matrix-like objects or a lists in which case comparisons are made element-wise. Note: interval endpoints are sorted internally thus ensuring the conditions a1 <= b1 and a2 <= b2 is not necessary.

c(2, 3) %[o]% c(0, 1)
list(0:4, 1:5) %[o]% c(2, 3)
cbind(0:4, 1:5) %[o]% c(2, 3)
data.frame(a=0:4, b=1:5) %[o]% c(2, 3)

If lengths do not match, shorter objects are recycled. These value-to-interval operators work for numeric (integer, real) and ordered vectors, and object types which are measured at least on ordinal scale (e.g. dates).

%)o(% is used for the negation, directional evaluation is done via the operators %[<o]% and %[o>]%.

Equal	Not equal	Less than	Greater than
%[o]%	%)o(%	%[<o]%	%[o>]%

Operators for discrete variables

The previous operators will return NA for unordered factors. Set overlap can be evaluated by the base %in% operator and its negation %ni%.

Versions

Install from CRAN:

install.packages("intrval")

Install development version from GitHub:

devtools::install_github("psolymos/intrval")

User visible changes are listed in the NEWS file.

Report a problem

Use the issue tracker to report a problem.

License

GPL-2

Examples

## bounding box
set.seed(1)
n <- 10^4
x <- runif(n, -2, 2)
y <- runif(n, -2, 2)
d <- sqrt(x^2 + y^2)
iv1 <- x %[]% c(-0.25, 0.25) & y %[]% c(-1.5, 1.5)
iv2 <- x %[]% c(-1.5, 1.5) & y %[]% c(-0.25, 0.25)
iv3 <- d %()% c(1, 1.5)
plot(x, y, pch = 19, cex = 0.25, col = iv1 + iv2 + 1,
    main = "Intersecting bounding boxes")
plot(x, y, pch = 19, cex = 0.25, col = iv3 + 1,
     main = "Deck the halls:\ndistance range from center")

## time series filtering
x <- seq(0, 4*24*60*60, 60*60)
dt <- as.POSIXct(x, origin="2000-01-01 00:00:00")
f <- as.POSIXlt(dt)$hour %[]% c(0, 11)
plot(sin(x) ~ dt, type="l", col="grey",
    main = "Filtering date/time objects")
points(sin(x) ~ dt, pch = 19, col = f + 1)

## QCC
library(qcc)
data(pistonrings)
mu <- mean(pistonrings$diameter[pistonrings$trial])
SD <- sd(pistonrings$diameter[pistonrings$trial])
x <- pistonrings$diameter[!pistonrings$trial]
iv <- mu + 3 * c(-SD, SD)
plot(x, pch = 19, col = x %)(% iv +1, type = "b", ylim = mu + 5 * c(-SD, SD),
    main = "Shewhart quality control chart\ndiameter of piston rings")
abline(h = mu)
abline(h = iv, lty = 2)


## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 9: Plant Weight Data.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2, 10, 20, labels = c("Ctl","Trt"))
weight <- c(ctl, trt)

lm.D9 <- lm(weight ~ group)
## compare 95% confidence intervals with 0
(CI.D9 <- confint(lm.D9))
#                2.5 %    97.5 %
# (Intercept)  4.56934 5.4946602
# groupTrt    -1.02530 0.2833003
0 %[]% CI.D9
# (Intercept)    groupTrt
#       FALSE        TRUE

lm.D90 <- lm(weight ~ group - 1) # omitting intercept
## compare 95% confidence of the 2 groups to each other
(CI.D90 <- confint(lm.D90))
#            2.5 %  97.5 %
# groupCtl 4.56934 5.49466
# groupTrt 4.19834 5.12366
CI.D90[1,] %[o]% CI.D90[2,]
# 2.5 %
#  TRUE

DATE <- as.Date(c("2000-01-01","2000-02-01", "2000-03-31"))
DATE %[<]% as.Date(c("2000-01-15", "2000-03-15"))
# [1]  TRUE FALSE FALSE
DATE %[]% as.Date(c("2000-01-15", "2000-03-15"))
# [1] FALSE  TRUE FALSE
DATE %[>]% as.Date(c("2000-01-15", "2000-03-15"))
# [1] FALSE FALSE  TRUE