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.
Install
Install from CRAN:
install.packages("intrval")Install development version from GitHub:
if (!requireNamespace("remotes")) install.packages("remotes")
remotes::install_github("psolymos/intrval")User visible changes are listed in the NEWS file.
Use the issue tracker to report a problem.
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) # listIf 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 |
|---|---|---|---|
%[]% |
%)(% |
%[<]% |
%[>]% |
%[)% |
%)[% |
%[<)% |
%[>)% |
%(]% |
%](% |
%(<]% |
%(>]% |
%()% |
%][% |
%(<)% |
%(>)% |
Dividing a range into 3 intervals
The functions %[c]%, %[c)%, %(c]%, and %(c)% return an integer vector taking values (the c within the brackets refer to ‘cut’):
-
-1Lwhen the value is less than or equal toa(a <= b), depending on the interval type, -
0Lwhen the value is inside the interval, or -
1Lwhen the value is greater than or equal tob(a <= b), depending on the interval type.
| Expression | Evaluates to -1 | Evaluates to 0 | Evaluates to 1 |
|---|---|---|---|
x %[c]% c(a, b) |
x < a |
x >= a & x <= b |
x > b |
x %[c)% c(a, b) |
x < a |
x >= a & x < b |
x >= b |
x %(c]% c(a, b) |
x <= a |
x > a & x <= b |
x > b |
x %(c)% c(a, b) |
x <= a |
x > a & x < b |
x >= b |
Interval-to-interval relations
The operators define the open/closed nature of the lower/upper limits of the intervals on the left and right hand side of the o in the middle.
| Intervals | Int. 2: []
|
Int. 2: [)
|
Int. 2: (]
|
Int. 2: ()
|
|---|---|---|---|---|
Int. 1: [] |
%[]o[]% |
%[]o[)% |
%[]o(]% |
%[]o()% |
Int. 1: [) |
%[)o[]% |
%[)o[)% |
%[)o(]% |
%[)o()% |
Int. 1: (] |
%(]o[]% |
%(]o[)% |
%(]o(]% |
%(]o()% |
Int. 1: () |
%()o[]% |
%()o[)% |
%()o(]% |
%()o()% |
The overlap of two closed intervals, [a1, b1] and [a2, b2], is evaluated by the %[o]% (alias for %[]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. 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), see Examples. 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 of two closed interval overlap, directional evaluation is done via the operators %[<o]% and %[o>]%. The overlap of two open intervals is evaluated by the %(o)% (alias for %()o()%). %]o[% is used for the negation of two open interval overlap, directional evaluation is done via the operators %(<o)% and %(o>)%.
| Equal | Not equal | Less than | Greater than |
|---|---|---|---|
%[o]% |
%)o(% |
%[<o]% |
%[o>]% |
%(o)% |
%]o[% |
%(<o)% |
%(o>)% |
Overlap operators with mixed endpoint do not have negation and directional counterparts.
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% (as in not in, the opposite of in). %nin% and %notin% are aliases for better code readability (%in% can look very much like %ni%).
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)$hour %[]% c(0, 11)
plot(sin(x) ~ dt, type="l", col="grey",
main = "Filtering date/time objects")
points(sin(x) ~ dt, pch = 19, col = f + 1)Quality control chart (QCC)
library(qcc)
data(pistonrings)
mu <- mean(pistonrings$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)Confidence intervals and hypothesis testing
## 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 %
# TRUEDates
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
dt1 <- as.Date(c("2000-01-01", "2000-03-15"))
dt2 <- as.Date(c("2000-03-15", "2000-06-07"))
dt1 %[]o[]% dt2
# [1] TRUE
dt1 %[]o[)% dt2
# [1] TRUE
dt1 %[]o(]% dt2
# [1] FALSE
dt1 %[]o()% dt2
# [1] FALSEFloating point number comparisons
The intrval package used fpCompare to reliable numeric-to-numeric comparisons. The behavior can be turned off to use the less reliable base R implementation:
x1 <- 0.5 - 0.3
x2 <- 0.3 - 0.1
op <- intrval_options(use_fpCompare = FALSE)
## this is the base R behavior
x1 %[]% c(0.2, 0.6)
# [1] TRUE
x2 %[]% c(0.2, 0.6)
# [1] FALSE
## reset defaults
intrval_options(op)
## using fpCompare
x1 %[]% c(0.2, 0.6)
# [1] TRUE
x2 %[]% c(0.2, 0.6)
# [1] TRUETruncated distributions
Find the math here, as implemented in the package truncdist.
dtrunc <- function(x, ..., distr, lwr=-Inf, upr=Inf) {
f <- get(paste0("d", distr), mode = "function")
F <- get(paste0("p", distr), mode = "function")
Fx_lwr <- F(lwr, ..., log=FALSE)
Fx_upr <- F(upr, ..., log=FALSE)
fx <- f(x, ..., log=FALSE)
fx / (Fx_upr - Fx_lwr) * (x %[]% c(lwr, upr))
}
n <- 10^4
curve(dtrunc(x, distr="norm"), -2.5, 2.5, ylim=c(0, 2), ylab="f(x)")
curve(dtrunc(x, distr="norm", lwr=-0.5, upr=0.1), add=TRUE, col=4, n=n)
curve(dtrunc(x, distr="norm", lwr=-0.75, upr=0.25), add=TRUE, col=3, n=n)
curve(dtrunc(x, distr="norm", lwr=-1, upr=1), add=TRUE, col=2, n=n)Shiny example 1: regular slider
library(shiny)
library(intrval)
library(qcc)
data(pistonrings)
mu <- mean(pistonrings$diameter[pistonrings$trial])
SD <- sd(pistonrings$diameter[pistonrings$trial])
x <- pistonrings$diameter[!pistonrings$trial]
## UI function
ui <- fluidPage(
plotOutput("plot"),
sliderInput("x", "x SD:",
min=0, max=5, value=0, step=0.1,
animate=animationOptions(100)
)
)
# Server logic
server <- function(input, output) {
output$plot <- renderPlot({
Main <- paste("Shewhart quality control chart",
"diameter of piston rings", sprintf("+/- %.1f SD", input$x),
sep="\n")
iv <- mu + input$x * c(-SD, SD)
plot(x, pch = 19, col = x %)(% iv +1, type = "b",
ylim = mu + 5 * c(-SD, SD), main = Main)
abline(h = mu)
abline(h = iv, lty = 2)
})
}
## Run shiny app
if (interactive()) shinyApp(ui, server)Shiny example 2: range slider
library(shiny)
library(intrval)
set.seed(1)
n <- 10^4
x <- round(runif(n, -2, 2), 2)
y <- round(runif(n, -2, 2), 2)
d <- round(sqrt(x^2 + y^2), 2)
## UI function
ui <- fluidPage(
titlePanel("intrval example with shiny"),
sidebarLayout(
sidebarPanel(
sliderInput("bb_x", "x value:",
min=min(x), max=max(x), value=range(x),
step=round(diff(range(x))/20, 1), animate=TRUE
),
sliderInput("bb_y", "y value:",
min = min(y), max = max(y), value = range(y),
step=round(diff(range(y))/20, 1), animate=TRUE
),
sliderInput("bb_d", "radial distance:",
min = 0, max = max(d), value = c(0, max(d)/2),
step=round(max(d)/20, 1), animate=TRUE
)
),
mainPanel(
plotOutput("plot")
)
)
)
# Server logic
server <- function(input, output) {
output$plot <- renderPlot({
iv1 <- x %[]% input$bb_x & y %[]% input$bb_y
iv2 <- x %[]% input$bb_y & y %[]% input$bb_x
iv3 <- d %()% input$bb_d
op <- par(mfrow=c(1,2))
plot(x, y, pch = 19, cex = 0.25, col = iv1 + iv2 + 3,
main = "Intersecting bounding boxes")
plot(x, y, pch = 19, cex = 0.25, col = iv3 + 1,
main = "Deck the halls:\ndistance range from center")
par(op)
})
}
## Run shiny app
if (interactive()) shinyApp(ui, server)