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 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.
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).
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 |
| Equal | Not equal | Less than | Greater than |
|---|---|---|---|
%[]% |
%)(% |
%[<]% |
%[>]% |
%[)% |
%)[% |
%[<)% |
%[>)% |
%(]% |
%](% |
%(<]% |
%(>]% |
%()% |
%][% |
%(<)% |
%(>)% |
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, or1Lwhen 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 |
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.
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%).
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")x <- seq(0, 4*24*60*60, 60*60)
dt <- as.POSIXct(x, origin="2000-01-01 00:00:00")
f <- as.POSIXlt(dt)$hour %[]% c(0, 11)
plot(sin(x) ~ dt, type="l", col="grey",
main = "Filtering date/time objects")
points(sin(x) ~ dt, pch = 19, col = f + 1)library(qcc)
data(pistonrings)
mu <- mean(pistonrings$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 %
# TRUEDATE <- 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] FALSE(2 * 1:5) %[]% (c(2, 3) * 2)
# [1] FALSE TRUE TRUE FALSE FALSE
2 * 1:5 %[]% (c(2, 3) * 2)
# [1] 0 0 0 2 2
(2 * 1:5) %[]% c(2, 3) * 2
# [1] 2 0 0 0 0
2 * 1:5 %[]% c(2, 3) * 2
# [1] 0 4 4 0 0The 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] TRUE
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)
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)
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)