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 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")-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 %
-# TRUE-Dates
-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] FALSE-Truncated 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)
