From 3c71f470d7231a541ebf41dcfd119853b3d3e5b6 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 4 Sep 2022 12:03:48 -0400 Subject: [PATCH 01/80] fix some CMD check errors --- DESCRIPTION | 2 +- R/ggbiplot.r | 11 +++++++---- R/ggscreeplot.r | 6 ++++-- man/wine.Rd | 4 +++- 4 files changed, 15 insertions(+), 8 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index f90b3a7..d301b2a 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -8,7 +8,7 @@ Maintainer: Vincent Q. Vu Description: A ggplot2 based biplot. It provides a drop-in replacement for biplot.princomp(). It implements a biplot and scree plot using ggplot2. -Depends: +Imports: ggplot2, plyr, scales, grid License: GPL-2 URL: http://github.com/vqv/ggbiplot diff --git a/R/ggbiplot.r b/R/ggbiplot.r index e0e06e6..e16f8d6 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -33,11 +33,14 @@ #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) #' @param circle draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1) +#' @param circle.prob size of circle #' @param var.axes draw arrows for the variables? #' @param varname.size size of the text for variable names #' @param varname.adjust adjustment factor the placement of the variable names, >= 1 means farther from the arrow #' @param varname.abbrev whether or not to abbreviate the variable names #' +#' @importFrom stats predict qchisq var +#' @importFrom scales muted #' @return a ggplot2 plot #' @export #' @examples @@ -54,10 +57,10 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, varname.size = 3, varname.adjust = 1.5, varname.abbrev = FALSE, ...) { - library(ggplot2) - library(plyr) - library(scales) - library(grid) + # library(ggplot2) + # library(plyr) + # library(scales) + # library(grid) stopifnot(length(choices) == 2) diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index d6347e0..8318aba 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -20,8 +20,10 @@ #' Screeplot for Principal Components #' -#' @param pcobj an object returned by prcomp() or princomp() -#' @param type the type of scree plot. 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace. +#' @param pcobj an object returned by prcomp() or princomp() +#' @param type the type of scree plot. +#' 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. +#' 'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace. #' @export #' @examples #' data(wine) diff --git a/man/wine.Rd b/man/wine.Rd index ec50e7f..79ce44c 100644 --- a/man/wine.Rd +++ b/man/wine.Rd @@ -1,5 +1,6 @@ \name{wine} \alias{wine} +\alias{wine.class} \docType{data} \title{ Chemical composition of three cultivars of wine @@ -20,6 +21,7 @@ http://archive.ics.uci.edu/ml/datasets/Wine data(wine) wine.pca <- prcomp(wine, scale. = TRUE) print(ggscreeplot(wine.pca)) -print(ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, groups = wine.class, ellipse = TRUE, circle = TRUE)) +print(ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, + groups = wine.class, ellipse = TRUE, circle = TRUE)) } \keyword{datasets} From 38a99daaff40ff0fd49b0460f35ded39151f1dcc Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 4 Sep 2022 12:49:18 -0400 Subject: [PATCH 02/80] fix more errors & warnings; use roxygen2 for .Rd --- DESCRIPTION | 5 +-- NAMESPACE | 7 ++++ R/ggbiplot.r | 10 ++++- R/ggscreeplot.r | 2 +- R/wine.R | 29 ++++++++++++++ man/ggbiplot.Rd | 99 +++++++++++++++++++++++++--------------------- man/ggscreeplot.Rd | 25 ++++++------ man/wine.Rd | 39 ++++++++++-------- 8 files changed, 136 insertions(+), 80 deletions(-) create mode 100644 R/wine.R diff --git a/DESCRIPTION b/DESCRIPTION index d301b2a..aa551ce 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -11,7 +11,6 @@ Description: A ggplot2 based biplot. It provides a drop-in Imports: ggplot2, plyr, scales, grid License: GPL-2 +Encoding: UTF-8 URL: http://github.com/vqv/ggbiplot -Collate: - 'ggbiplot.r' - 'ggscreeplot.r' +RoxygenNote: 7.2.1 diff --git a/NAMESPACE b/NAMESPACE index eef88a6..993b9b2 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -1,2 +1,9 @@ +# Generated by roxygen2: do not edit by hand + export(ggbiplot) export(ggscreeplot) +import(ggplot2) +importFrom(scales,muted) +importFrom(stats,predict) +importFrom(stats,qchisq) +importFrom(stats,var) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index e16f8d6..4a7e443 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -38,15 +38,21 @@ #' @param varname.size size of the text for variable names #' @param varname.adjust adjustment factor the placement of the variable names, >= 1 means farther from the arrow #' @param varname.abbrev whether or not to abbreviate the variable names +#' @param ... other arguments passed down #' +#' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted -#' @return a ggplot2 plot +#' @return a ggplot2 plot object #' @export #' @examples #' data(wine) +#' library(ggplot2) #' wine.pca <- prcomp(wine, scale. = TRUE) -#' print(ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, groups = wine.class, ellipse = TRUE, circle = TRUE)) +#' ggbiplot(wine.pca, +#' obs.scale = 1, var.scale = 1, +#' groups = wine.class, +#' ellipse = TRUE, circle = TRUE) #' ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale, diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index 8318aba..c05a67d 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -28,7 +28,7 @@ #' @examples #' data(wine) #' wine.pca <- prcomp(wine, scale. = TRUE) -#' print(ggscreeplot(wine.pca)) +#' ggscreeplot(wine.pca) #' ggscreeplot <- function(pcobj, type = c('pev', 'cev')) { diff --git a/R/wine.R b/R/wine.R new file mode 100644 index 0000000..73876c4 --- /dev/null +++ b/R/wine.R @@ -0,0 +1,29 @@ +#' @title Wine dataset +#' @name wine +#' @aliases wine.class +#' @description +#' Results of a chemical analysis of wines grown in the same region in Italy, +#' derived from three different cultivars. The analysis determined the +#' quantities of 13 chemical constituents found in each of the three types of wines. +#' +#' The cultivars, 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. +#' +#' +#' @docType data +#' @usage data(wine) +#' @format +#' A \code{wine} data frame consisting of 178 observations (rows) and +#' 13 columns and vector \code{wine.class} of factors indicating the cultivars. +#' @source UCI Machine Learning Repository (\url{http://archive.ics.uci.edu/ml/datasets/Wine}) +#' +#' @examples +#' data(wine) +#' table(wine.class) +#' +#' wine.pca <- prcomp(wine, scale. = TRUE) +#' ggscreeplot(wine.pca) +#' ggbiplot(wine.pca, +#' obs.scale = 1, var.scale = 1, +#' groups = wine.class, ellipse = TRUE, circle = TRUE) + +NULL diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 82e2070..c3c7c34 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -1,74 +1,83 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/ggbiplot.r \name{ggbiplot} \alias{ggbiplot} \title{Biplot for Principal Components using ggplot2} \usage{ - ggbiplot(pcobj, choices = 1:2, scale = 1, pc.biplot = - TRUE, obs.scale = 1 - scale, var.scale = scale, groups = - NULL, ellipse = FALSE, ellipse.prob = 0.68, labels = - NULL, labels.size = 3, alpha = 1, var.axes = TRUE, circle - = FALSE, circle.prob = 0.69, varname.size = 3, - varname.adjust = 1.5, varname.abbrev = FALSE, ...) +ggbiplot( + pcobj, + choices = 1:2, + scale = 1, + pc.biplot = TRUE, + obs.scale = 1 - scale, + var.scale = scale, + groups = NULL, + ellipse = FALSE, + ellipse.prob = 0.68, + labels = NULL, + labels.size = 3, + alpha = 1, + var.axes = TRUE, + circle = FALSE, + circle.prob = 0.69, + varname.size = 3, + varname.adjust = 1.5, + varname.abbrev = FALSE, + ... +) } \arguments{ - \item{pcobj}{an object returned by prcomp() or - princomp()} +\item{pcobj}{an object returned by prcomp() or princomp()} - \item{choices}{which PCs to plot} +\item{choices}{which PCs to plot} - \item{scale}{covariance biplot (scale = 1), form biplot - (scale = 0). When scale = 1, the inner product between - the variables approximates the covariance and the - distance between the points approximates the Mahalanobis - distance.} +\item{scale}{covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance.} - \item{obs.scale}{scale factor to apply to observations} +\item{pc.biplot}{for compatibility with biplot.princomp()} - \item{var.scale}{scale factor to apply to variables} +\item{obs.scale}{scale factor to apply to observations} - \item{pc.biplot}{for compatibility with - biplot.princomp()} +\item{var.scale}{scale factor to apply to variables} - \item{groups}{optional factor variable indicating the - groups that the observations belong to. If provided the - points will be colored according to groups} +\item{groups}{optional factor variable indicating the groups that the observations belong to. If provided the points will be colored according to groups} - \item{ellipse}{draw a normal data ellipse for each - group?} +\item{ellipse}{draw a normal data ellipse for each group?} - \item{ellipse.prob}{size of the ellipse in Normal - probability} +\item{ellipse.prob}{size of the ellipse in Normal probability} - \item{labels}{optional vector of labels for the - observations} +\item{labels}{optional vector of labels for the observations} - \item{labels.size}{size of the text used for the labels} +\item{labels.size}{size of the text used for the labels} - \item{alpha}{alpha transparency value for the points (0 = - TRUEransparent, 1 = opaque)} +\item{alpha}{alpha transparency value for the points (0 = transparent, 1 = opaque)} - \item{circle}{draw a correlation circle? (only applies - when prcomp was called with scale = TRUE and when - var.scale = 1)} +\item{var.axes}{draw arrows for the variables?} - \item{var.axes}{draw arrows for the variables?} +\item{circle}{draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1)} - \item{varname.size}{size of the text for variable names} +\item{circle.prob}{size of circle} - \item{varname.adjust}{adjustment factor the placement of - the variable names, >= 1 means farther from the arrow} +\item{varname.size}{size of the text for variable names} - \item{varname.abbrev}{whether or not to abbreviate the - variable names} +\item{varname.adjust}{adjustment factor the placement of the variable names, >= 1 means farther from the arrow} + +\item{varname.abbrev}{whether or not to abbreviate the variable names} + +\item{...}{other arguments passed down} } \value{ - a ggplot2 plot +a ggplot2 plot object } \description{ - Biplot for Principal Components using ggplot2 +Biplot for Principal Components using ggplot2 } \examples{ -data(wine) -wine.pca <- prcomp(wine, scale. = TRUE) -print(ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, groups = wine.class, ellipse = TRUE, circle = TRUE)) -} + data(wine) + library(ggplot2) + wine.pca <- prcomp(wine, scale. = TRUE) + ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + groups = wine.class, + ellipse = TRUE, circle = TRUE) +} diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd index 1e7ce96..e0b6cfd 100644 --- a/man/ggscreeplot.Rd +++ b/man/ggscreeplot.Rd @@ -1,25 +1,24 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/ggscreeplot.r \name{ggscreeplot} \alias{ggscreeplot} \title{Screeplot for Principal Components} \usage{ - ggscreeplot(pcobj, type = c("pev", "cev")) +ggscreeplot(pcobj, type = c("pev", "cev")) } \arguments{ - \item{pcobj}{an object returned by prcomp() or - princomp()} +\item{pcobj}{an object returned by prcomp() or princomp()} - \item{type}{the type of scree plot. 'pev' corresponds - proportion of explained variance, i.e. the eigenvalues - divided by the trace. 'cev' corresponds to the cumulative - proportion of explained variance, i.e. the partial sum of - the first k eigenvalues divided by the trace.} +\item{type}{the type of scree plot. +'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. +'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.} } \description{ - Screeplot for Principal Components +Screeplot for Principal Components } \examples{ -data(wine) -wine.pca <- prcomp(wine, scale. = TRUE) -print(ggscreeplot(wine.pca)) -} + data(wine) + wine.pca <- prcomp(wine, scale. = TRUE) + ggscreeplot(wine.pca) +} diff --git a/man/wine.Rd b/man/wine.Rd index 79ce44c..c3fa1bf 100644 --- a/man/wine.Rd +++ b/man/wine.Rd @@ -1,27 +1,34 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/wine.R +\docType{data} \name{wine} \alias{wine} \alias{wine.class} -\docType{data} -\title{ -Chemical composition of three cultivars of wine -} -\description{ -Chemical constituents of wines from three different cultivars grown in the same region in Italy. The cultivars, -'barolo', 'barbera', and 'grignolino', are indicated in wine.class. -} -\usage{data(wine)} +\title{Wine dataset} \format{ - The format is: - chr "wine" +A \code{wine} data frame consisting of 178 observations (rows) and +13 columns and vector \code{wine.class} of factors indicating the cultivars. } \source{ -http://archive.ics.uci.edu/ml/datasets/Wine +UCI Machine Learning Repository (\url{http://archive.ics.uci.edu/ml/datasets/Wine}) +} +\usage{ +data(wine) +} +\description{ +Results of a chemical analysis of wines grown in the same region in Italy, + derived from three different cultivars. The analysis determined the + quantities of 13 chemical constituents found in each of the three types of wines. + + The cultivars, 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. } \examples{ data(wine) +table(wine.class) + wine.pca <- prcomp(wine, scale. = TRUE) -print(ggscreeplot(wine.pca)) -print(ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, - groups = wine.class, ellipse = TRUE, circle = TRUE)) +ggscreeplot(wine.pca) +ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + groups = wine.class, ellipse = TRUE, circle = TRUE) } -\keyword{datasets} From 91dc59ddd4b33f3bac4bdde03c025040a70da808 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Mon, 5 Sep 2022 12:36:25 -0400 Subject: [PATCH 03/80] add varname.color, point.size args --- .Rbuildignore | 1 + DESCRIPTION | 2 +- NAMESPACE | 1 + NEWS.md | 10 ++++++++++ R/ggbiplot.r | 50 +++++++++++++++++++++++++++++++++---------------- extra/testing.R | 36 +++++++++++++++++++++++++++++++++++ man/ggbiplot.Rd | 14 ++++++++++++-- 7 files changed, 95 insertions(+), 19 deletions(-) create mode 100644 NEWS.md create mode 100644 extra/testing.R diff --git a/.Rbuildignore b/.Rbuildignore index 8453a6f..c3934f2 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -2,3 +2,4 @@ ^\.Rproj\.user$ ^README\.Rmd$ ^README-.*\.png$ +^extra/$ diff --git a/DESCRIPTION b/DESCRIPTION index aa551ce..42e2279 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: ggbiplot Type: Package Title: A ggplot2 based biplot -Version: 0.55 +Version: 0.56 Date: 2011-10-23 Author: Vincent Q. Vu Maintainer: Vincent Q. Vu diff --git a/NAMESPACE b/NAMESPACE index 993b9b2..a3ecdfd 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -3,6 +3,7 @@ export(ggbiplot) export(ggscreeplot) import(ggplot2) +importFrom(plyr,ddply) importFrom(scales,muted) importFrom(stats,predict) importFrom(stats,qchisq) diff --git a/NEWS.md b/NEWS.md new file mode 100644 index 0000000..f07fcf6 --- /dev/null +++ b/NEWS.md @@ -0,0 +1,10 @@ +## Version 0.56 + +- Fixed many documentation errors and warnings +- Use roxygen2 for documentation +- added varname.color to replace fixed 'muted("red")' +- tweaked arrow style +- increased default thickness of variable vectors +- add point.size argument + + diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 4a7e443..1db6092 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -26,9 +26,12 @@ #' @param obs.scale scale factor to apply to observations #' @param var.scale scale factor to apply to variables #' @param pc.biplot for compatibility with biplot.princomp() -#' @param groups optional factor variable indicating the groups that the observations belong to. If provided the points will be colored according to groups +#' @param groups optional factor variable indicating the groups that the observations belong to. +#' If provided the points will be colored according to groups. +#' @param point.size Size of observation points. #' @param ellipse draw a normal data ellipse for each group? -#' @param ellipse.prob size of the ellipse in Normal probability +#' @param ellipse.prob coverage size of the data ellipse in Normal probability +#' @param ellipse.size thickness of the line outlining the ellipses #' @param labels optional vector of labels for the observations #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) @@ -36,6 +39,7 @@ #' @param circle.prob size of circle #' @param var.axes draw arrows for the variables? #' @param varname.size size of the text for variable names +#' @param varname.color color for the variable vectors and names #' @param varname.adjust adjustment factor the placement of the variable names, >= 1 means farther from the arrow #' @param varname.abbrev whether or not to abbreviate the variable names #' @param ... other arguments passed down @@ -43,6 +47,7 @@ #' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted +#' @importFrom plyr ddply #' @return a ggplot2 plot object #' @export #' @examples @@ -55,13 +60,18 @@ #' ellipse = TRUE, circle = TRUE) #' ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, - obs.scale = 1 - scale, var.scale = scale, - groups = NULL, ellipse = FALSE, ellipse.prob = 0.68, - labels = NULL, labels.size = 3, alpha = 1, - var.axes = TRUE, - circle = FALSE, circle.prob = 0.69, - varname.size = 3, varname.adjust = 1.5, - varname.abbrev = FALSE, ...) + obs.scale = 1 - scale, var.scale = scale, + groups = NULL, + point.size = 1.5, + ellipse = FALSE, ellipse.prob = 0.68, ellipse.size = NULL, + labels = NULL, labels.size = 3, + alpha = 1, + var.axes = TRUE, + circle = FALSE, circle.prob = 0.69, + varname.size = 3, + varname.adjust = 1.5, + varname.color = 'darkred', + varname.abbrev = FALSE, ...) { # library(ggplot2) # library(plyr) @@ -96,6 +106,9 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, stop('Expected a object of class prcomp, princomp, PCA, or lda') } + # shutup 'no visible binding...' +# utils::globalVariables(c("xvar", "yvar", "varname", "angle", "hjust")) + # Scores choices <- pmin(choices, ncol(u)) df.u <- as.data.frame(sweep(u[,choices], 2, d[choices]^obs.scale, FUN='*')) @@ -154,7 +167,9 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # Base plot g <- ggplot(data = df.u, aes(x = xvar, y = yvar)) + - xlab(u.axis.labs[1]) + ylab(u.axis.labs[2]) + coord_equal() + xlab(u.axis.labs[1]) + + ylab(u.axis.labs[2]) + + coord_equal() if(var.axes) { # Draw circle @@ -162,16 +177,18 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, { theta <- c(seq(-pi, pi, length = 50), seq(pi, -pi, length = 50)) circle <- data.frame(xvar = r * cos(theta), yvar = r * sin(theta)) - g <- g + geom_path(data = circle, color = muted('white'), + g <- g + geom_path(data = circle, color = scales::muted('white'), size = 1/2, alpha = 1/3) } # Draw directions + arrow_style <- arrow(length = unit(1/2, 'picas'), type="closed", angle=15) g <- g + geom_segment(data = df.v, aes(x = 0, y = 0, xend = xvar, yend = yvar), - arrow = arrow(length = unit(1/2, 'picas')), - color = muted('red')) + arrow = arrow_style, + color = varname.color, + size = 1.2) } # Draw either labels or points @@ -184,7 +201,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, } } else { if(!is.null(df.u$groups)) { - g <- g + geom_point(aes(color = groups), alpha = alpha) + g <- g + geom_point(aes(color = groups), alpha = alpha, size = point.size) } else { g <- g + geom_point(alpha = alpha) } @@ -206,7 +223,8 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, groups = x$groups[1]) }) names(ell)[1:2] <- c('xvar', 'yvar') - g <- g + geom_path(data = ell, aes(color = groups, group = groups)) + g <- g + geom_path(data = ell, aes(color = groups, group = groups, size = ellipse.size)) +# g <- g + geom_polygon(data = ell, aes(color = groups, group = groups, size = ellipse.size)) } # Label the variable axes @@ -215,7 +233,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, geom_text(data = df.v, aes(label = varname, x = xvar, y = yvar, angle = angle, hjust = hjust), - color = 'darkred', size = varname.size) + color = varname.color, size = varname.size) } # Change the name of the legend for groups # if(!is.null(groups)) { diff --git a/extra/testing.R b/extra/testing.R new file mode 100644 index 0000000..0df0446 --- /dev/null +++ b/extra/testing.R @@ -0,0 +1,36 @@ +data(wine, package="ggbiplot") +wine.pca <- prcomp(wine, scale. = TRUE) +ggbiplot(wine.pca, groups=wine.class, + ellipse = TRUE, + circle = TRUE, + varname.color = "darkred", + varname.size = 4) + + +library(dplyr) +library(ggplot2) +data(penguins, package = "palmerpenguins") +peng <- penguins |> + rename( + bill_length = bill_length_mm, + bill_depth = bill_depth_mm, + flipper_length = flipper_length_mm, + body_mass = body_mass_g + ) |> + filter(!is.na(bill_depth), + !is.na(sex)) + + +peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, + data=peng, + na.action=na.omit, + scale. = TRUE) + +ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, + groups = peng$species, point.size=2, + varname.size = 5, varname.color = scales::muted("red"), + ellipse = TRUE, + circle = TRUE) + + scale_color_discrete(name = 'Penguin Species') + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index c3c7c34..73101f7 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -12,8 +12,10 @@ ggbiplot( obs.scale = 1 - scale, var.scale = scale, groups = NULL, + point.size = 1.5, ellipse = FALSE, ellipse.prob = 0.68, + ellipse.size = NULL, labels = NULL, labels.size = 3, alpha = 1, @@ -22,6 +24,7 @@ ggbiplot( circle.prob = 0.69, varname.size = 3, varname.adjust = 1.5, + varname.color = "darkred", varname.abbrev = FALSE, ... ) @@ -39,11 +42,16 @@ ggbiplot( \item{var.scale}{scale factor to apply to variables} -\item{groups}{optional factor variable indicating the groups that the observations belong to. If provided the points will be colored according to groups} +\item{groups}{optional factor variable indicating the groups that the observations belong to. +If provided the points will be colored according to groups.} + +\item{point.size}{Size of observation points.} \item{ellipse}{draw a normal data ellipse for each group?} -\item{ellipse.prob}{size of the ellipse in Normal probability} +\item{ellipse.prob}{coverage size of the data ellipse in Normal probability} + +\item{ellipse.size}{thickness of the line outlining the ellipses} \item{labels}{optional vector of labels for the observations} @@ -61,6 +69,8 @@ ggbiplot( \item{varname.adjust}{adjustment factor the placement of the variable names, >= 1 means farther from the arrow} +\item{varname.color}{color for the variable vectors and names} + \item{varname.abbrev}{whether or not to abbreviate the variable names} \item{...}{other arguments passed down} From 673e20f69b8af7f502be628f6f9c0e3ff1f23cbe Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Thu, 29 Jun 2023 16:51:07 -0400 Subject: [PATCH 04/80] replace plyr w/ dplyr --- .Rbuildignore | 2 +- DESCRIPTION | 8 ++++---- NAMESPACE | 8 +++++++- R/ggbiplot.r | 49 +++++++++++++++++++++++++++++++++++-------------- 4 files changed, 47 insertions(+), 20 deletions(-) diff --git a/.Rbuildignore b/.Rbuildignore index c3934f2..2fdf9ba 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -2,4 +2,4 @@ ^\.Rproj\.user$ ^README\.Rmd$ ^README-.*\.png$ -^extra/$ +extra/ diff --git a/DESCRIPTION b/DESCRIPTION index 42e2279..60b8c1f 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,16 +1,16 @@ Package: ggbiplot Type: Package Title: A ggplot2 based biplot -Version: 0.56 -Date: 2011-10-23 +Version: 0.6.0 +Date: 2023-06-29 Author: Vincent Q. Vu Maintainer: Vincent Q. Vu Description: A ggplot2 based biplot. It provides a drop-in replacement for biplot.princomp(). It implements a biplot and scree plot using ggplot2. Imports: - ggplot2, plyr, scales, grid + ggplot2, dplyr, scales, tidyr, purrr License: GPL-2 Encoding: UTF-8 URL: http://github.com/vqv/ggbiplot -RoxygenNote: 7.2.1 +RoxygenNote: 7.2.3 diff --git a/NAMESPACE b/NAMESPACE index a3ecdfd..59568a7 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -3,8 +3,14 @@ export(ggbiplot) export(ggscreeplot) import(ggplot2) -importFrom(plyr,ddply) +importFrom(dplyr,filter) +importFrom(dplyr,group_by) +importFrom(dplyr,n) +importFrom(dplyr,select) +importFrom(dplyr,summarize) +importFrom(purrr,map) importFrom(scales,muted) importFrom(stats,predict) importFrom(stats,qchisq) importFrom(stats,var) +importFrom(tidyr,unnest) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 1db6092..6bded6b 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -47,7 +47,10 @@ #' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted -#' @importFrom plyr ddply +## @importFrom plyr ddply +#' @importFrom dplyr filter n summarize select group_by +#' @importFrom tidyr unnest +#' @importFrom purrr map #' @return a ggplot2 plot object #' @export #' @examples @@ -107,7 +110,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, } # shutup 'no visible binding...' -# utils::globalVariables(c("xvar", "yvar", "varname", "angle", "hjust")) + utils::globalVariables(c("xvar", "yvar", "varname", "angle", "hjust")) # Scores choices <- pmin(choices, ncol(u)) @@ -188,7 +191,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, aes(x = 0, y = 0, xend = xvar, yend = yvar), arrow = arrow_style, color = varname.color, - size = 1.2) + linewidth = 1.2) } # Draw either labels or points @@ -212,17 +215,35 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, theta <- c(seq(-pi, pi, length = 50), seq(pi, -pi, length = 50)) circle <- cbind(cos(theta), sin(theta)) - ell <- ddply(df.u, 'groups', function(x) { - if(nrow(x) <= 2) { - return(NULL) - } - sigma <- var(cbind(x$xvar, x$yvar)) - mu <- c(mean(x$xvar), mean(x$yvar)) - ed <- sqrt(qchisq(ellipse.prob, df = 2)) - data.frame(sweep(circle %*% chol(sigma) * ed, 2, mu, FUN = '+'), - groups = x$groups[1]) - }) - names(ell)[1:2] <- c('xvar', 'yvar') + # ell <- ddply(df.u, 'groups', function(x) { + # if(nrow(x) <= 2) { + # return(NULL) + # } + # sigma <- var(cbind(x$xvar, x$yvar)) + # mu <- c(mean(x$xvar), mean(x$yvar)) + # ed <- sqrt(qchisq(ellipse.prob, df = 2)) + # data.frame(sweep(circle %*% chol(sigma) * ed, 2, mu, FUN = '+'), + # groups = x$groups[1]) + # }) + # names(ell)[1:2] <- c('xvar', 'yvar') + + ell <- + df.u |> + group_by(groups) |> + filter(n() > 2) |> + summarize( + sigma = list(var(cbind(xvar, yvar))), + mu = list(c(mean(xvar), mean(yvar))), + ed = sqrt(qchisq(ellipse.prob, df = 2)), + circle_chol = list(circle %*% chol(sigma[[1]]) * ed), + ell = list(sweep(circle_chol[[1]], 2, mu[[1]], FUN = "+")), + xvar = map(ell, ~.x[,1]), + yvar = map(ell, ~.x[,2]), + .groups = "drop" + ) |> + select(xvar, yvar, groups) |> + tidyr::unnest(c(xvar, yvar)) + g <- g + geom_path(data = ell, aes(color = groups, group = groups, size = ellipse.size)) # g <- g + geom_polygon(data = ell, aes(color = groups, group = groups, size = ellipse.size)) } From e7a60ce10197755ecd0335f5b596952a5f8b8c72 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Thu, 29 Jun 2023 16:59:47 -0400 Subject: [PATCH 05/80] fix undef'd global vars, etc --- R/ggbiplot.r | 3 ++- R/ggscreeplot.r | 1 + 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 6bded6b..b15c0b1 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -110,7 +110,8 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, } # shutup 'no visible binding...' - utils::globalVariables(c("xvar", "yvar", "varname", "angle", "hjust")) +# utils::globalVariables(c("xvar", "yvar", "varname", "angle", "hjust")) + angle <- circle_chol <- ed <- hjust <- mu <- sigma <- varname <- xvar <- yvar <-NULL # Scores choices <- pmin(choices, ncol(u)) diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index c05a67d..ffcbc54 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -42,6 +42,7 @@ ggscreeplot <- function(pcobj, type = c('pev', 'cev')) pev = 'proportion of explained variance', cev = 'cumulative proportion of explained variance') + PC <- NULL df <- data.frame(PC = 1:length(d), yvar = yvar) ggplot(data = df, aes(x = PC, y = yvar)) + From d10dc115be7fc6f7d306ac457f8b061445ece628 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Fri, 30 Jun 2023 05:36:21 -0400 Subject: [PATCH 06/80] fix linewidths; add MF as author --- DESCRIPTION | 7 +++++-- R/ggbiplot.r | 27 +++++++++++++++++++-------- extra/testing.R | 5 ++++- 3 files changed, 28 insertions(+), 11 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 60b8c1f..c06133f 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -3,8 +3,11 @@ Type: Package Title: A ggplot2 based biplot Version: 0.6.0 Date: 2023-06-29 -Author: Vincent Q. Vu -Maintainer: Vincent Q. Vu +Authors@R: c( + person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut", "cre")), + person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut"), + comment = c(ORCID = "0000-0002-3237-0941")) + ) Description: A ggplot2 based biplot. It provides a drop-in replacement for biplot.princomp(). It implements a biplot and scree plot using ggplot2. diff --git a/R/ggbiplot.r b/R/ggbiplot.r index b15c0b1..5757ade 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -31,7 +31,7 @@ #' @param point.size Size of observation points. #' @param ellipse draw a normal data ellipse for each group? #' @param ellipse.prob coverage size of the data ellipse in Normal probability -#' @param ellipse.size thickness of the line outlining the ellipses +#' @param ellipse.linewidth thickness of the line outlining the ellipses #' @param labels optional vector of labels for the observations #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) @@ -66,11 +66,13 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale, groups = NULL, point.size = 1.5, - ellipse = FALSE, ellipse.prob = 0.68, ellipse.size = NULL, + ellipse = FALSE, + ellipse.prob = 0.68, + ellipse.linewidth = NULL, labels = NULL, labels.size = 3, alpha = 1, var.axes = TRUE, - circle = FALSE, circle.prob = 0.69, + circle = FALSE, circle.prob = 0.68, varname.size = 3, varname.adjust = 1.5, varname.color = 'darkred', @@ -145,7 +147,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # Append the proportion of explained variance to the axis labels u.axis.labs <- paste(u.axis.labs, - sprintf('(%0.1f%% explained var.)', + sprintf('(%0.1f%%)', 100 * pcobj$sdev[choices]^2/sum(pcobj$sdev^2))) # Score Labels @@ -181,8 +183,9 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, { theta <- c(seq(-pi, pi, length = 50), seq(pi, -pi, length = 50)) circle <- data.frame(xvar = r * cos(theta), yvar = r * sin(theta)) - g <- g + geom_path(data = circle, color = scales::muted('white'), - size = 1/2, alpha = 1/3) + g <- g + geom_path(data = circle, + color = scales::muted('white'), + linewidth = 1/2, alpha = 1/3) } # Draw directions @@ -245,8 +248,16 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, select(xvar, yvar, groups) |> tidyr::unnest(c(xvar, yvar)) - g <- g + geom_path(data = ell, aes(color = groups, group = groups, size = ellipse.size)) -# g <- g + geom_polygon(data = ell, aes(color = groups, group = groups, size = ellipse.size)) + # g <- g + geom_path(data = ell, + # aes(color = groups, + # group = groups), + # linewidth = ellipse.linewidth) + g <- g + geom_polygon(data = ell, + aes(color = groups, + fill = groups +# , group = groups + ), + linewidth = ellipse.linewidth) } # Label the variable axes diff --git a/extra/testing.R b/extra/testing.R index 0df0446..57c7d33 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -2,9 +2,12 @@ data(wine, package="ggbiplot") wine.pca <- prcomp(wine, scale. = TRUE) ggbiplot(wine.pca, groups=wine.class, ellipse = TRUE, + ellipse.linewidth = 1.2, circle = TRUE, varname.color = "darkred", - varname.size = 4) + varname.size = 4) + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') library(dplyr) From 4396103e7b8b95a76d1dbba77cf44953411451fd Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 1 Jul 2023 03:46:30 -0400 Subject: [PATCH 07/80] make MF maintainer --- DESCRIPTION | 4 ++-- R/ggbiplot.r | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index c06133f..9a0ac0f 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -4,8 +4,8 @@ Title: A ggplot2 based biplot Version: 0.6.0 Date: 2023-06-29 Authors@R: c( - person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut", "cre")), - person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut"), + person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut"), + person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre")), comment = c(ORCID = "0000-0002-3237-0941")) ) Description: A ggplot2 based biplot. It provides a drop-in diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 5757ade..f221cb5 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -254,8 +254,8 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # linewidth = ellipse.linewidth) g <- g + geom_polygon(data = ell, aes(color = groups, - fill = groups -# , group = groups + fill = groups, + group = groups ), linewidth = ellipse.linewidth) } From 87acace5c8aa74e58e9e9100b43f6a30340a9af8 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 11:47:20 -0400 Subject: [PATCH 08/80] ellipse.size -> ellipse.linewidth --- DESCRIPTION | 4 ++-- R/ggbiplot.r | 6 +++--- man/ggbiplot.Rd | 6 +++--- 3 files changed, 8 insertions(+), 8 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 9a0ac0f..48c80c1 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -4,8 +4,8 @@ Title: A ggplot2 based biplot Version: 0.6.0 Date: 2023-06-29 Authors@R: c( - person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut"), - person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre")), + person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut")), + person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre"), comment = c(ORCID = "0000-0002-3237-0941")) ) Description: A ggplot2 based biplot. It provides a drop-in diff --git a/R/ggbiplot.r b/R/ggbiplot.r index f221cb5..a3fe1b2 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -189,13 +189,13 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, } # Draw directions - arrow_style <- arrow(length = unit(1/2, 'picas'), type="closed", angle=15) + arrow_style <- arrow(length = unit(1/2, 'picas'), type="closed", angle=15) # MF: was angle=15 g <- g + geom_segment(data = df.v, aes(x = 0, y = 0, xend = xvar, yend = yvar), arrow = arrow_style, color = varname.color, - linewidth = 1.2) + linewidth = 1.4) # MR: was 1.2 } # Draw either labels or points @@ -245,7 +245,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, yvar = map(ell, ~.x[,2]), .groups = "drop" ) |> - select(xvar, yvar, groups) |> + dplyr::select(xvar, yvar, groups) |> tidyr::unnest(c(xvar, yvar)) # g <- g + geom_path(data = ell, diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 73101f7..02836e3 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -15,13 +15,13 @@ ggbiplot( point.size = 1.5, ellipse = FALSE, ellipse.prob = 0.68, - ellipse.size = NULL, + ellipse.linewidth = NULL, labels = NULL, labels.size = 3, alpha = 1, var.axes = TRUE, circle = FALSE, - circle.prob = 0.69, + circle.prob = 0.68, varname.size = 3, varname.adjust = 1.5, varname.color = "darkred", @@ -51,7 +51,7 @@ If provided the points will be colored according to groups.} \item{ellipse.prob}{coverage size of the data ellipse in Normal probability} -\item{ellipse.size}{thickness of the line outlining the ellipses} +\item{ellipse.linewidth}{thickness of the line outlining the ellipses} \item{labels}{optional vector of labels for the observations} From 4d7649dd571ee31f72433967abc04fdef1ff0733 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 12:40:47 -0400 Subject: [PATCH 09/80] Added `var.factor` argument --- NEWS.md | 10 ++++++++-- R/ggbiplot.r | 39 ++++++++++++++++++++++----------------- extra/testing.R | 27 +++++++++++++++++++++++++-- man/ggbiplot.Rd | 4 ++++ 4 files changed, 59 insertions(+), 21 deletions(-) diff --git a/NEWS.md b/NEWS.md index f07fcf6..e8b5129 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,10 +1,16 @@ +## Version 0.6.0 + +- Use `geom_polygon()` rather than `geom_path()` for ellipses +- Added `var.factor` argument to expand or reflect the variable vectors +- moved points/labels code earlier so ellipses and variable vectors are not obscured + ## Version 0.56 - Fixed many documentation errors and warnings - Use roxygen2 for documentation -- added varname.color to replace fixed 'muted("red")' +- added `varname.color` to replace fixed `muted("red")` - tweaked arrow style - increased default thickness of variable vectors -- add point.size argument +- add `point.size` argument diff --git a/R/ggbiplot.r b/R/ggbiplot.r index a3fe1b2..eb4dbf7 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -25,6 +25,8 @@ #' @param scale covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance. #' @param obs.scale scale factor to apply to observations #' @param var.scale scale factor to apply to variables +#' @param var.factor factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +#' (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility. #' @param pc.biplot for compatibility with biplot.princomp() #' @param groups optional factor variable indicating the groups that the observations belong to. #' If provided the points will be colored according to groups. @@ -63,7 +65,9 @@ #' ellipse = TRUE, circle = TRUE) #' ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, - obs.scale = 1 - scale, var.scale = scale, + obs.scale = 1 - scale, + var.scale = scale, + var.factor = 1, # MF groups = NULL, point.size = 1.5, ellipse = FALSE, @@ -122,6 +126,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # Directions v <- sweep(v, 2, d^var.scale, FUN='*') df.v <- as.data.frame(v[, choices]) + df.v <- var.factor * df.v names(df.u) <- c('xvar', 'yvar') names(df.v) <- names(df.u) @@ -177,6 +182,22 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, ylab(u.axis.labs[2]) + coord_equal() + # Draw either labels or points + if(!is.null(df.u$labels)) { + if(!is.null(df.u$groups)) { + g <- g + geom_text(aes(label = labels, color = groups), + size = labels.size) + } else { + g <- g + geom_text(aes(label = labels), size = labels.size) + } + } else { + if(!is.null(df.u$groups)) { + g <- g + geom_point(aes(color = groups), alpha = alpha, size = point.size) + } else { + g <- g + geom_point(alpha = alpha) + } + } + if(var.axes) { # Draw circle if(circle) @@ -198,22 +219,6 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, linewidth = 1.4) # MR: was 1.2 } - # Draw either labels or points - if(!is.null(df.u$labels)) { - if(!is.null(df.u$groups)) { - g <- g + geom_text(aes(label = labels, color = groups), - size = labels.size) - } else { - g <- g + geom_text(aes(label = labels), size = labels.size) - } - } else { - if(!is.null(df.u$groups)) { - g <- g + geom_point(aes(color = groups), alpha = alpha, size = point.size) - } else { - g <- g + geom_point(alpha = alpha) - } - } - # Overlay a concentration ellipse if there are groups if(!is.null(df.u$groups) && ellipse) { theta <- c(seq(-pi, pi, length = 50), seq(pi, -pi, length = 50)) diff --git a/extra/testing.R b/extra/testing.R index 57c7d33..7f548fd 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -30,10 +30,33 @@ peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, scale. = TRUE) ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, + groups = peng$species, point.size=2, + varname.size = 5, varname.color = scales::muted("black"), + ellipse = TRUE, ellipse.linewidth = 1.4, + circle = TRUE) + +# scale_fill_discrete(name = 'Species') + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') + +ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, + var.factor = -1.1, + groups = peng$species, point.size=2, + varname.size = 5, varname.color = scales::muted("black"), + ellipse = TRUE, ellipse.linewidth = 1.4, + circle = TRUE) + + # scale_fill_discrete(name = 'Species') + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') + + +# last two dimensions: outliers +ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, groups = peng$species, point.size=2, varname.size = 5, varname.color = scales::muted("red"), - ellipse = TRUE, + ellipse = TRUE, ellipse.linewidth = 1.4, circle = TRUE) + - scale_color_discrete(name = 'Penguin Species') + + # scale_fill_discrete(name = 'Species') + theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') + + diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 02836e3..08f6f41 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -11,6 +11,7 @@ ggbiplot( pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale, + var.factor = 1, groups = NULL, point.size = 1.5, ellipse = FALSE, @@ -42,6 +43,9 @@ ggbiplot( \item{var.scale}{scale factor to apply to variables} +\item{var.factor}{factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +(\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility.} + \item{groups}{optional factor variable indicating the groups that the observations belong to. If provided the points will be colored according to groups.} From b8889f953ed002689d37eef7a617a878a522b5ed Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 13:13:09 -0400 Subject: [PATCH 10/80] default ellipse.linewidth=1.3, not NULL --- R/ggbiplot.r | 10 ++++++---- extra/testing.R | 1 + 2 files changed, 7 insertions(+), 4 deletions(-) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index eb4dbf7..d1e0ead 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -61,6 +61,7 @@ #' wine.pca <- prcomp(wine, scale. = TRUE) #' ggbiplot(wine.pca, #' obs.scale = 1, var.scale = 1, +#' varname.size = 4, #' groups = wine.class, #' ellipse = TRUE, circle = TRUE) #' @@ -72,7 +73,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, point.size = 1.5, ellipse = FALSE, ellipse.prob = 0.68, - ellipse.linewidth = NULL, + ellipse.linewidth = 1.3, labels = NULL, labels.size = 3, alpha = 1, var.axes = TRUE, @@ -210,7 +211,7 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, } # Draw directions - arrow_style <- arrow(length = unit(1/2, 'picas'), type="closed", angle=15) # MF: was angle=15 + arrow_style <- arrow(length = unit(1/2, 'picas'), type="closed", angle=15) g <- g + geom_segment(data = df.v, aes(x = 0, y = 0, xend = xvar, yend = yvar), @@ -259,9 +260,10 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # linewidth = ellipse.linewidth) g <- g + geom_polygon(data = ell, aes(color = groups, - fill = groups, - group = groups + fill = groups + # group = groups ), + alpha = 0.4, # MF: why doesn't this have any effect? linewidth = ellipse.linewidth) } diff --git a/extra/testing.R b/extra/testing.R index 7f548fd..edaf22a 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -38,6 +38,7 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') +# try reflecting & scaline var vectors ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, var.factor = -1.1, groups = peng$species, point.size=2, From 9b19c4fea56e220ab58865aa6dc5a0d9a26f98ef Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 13:45:26 -0400 Subject: [PATCH 11/80] add Agashi as contributor --- DESCRIPTION | 8 +++++--- man/ggbiplot.Rd | 3 ++- 2 files changed, 7 insertions(+), 4 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 48c80c1..f5bca5c 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -6,14 +6,16 @@ Date: 2023-06-29 Authors@R: c( person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut")), person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre"), - comment = c(ORCID = "0000-0002-3237-0941")) + comment = c(ORCID = "0000-0002-3237-0941")), + person("Aghasi", "Tavadyan", , "a.tavadyan@gmail.com", role = "ctb") ) Description: A ggplot2 based biplot. It provides a drop-in - replacement for biplot.princomp(). It implements a + replacement for biplot.princomp(), but with many enhancements. It implements a biplot and scree plot using ggplot2. Imports: ggplot2, dplyr, scales, tidyr, purrr License: GPL-2 Encoding: UTF-8 -URL: http://github.com/vqv/ggbiplot +URL: https://github.com/friendly/ggbiplot RoxygenNote: 7.2.3 + diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 08f6f41..12f3926 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -16,7 +16,7 @@ ggbiplot( point.size = 1.5, ellipse = FALSE, ellipse.prob = 0.68, - ellipse.linewidth = NULL, + ellipse.linewidth = 1.3, labels = NULL, labels.size = 3, alpha = 1, @@ -91,6 +91,7 @@ Biplot for Principal Components using ggplot2 wine.pca <- prcomp(wine, scale. = TRUE) ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, + varname.size = 4, groups = wine.class, ellipse = TRUE, circle = TRUE) From b5409988502c2ff67895580aa13c61e857c22877 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 15:35:14 -0400 Subject: [PATCH 12/80] change date for win-builder --- DESCRIPTION | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/DESCRIPTION b/DESCRIPTION index f5bca5c..75482f8 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -2,7 +2,7 @@ Package: ggbiplot Type: Package Title: A ggplot2 based biplot Version: 0.6.0 -Date: 2023-06-29 +Date: 2023-09-12 Authors@R: c( person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut")), person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre"), From 694dc9fc24bcd8f691d5d44b989c51bfbd0af6a4 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 15:39:27 -0400 Subject: [PATCH 13/80] add cran-comments --- .Rbuildignore | 1 + cran-comments.md | 10 ++++++++++ 2 files changed, 11 insertions(+) create mode 100644 cran-comments.md diff --git a/.Rbuildignore b/.Rbuildignore index 2fdf9ba..0b73413 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -3,3 +3,4 @@ ^README\.Rmd$ ^README-.*\.png$ extra/ +^cran-comments\.md$ diff --git a/cran-comments.md b/cran-comments.md new file mode 100644 index 0000000..e94b950 --- /dev/null +++ b/cran-comments.md @@ -0,0 +1,10 @@ +## Test environments + +* Windows 10, R version 4.2.3 (2023-03-15 ucrt) +* win-builder + +## R CMD check results + +0 errors | 0 warnings | 1 note + +* This is a new release. From 9cd3a832a6f1e440731b4a5d1fe7d5efe10396e2 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 16:33:24 -0400 Subject: [PATCH 14/80] Title Case in Title --- DESCRIPTION | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 75482f8..7424d24 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ Package: ggbiplot Type: Package -Title: A ggplot2 based biplot +Title: A ggplot2 Based Biplot Version: 0.6.0 Date: 2023-09-12 Authors@R: c( @@ -9,7 +9,7 @@ Authors@R: c( comment = c(ORCID = "0000-0002-3237-0941")), person("Aghasi", "Tavadyan", , "a.tavadyan@gmail.com", role = "ctb") ) -Description: A ggplot2 based biplot. It provides a drop-in +Description: A ggplot2 based biplot. It provides a replacement for biplot.princomp(), but with many enhancements. It implements a biplot and scree plot using ggplot2. Imports: From ec594e170f9d1abc93f15832cebada640d05a24e Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Wed, 13 Sep 2023 16:34:59 -0400 Subject: [PATCH 15/80] add win-builder --- cran-comments.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/cran-comments.md b/cran-comments.md index e94b950..7a4afee 100644 --- a/cran-comments.md +++ b/cran-comments.md @@ -1,7 +1,7 @@ ## Test environments * Windows 10, R version 4.2.3 (2023-03-15 ucrt) -* win-builder +* win-builder, R Under development (unstable) (2023-09-12 r85134 ucrt) ## R CMD check results From 866a3cbef52313d70cc7b1313caafbe15a4f3b3a Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Thu, 14 Sep 2023 10:57:44 -0400 Subject: [PATCH 16/80] work on README --- DESCRIPTION | 1 + R/wine.R | 2 +- README-wine-example-1.png | Bin 54761 -> 0 bytes README.Rmd | 51 +++++++++++++++---- README.md | 65 +++++++++++++++++++----- man/figures/README-wine-biplot-1.png | Bin 0 -> 21689 bytes man/figures/README-wine-example-1.png | Bin 0 -> 21502 bytes man/figures/README-wine-screeplot-1.png | Bin 0 -> 5899 bytes 8 files changed, 93 insertions(+), 26 deletions(-) delete mode 100644 README-wine-example-1.png create mode 100644 man/figures/README-wine-biplot-1.png create mode 100644 man/figures/README-wine-example-1.png create mode 100644 man/figures/README-wine-screeplot-1.png diff --git a/DESCRIPTION b/DESCRIPTION index 7424d24..2e9f3ee 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -17,5 +17,6 @@ Imports: License: GPL-2 Encoding: UTF-8 URL: https://github.com/friendly/ggbiplot +BugReports: https://github.com/friendly/ggbiplot/issues RoxygenNote: 7.2.3 diff --git a/R/wine.R b/R/wine.R index 73876c4..3c5d00f 100644 --- a/R/wine.R +++ b/R/wine.R @@ -6,7 +6,7 @@ #' derived from three different cultivars. The analysis determined the #' quantities of 13 chemical constituents found in each of the three types of wines. #' -#' The cultivars, 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. +#' The grape varieties (cultivars), 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. #' #' #' @docType data diff --git a/README-wine-example-1.png b/README-wine-example-1.png deleted file mode 100644 index 3e0873e66c26ae9e38d8ebbb4e5088710756e2d0..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 54761 zcmd>mRa9J2(`6GpcyK2{13`j2!QI{6J-7!5A-Fq@ySux)ySuwPbMyT(53|Kjd+Jo}s=bRKIT=x;k9Z$JAP|zcn2-Vp^dSQTg4lrj0Q~0mOw15C!P|+c zJAgpQ-T!_d`fUr0Kp+y3xDdaRYwF3Wsg|NDKImfKg#Odr8a^}>TZ3t7*4A2ZR$bj} zopS-$xg~sVPQ|*^Bce%kRns0a7*gmCW)T%m{l1NON?{1`^Jmob_Xrf+{j_H?h_qCP zaT2QF55G|b;Bc{$+aQ0yef}MJr|%~UoDoqeT!A+RK>xqK6kLZO$PO z0v9FLvuRiJNue483u|ci3QI)*^>@_o2L#6j(N&S2vB}>+D%&R-mNO&FurBfEd{yTh^NbR 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zl*{4#V0RM)fgIZ-3kKI1!5CO)8(%Fcb$<__3`Yf0<<-x>DxP092|qkhVSN49M~|jy z;x~DQ^?E%ju!hzM-L>)YFjh60A8K+2wdw9;7EQk;$eE2HPS^t&H}(icqTbV|xe2A+ zy2k|z5PzWYfm-h-UCfVlW-L04Ts4Cm0g(OkejdZqtRvZs)NoCc{8Cuq)-=~i%1Z7tP8zc2Lyod4r M261v -**NEWS**: Active development of ggbiplot has moved to the [experimental branch](https://github.com/vqv/ggbiplot/tree/experimental) + +[![CRAN status](https://www.r-pkg.org/badges/version/ggbiplot)](https://CRAN.R-project.org/package=ggbiplot) +[![Last Commit](https://img.shields.io/github/last-commit/friendly/ggbiplot)](https://github.com/friendly/ggbiplot) + + + + +This repo for the [ggbiplot package](https://CRAN.R-project.org/package=ggbiplot) +was forked from [https://github.com/vqv/ggbiplot](https://github.com/vqv/ggbiplot) by Vince Yu, which has been dormant +since 2015. + +The goal is to complete that development and publish a new version on CRAN. +There is also an [experimental branch](https://github.com/friendly/ggbiplot/tree/experimental) which attempts to +simplify the code, but this has some unresolved problems. ```{r, echo = FALSE} knitr::opts_chunk$set( collapse = TRUE, + message = FALSE, + warning = FALSE, comment = "#>", - fig.path = "README-" + fig.path = "man/figures/README-" ) ``` @@ -23,25 +36,41 @@ An implementation of the biplot using ggplot2. The package provides two functio `ggbiplot` aims to be a drop-in replacement for the built-in R function `biplot.princomp()` with extended functionality for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids. -*The development of this software was supported in part by NSF Postdoctoral Fellowship DMS-0903120* Installation ------------ +Install the current master branch with: + ```r -library(devtools) -install_github("vqv/ggbiplot") +remotes::install_github("friendly/ggbiplot") ``` Example Usage ------------- +The `wine` data contains results of a chemical analysis of wines grown in the same region in Italy, +derived from three different cultivars. The analysis determined the +quantities of 13 chemical constituents found in each of the three types of wines. +The grape varieties (cultivars), 'barolo', 'barbera', and 'grignolino', are given in `wine.class`. -```{r wine-example, message = FALSE, warning = FALSE} +What can we understand about the differences among these wines from a biplot? + +```{r wine-screeplot} library(ggbiplot) +library(ggplot2) data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, - groups = wine.class, ellipse = TRUE, circle = TRUE) + +ggscreeplot(wine.pca) +``` + + +Plot the first two PCA dimensions: +```{r wine-biplot} +ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + groups = wine.class, + ellipse = TRUE, + circle = TRUE) + scale_color_discrete(name = '') + theme(legend.direction = 'horizontal', legend.position = 'top') ``` diff --git a/README.md b/README.md index f4e3aeb..30d17b0 100644 --- a/README.md +++ b/README.md @@ -1,33 +1,70 @@ + + + +[![CRAN +status](https://www.r-pkg.org/badges/version/ggbiplot)](https://CRAN.R-project.org/package=ggbiplot) +[![Last +Commit](https://img.shields.io/github/last-commit/friendly/ggbiplot)](https://github.com/friendly/ggbiplot) + + +This repo for the [ggbiplot +package](https://CRAN.R-project.org/package=ggbiplot) was forked from + by Vince Yu, which has been dormant +since 2015. -**NEWS**: Active development of ggbiplot has moved to the [experimental branch](https://github.com/vqv/ggbiplot/tree/experimental) +The goal is to complete that development and publish a new version on +CRAN. There is also an [experimental +branch](https://github.com/friendly/ggbiplot/tree/experimental) which +attempts to simplify the code, but this has some unresolved problems. -ggbiplot -======== +# ggbiplot -An implementation of the biplot using ggplot2. The package provides two functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a drop-in replacement for the built-in R function `biplot.princomp()` with extended functionality for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids. +An implementation of the biplot using ggplot2. The package provides two +functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a +drop-in replacement for the built-in R function `biplot.princomp()` with +extended functionality for labeling groups, drawing a correlation +circle, and adding Normal probability ellipsoids. -*The development of this software was supported in part by NSF Postdoctoral Fellowship DMS-0903120* +## Installation -Installation ------------- +Install the current master branch with: ``` r -library(devtools) -install_github("vqv/ggbiplot") +remotes::install_github("friendly/ggbiplot") ``` -Example Usage -------------- +## Example Usage + +The `wine` data contains results of a chemical analysis of wines grown +in the same region in Italy, derived from three different cultivars. The +analysis determined the quantities of 13 chemical constituents found in +each of the three types of wines. The grape varieties (cultivars), +‘barolo’, ‘barbera’, and ‘grignolino’, are given in `wine.class`. + +What can we understand about the differences among these wines from a +biplot? ``` r library(ggbiplot) +library(ggplot2) data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, - groups = wine.class, ellipse = TRUE, circle = TRUE) + +ggscreeplot(wine.pca) +``` + +![](man/figures/README-wine-screeplot-1.png) + +Plot the first two PCA dimensions: + +``` r +ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + groups = wine.class, + ellipse = TRUE, + circle = TRUE) + scale_color_discrete(name = '') + theme(legend.direction = 'horizontal', legend.position = 'top') ``` -![](README-wine-example-1.png) +![](man/figures/README-wine-biplot-1.png) diff --git a/man/figures/README-wine-biplot-1.png b/man/figures/README-wine-biplot-1.png new file mode 100644 index 0000000000000000000000000000000000000000..32a0239dca98fcd329246e499a824ff5d55d3653 GIT 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Date: Fri, 15 Sep 2023 21:40:37 -0400 Subject: [PATCH 17/80] fix ellipse fill problem --- R/ggbiplot.r | 26 ++++++++++++++++++-------- 1 file changed, 18 insertions(+), 8 deletions(-) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index d1e0ead..5dc1134 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -253,18 +253,28 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, ) |> dplyr::select(xvar, yvar, groups) |> tidyr::unnest(c(xvar, yvar)) - + # g <- g + geom_path(data = ell, # aes(color = groups, # group = groups), # linewidth = ellipse.linewidth) - g <- g + geom_polygon(data = ell, - aes(color = groups, - fill = groups - # group = groups - ), - alpha = 0.4, # MF: why doesn't this have any effect? - linewidth = ellipse.linewidth) + # g <- g + geom_polygon(data = ell, + # aes(color = groups, + # fill = groups + # # group = groups + # ), + # alpha = 0.4, # MF: why doesn't this have any effect? + # linewidth = ellipse.linewidth) + + # Overlay a concentration ellipse if there are groups + g <- g + stat_ellipse(geom="polygon", + aes(group = groups, + color = groups, + fill = groups), + alpha = 0.2, + linewidth = ellipse.linewidth, + type = "norm", level = ellipse.prob) + } # Label the variable axes From a65e52781f2dff168c690b6c9832c7b03857e408 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 16 Sep 2023 12:59:00 -0400 Subject: [PATCH 18/80] add ellipse.fill, ellipse.alpha --- DESCRIPTION | 2 +- NAMESPACE | 2 -- R/ggbiplot.r | 57 +++++++++++++++++++++++++++---------------------- man/ggbiplot.Rd | 6 ++++++ man/wine.Rd | 2 +- 5 files changed, 39 insertions(+), 30 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 2e9f3ee..5f27d96 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -13,7 +13,7 @@ Description: A ggplot2 based biplot. It provides a replacement for biplot.princomp(), but with many enhancements. It implements a biplot and scree plot using ggplot2. Imports: - ggplot2, dplyr, scales, tidyr, purrr + ggplot2, dplyr, scales License: GPL-2 Encoding: UTF-8 URL: https://github.com/friendly/ggbiplot diff --git a/NAMESPACE b/NAMESPACE index 59568a7..c93d946 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -8,9 +8,7 @@ importFrom(dplyr,group_by) importFrom(dplyr,n) importFrom(dplyr,select) importFrom(dplyr,summarize) -importFrom(purrr,map) importFrom(scales,muted) importFrom(stats,predict) importFrom(stats,qchisq) importFrom(stats,var) -importFrom(tidyr,unnest) diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 5dc1134..c396a09 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -34,6 +34,8 @@ #' @param ellipse draw a normal data ellipse for each group? #' @param ellipse.prob coverage size of the data ellipse in Normal probability #' @param ellipse.linewidth thickness of the line outlining the ellipses +#' @param ellipse.fill logical; should the ellipses be filled? +#' @param ellipse.alpha transparency value (0 - 1) for filled ellipses #' @param labels optional vector of labels for the observations #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) @@ -51,8 +53,8 @@ #' @importFrom scales muted ## @importFrom plyr ddply #' @importFrom dplyr filter n summarize select group_by -#' @importFrom tidyr unnest -#' @importFrom purrr map +## @importFrom tidyr unnest +## @importFrom purrr map #' @return a ggplot2 plot object #' @export #' @examples @@ -65,7 +67,8 @@ #' groups = wine.class, #' ellipse = TRUE, circle = TRUE) #' -ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, +ggbiplot <- function(pcobj, choices = 1:2, + scale = 1, pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale, var.factor = 1, # MF @@ -74,6 +77,8 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, ellipse = FALSE, ellipse.prob = 0.68, ellipse.linewidth = 1.3, + ellipse.fill = TRUE, + ellipse.alpha = 0.3, labels = NULL, labels.size = 3, alpha = 1, var.axes = TRUE, @@ -83,12 +88,11 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, varname.color = 'darkred', varname.abbrev = FALSE, ...) { - # library(ggplot2) - # library(plyr) - # library(scales) - # library(grid) - stopifnot(length(choices) == 2) + if(length(choices) > 2) { + warning("choices = ", choices, " is not of length 2. Only the first 2 will be used") + choices <- choices[1:2] + } # Recover the SVD if(inherits(pcobj, 'prcomp')){ @@ -237,22 +241,22 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # }) # names(ell)[1:2] <- c('xvar', 'yvar') - ell <- - df.u |> - group_by(groups) |> - filter(n() > 2) |> - summarize( - sigma = list(var(cbind(xvar, yvar))), - mu = list(c(mean(xvar), mean(yvar))), - ed = sqrt(qchisq(ellipse.prob, df = 2)), - circle_chol = list(circle %*% chol(sigma[[1]]) * ed), - ell = list(sweep(circle_chol[[1]], 2, mu[[1]], FUN = "+")), - xvar = map(ell, ~.x[,1]), - yvar = map(ell, ~.x[,2]), - .groups = "drop" - ) |> - dplyr::select(xvar, yvar, groups) |> - tidyr::unnest(c(xvar, yvar)) + # ell <- + # df.u |> + # group_by(groups) |> + # filter(n() > 2) |> + # summarize( + # sigma = list(var(cbind(xvar, yvar))), + # mu = list(c(mean(xvar), mean(yvar))), + # ed = sqrt(qchisq(ellipse.prob, df = 2)), + # circle_chol = list(circle %*% chol(sigma[[1]]) * ed), + # ell = list(sweep(circle_chol[[1]], 2, mu[[1]], FUN = "+")), + # xvar = map(ell, ~.x[,1]), + # yvar = map(ell, ~.x[,2]), + # .groups = "drop" + # ) |> + # dplyr::select(xvar, yvar, groups) |> + # tidyr::unnest(c(xvar, yvar)) # g <- g + geom_path(data = ell, # aes(color = groups, @@ -267,11 +271,12 @@ ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, # linewidth = ellipse.linewidth) # Overlay a concentration ellipse if there are groups - g <- g + stat_ellipse(geom="polygon", + geom <- if(isTRUE(ellipse.fill)) "polygon" else "path" + g <- g + stat_ellipse(geom=geom, aes(group = groups, color = groups, fill = groups), - alpha = 0.2, + alpha = ellipse.alpha, linewidth = ellipse.linewidth, type = "norm", level = ellipse.prob) diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 12f3926..8b2f1d2 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -17,6 +17,8 @@ ggbiplot( ellipse = FALSE, ellipse.prob = 0.68, ellipse.linewidth = 1.3, + ellipse.fill = TRUE, + ellipse.alpha = 0.3, labels = NULL, labels.size = 3, alpha = 1, @@ -57,6 +59,10 @@ If provided the points will be colored according to groups.} \item{ellipse.linewidth}{thickness of the line outlining the ellipses} +\item{ellipse.fill}{logical; should the ellipses be filled?} + +\item{ellipse.alpha}{transparency value (0 - 1) for filled ellipses} + \item{labels}{optional vector of labels for the observations} \item{labels.size}{size of the text used for the labels} diff --git a/man/wine.Rd b/man/wine.Rd index c3fa1bf..6bf000d 100644 --- a/man/wine.Rd +++ b/man/wine.Rd @@ -20,7 +20,7 @@ Results of a chemical analysis of wines grown in the same region in Italy, derived from three different cultivars. The analysis determined the quantities of 13 chemical constituents found in each of the three types of wines. - The cultivars, 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. + The grape varieties (cultivars), 'barolo', 'barbera', and 'grignolino', are indicated in \code{wine.class}. } \examples{ data(wine) From c61fbd35fe395e634c64e8e08a799eda1fbeeba9 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 16 Sep 2023 14:35:00 -0400 Subject: [PATCH 19/80] add hex logo; tweak some ooption defaults --- NEWS.md | 5 ++++- R/ggbiplot.r | 22 +++++++++++++----- README.Rmd | 7 +++--- README.md | 8 +++---- extra/testing.R | 32 ++++++++++++++++++++------- man/figures/README-wine-biplot-1.png | Bin 21689 -> 22408 bytes man/figures/logo.png | Bin 0 -> 35061 bytes 7 files changed, 51 insertions(+), 23 deletions(-) create mode 100644 man/figures/logo.png diff --git a/NEWS.md b/NEWS.md index e8b5129..601b931 100644 --- a/NEWS.md +++ b/NEWS.md @@ -2,7 +2,10 @@ - Use `geom_polygon()` rather than `geom_path()` for ellipses - Added `var.factor` argument to expand or reflect the variable vectors -- moved points/labels code earlier so ellipses and variable vectors are not obscured +- Moved points/labels code earlier so ellipses and variable vectors are not obscured +- Replaced internal calculation of ellipses with `stat_ellipse()` +- Now allow ellipses to be filled (`geom_polygon()`) or unfilled (`geom_path()`) +- Added hex logo ## Version 0.56 diff --git a/R/ggbiplot.r b/R/ggbiplot.r index c396a09..bc4689f 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -51,7 +51,6 @@ #' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted -## @importFrom plyr ddply #' @importFrom dplyr filter n summarize select group_by ## @importFrom tidyr unnest ## @importFrom purrr map @@ -78,13 +77,15 @@ ggbiplot <- function(pcobj, choices = 1:2, ellipse.prob = 0.68, ellipse.linewidth = 1.3, ellipse.fill = TRUE, - ellipse.alpha = 0.3, - labels = NULL, labels.size = 3, + ellipse.alpha = 0.25, + labels = NULL, + labels.size = 3, alpha = 1, var.axes = TRUE, - circle = FALSE, circle.prob = 0.68, + circle = FALSE, + circle.prob = 0.68, varname.size = 3, - varname.adjust = 1.5, + varname.adjust = 1.25, varname.color = 'darkred', varname.abbrev = FALSE, ...) { @@ -272,13 +273,22 @@ ggbiplot <- function(pcobj, choices = 1:2, # Overlay a concentration ellipse if there are groups geom <- if(isTRUE(ellipse.fill)) "polygon" else "path" - g <- g + stat_ellipse(geom=geom, + if (isTRUE(ellipse.fill)) { + g <- g + stat_ellipse(geom="polygon", aes(group = groups, color = groups, fill = groups), alpha = ellipse.alpha, linewidth = ellipse.linewidth, type = "norm", level = ellipse.prob) + } + else { + g <- g + stat_ellipse(geom="path", + aes(group = groups, + color = groups), + linewidth = ellipse.linewidth, + type = "norm", level = ellipse.prob) + } } diff --git a/README.Rmd b/README.Rmd index f507c16..880726d 100644 --- a/README.Rmd +++ b/README.Rmd @@ -29,10 +29,9 @@ knitr::opts_chunk$set( ) ``` -ggbiplot -======== +# ggbiplot -An implementation of the biplot using ggplot2. The package provides two functions: `ggscreeplot()` and `ggbiplot()`. +An implementation of the biplot using `ggplot2`. The package provides two functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a drop-in replacement for the built-in R function `biplot.princomp()` with extended functionality for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids. @@ -71,6 +70,6 @@ ggbiplot(wine.pca, groups = wine.class, ellipse = TRUE, circle = TRUE) + - scale_color_discrete(name = '') + + labs(fill = "Cultivar", color = "Cultivar") + theme(legend.direction = 'horizontal', legend.position = 'top') ``` diff --git a/README.md b/README.md index 30d17b0..94a2b48 100644 --- a/README.md +++ b/README.md @@ -18,10 +18,10 @@ CRAN. There is also an [experimental branch](https://github.com/friendly/ggbiplot/tree/experimental) which attempts to simplify the code, but this has some unresolved problems. -# ggbiplot +# ggbiplot -An implementation of the biplot using ggplot2. The package provides two -functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a +An implementation of the biplot using `ggplot2`. The package provides +two functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a drop-in replacement for the built-in R function `biplot.princomp()` with extended functionality for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids. @@ -63,7 +63,7 @@ ggbiplot(wine.pca, groups = wine.class, ellipse = TRUE, circle = TRUE) + - scale_color_discrete(name = '') + + labs(fill = "Cultivar", color = "Cultivar") + theme(legend.direction = 'horizontal', legend.position = 'top') ``` diff --git a/extra/testing.R b/extra/testing.R index edaf22a..fd703e3 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -1,17 +1,28 @@ +library(ggbiplot) +library(ggplot2) data(wine, package="ggbiplot") wine.pca <- prcomp(wine, scale. = TRUE) ggbiplot(wine.pca, groups=wine.class, ellipse = TRUE, - ellipse.linewidth = 1.2, + ellipse.linewidth = 1.1, circle = TRUE, varname.color = "darkred", varname.size = 4) + theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') +ggbiplot(wine.pca, groups=wine.class, + ellipse = TRUE, + ellipse.linewidth = 1.2, ellipse.fill = FALSE, + circle = TRUE, + varname.color = "darkred", + varname.size = 4) + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') + + library(dplyr) -library(ggplot2) data(penguins, package = "palmerpenguins") peng <- penguins |> rename( @@ -31,21 +42,25 @@ peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, groups = peng$species, point.size=2, - varname.size = 5, varname.color = scales::muted("black"), + varname.size = 5, + varname.color = scales::muted("black"), ellipse = TRUE, ellipse.linewidth = 1.4, circle = TRUE) + -# scale_fill_discrete(name = 'Species') + + # scale_fill_discrete(name = 'Species') + + # scale_color_discrete(name = 'Species') + + labs(fill = "Species", color = "Species") + theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') # try reflecting & scaline var vectors ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, - var.factor = -1.1, + var.factor = -1, + varname.adjust = 1, groups = peng$species, point.size=2, varname.size = 5, varname.color = scales::muted("black"), ellipse = TRUE, ellipse.linewidth = 1.4, circle = TRUE) + - # scale_fill_discrete(name = 'Species') + + labs(fill = "Species", color = "Species") + theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') @@ -53,10 +68,11 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, # last two dimensions: outliers ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, groups = peng$species, point.size=2, + var.factor = 2.1, varname.adjust = 1, varname.size = 5, varname.color = scales::muted("red"), - ellipse = TRUE, ellipse.linewidth = 1.4, + ellipse = TRUE, ellipse.alpha = 0.1, circle = TRUE) + - # scale_fill_discrete(name = 'Species') + + labs(fill = "Species", color = "Species") + 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zQFp#;=fyx(T`*Yhl{&pq6ds(`3|VIR%hsDH*2!>0K-!`8ms*@SO267ldknxs@2&mOHj-7E5PAxkaN8HwPD@-|B*EQrqLPp2aBzVB z>OPFJ!5|*eM1CeatW^lfqf=2S2`ml*A#mK$VP!0ZX*7O*0{-hzk`0qA(kwNY`sVfo z7|PzTspp6%rcdxveXjVBEFSEi36s^;)fT&LwSknUL6(6Qc6Lg&ie$f*ZUE+o)%3Eh zBLo5*V8?*r7tP4>2hhR@QK(h`Eg@}d%L>41^W4eF2`1gb05hZKX3AU6)v?167ji5) zHSJFW>ZZGaoa&1gE-2`?f7~eB9D)N<|Dd#a8>%SQ7cr?{a`D4D(N97;jgwXLvr54l zcM^p4x1iaQRpg11riM-dHZJz)jUS8zSOMkGWxI*kgd&m4zc+8b_J3jB5{~B^T^`~9 zqzpv&Gn?zteXSb?JqC_VS7+Ax(A>>(&ldvWRz_xqe5khet9%^aL6|!sET|Y!O%_l8 z0Tv1Y2Mm6y3hIn{b2BR! zS9Q%bqk9pAg(F{R=ic%U2w*W7<`odwiFWKfXAY)o35g(v~4Yyt&04dT*Z{JWWblnldHXiLk_L}XkWovdFJZ#UqO0z z>cXJi*;=K^T06tAcgwMw2E!~@yOmbu9GAb+n|!yr`+WPRbjK&##3fvScCD~90L#`1 zGYgB!VYw4rTKS%JyscTiG{z|SOXM6SqW4sP}kI4 zTu1fICx8~=@MqZ`9Q^wSuoo^nuzL_2>s)^&j4u=d6^;D7)flCsD+9qN!VTwWxa`n( zj)XW+$SXP%2I^H@Ozg%JW5JI7#~hRzkln$M9Idc$N+mng;ISc$07y-(WPh`b(eU9w zt78}>=3;u`Na^$lxBdAQS?SJ<5?%&ie1vJxnOZoWJwI}n0g9?phtNJENw zpQfB4pai}I?D7BO@gyfbJv~?c1CS2vZ#L7cEG0EG2*Mc-720nz){2UXaP`DoR%$E* d;TvXa*BzuK6l_7v9timFnUtbriTF$Z{{eug@e}|6 literal 0 HcmV?d00001 From fbc65cb9fd61c915003a4dfbcd1a3c13929953ab Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 16 Sep 2023 16:33:32 -0400 Subject: [PATCH 20/80] add iris example to README --- R/ggbiplot.r | 33 ++++++--- R/ggscreeplot.r | 13 ++-- README.Rmd | 79 +++++++++++++++++++-- README.md | 87 +++++++++++++++++++++++- extra/testing.R | 63 ++++++++++++++--- man/figures/README-iris-biplot0-1.png | Bin 0 -> 24111 bytes man/figures/README-iris-biplot1-1.png | Bin 0 -> 24600 bytes man/figures/README-wine-biplot-1.png | Bin 22408 -> 22094 bytes man/figures/README-wine-screeplot-1.png | Bin 5899 -> 7262 bytes 9 files changed, 243 insertions(+), 32 deletions(-) create mode 100644 man/figures/README-iris-biplot0-1.png create mode 100644 man/figures/README-iris-biplot1-1.png diff --git a/R/ggbiplot.r b/R/ggbiplot.r index bc4689f..c03c8a5 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -57,15 +57,30 @@ #' @return a ggplot2 plot object #' @export #' @examples -#' data(wine) -#' library(ggplot2) -#' wine.pca <- prcomp(wine, scale. = TRUE) -#' ggbiplot(wine.pca, -#' obs.scale = 1, var.scale = 1, -#' varname.size = 4, -#' groups = wine.class, -#' ellipse = TRUE, circle = TRUE) +#' data(wine) +#' library(ggplot2) +#' wine.pca <- prcomp(wine, scale. = TRUE) +#' ggbiplot(wine.pca, +#' obs.scale = 1, var.scale = 1, +#' varname.size = 4, +#' groups = wine.class, +#' ellipse = TRUE, circle = TRUE) #' +#' data(iris) +#' iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, +#' data=iris, +#' scale. = TRUE) +#' ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, +#' groups = iris$Species, point.size=2, +#' varname.size = 5, +#' varname.color = "black", +#' varname.adjust = 1.2, +#' ellipse = TRUE, +#' circle = TRUE) + +#' labs(fill = "Species", color = "Species") + +#' theme_minimal(base_size = 14) + +#' theme(legend.direction = 'horizontal', legend.position = 'top') + ggbiplot <- function(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, obs.scale = 1 - scale, @@ -86,7 +101,7 @@ ggbiplot <- function(pcobj, choices = 1:2, circle.prob = 0.68, varname.size = 3, varname.adjust = 1.25, - varname.color = 'darkred', + varname.color = "black", varname.abbrev = FALSE, ...) { diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index ffcbc54..6ced80b 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -24,13 +24,16 @@ #' @param type the type of scree plot. #' 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. #' 'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace. +#' @param size point size #' @export #' @examples #' data(wine) #' wine.pca <- prcomp(wine, scale. = TRUE) #' ggscreeplot(wine.pca) #' -ggscreeplot <- function(pcobj, type = c('pev', 'cev')) +ggscreeplot <- function(pcobj, + type = c('pev', 'cev'), + size = 4) { type <- match.arg(type) d <- pcobj$sdev^2 @@ -39,13 +42,13 @@ ggscreeplot <- function(pcobj, type = c('pev', 'cev')) cev = cumsum(d) / sum(d)) yvar.lab <- switch(type, - pev = 'proportion of explained variance', - cev = 'cumulative proportion of explained variance') + pev = 'Proportion of explained variance', + cev = 'Cumulative proportion of explained variance') PC <- NULL df <- data.frame(PC = 1:length(d), yvar = yvar) ggplot(data = df, aes(x = PC, y = yvar)) + - xlab('principal component number') + ylab(yvar.lab) + - geom_point() + geom_path() + xlab('Principal component number') + ylab(yvar.lab) + + geom_point(size = size) + geom_path() } diff --git a/README.Rmd b/README.Rmd index 880726d..7bab24f 100644 --- a/README.Rmd +++ b/README.Rmd @@ -36,8 +36,7 @@ An implementation of the biplot using `ggplot2`. The package provides two funct for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids. -Installation ------------- +## Installation Install the current master branch with: @@ -45,25 +44,31 @@ Install the current master branch with: remotes::install_github("friendly/ggbiplot") ``` -Example Usage -------------- +## Example Usage + +### Wine data + The `wine` data contains results of a chemical analysis of wines grown in the same region in Italy, derived from three different cultivars. The analysis determined the quantities of 13 chemical constituents found in each of the three types of wines. -The grape varieties (cultivars), 'barolo', 'barbera', and 'grignolino', are given in `wine.class`. +The grape varieties (cultivars), **barolo**, **barbera**, and **grignolino**, are given in `wine.class`. What can we understand about the differences among these wines from a biplot? ```{r wine-screeplot} library(ggbiplot) library(ggplot2) +library(dplyr) + data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggscreeplot(wine.pca) +ggscreeplot(wine.pca) + + theme_bw(base_size = 14) ``` +Hmm. The screeplot shows that more than two dimensions are necessary to account for most of the variance. -Plot the first two PCA dimensions: +Plot the first two PCA dimensions, accounting for 55% of the variance. ```{r wine-biplot} ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, @@ -73,3 +78,63 @@ ggbiplot(wine.pca, labs(fill = "Cultivar", color = "Cultivar") + theme(legend.direction = 'horizontal', legend.position = 'top') ``` + +The three cultivars are arranged along the first dimension, in the order barolo < grignolino < barbera. +These are distinguished largely by a conrtast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`). +The second dimension is represented by the cluster of variables `Mg`, `Alcohol`, `Ash`, `Color`, which distinguishes +grignolino from the other two. + +### Iris data + +```{r iris-pca} +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) +summary(iris.pca) +``` + +Plot the first two dimensions: + +```{r iris-biplot0} +iris.gg <- +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + +iris.gg +``` + +It is possible to add annotations to the biplot by making use of the fact that `ggplot()` returns a lot of +information in the `"gg"` object. In particular, the `$data` component contains the scores on the principal +components that are plotted as points here. +Here we add direct labels for the groups and suppress the legend. + +```{r iris-labs} +# get means of coordinates by group +group.labs <- + iris.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +group.labs +``` + +Now, just use `geom_label` to draw labels for the groups. +```{r iris-biplot1} +iris.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") + +``` + + + diff --git a/README.md b/README.md index 94a2b48..944e149 100644 --- a/README.md +++ b/README.md @@ -36,11 +36,13 @@ remotes::install_github("friendly/ggbiplot") ## Example Usage +### Wine data + The `wine` data contains results of a chemical analysis of wines grown in the same region in Italy, derived from three different cultivars. The analysis determined the quantities of 13 chemical constituents found in each of the three types of wines. The grape varieties (cultivars), -‘barolo’, ‘barbera’, and ‘grignolino’, are given in `wine.class`. +**barolo**, **barbera**, and **grignolino**, are given in `wine.class`. What can we understand about the differences among these wines from a biplot? @@ -48,14 +50,20 @@ biplot? ``` r library(ggbiplot) library(ggplot2) +library(dplyr) + data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggscreeplot(wine.pca) +ggscreeplot(wine.pca) + + theme_bw(base_size = 14) ``` ![](man/figures/README-wine-screeplot-1.png) -Plot the first two PCA dimensions: +Hmm. The screeplot shows that more than two dimensions are necessary to +account for most of the variance. + +Plot the first two PCA dimensions, accounting for 55% of the variance. ``` r ggbiplot(wine.pca, @@ -68,3 +76,76 @@ ggbiplot(wine.pca, ``` ![](man/figures/README-wine-biplot-1.png) + +The three cultivars are arranged along the first dimension, in the order +barolo \< grignolino \< barbera. These are distinguished largely by a +conrtast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`). +The second dimension is represented by the cluster of variables `Mg`, +`Alcohol`, `Ash`, `Color`, which distinguishes grignolino from the other +two. + +### Iris data + +``` r +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) +summary(iris.pca) +#> Importance of components: +#> PC1 PC2 PC3 PC4 +#> Standard deviation 1.7084 0.9560 0.38309 0.14393 +#> Proportion of Variance 0.7296 0.2285 0.03669 0.00518 +#> Cumulative Proportion 0.7296 0.9581 0.99482 1.00000 +``` + +Plot the first two dimensions: + +``` r +iris.gg <- +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + +iris.gg +``` + +![](man/figures/README-iris-biplot0-1.png) + +It is possible to add annotations to the biplot by making use of the +fact that `ggplot()` returns a lot of information in the `"gg"` object. +In particular, the `$data` component contains the scores on the +principal components that are plotted as points here. Here we add direct +labels for the groups and suppress the legend. + +``` r +# get means of coordinates by group +group.labs <- + iris.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +group.labs +#> groups xvar yvar +#> 1 setosa -2.2173249 -0.2879627 +#> 2 versicolor 0.4947904 0.5483335 +#> 3 virginica 1.7225345 -0.2603708 +``` + +Now, just use `geom_label` to draw labels for the groups. + +``` r +iris.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") +``` + +![](man/figures/README-iris-biplot1-1.png) diff --git a/extra/testing.R b/extra/testing.R index fd703e3..c8913b8 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -1,5 +1,11 @@ +#' --- +#' title: test cases for ggbiplot +#' --- + library(ggbiplot) library(ggplot2) +library(dplyr) + data(wine, package="ggbiplot") wine.pca <- prcomp(wine, scale. = TRUE) ggbiplot(wine.pca, groups=wine.class, @@ -11,6 +17,7 @@ ggbiplot(wine.pca, groups=wine.class, theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') +# unfilled ggbiplot(wine.pca, groups=wine.class, ellipse = TRUE, ellipse.linewidth = 1.2, ellipse.fill = FALSE, @@ -21,8 +28,8 @@ ggbiplot(wine.pca, groups=wine.class, theme(legend.direction = 'horizontal', legend.position = 'top') - -library(dplyr) +#' ## penguins data +#' data(penguins, package = "palmerpenguins") peng <- penguins |> rename( @@ -40,18 +47,31 @@ peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, na.action=na.omit, scale. = TRUE) +peng.gg <- ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, groups = peng$species, point.size=2, - varname.size = 5, - varname.color = scales::muted("black"), - ellipse = TRUE, ellipse.linewidth = 1.4, + varname.size = 6, + varname.color = "black", #scales::muted("black"), + ellipse = TRUE, ellipse.linewidth = 1.2, circle = TRUE) + - # scale_fill_discrete(name = 'Species') + - # scale_color_discrete(name = 'Species') + labs(fill = "Species", color = "Species") + - theme_minimal() + + theme_minimal(base_size = 14) + theme(legend.direction = 'horizontal', legend.position = 'top') +# label the ellipses +group.labs <- + peng.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +peng.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") + + + + # try reflecting & scaline var vectors ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, var.factor = -1, @@ -76,4 +96,31 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') +#' ## iris data +#' +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) + +iris.gg <- +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + 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zRAzQn^~O&hs8lassvnu~D}+jaZKOg0CSt@0ql-y_Rbs?S4bx;(@JjOaY9@U=saNpk z@oBr(o>W6Y*|m41fTk$(n4cm)Qq2KVF=7t7m$ozecwBk+N28NbFINMXCFTeFPJedy ze5S9@a~^{ix6s2lEx{-o+~3|8?QW>gZ?&9ihjKit)Gr=Fe1C(SJoA-|%uZ>r3V@A} klgL%D{tYB+x3P1AWaQFkzW%T#au(^b From b1918c71ae1ad925b1d9ebf96b86443de48178ea Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 16 Sep 2023 18:43:58 -0400 Subject: [PATCH 21/80] more testing examples --- DESCRIPTION | 8 +++-- NAMESPACE | 5 --- NEWS.md | 2 ++ R/ggbiplot.r | 47 ++++++++++++++++++--------- R/ggscreeplot.r | 17 ++++++++++ extra/test-iris.R | 67 ++++++++++++++++++++++++++++++++++++++ extra/testing.R | 52 ++++++++++++++--------------- man/ggbiplot.Rd | 81 +++++++++++++++++++++++++++++++--------------- man/ggscreeplot.Rd | 4 ++- 9 files changed, 208 insertions(+), 75 deletions(-) create mode 100644 extra/test-iris.R diff --git a/DESCRIPTION b/DESCRIPTION index 5f27d96..4ea89e7 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -11,9 +11,13 @@ Authors@R: c( ) Description: A ggplot2 based biplot. It provides a replacement for biplot.princomp(), but with many enhancements. It implements a - biplot and scree plot using ggplot2. + biplot and scree plot using ggplot2 which can be used with prcomp(), princomp(), + FactoMineR::PCA() or MASS::lda(). Imports: - ggplot2, dplyr, scales + ggplot2, scales +Suggests: + dplyr, + MASS License: GPL-2 Encoding: UTF-8 URL: https://github.com/friendly/ggbiplot diff --git a/NAMESPACE b/NAMESPACE index c93d946..993b9b2 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -3,11 +3,6 @@ export(ggbiplot) export(ggscreeplot) import(ggplot2) -importFrom(dplyr,filter) -importFrom(dplyr,group_by) -importFrom(dplyr,n) -importFrom(dplyr,select) -importFrom(dplyr,summarize) importFrom(scales,muted) importFrom(stats,predict) importFrom(stats,qchisq) diff --git a/NEWS.md b/NEWS.md index 601b931..36f08e5 100644 --- a/NEWS.md +++ b/NEWS.md @@ -6,6 +6,8 @@ - Replaced internal calculation of ellipses with `stat_ellipse()` - Now allow ellipses to be filled (`geom_polygon()`) or unfilled (`geom_path()`) - Added hex logo +- Added iris example to README +- Removed Imports: dplyr, purrr as no longer needed ## Version 0.56 diff --git a/R/ggbiplot.r b/R/ggbiplot.r index c03c8a5..868a4ee 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -19,24 +19,32 @@ # #' Biplot for Principal Components using ggplot2 +#' +#' A biplot simultaneously displays information on the observations (as points) +#' and the variables (as vectors) in a multidimensional dataset. The 2D biplot +#' is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data. #' -#' @param pcobj an object returned by prcomp() or princomp() -#' @param choices which PCs to plot -#' @param scale covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance. -#' @param obs.scale scale factor to apply to observations -#' @param var.scale scale factor to apply to variables -#' @param var.factor factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +#' @param pcobj an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +#' \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}} +#' @param choices Which components to plot? A vector of length 2. +#' @param scale Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product +#' between the variables approximates the covariance and the distance between the points +#' approximates the Mahalanobis distance. +#' @param obs.scale Scale factor to apply to observations +#' @param var.scale Scale factor to apply to variables +#' @param var.factor Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected #' (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility. -#' @param pc.biplot for compatibility with biplot.princomp() +#' @param pc.biplot For compatibility with \code{biplot.princomp()} #' @param groups optional factor variable indicating the groups that the observations belong to. #' If provided the points will be colored according to groups. #' @param point.size Size of observation points. #' @param ellipse draw a normal data ellipse for each group? -#' @param ellipse.prob coverage size of the data ellipse in Normal probability -#' @param ellipse.linewidth thickness of the line outlining the ellipses -#' @param ellipse.fill logical; should the ellipses be filled? -#' @param ellipse.alpha transparency value (0 - 1) for filled ellipses -#' @param labels optional vector of labels for the observations +#' @param ellipse.prob Coverage size of the data ellipse in Normal probability +#' @param ellipse.linewidth Thickness of the line outlining the ellipses +#' @param ellipse.fill Logical; should the ellipses be filled? +#' @param ellipse.alpha Transparency value (0 - 1) for filled ellipses +#' @param labels Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()} +#' of the dataset. #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) #' @param circle draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1) @@ -51,10 +59,19 @@ #' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted -#' @importFrom dplyr filter n summarize select group_by +## @importFrom dplyr filter n summarize select group_by ## @importFrom tidyr unnest ## @importFrom purrr map -#' @return a ggplot2 plot object +#' +#' @seealso \code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} +#' +#' @references +#' K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. +#' \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. +#' +#' J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall +#' +#' @return a ggplot2 plot object of class \code{c("gg", "ggplot")} #' @export #' @examples #' data(wine) @@ -133,7 +150,7 @@ ggbiplot <- function(pcobj, choices = 1:2, v <- pcobj$scaling d.total <- sum(d^2) } else { - stop('Expected a object of class prcomp, princomp, PCA, or lda') + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') } # shutup 'no visible binding...' diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index 6ced80b..084bee6 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -35,6 +35,23 @@ ggscreeplot <- function(pcobj, type = c('pev', 'cev'), size = 4) { + # Recover the SVD + if(inherits(pcobj, 'prcomp')){ + nobs.factor <- sqrt(nrow(pcobj$x) - 1) + d <- pcobj$sdev + } else if(inherits(pcobj, 'princomp')) { + nobs.factor <- sqrt(pcobj$n.obs) + d <- pcobj$sdev + } else if(inherits(pcobj, 'PCA')) { + nobs.factor <- sqrt(nrow(pcobj$call$X)) + d <- unlist(sqrt(pcobj$eig)[1]) + } else if(inherits(pcobj, "lda")) { + d <- pcobj$svd + } else { + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') + } + + type <- match.arg(type) d <- pcobj$sdev^2 yvar <- switch(type, diff --git a/extra/test-iris.R b/extra/test-iris.R new file mode 100644 index 0000000..7f001aa --- /dev/null +++ b/extra/test-iris.R @@ -0,0 +1,67 @@ +#' --- +#' title: test iris data for ggbiplot +#' --- + +library(ggbiplot) +library(ggplot2) +library(dplyr) +library(MASS) + + + +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) + +iris.gg <- + ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + +#' ## label the ellipses +group.labs <- + iris.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +iris.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") + +# show point labels +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, + point.size=2, + labels = row.names(iris), + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = FALSE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + + +#' ## Try lda() + +iris.lda <- lda(Species ~ ., data = iris) + +ggbiplot(iris.lda, + groups = iris$Species, + ellipse = TRUE, + varname.size = 5) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + + diff --git a/extra/testing.R b/extra/testing.R index c8913b8..fee5414 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -44,7 +44,6 @@ peng <- penguins |> peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, data=peng, - na.action=na.omit, scale. = TRUE) peng.gg <- @@ -85,9 +84,11 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, theme(legend.direction = 'horizontal', legend.position = 'top') -# last two dimensions: outliers +# last two dimensions: outliers; use observation labels ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, - groups = peng$species, point.size=2, + groups = peng$species, + labels = row.names(peng), + point.size=2, var.factor = 2.1, varname.adjust = 1, varname.size = 5, varname.color = scales::muted("red"), ellipse = TRUE, ellipse.alpha = 0.1, @@ -96,31 +97,30 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') -#' ## iris data -#' -data(iris) -iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, - data=iris, - scale. = TRUE) +#' USArrests -iris.gg <- -ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, - groups = iris$Species, point.size=2, - varname.size = 5, - varname.color = "black", - varname.adjust = 1.2, - ellipse = TRUE, - circle = TRUE) + - labs(fill = "Species", color = "Species") + +data("USArrests") +arrests.pca <- + prcomp (~ Murder + Assault + UrbanPop + Rape, + data=USArrests, + scale. = TRUE) + +ggbiplot(arrests.pca, + labels = state.abb[match(row.names(USArrests), state.name)] , + circle = TRUE, + varname.size = 4, + varname.color = "red") + theme_minimal(base_size = 14) + theme(legend.direction = 'horizontal', legend.position = 'top') -group.labs <- - iris.gg$data |> - summarise(xvar = mean(xvar), - yvar = mean(yvar), .by = groups) +ggbiplot(arrests.pca, + groups = state.region, + labels = state.abb[match(row.names(USArrests), state.name)], + labels.size = 4, + ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1, + circle = TRUE, + varname.size = 4, + varname.color = "black") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') -iris.gg + geom_label(data = group.labs, - aes(x = xvar, y=yvar, label=groups), - size = 5) + - theme(legend.position = "none") diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 8b2f1d2..38455f0 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -18,7 +18,7 @@ ggbiplot( ellipse.prob = 0.68, ellipse.linewidth = 1.3, ellipse.fill = TRUE, - ellipse.alpha = 0.3, + ellipse.alpha = 0.25, labels = NULL, labels.size = 3, alpha = 1, @@ -26,26 +26,29 @@ ggbiplot( circle = FALSE, circle.prob = 0.68, varname.size = 3, - varname.adjust = 1.5, - varname.color = "darkred", + varname.adjust = 1.25, + varname.color = "black", varname.abbrev = FALSE, ... ) } \arguments{ -\item{pcobj}{an object returned by prcomp() or princomp()} +\item{pcobj}{an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +\code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}} -\item{choices}{which PCs to plot} +\item{choices}{Which components to plot? A vector of length 2.} -\item{scale}{covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance.} +\item{scale}{Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product +between the variables approximates the covariance and the distance between the points +approximates the Mahalanobis distance.} -\item{pc.biplot}{for compatibility with biplot.princomp()} +\item{pc.biplot}{For compatibility with \code{biplot.princomp()}} -\item{obs.scale}{scale factor to apply to observations} +\item{obs.scale}{Scale factor to apply to observations} -\item{var.scale}{scale factor to apply to variables} +\item{var.scale}{Scale factor to apply to variables} -\item{var.factor}{factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +\item{var.factor}{Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility.} \item{groups}{optional factor variable indicating the groups that the observations belong to. @@ -55,15 +58,16 @@ If provided the points will be colored according to groups.} \item{ellipse}{draw a normal data ellipse for each group?} -\item{ellipse.prob}{coverage size of the data ellipse in Normal probability} +\item{ellipse.prob}{Coverage size of the data ellipse in Normal probability} -\item{ellipse.linewidth}{thickness of the line outlining the ellipses} +\item{ellipse.linewidth}{Thickness of the line outlining the ellipses} -\item{ellipse.fill}{logical; should the ellipses be filled?} +\item{ellipse.fill}{Logical; should the ellipses be filled?} -\item{ellipse.alpha}{transparency value (0 - 1) for filled ellipses} +\item{ellipse.alpha}{Transparency value (0 - 1) for filled ellipses} -\item{labels}{optional vector of labels for the observations} +\item{labels}{Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()} +of the dataset.} \item{labels.size}{size of the text used for the labels} @@ -86,19 +90,44 @@ If provided the points will be colored according to groups.} \item{...}{other arguments passed down} } \value{ -a ggplot2 plot object +a ggplot2 plot object of class \code{c("gg", "ggplot")} } \description{ -Biplot for Principal Components using ggplot2 +A biplot simultaneously displays information on the observations (as points) +and the variables (as vectors) in a multidimensional dataset. The 2D biplot +is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data. } \examples{ - data(wine) - library(ggplot2) - wine.pca <- prcomp(wine, scale. = TRUE) - ggbiplot(wine.pca, - obs.scale = 1, var.scale = 1, - varname.size = 4, - groups = wine.class, - ellipse = TRUE, circle = TRUE) - +data(wine) +library(ggplot2) +wine.pca <- prcomp(wine, scale. = TRUE) +ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + varname.size = 4, + groups = wine.class, + ellipse = TRUE, circle = TRUE) + +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') +} +\references{ +K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. + \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. + + J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall +} +\seealso{ +\code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} } diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd index e0b6cfd..2d3531e 100644 --- a/man/ggscreeplot.Rd +++ b/man/ggscreeplot.Rd @@ -4,7 +4,7 @@ \alias{ggscreeplot} \title{Screeplot for Principal Components} \usage{ -ggscreeplot(pcobj, type = c("pev", "cev")) +ggscreeplot(pcobj, type = c("pev", "cev"), size = 4) } \arguments{ \item{pcobj}{an object returned by prcomp() or princomp()} @@ -12,6 +12,8 @@ ggscreeplot(pcobj, type = c("pev", "cev")) \item{type}{the type of scree plot. 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.} + +\item{size}{point size} } \description{ Screeplot for Principal Components From 76b2976791681d2184e86edb9122fc6a012c6864 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sat, 16 Sep 2023 18:43:58 -0400 Subject: [PATCH 22/80] more testing examples --- DESCRIPTION | 8 +++-- NAMESPACE | 5 --- NEWS.md | 2 ++ R/ggbiplot.r | 47 ++++++++++++++++++--------- R/ggscreeplot.r | 17 ++++++++++ extra/test-iris.R | 67 ++++++++++++++++++++++++++++++++++++++ extra/testing.R | 54 +++++++++++++++---------------- man/ggbiplot.Rd | 81 +++++++++++++++++++++++++++++++--------------- man/ggscreeplot.Rd | 4 ++- 9 files changed, 209 insertions(+), 76 deletions(-) create mode 100644 extra/test-iris.R diff --git a/DESCRIPTION b/DESCRIPTION index 5f27d96..4ea89e7 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -11,9 +11,13 @@ Authors@R: c( ) Description: A ggplot2 based biplot. It provides a replacement for biplot.princomp(), but with many enhancements. It implements a - biplot and scree plot using ggplot2. + biplot and scree plot using ggplot2 which can be used with prcomp(), princomp(), + FactoMineR::PCA() or MASS::lda(). Imports: - ggplot2, dplyr, scales + ggplot2, scales +Suggests: + dplyr, + MASS License: GPL-2 Encoding: UTF-8 URL: https://github.com/friendly/ggbiplot diff --git a/NAMESPACE b/NAMESPACE index c93d946..993b9b2 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -3,11 +3,6 @@ export(ggbiplot) export(ggscreeplot) import(ggplot2) -importFrom(dplyr,filter) -importFrom(dplyr,group_by) -importFrom(dplyr,n) -importFrom(dplyr,select) -importFrom(dplyr,summarize) importFrom(scales,muted) importFrom(stats,predict) importFrom(stats,qchisq) diff --git a/NEWS.md b/NEWS.md index 601b931..36f08e5 100644 --- a/NEWS.md +++ b/NEWS.md @@ -6,6 +6,8 @@ - Replaced internal calculation of ellipses with `stat_ellipse()` - Now allow ellipses to be filled (`geom_polygon()`) or unfilled (`geom_path()`) - Added hex logo +- Added iris example to README +- Removed Imports: dplyr, purrr as no longer needed ## Version 0.56 diff --git a/R/ggbiplot.r b/R/ggbiplot.r index c03c8a5..868a4ee 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -19,24 +19,32 @@ # #' Biplot for Principal Components using ggplot2 +#' +#' A biplot simultaneously displays information on the observations (as points) +#' and the variables (as vectors) in a multidimensional dataset. The 2D biplot +#' is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data. #' -#' @param pcobj an object returned by prcomp() or princomp() -#' @param choices which PCs to plot -#' @param scale covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance. -#' @param obs.scale scale factor to apply to observations -#' @param var.scale scale factor to apply to variables -#' @param var.factor factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +#' @param pcobj an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +#' \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}} +#' @param choices Which components to plot? A vector of length 2. +#' @param scale Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product +#' between the variables approximates the covariance and the distance between the points +#' approximates the Mahalanobis distance. +#' @param obs.scale Scale factor to apply to observations +#' @param var.scale Scale factor to apply to variables +#' @param var.factor Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected #' (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility. -#' @param pc.biplot for compatibility with biplot.princomp() +#' @param pc.biplot For compatibility with \code{biplot.princomp()} #' @param groups optional factor variable indicating the groups that the observations belong to. #' If provided the points will be colored according to groups. #' @param point.size Size of observation points. #' @param ellipse draw a normal data ellipse for each group? -#' @param ellipse.prob coverage size of the data ellipse in Normal probability -#' @param ellipse.linewidth thickness of the line outlining the ellipses -#' @param ellipse.fill logical; should the ellipses be filled? -#' @param ellipse.alpha transparency value (0 - 1) for filled ellipses -#' @param labels optional vector of labels for the observations +#' @param ellipse.prob Coverage size of the data ellipse in Normal probability +#' @param ellipse.linewidth Thickness of the line outlining the ellipses +#' @param ellipse.fill Logical; should the ellipses be filled? +#' @param ellipse.alpha Transparency value (0 - 1) for filled ellipses +#' @param labels Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()} +#' of the dataset. #' @param labels.size size of the text used for the labels #' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) #' @param circle draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1) @@ -51,10 +59,19 @@ #' @import ggplot2 #' @importFrom stats predict qchisq var #' @importFrom scales muted -#' @importFrom dplyr filter n summarize select group_by +## @importFrom dplyr filter n summarize select group_by ## @importFrom tidyr unnest ## @importFrom purrr map -#' @return a ggplot2 plot object +#' +#' @seealso \code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} +#' +#' @references +#' K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. +#' \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. +#' +#' J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall +#' +#' @return a ggplot2 plot object of class \code{c("gg", "ggplot")} #' @export #' @examples #' data(wine) @@ -133,7 +150,7 @@ ggbiplot <- function(pcobj, choices = 1:2, v <- pcobj$scaling d.total <- sum(d^2) } else { - stop('Expected a object of class prcomp, princomp, PCA, or lda') + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') } # shutup 'no visible binding...' diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r index 6ced80b..084bee6 100644 --- a/R/ggscreeplot.r +++ b/R/ggscreeplot.r @@ -35,6 +35,23 @@ ggscreeplot <- function(pcobj, type = c('pev', 'cev'), size = 4) { + # Recover the SVD + if(inherits(pcobj, 'prcomp')){ + nobs.factor <- sqrt(nrow(pcobj$x) - 1) + d <- pcobj$sdev + } else if(inherits(pcobj, 'princomp')) { + nobs.factor <- sqrt(pcobj$n.obs) + d <- pcobj$sdev + } else if(inherits(pcobj, 'PCA')) { + nobs.factor <- sqrt(nrow(pcobj$call$X)) + d <- unlist(sqrt(pcobj$eig)[1]) + } else if(inherits(pcobj, "lda")) { + d <- pcobj$svd + } else { + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') + } + + type <- match.arg(type) d <- pcobj$sdev^2 yvar <- switch(type, diff --git a/extra/test-iris.R b/extra/test-iris.R new file mode 100644 index 0000000..7f001aa --- /dev/null +++ b/extra/test-iris.R @@ -0,0 +1,67 @@ +#' --- +#' title: test iris data for ggbiplot +#' --- + +library(ggbiplot) +library(ggplot2) +library(dplyr) +library(MASS) + + + +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) + +iris.gg <- + ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + +#' ## label the ellipses +group.labs <- + iris.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +iris.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") + +# show point labels +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, + point.size=2, + labels = row.names(iris), + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = FALSE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + + +#' ## Try lda() + +iris.lda <- lda(Species ~ ., data = iris) + +ggbiplot(iris.lda, + groups = iris$Species, + ellipse = TRUE, + varname.size = 5) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + + diff --git a/extra/testing.R b/extra/testing.R index c8913b8..67e1ce5 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -44,7 +44,6 @@ peng <- penguins |> peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, data=peng, - na.action=na.omit, scale. = TRUE) peng.gg <- @@ -85,9 +84,11 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, theme(legend.direction = 'horizontal', legend.position = 'top') -# last two dimensions: outliers +# last two dimensions: outliers; use observation labels ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, - groups = peng$species, point.size=2, + groups = peng$species, + labels = row.names(peng), + point.size=2, var.factor = 2.1, varname.adjust = 1, varname.size = 5, varname.color = scales::muted("red"), ellipse = TRUE, ellipse.alpha = 0.1, @@ -96,31 +97,30 @@ ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, theme_minimal() + theme(legend.direction = 'horizontal', legend.position = 'top') -#' ## iris data -#' -data(iris) -iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, - data=iris, - scale. = TRUE) +#' USArrests -iris.gg <- -ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, - groups = iris$Species, point.size=2, - varname.size = 5, - varname.color = "black", - varname.adjust = 1.2, - ellipse = TRUE, - circle = TRUE) + - labs(fill = "Species", color = "Species") + +data("USArrests") +arrests.pca <- + prcomp (~ Murder + Assault + UrbanPop + Rape, + data=USArrests, + scale. = TRUE) + + +ggbiplot(arrests.pca, + labels = state.abb[match(row.names(USArrests), state.name)] , + circle = TRUE, + varname.size = 4, + varname.color = "red") + + theme_minimal(base_size = 14) + +ggbiplot(arrests.pca, + groups = state.region, + labels = state.abb[match(row.names(USArrests), state.name)], + labels.size = 4, + ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1, + circle = TRUE, + varname.size = 4, + varname.color = "black") + theme_minimal(base_size = 14) + theme(legend.direction = 'horizontal', legend.position = 'top') -group.labs <- - iris.gg$data |> - summarise(xvar = mean(xvar), - yvar = mean(yvar), .by = groups) - -iris.gg + geom_label(data = group.labs, - aes(x = xvar, y=yvar, label=groups), - size = 5) + - theme(legend.position = "none") diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 8b2f1d2..38455f0 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -18,7 +18,7 @@ ggbiplot( ellipse.prob = 0.68, ellipse.linewidth = 1.3, ellipse.fill = TRUE, - ellipse.alpha = 0.3, + ellipse.alpha = 0.25, labels = NULL, labels.size = 3, alpha = 1, @@ -26,26 +26,29 @@ ggbiplot( circle = FALSE, circle.prob = 0.68, varname.size = 3, - varname.adjust = 1.5, - varname.color = "darkred", + varname.adjust = 1.25, + varname.color = "black", varname.abbrev = FALSE, ... ) } \arguments{ -\item{pcobj}{an object returned by prcomp() or princomp()} +\item{pcobj}{an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +\code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}} -\item{choices}{which PCs to plot} +\item{choices}{Which components to plot? A vector of length 2.} -\item{scale}{covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance.} +\item{scale}{Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product +between the variables approximates the covariance and the distance between the points +approximates the Mahalanobis distance.} -\item{pc.biplot}{for compatibility with biplot.princomp()} +\item{pc.biplot}{For compatibility with \code{biplot.princomp()}} -\item{obs.scale}{scale factor to apply to observations} +\item{obs.scale}{Scale factor to apply to observations} -\item{var.scale}{scale factor to apply to variables} +\item{var.scale}{Scale factor to apply to variables} -\item{var.factor}{factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected +\item{var.factor}{Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility.} \item{groups}{optional factor variable indicating the groups that the observations belong to. @@ -55,15 +58,16 @@ If provided the points will be colored according to groups.} \item{ellipse}{draw a normal data ellipse for each group?} -\item{ellipse.prob}{coverage size of the data ellipse in Normal probability} +\item{ellipse.prob}{Coverage size of the data ellipse in Normal probability} -\item{ellipse.linewidth}{thickness of the line outlining the ellipses} +\item{ellipse.linewidth}{Thickness of the line outlining the ellipses} -\item{ellipse.fill}{logical; should the ellipses be filled?} +\item{ellipse.fill}{Logical; should the ellipses be filled?} -\item{ellipse.alpha}{transparency value (0 - 1) for filled ellipses} +\item{ellipse.alpha}{Transparency value (0 - 1) for filled ellipses} -\item{labels}{optional vector of labels for the observations} +\item{labels}{Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()} +of the dataset.} \item{labels.size}{size of the text used for the labels} @@ -86,19 +90,44 @@ If provided the points will be colored according to groups.} \item{...}{other arguments passed down} } \value{ -a ggplot2 plot object +a ggplot2 plot object of class \code{c("gg", "ggplot")} } \description{ -Biplot for Principal Components using ggplot2 +A biplot simultaneously displays information on the observations (as points) +and the variables (as vectors) in a multidimensional dataset. The 2D biplot +is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data. } \examples{ - data(wine) - library(ggplot2) - wine.pca <- prcomp(wine, scale. = TRUE) - ggbiplot(wine.pca, - obs.scale = 1, var.scale = 1, - varname.size = 4, - groups = wine.class, - ellipse = TRUE, circle = TRUE) - +data(wine) +library(ggplot2) +wine.pca <- prcomp(wine, scale. = TRUE) +ggbiplot(wine.pca, + obs.scale = 1, var.scale = 1, + varname.size = 4, + groups = wine.class, + ellipse = TRUE, circle = TRUE) + +data(iris) +iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, + data=iris, + scale. = TRUE) +ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, + groups = iris$Species, point.size=2, + varname.size = 5, + varname.color = "black", + varname.adjust = 1.2, + ellipse = TRUE, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') +} +\references{ +K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. + \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. + + J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall +} +\seealso{ +\code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} } diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd index e0b6cfd..2d3531e 100644 --- a/man/ggscreeplot.Rd +++ b/man/ggscreeplot.Rd @@ -4,7 +4,7 @@ \alias{ggscreeplot} \title{Screeplot for Principal Components} \usage{ -ggscreeplot(pcobj, type = c("pev", "cev")) +ggscreeplot(pcobj, type = c("pev", "cev"), size = 4) } \arguments{ \item{pcobj}{an object returned by prcomp() or princomp()} @@ -12,6 +12,8 @@ ggscreeplot(pcobj, type = c("pev", "cev")) \item{type}{the type of scree plot. 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.} + +\item{size}{point size} } \description{ Screeplot for Principal Components From 36de0fe25c968bec1f2b57d0c43ec204a466dad8 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 17 Sep 2023 19:06:26 -0400 Subject: [PATCH 23/80] add crime data --- DESCRIPTION | 1 + R/crime.R | 48 ++++++++++++++++++++++++++++++++++++++++ R/ggbiplot.r | 5 ++++- R/wine.R | 1 + data/crime.RData | Bin 0 -> 1940 bytes extra/test-crime.R | 44 ++++++++++++++++++++++++++++++++++++ man/crime.Rd | 54 +++++++++++++++++++++++++++++++++++++++++++++ man/ggbiplot.Rd | 7 ++++-- man/ggscreeplot.Rd | 2 +- man/wine.Rd | 1 + 10 files changed, 159 insertions(+), 4 deletions(-) create mode 100644 R/crime.R create mode 100644 data/crime.RData create mode 100644 extra/test-crime.R create mode 100644 man/crime.Rd diff --git a/DESCRIPTION b/DESCRIPTION index 4ea89e7..68ef2f9 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -13,6 +13,7 @@ Description: A ggplot2 based biplot. It provides a replacement for biplot.princomp(), but with many enhancements. It implements a biplot and scree plot using ggplot2 which can be used with prcomp(), princomp(), FactoMineR::PCA() or MASS::lda(). +Depends: R (>= 3.5.0) Imports: ggplot2, scales Suggests: diff --git a/R/crime.R b/R/crime.R new file mode 100644 index 0000000..b54e3e8 --- /dev/null +++ b/R/crime.R @@ -0,0 +1,48 @@ +#' @title U. S. Crimes +#' @name crime +#' @description +#' This dataset gives rates of various crimes in each of the 50 U. S. states, +#' originally from the United States Statistical Abstracts (1970). The data +#' were analyzed by John Hartigan (1975) in his book \emph{Clustering Algorithms} and +#' were later reanalyzed by Friendly (1991). +#' +#' @docType data +#' @usage data(crime) +#' @format +#' A data frame with 50 observations on the following 10 variables. +#' \describe{ +#' \item{\code{state}}{state name, a character vector} +#' \item{\code{murder}}{a numeric vector} +#' \item{\code{rape}}{a numeric vector} +#' \item{\code{robbery}}{a numeric vector} +#' \item{\code{assault}}{a numeric vector} +#' \item{\code{burglary}}{a numeric vector} +#' \item{\code{larceny}}{a numeric vector} +#' \item{\code{auto}}{auto thefts, a numeric vector} +#' \item{\code{st}}{state abbreviation, a character vector} +#' \item{\code{region}}{region of the U.S., a factor with levels \code{Northeast} \code{South} \code{North Central} \code{West}} +#' } +#' @keywords dataset +#' @source +#' The data are originally from the United States Statistical Abstracts (1970). +#' @references +#' Friendly, M. (1991). \emph{SAS System for Statistical Graphics}. SAS Institute. +#' +#' Hartigan, J. A. (1975). \emph{Clustering Algorithms}. John Wiley and Sons. + +#' @examples +#' data(crime) +#' library(ggplot2) +#' crime.pca <- +#' crime |> +#' dplyr::select(where(is.numeric)) |> +#' prcomp(scale. = TRUE) +#' +#' ggbiplot(crime.pca, +#' labels = crime$st , +#' circle = TRUE, +#' varname.size = 4, +#' varname.color = "red") + +#' theme_minimal(base_size = 14) + +NULL diff --git a/R/ggbiplot.r b/R/ggbiplot.r index 868a4ee..d4dd7a1 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -66,9 +66,12 @@ #' @seealso \code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} #' #' @references -#' K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. +#' Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. #' \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. #' +#' Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. +#' In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. +#' #' J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall #' #' @return a ggplot2 plot object of class \code{c("gg", "ggplot")} diff --git a/R/wine.R b/R/wine.R index 3c5d00f..0967c6b 100644 --- a/R/wine.R +++ b/R/wine.R @@ -15,6 +15,7 @@ #' A \code{wine} data frame consisting of 178 observations (rows) and #' 13 columns and vector \code{wine.class} of factors indicating the cultivars. #' @source UCI Machine Learning Repository (\url{http://archive.ics.uci.edu/ml/datasets/Wine}) +#' @keywords dataset #' #' @examples #' data(wine) diff --git a/data/crime.RData b/data/crime.RData new file mode 100644 index 0000000000000000000000000000000000000000..9e29c287147b925dc8c27388b1e5c914ac01f016 GIT binary patch literal 1940 zcmV;F2W$8riwFP!0000025ne-Y*SSj@7C_gc!fwnF%E$c5P6NKyt;IZmC<%?-O3Pw z)AqEz^!DEE-rH?OKp+_85yE(8yyOi5Tzn)XDlx{tj6s6I#E=-Hi81~`3`RnTe}K3B ze&@8S-cY{B`M%%xJKs6?Ea$d1tgWkFTkUW-oDNs1)8Q<$RYzHSu<`Xp4%=fJB@UOP zD(j3GN{ZWoV{9XvG0OhU#b8Cf%EBzgV3ymanPhU%P`2orFe~egB-2c0!mjo(Rf*|_ zrpO47uIdJh>ad4-bWP(CONpc{5z@d_*2@eoYBbszN>r9y#dRYt0n3~0SVa*t@kUuf zU{`uoRnc@su&MBBQH4peF0bAzQJM>BS2lCaN=K3z*i~!vv|<*dmid^X34WD6W@J>R zMPU#3G1Fv`MB3z*B_VxEB%#EaCLn!^J#SOD1mrNEVw%~1U0q5($29e{A?ymDu332! zm3|&J3f7|B&wH3`({MlUt!-kdE;FIXR#s=7tGQwFOrgie`;>^DhwZKH)Qu$U5q{mU z615&?=yo>+d<}UUSTa8aS0JHClt5CoS0cY{0tS!kV)ivHT+_^q+QafYqoy^XM|rK+ zENJD3Ha-16waGiAc2$sP`)P79)v_S(lMCuPl+jamUY2$C?QzeDg+0D5 z_qa#h$v)q?$H6}t`BNb$V04>i(|B5Hbdlhk`5hwar zj&bmp>#`VeUeu`{Pq<5f-}EVsuLRC)#4Y-r@I0_rAaC&wimOAt`51o#e)Pe;0C;uC zTMoR};IBviJmh;!%BvIj;J0)Qjn4+pxxi~WKz`Bx`M~wSzYP94@Qc1J0p2q3^!$yw z7@q>^1`ok^8S1++k9okE1^x?Ri+)W<{b{i0Q=VLxwWu#7Yoz!f;=3PFUEV?dO|!|4 zoFf_EN^$HE*_*`tk-u4?K5c;AfPQw)AUlY9>?iQp!#-d-ASN4<66F$e1qUQBkR zhU&bDy2~-|5OCIk$4cy<)sUVCL*JL~DEj{u)iZaKtzh0g)M&Ti2S4yhpr2buligKG zaV@CNu}+(7v5r{J4$L=(@eTLMww_}B-6VT7!cnnbyQiTq$d6wnnG*X1eO-@r>4Cou z`y`I_P4^J4`4`2TzoAd)Zw$B!`rrL0<_#PL^VuGxya@0V?9a`Ze;E6*6Yoj%7UqL> z==h9e-~smE?OdE(m;NuQ&e6M+e<4V`4r0B|-6DB*Dam8#|H;)<=gdgLJvIUM&oq80 zNjQfd!+uKnd!u9@0iXSNFAgt&|0v-c`-SWik0|fNwb07+(18gs^HT|a$o`F?fe0}2N7RG{=?YE z$3~I=;P-?xFqZtgZV;b+z2Luo=(?PVQ~dQdk{_Gs?>Le-LgXLZPWGh?$(yvk?!gk` zb?!0w2hWlJQh@4R8IL}_hx~uYe>n!8Psx9=8T;aGvaj7Id0_;_T^j_>GxTpG$qSDt z?(%iSk0bn#EQ|*T_wt97e|0D7-zNKmAIUy_hwRIE|Ia7Le^IB(zo0z7fv zg}VsP#JSgpbHMro^^Q=S3LZV^M-=B=5`F2We8A zlk*748lg^y!#O;+_O@mJT=*60C9q42{LZ4E7%wT1g=5ZwJb_zMRHHDyFs8JqMq!R? zDE^SoDdj5f;i`!p?h-e~+>MztQ`|hua@SaSU8h?%*DQmn;@X + dplyr::select(where(is.numeric)) |> + prcomp(scale. = TRUE) + +biplot(crime.pca) + +# reflect dims 1:2 +crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] +crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] + +biplot(crime.pca) + + +ggbiplot(crime.pca, + labels = crime$st , + circle = TRUE, + varname.size = 4, + varname.color = "red") + + theme_minimal(base_size = 14) + +ggbiplot(crime.pca, + groups = crime$region, + labels = crime$st, + labels.size = 4, + var.factor = 1.4, + ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1, + circle = TRUE, + varname.size = 4, + varname.color = "black") + + labs(fill = "Region", color = "Region") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + + diff --git a/man/crime.Rd b/man/crime.Rd new file mode 100644 index 0000000..663164f --- /dev/null +++ b/man/crime.Rd @@ -0,0 +1,54 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/crime.R +\docType{data} +\name{crime} +\alias{crime} +\title{U. S. Crimes} +\format{ +A data frame with 50 observations on the following 10 variables. +\describe{ + \item{\code{state}}{state name, a character vector} + \item{\code{murder}}{a numeric vector} + \item{\code{rape}}{a numeric vector} + \item{\code{robbery}}{a numeric vector} + \item{\code{assault}}{a numeric vector} + \item{\code{burglary}}{a numeric vector} + \item{\code{larceny}}{a numeric vector} + \item{\code{auto}}{auto thefts, a numeric vector} + \item{\code{st}}{state abbreviation, a character vector} + \item{\code{region}}{region of the U.S., a factor with levels \code{Northeast} \code{South} \code{North Central} \code{West}} +} +} +\source{ +The data are originally from the United States Statistical Abstracts (1970). +} +\usage{ +data(crime) +} +\description{ +This dataset gives rates of various crimes in each of the 50 U. S. states, +originally from the United States Statistical Abstracts (1970). The data +were analyzed by John Hartigan (1975) in his book \emph{Clustering Algorithms} and +were later reanalyzed by Friendly (1991). +} +\examples{ +data(crime) +library(ggplot2) +crime.pca <- + crime |> + dplyr::select(where(is.numeric)) |> + prcomp(scale. = TRUE) + +ggbiplot(crime.pca, + labels = crime$st , + circle = TRUE, + varname.size = 4, + varname.color = "red") + + theme_minimal(base_size = 14) +} +\references{ +Friendly, M. (1991). \emph{SAS System for Statistical Graphics}. SAS Institute. + +Hartigan, J. A. (1975). \emph{Clustering Algorithms}. John Wiley and Sons. +} +\keyword{dataset} diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd index 38455f0..bfa08f9 100644 --- a/man/ggbiplot.Rd +++ b/man/ggbiplot.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/ggbiplot.r +% Please edit documentation in R/ggbiplot.R \name{ggbiplot} \alias{ggbiplot} \title{Biplot for Principal Components using ggplot2} @@ -123,9 +123,12 @@ ggbiplot(iris.pca, obs.scale = 1, var.scale = 1, theme(legend.direction = 'horizontal', legend.position = 'top') } \references{ -K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. +Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}. + Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. + In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. + J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall } \seealso{ diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd index 2d3531e..e717218 100644 --- a/man/ggscreeplot.Rd +++ b/man/ggscreeplot.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/ggscreeplot.r +% Please edit documentation in R/ggscreeplot.R \name{ggscreeplot} \alias{ggscreeplot} \title{Screeplot for Principal Components} diff --git a/man/wine.Rd b/man/wine.Rd index 6bf000d..19d265f 100644 --- a/man/wine.Rd +++ b/man/wine.Rd @@ -32,3 +32,4 @@ ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, groups = wine.class, ellipse = TRUE, circle = TRUE) } +\keyword{dataset} From bb3484a65a2aceeec1dd8e24dc01b31c81ac827e Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 17 Sep 2023 19:21:29 -0400 Subject: [PATCH 24/80] add wine variable descriptions --- R/wine.R | 17 +++++++++++++++++ man/wine.Rd | 16 ++++++++++++++++ 2 files changed, 33 insertions(+) diff --git a/R/wine.R b/R/wine.R index 0967c6b..ed52612 100644 --- a/R/wine.R +++ b/R/wine.R @@ -14,6 +14,23 @@ #' @format #' A \code{wine} data frame consisting of 178 observations (rows) and #' 13 columns and vector \code{wine.class} of factors indicating the cultivars. +#' The variables are: +#' \describe{ +#' \item{\code{Alcohol}}{a numeric vector} +#' \item{\code{MalicAcid}}{Malic acid, a numeric vector} +#' \item{\code{Ash}}{Ash, a numeric vector} +#' \item{\code{AlcAsh}}{Alcalinity of ash, a numeric vector} +#' \item{\code{Mg}}{Magnesium, a numeric vector} +#' \item{\code{Phenols}}{total phenols, a numeric vector} +#' \item{\code{Flav}}{Flavanoids, a numeric vector} +#' \item{\code{NonFlavPhenols}}{Nonflavanoid phenols, a numeric vector} +#' \item{\code{Proa}}{Proanthocyanins, a numeric vector} +#' \item{\code{Color}}{Color intensity, a numeric vector} +#' \item{\code{Hue}}{a numeric vector} +#' \item{\code{OD}}{D280/OD315 of diluted wines, a numeric vector} +#' \item{\code{Proline}}{a numeric vector} +#' } + #' @source UCI Machine Learning Repository (\url{http://archive.ics.uci.edu/ml/datasets/Wine}) #' @keywords dataset #' diff --git a/man/wine.Rd b/man/wine.Rd index 19d265f..4f414bc 100644 --- a/man/wine.Rd +++ b/man/wine.Rd @@ -8,6 +8,22 @@ \format{ A \code{wine} data frame consisting of 178 observations (rows) and 13 columns and vector \code{wine.class} of factors indicating the cultivars. +The variables are: + \describe{ + \item{\code{Alcohol}}{a numeric vector} + \item{\code{MalicAcid}}{Malic acid, a numeric vector} + \item{\code{Ash}}{Ash, a numeric vector} + \item{\code{AlcAsh}}{Alcalinity of ash, a numeric vector} + \item{\code{Mg}}{Magnesium, a numeric vector} + \item{\code{Phenols}}{total phenols, a numeric vector} + \item{\code{Flav}}{Flavanoids, a numeric vector} + \item{\code{NonFlavPhenols}}{Nonflavanoid phenols, a numeric vector} + \item{\code{Proa}}{Proanthocyanins, a numeric vector} + \item{\code{Color}}{Color intensity, a numeric vector} + \item{\code{Hue}}{a numeric vector} + \item{\code{OD}}{D280/OD315 of diluted wines, a numeric vector} + \item{\code{Proline}}{a numeric vector} + } } \source{ UCI Machine Learning Repository (\url{http://archive.ics.uci.edu/ml/datasets/Wine}) From d04c871e849e871454758d346077b1e420a00b4c Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 17 Sep 2023 21:30:15 -0400 Subject: [PATCH 25/80] added reflect() --- NAMESPACE | 1 + R/reflect.R | 57 ++++++++++++++++++++++++++++++++++++++++++++++++++ man/reflect.Rd | 31 +++++++++++++++++++++++++++ 3 files changed, 89 insertions(+) create mode 100644 R/reflect.R create mode 100644 man/reflect.Rd diff --git a/NAMESPACE b/NAMESPACE index 993b9b2..07fb16c 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -2,6 +2,7 @@ export(ggbiplot) export(ggscreeplot) +export(reflect) import(ggplot2) importFrom(scales,muted) importFrom(stats,predict) diff --git a/R/reflect.R b/R/reflect.R new file mode 100644 index 0000000..9a748e1 --- /dev/null +++ b/R/reflect.R @@ -0,0 +1,57 @@ + +#' Reflect columns in a principal component-like object +#' +#' Principle component like objects have variable loadings whose +#' signs are arbitrary, in the sense that a given column can be +#' reflected (multiplied by -1) without changing the fit. +#' +#' This function allows one to reflect any columns of the variable +#' loadings (and corresponding observation scores). +#' +#' @param pcobj an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +#' \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}} +#' @param columns a vector of indices of the columns to reflect +#' +#' @return The pca-like object with specified columns of the +#' variable loadings and observation scores multiplied +#' by -1. +#' @export +#' +#' @examples +#' # none yet +reflect <- function(pcobj, columns = 1:2){ + + check <- function(x, cols){ + if(!all(cols %in% 1:ncol(x))) stop("Illegl columns selected:", + paste(cols, collapse = ", ")) + } + + if(inherits(pcobj, 'prcomp')){ + check(pcobj$rotation, columns) + pcobj$rotation[, columns] <- -1 * pcobj$rotation[, columns] + pcobj$x[, columns] <- -1 * pcobj$x[, columns] + } + else if(inherits(pcobj, 'princomp')) { + check(pcobj$loadings, columns) + pcobj$loadings[, columns] <- -1 * pcobj$loadings[, columns] + pcobj$scores[, columns] <- -1 * pcobj$scores[, columns] + } + else if(inherits(pcobj, 'PCA')) { + check(pcobj$var$coord, columns) + pcobj$var$coord[, columns] <- -1 * pcobj$var$coord[, columns] + pcobj$ind$coord[, columns] <- -1 * pcobj$ind$coord[, columns] + } + else if(inherits(pcobj, "lda")) { + warning("Can't reflect an 'lda' object") + # u <- predict(pcobj)$x + # check(u, columns) + # pcobj$scaling[, columns] <- -1 * pcobj$scaling[, columns] + # pcobj$x[, columns] <- -1 * pcobj$x[, columns] + } + else { + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') + } + + pcobj + +} \ No newline at end of file diff --git a/man/reflect.Rd b/man/reflect.Rd new file mode 100644 index 0000000..570d469 --- /dev/null +++ b/man/reflect.Rd @@ -0,0 +1,31 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/reflect.R +\name{reflect} +\alias{reflect} +\title{Reflect columns in a principal component-like object} +\usage{ +reflect(pcobj, columns = 1:2) +} +\arguments{ +\item{pcobj}{an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +\code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}} + +\item{columns}{a vector of indices of the columns to reflect} +} +\value{ +The pca-like object with specified columns of the + variable loadings and observation scores multiplied + by -1. +} +\description{ +Principle component like objects have variable loadings whose +signs are arbitrary, in the sense that a given column can be +reflected (multiplied by -1) without changing the fit. +} +\details{ +This function allows one to reflect any columns of the variable +loadings (and corresponding observation scores). +} +\examples{ +# none yet +} From 8c42d1e6f0e48eccce8269f9e8d108ad66b127e3 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 17 Sep 2023 21:30:15 -0400 Subject: [PATCH 26/80] added reflect() --- NAMESPACE | 1 + R/reflect.R | 58 ++++++++++++++++++++++++++++++++++++++++++++++++++ man/reflect.Rd | 32 ++++++++++++++++++++++++++++ 3 files changed, 91 insertions(+) create mode 100644 R/reflect.R create mode 100644 man/reflect.Rd diff --git a/NAMESPACE b/NAMESPACE index 993b9b2..07fb16c 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -2,6 +2,7 @@ export(ggbiplot) export(ggscreeplot) +export(reflect) import(ggplot2) importFrom(scales,muted) importFrom(stats,predict) diff --git a/R/reflect.R b/R/reflect.R new file mode 100644 index 0000000..e123a05 --- /dev/null +++ b/R/reflect.R @@ -0,0 +1,58 @@ + +#' Reflect columns in a principal component-like object +#' +#' Principle component like objects have variable loadings whose +#' signs are arbitrary, in the sense that a given column can be +#' reflected (multiplied by -1) without changing the fit. +#' +#' This function allows one to reflect any columns of the variable +#' loadings (and corresponding observation scores). This is often +#' useful for interpreting a biplot. +#' +#' @param pcobj an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +#' \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}} +#' @param columns a vector of indices of the columns to reflect +#' +#' @return The pca-like object with specified columns of the +#' variable loadings and observation scores multiplied +#' by -1. +#' @export +#' +#' @examples +#' # none yet +reflect <- function(pcobj, columns = 1:2){ + + check <- function(x, cols){ + if(!all(cols %in% 1:ncol(x))) stop("Illegal columns selected:", + paste(cols, collapse = ", ")) + } + + if(inherits(pcobj, 'prcomp')){ + check(pcobj$rotation, columns) + pcobj$rotation[, columns] <- -1 * pcobj$rotation[, columns] + pcobj$x[, columns] <- -1 * pcobj$x[, columns] + } + else if(inherits(pcobj, 'princomp')) { + check(pcobj$loadings, columns) + pcobj$loadings[, columns] <- -1 * pcobj$loadings[, columns] + pcobj$scores[, columns] <- -1 * pcobj$scores[, columns] + } + else if(inherits(pcobj, 'PCA')) { + check(pcobj$var$coord, columns) + pcobj$var$coord[, columns] <- -1 * pcobj$var$coord[, columns] + pcobj$ind$coord[, columns] <- -1 * pcobj$ind$coord[, columns] + } + else if(inherits(pcobj, "lda")) { + warning("Can't reflect an 'lda' object") + # u <- predict(pcobj)$x + # check(u, columns) + # pcobj$scaling[, columns] <- -1 * pcobj$scaling[, columns] + # pcobj$x[, columns] <- -1 * pcobj$x[, columns] + } + else { + stop('Expected a object of class "prcomp", "princomp", "PCA", or "lda"') + } + + pcobj + +} \ No newline at end of file diff --git a/man/reflect.Rd b/man/reflect.Rd new file mode 100644 index 0000000..38c6ca1 --- /dev/null +++ b/man/reflect.Rd @@ -0,0 +1,32 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/reflect.R +\name{reflect} +\alias{reflect} +\title{Reflect columns in a principal component-like object} +\usage{ +reflect(pcobj, columns = 1:2) +} +\arguments{ +\item{pcobj}{an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, +\code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}} + +\item{columns}{a vector of indices of the columns to reflect} +} +\value{ +The pca-like object with specified columns of the + variable loadings and observation scores multiplied + by -1. +} +\description{ +Principle component like objects have variable loadings whose +signs are arbitrary, in the sense that a given column can be +reflected (multiplied by -1) without changing the fit. +} +\details{ +This function allows one to reflect any columns of the variable +loadings (and corresponding observation scores). This is often +useful for interpreting a biplot. +} +\examples{ +# none yet +} From 918ece54f08a9e510d66fa72ffabbb31b617f8a4 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Sun, 17 Sep 2023 22:51:05 -0400 Subject: [PATCH 27/80] re-org examples --- R/reflect.R | 12 ++++- extra/{test-crime.R => crime=ex.R} | 10 +++-- extra/penguins-ex.R | 71 ++++++++++++++++++++++++++++++ extra/testing.R | 68 ---------------------------- 4 files changed, 88 insertions(+), 73 deletions(-) rename extra/{test-crime.R => crime=ex.R} (81%) create mode 100644 extra/penguins-ex.R diff --git a/R/reflect.R b/R/reflect.R index e123a05..fe106fa 100644 --- a/R/reflect.R +++ b/R/reflect.R @@ -19,7 +19,17 @@ #' @export #' #' @examples -#' # none yet +#' data(crime) +#' crime.pca <- +#' crime |> +#' dplyr::select(where(is.numeric)) |> +#' prcomp(scale. = TRUE) +#' +#' biplot(crime.pca) +#' +#' crime.pca <- reflect(crime.pca) +#' biplot(crime.pca) + reflect <- function(pcobj, columns = 1:2){ check <- function(x, cols){ diff --git a/extra/test-crime.R b/extra/crime=ex.R similarity index 81% rename from extra/test-crime.R rename to extra/crime=ex.R index 756b66d..0d3a4c0 100644 --- a/extra/test-crime.R +++ b/extra/crime=ex.R @@ -4,8 +4,8 @@ library(ggbiplot) library(dplyr) - -load(here::here("data", "crime.RData")) +data(crime) +#load(here::here("data", "crime.RData")) crime.pca <- crime |> @@ -15,8 +15,10 @@ crime.pca <- biplot(crime.pca) # reflect dims 1:2 -crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] -crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] +# crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] +# crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] + +crime.pca <- reflect(crime.pca) biplot(crime.pca) diff --git a/extra/penguins-ex.R b/extra/penguins-ex.R new file mode 100644 index 0000000..9dadbde --- /dev/null +++ b/extra/penguins-ex.R @@ -0,0 +1,71 @@ +#' --- +#' title: penguins data examples +#' --- +#' + +data(penguins, package = "palmerpenguins") +peng <- penguins |> + rename( + bill_length = bill_length_mm, + bill_depth = bill_depth_mm, + flipper_length = flipper_length_mm, + body_mass = body_mass_g + ) |> + filter(!is.na(bill_depth), + !is.na(sex)) + + +peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, + data=peng, + scale. = TRUE) + +peng.gg <- + ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, + groups = peng$species, point.size=2, + varname.size = 6, + varname.color = "black", #scales::muted("black"), + ellipse = TRUE, ellipse.linewidth = 1.2, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal(base_size = 14) + + theme(legend.direction = 'horizontal', legend.position = 'top') + +# label the ellipses +group.labs <- + peng.gg$data |> + summarise(xvar = mean(xvar), + yvar = mean(yvar), .by = groups) + +peng.gg + geom_label(data = group.labs, + aes(x = xvar, y=yvar, label=groups), + size = 5) + + theme(legend.position = "none") + + + + +# try reflecting & scaline var vectors +ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, + var.factor = -1, + varname.adjust = 1, + groups = peng$species, point.size=2, + varname.size = 5, varname.color = scales::muted("black"), + ellipse = TRUE, ellipse.linewidth = 1.4, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') + + +# last two dimensions: outliers; use observation labels +ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, + groups = peng$species, + labels = row.names(peng), + point.size=2, + var.factor = 2.1, varname.adjust = 1, + varname.size = 5, varname.color = scales::muted("red"), + ellipse = TRUE, ellipse.alpha = 0.1, + circle = TRUE) + + labs(fill = "Species", color = "Species") + + theme_minimal() + + theme(legend.direction = 'horizontal', legend.position = 'top') diff --git a/extra/testing.R b/extra/testing.R index 67e1ce5..968e6cf 100644 --- a/extra/testing.R +++ b/extra/testing.R @@ -28,74 +28,6 @@ ggbiplot(wine.pca, groups=wine.class, theme(legend.direction = 'horizontal', legend.position = 'top') -#' ## penguins data -#' -data(penguins, package = "palmerpenguins") -peng <- penguins |> - rename( - bill_length = bill_length_mm, - bill_depth = bill_depth_mm, - flipper_length = flipper_length_mm, - body_mass = body_mass_g - ) |> - filter(!is.na(bill_depth), - !is.na(sex)) - - -peng.pca <- prcomp (~ bill_length + bill_depth + flipper_length + body_mass, - data=peng, - scale. = TRUE) - -peng.gg <- -ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, - groups = peng$species, point.size=2, - varname.size = 6, - varname.color = "black", #scales::muted("black"), - ellipse = TRUE, ellipse.linewidth = 1.2, - circle = TRUE) + - labs(fill = "Species", color = "Species") + - theme_minimal(base_size = 14) + - theme(legend.direction = 'horizontal', legend.position = 'top') - -# label the ellipses -group.labs <- - peng.gg$data |> - summarise(xvar = mean(xvar), - yvar = mean(yvar), .by = groups) - -peng.gg + geom_label(data = group.labs, - aes(x = xvar, y=yvar, label=groups), - size = 5) + - theme(legend.position = "none") - - - - -# try reflecting & scaline var vectors -ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, - var.factor = -1, - varname.adjust = 1, - groups = peng$species, point.size=2, - varname.size = 5, varname.color = scales::muted("black"), - ellipse = TRUE, ellipse.linewidth = 1.4, - circle = TRUE) + - labs(fill = "Species", color = "Species") + - theme_minimal() + - theme(legend.direction = 'horizontal', legend.position = 'top') - - -# last two dimensions: outliers; use observation labels -ggbiplot(peng.pca, obs.scale = 1, var.scale = 1, choices = 3:4, - groups = peng$species, - labels = row.names(peng), - point.size=2, - var.factor = 2.1, varname.adjust = 1, - varname.size = 5, varname.color = scales::muted("red"), - ellipse = TRUE, ellipse.alpha = 0.1, - circle = TRUE) + - labs(fill = "Species", color = "Species") + - theme_minimal() + - theme(legend.direction = 'horizontal', legend.position = 'top') #' USArrests From 27e4673bb1458f654221e8794a90d177800fb234 Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Mon, 18 Sep 2023 21:00:31 -0400 Subject: [PATCH 28/80] fix crime-ex.R --- extra/{crime=ex.R => crime-ex.R} | 16 +++++++++++++--- extra/penguins-ex.R | 3 ++- 2 files changed, 15 insertions(+), 4 deletions(-) rename extra/{crime=ex.R => crime-ex.R} (67%) diff --git a/extra/crime=ex.R b/extra/crime-ex.R similarity index 67% rename from extra/crime=ex.R rename to extra/crime-ex.R index 0d3a4c0..c0facdb 100644 --- a/extra/crime=ex.R +++ b/extra/crime-ex.R @@ -15,14 +15,15 @@ crime.pca <- biplot(crime.pca) # reflect dims 1:2 -# crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] -# crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] +crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] +crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] -crime.pca <- reflect(crime.pca) +crime.pca <- reflect(crime) biplot(crime.pca) +# default scaling: standardized components ggbiplot(crime.pca, labels = crime$st , circle = TRUE, @@ -30,6 +31,15 @@ ggbiplot(crime.pca, varname.color = "red") + theme_minimal(base_size = 14) +ggbiplot(crime.pca, + obs.scale = 1, var.scale = 1, + labels = crime$st , + circle = TRUE, + varname.size = 4, + varname.color = "red") + + theme_minimal(base_size = 14) + +# regions as groups, with ellipses ggbiplot(crime.pca, groups = crime$region, labels = crime$st, diff --git a/extra/penguins-ex.R b/extra/penguins-ex.R index 9dadbde..5b200d1 100644 --- a/extra/penguins-ex.R +++ b/extra/penguins-ex.R @@ -2,7 +2,8 @@ #' title: penguins data examples #' --- #' - + +library(ggplot2) data(penguins, package = "palmerpenguins") peng <- penguins |> rename( From bd7e9fa82398dade376960b332e44c9580c51a1c Mon Sep 17 00:00:00 2001 From: Michael Friendly Date: Tue, 19 Sep 2023 13:28:39 -0400 Subject: [PATCH 29/80] document ggbiplot details; use crime data in README --- DESCRIPTION | 1 + R/crime.R | 2 +- R/ggbiplot.r | 99 +++++++++++++++++---- README.Rmd | 84 +++++++++++++++++- README.md | 112 +++++++++++++++++++++--- extra/crime-ex.R | 10 ++- man/crime.Rd | 2 +- man/figures/README-crime-biplot0-1.png | Bin 0 -> 23888 bytes man/figures/README-crime-biplot1-1.png | Bin 0 -> 41117 bytes man/figures/README-crime-corrplot-1.png | Bin 0 -> 16394 bytes man/figures/README-iris-biplot0-1.png | Bin 24111 -> 26275 bytes man/figures/README-iris-biplot1-1.png | Bin 24600 -> 25467 bytes man/figures/README-wine-biplot-1.png | Bin 22094 -> 24302 bytes man/figures/README-wine-screeplot-1.png | Bin 7262 -> 7803 bytes man/ggbiplot.Rd | 93 ++++++++++++++++---- man/reflect.Rd | 11 ++- 16 files changed, 358 insertions(+), 56 deletions(-) create mode 100644 man/figures/README-crime-biplot0-1.png create mode 100644 man/figures/README-crime-biplot1-1.png create mode 100644 man/figures/README-crime-corrplot-1.png diff --git a/DESCRIPTION b/DESCRIPTION index 68ef2f9..73974e7 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -17,6 +17,7 @@ Depends: R (>= 3.5.0) Imports: ggplot2, scales Suggests: + corrplot, dplyr, MASS License: GPL-2 diff --git a/R/crime.R b/R/crime.R index b54e3e8..070c127 100644 --- a/R/crime.R +++ b/R/crime.R @@ -1,7 +1,7 @@ #' @title U. S. Crimes #' @name crime #' @description -#' This dataset gives rates of various crimes in each of the 50 U. S. states, +#' This dataset gives rates of various serious crimes in each of the 50 U. S. states, #' originally from the United States Statistical Abstracts (1970). The data #' were analyzed by John Hartigan (1975) in his book \emph{Clustering Algorithms} and #' were later reanalyzed by Friendly (1991). diff --git a/R/ggbiplot.r b/R/ggbiplot.r index d4dd7a1..5435486 100644 --- a/R/ggbiplot.r +++ b/R/ggbiplot.r @@ -20,40 +20,94 @@ #' Biplot for Principal Components using ggplot2 #' +#' @description #' A biplot simultaneously displays information on the observations (as points) #' and the variables (as vectors) in a multidimensional dataset. The 2D biplot -#' is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data. +#' is typically based on the first two principal components of a dataset, giving a rank 2 approximation +#' to the data. +#' +#' The biplot method for principal component analysis was originally defined by Gabriel (1971, 1981). +#' Gower & Hand (1996) give a more complete treatment. Gower et al. (2011) is the most up to date +#' exposition of biplot methodology. +#' +#' @details +#' The biplot is constructed by using the singular value decomposition (SVD) to obtain a low-rank +#' approximation to the data matrix \eqn{\mathbf{X}_{n \times p}} (centered, and optionally scaled to unit variances) +#' whose \eqn{n} rows are the observations +#' and whose \eqn{p} columns are the variables. +#' +#' Using the SVD, the matrix \eqn{\mathbf{X}}, of rank \eqn{r \le p} +#' can be expressed \emph{exactly} as +#' \deqn{\mathbf{X} = \mathbf{U} \mathbf{\Lambda} \mathbf{V}' +#' = \Sigma_i^r \lambda_i \mathbf{u}_i \mathbf{v}_i' \; ,} +#' +#' where +#' \itemize{ +#' \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores and also the eigenvectors +#' of \eqn{\mathbf{X} \mathbf{X}'}, +#' \item \eqn{\mathbf{\Lambda}} is an \eqn{r \times r} diagonal matrix of singular values, +#' \eqn{\lambda_1 \ge \lambda_2 \ge \cdots \lambda_r} +#' % which are also the square roots +#' % of the eigenvalues of \eqn{\mathbf{X} \mathbf{X}'}. +#' \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of observation scores and also the eigenvectors +#' of \eqn{\mathbf{X}' \mathbf{X}}. +#' } +#' +#' Then, a rank 2 (or 3) PCA approximation \eqn{\widehat{\mathbf{X}}} to the data matrix used in the biplot +#' can be obtained from the first 2 (or 3) +#' singular values \eqn{\lambda_i} +#' and the corresponding \eqn{\mathbf{u}_i, \mathbf{v}_i} as +#' +#' \deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2'} #' +#' The biplot is then obtained by overlaying two scatterplots that share a common set of axes and have a between-set scalar +#' product interpretation. Typically, the observations (rows of \eqn{\mathbf{X}}) are represented as points +#' and the variables (columns of \eqn{\mathbf{X}}) are represented as vectors from the origin. +#' +#' The \code{scale} factor, \eqn{\alpha} allows the variances of the components to be apportioned between the +#' row points and column vectors, with different interpretations, by representing the approximation +#' \eqn{\widehat{\mathbf{X}}} as the product of two matrices, +#' +#' \deqn{\widehat{\mathbf{X}} = (\mathbf{U} \mathbf{\Lambda}^\alpha) (\mathbf{\Lambda}^{1-\alpha} \mathbf{V}')} +#' #' @param pcobj an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, #' \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}} #' @param choices Which components to plot? A vector of length 2. -#' @param scale Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product +#' @param scale Covariance biplot (\code{scale = 1}), form biplot (\code{scale = 0}). +#' When \code{scale = 1} (the default), the inner product #' between the variables approximates the covariance and the distance between the points #' approximates the Mahalanobis distance. #' @param obs.scale Scale factor to apply to observations #' @param var.scale Scale factor to apply to variables #' @param var.factor Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected #' (\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility. -#' @param pc.biplot For compatibility with \code{biplot.princomp()} -#' @param groups optional factor variable indicating the groups that the observations belong to. -#' If provided the points will be colored according to groups. +#' \code{\link{reflect}} provides a simpler way to reflect the variables. +#' @param pc.biplot Logical, for compatibility with \code{biplot.princomp()}. If \code{TRUE}, use what Gabriel (1971) +#' refers to as a "principal component biplot", with \eqn{\alpha = 1} and observations scaled +#' up by sqrt(n) and variables scaled down by sqrt(n). Then inner products between +#' variables approximate covariances and distances between observations approximate +#' Mahalanobis distance. +#' @param groups Optional factor variable indicating the groups that the observations belong to. +#' If provided the points will be colored according to groups and this allows data ellipses also +#' to be drawn when \code{ellipse = TRUE}. #' @param point.size Size of observation points. -#' @param ellipse draw a normal data ellipse for each group? +#' @param ellipse Logical; draw a normal data ellipse for each group? #' @param ellipse.prob Coverage size of the data ellipse in Normal probability #' @param ellipse.linewidth Thickness of the line outlining the ellipses #' @param ellipse.fill Logical; should the ellipses be filled? #' @param ellipse.alpha Transparency value (0 - 1) for filled ellipses #' @param labels Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()} #' of the dataset. -#' @param labels.size size of the text used for the labels -#' @param alpha alpha transparency value for the points (0 = transparent, 1 = opaque) -#' @param circle draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1) -#' @param circle.prob size of circle -#' @param var.axes draw arrows for the variables? -#' @param varname.size size of the text for variable names -#' @param varname.color color for the variable vectors and names -#' @param varname.adjust adjustment factor the placement of the variable names, >= 1 means farther from the arrow -#' @param varname.abbrev whether or not to abbreviate the variable names +#' @param labels.size Size of the text used for the point labels +#' @param alpha Alpha transparency value for the points (0 = transparent, 1 = opaque) +#' @param circle draw a correlation circle? (only applies when prcomp was called with +#' \code{scale = TRUE} and when \code{var.scale = 1}) +#' @param circle.prob Size of the correlation circle +#' @param var.axes logical; draw arrows for the variables? +#' @param varname.size Size of the text for variable names +#' @param varname.color Color for the variable vectors and names +#' @param varname.adjust Adjustment factor the placement of the variable names, >= 1 means farther from the arrow +#' @param varname.abbrev logical; whether or not to abbreviate the variable names, using \code{\link{abbreviate}}. #' @param ... other arguments passed down #' #' @import ggplot2 @@ -63,7 +117,10 @@ ## @importFrom tidyr unnest ## @importFrom purrr map #' -#' @seealso \code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}} +#' @seealso +#' \code{\link{reflect}}, \code{\link{ggscreeplot}}; +#' \code{link[stats]{biplot}} for the original stats package version; +#' \code{link[factoextra]{fviz_pca_biplot}} for the factoextra package version. #' #' @references #' Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. @@ -72,7 +129,9 @@ #' Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. #' In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. #' -#' J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall +#' J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall. +#' +#' Gower, J. C., Lubbe, S. G., & Roux, N. J. L. (2011). \emph{Understanding Biplots}. Wiley. #' #' @return a ggplot2 plot object of class \code{c("gg", "ggplot")} #' @export @@ -101,8 +160,10 @@ #' theme_minimal(base_size = 14) + #' theme(legend.direction = 'horizontal', legend.position = 'top') -ggbiplot <- function(pcobj, choices = 1:2, - scale = 1, pc.biplot = TRUE, +ggbiplot <- function(pcobj, + choices = 1:2, + scale = 1, + pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale, var.factor = 1, # MF diff --git a/README.Rmd b/README.Rmd index 7bab24f..3722136 100644 --- a/README.Rmd +++ b/README.Rmd @@ -25,8 +25,12 @@ knitr::opts_chunk$set( message = FALSE, warning = FALSE, comment = "#>", + fig.height = 6, + fig.width = 6, fig.path = "man/figures/README-" ) + +options(digits = 3) ``` # ggbiplot @@ -44,7 +48,82 @@ Install the current master branch with: remotes::install_github("friendly/ggbiplot") ``` -## Example Usage +## Examples + +Load packages: + +```{r} +library(ggplot2) +library(ggbiplot) +library(dplyr) +library(corrplot) + +# set ggplot2 theme +theme_set(theme_minimal(base_size = 14)) +``` + +### Crime data + +The `crime` data gives rates of various serious crimes in each of the 50 U. S. states, +originally from the United States Statistical Abstracts (1970). + +Let's take a quick look at the correlations among these, using `corrplot::corrplot()` +and showing each correlation by an ellipse whose eccentricity and shading represents the value of +the correlation. + +```{r crime-corrplot} +data(crime) +crime |> + dplyr::select(where(is.numeric)) |> + cor() |> + corrplot(method = "ellipse") +``` + +The correlations are all positive. Note also that the variables in the dataset +are ordered in seriousness or violence, ranging from murder to auto theft. + +Carry out a PCA: + +```{r crime-pca} +crime.pca <- + crime |> + dplyr::select(where(is.numeric)) |> + prcomp(scale. = TRUE) + +crime.pca +``` + +The biplot, using default scaling (standardized components), and labeling the +states by their state abbreviation: + +```{r crime-biplot0} +ggbiplot(crime.pca, + labels = crime$st , + circle = TRUE, + varname.size = 4, + varname.color = "red") +``` + +The directions of the principal components are arbitrary; we are free to reflect +the variable vectors and component scores to facilitate interpretation. +Also, there seem to be differences among regions of the U.S., which can be +visualized using data ellipses for the component scores. + +```{r crime-biplot1} +crime.pca <- reflect(crime.pca) +ggbiplot(crime.pca, + groups = crime$region, + labels = crime$st, + labels.size = 4, + var.factor = 1.4, + ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1, + circle = TRUE, + varname.size = 4, + varname.color = "black") + + labs(fill = "Region", color = "Region") + + theme(legend.direction = 'horizontal', legend.position = 'top') +``` + ### Wine data @@ -62,8 +141,7 @@ library(dplyr) data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggscreeplot(wine.pca) + - theme_bw(base_size = 14) +ggscreeplot(wine.pca) ``` Hmm. The screeplot shows that more than two dimensions are necessary to account for most of the variance. diff --git a/README.md b/README.md index 944e149..f2f7ece 100644 --- a/README.md +++ b/README.md @@ -34,7 +34,98 @@ Install the current master branch with: remotes::install_github("friendly/ggbiplot") ``` -## Example Usage +## Examples + +Load packages: + +``` r +library(ggplot2) +library(ggbiplot) +library(dplyr) +library(corrplot) + +# set ggplot2 theme +theme_set(theme_minimal(base_size = 14)) +``` + +### Crime data + +The `crime` data gives rates of various serious crimes in each of the 50 +U. S. states, originally from the United States Statistical Abstracts +(1970). + +Let’s take a quick look at the correlations among these, using +`corrplot::corrplot()` and showing each correlation by an ellipse whose +eccentricity and shading represents the value of the correlation. + +``` r +data(crime) +crime |> + dplyr::select(where(is.numeric)) |> + cor() |> + corrplot(method = "ellipse") +``` + +![](man/figures/README-crime-corrplot-1.png) + +Carry out a PCA: + +``` r +crime.pca <- + crime |> + dplyr::select(where(is.numeric)) |> + prcomp(scale. = TRUE) + +crime.pca +#> Standard deviations (1, .., p=7): +#> [1] 2.029 1.113 0.852 0.563 0.508 0.471 0.352 +#> +#> Rotation (n x k) = (7 x 7): +#> PC1 PC2 PC3 PC4 PC5 PC6 PC7 +#> murder -0.300 -0.6292 0.1782 -0.2321 0.5381 0.2591 0.2676 +#> rape -0.432 -0.1694 -0.2442 0.0622 0.1885 -0.7733 -0.2965 +#> robbery -0.397 0.0422 0.4959 -0.5580 -0.5200 -0.1144 -0.0039 +#> assault -0.397 -0.3435 -0.0695 0.6298 -0.5067 0.1724 0.1917 +#> burglary -0.440 0.2033 -0.2099 -0.0576 0.1010 0.5360 -0.6481 +#> larceny -0.357 0.4023 -0.5392 -0.2349 0.0301 0.0394 0.6017 +#> auto -0.295 0.5024 0.5684 0.4192 0.3698 -0.0573 0.1470 +``` + +The biplot, using default scaling (standardized components), and +labeling the states by their state abbreviation: + +``` r +ggbiplot(crime.pca, + labels = crime$st , + circle = TRUE, + varname.size = 4, + varname.color = "red") +``` + +![](man/figures/README-crime-biplot0-1.png) + +The directions of the principal components are arbitrary; we are free to +reflect the variable vectors and component scores to facilitate +interpretation. Also, there seem to be differences among regions of the +U.S., which can be visualized using data ellipses for the component +scores. + +``` r +crime.pca <- reflect(crime.pca) +ggbiplot(crime.pca, + groups = crime$region, + labels = crime$st, + labels.size = 4, + var.factor = 1.4, + ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1, + circle = TRUE, + varname.size = 4, + varname.color = "black") + + labs(fill = "Region", color = "Region") + + theme(legend.direction = 'horizontal', legend.position = 'top') +``` + +![](man/figures/README-crime-biplot1-1.png) ### Wine data @@ -54,8 +145,7 @@ library(dplyr) data(wine) wine.pca <- prcomp(wine, scale. = TRUE) -ggscreeplot(wine.pca) + - theme_bw(base_size = 14) +ggscreeplot(wine.pca) ``` ![](man/figures/README-wine-screeplot-1.png) @@ -93,10 +183,10 @@ iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, scale. = TRUE) summary(iris.pca) #> Importance of components: -#> PC1 PC2 PC3 PC4 -#> Standard deviation 1.7084 0.9560 0.38309 0.14393 -#> Proportion of Variance 0.7296 0.2285 0.03669 0.00518 -#> Cumulative Proportion 0.7296 0.9581 0.99482 1.00000 +#> PC1 PC2 PC3 PC4 +#> Standard deviation 1.71 0.956 0.3831 0.14393 +#> Proportion of Variance 0.73 0.229 0.0367 0.00518 +#> Cumulative Proportion 0.73 0.958 0.9948 1.00000 ``` Plot the first two dimensions: @@ -133,10 +223,10 @@ group.labs <- yvar = mean(yvar), .by = groups) group.labs -#> groups xvar yvar -#> 1 setosa -2.2173249 -0.2879627 -#> 2 versicolor 0.4947904 0.5483335 -#> 3 virginica 1.7225345 -0.2603708 +#> groups xvar yvar +#> 1 setosa -2.217 -0.288 +#> 2 versicolor 0.495 0.548 +#> 3 virginica 1.723 -0.260 ``` Now, just use `geom_label` to draw labels for the groups. diff --git a/extra/crime-ex.R b/extra/crime-ex.R index c0facdb..171f23f 100644 --- a/extra/crime-ex.R +++ b/extra/crime-ex.R @@ -2,10 +2,16 @@ #' title: crime data #' --- +library(ggplot2) library(ggbiplot) library(dplyr) +library(corrplot) data(crime) -#load(here::here("data", "crime.RData")) + +crime |> + dplyr::select(where(is.numeric)) |> + cor() |> + corrplot(method = "ellipse") crime.pca <- crime |> @@ -18,7 +24,7 @@ biplot(crime.pca) crime.pca$rotation[,1:2] <- -1 * crime.pca$rotation[,1:2] crime.pca$x[,1:2] <- -1 * crime.pca$x[,1:2] -crime.pca <- reflect(crime) +crime.pca <- reflect(crime.pca) biplot(crime.pca) diff --git a/man/crime.Rd b/man/crime.Rd index 663164f..fd6a1cb 100644 --- a/man/crime.Rd +++ b/man/crime.Rd @@ -26,7 +26,7 @@ The data are originally from the United States Statistical Abstracts (1970). data(crime) } \description{ -This dataset gives rates of various crimes in each of the 50 U. S. states, +This dataset gives rates of various serious crimes in each of the 50 U. S. states, originally from the United States Statistical Abstracts (1970). 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diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd
index bfa08f9..78ab3f1 100644
--- a/man/ggbiplot.Rd
+++ b/man/ggbiplot.Rd
@@ -38,25 +38,32 @@ ggbiplot(
 
 \item{choices}{Which components to plot? A vector of length 2.}
 
-\item{scale}{Covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product 
+\item{scale}{Covariance biplot (\code{scale = 1}), form biplot (\code{scale = 0}). 
+When \code{scale = 1} (the default), the inner product 
 between the variables approximates the covariance and the distance between the points 
 approximates the Mahalanobis distance.}
 
-\item{pc.biplot}{For compatibility with \code{biplot.princomp()}}
+\item{pc.biplot}{Logical, for compatibility with \code{biplot.princomp()}. If \code{TRUE}, use what Gabriel (1971) 
+refers to as a "principal component biplot", with \eqn{\alpha = 1} and observations scaled 
+up by sqrt(n) and variables scaled down by sqrt(n). Then inner products between 
+variables approximate covariances and distances between observations approximate 
+Mahalanobis distance.}
 
 \item{obs.scale}{Scale factor to apply to observations}
 
 \item{var.scale}{Scale factor to apply to variables}
 
 \item{var.factor}{Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected
-(\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility.}
+(\code{var.factor = -1}) or expanded in length (\code{var.factor > 1}) for greater visibility.
+\code{\link{reflect}} provides a simpler way to reflect the variables.}
 
-\item{groups}{optional factor variable indicating the groups that the observations belong to. 
-If provided the points will be colored according to groups.}
+\item{groups}{Optional factor variable indicating the groups that the observations belong to. 
+If provided the points will be colored according to groups and this allows data ellipses also
+to be drawn when \code{ellipse = TRUE}.}
 
 \item{point.size}{Size of observation points.}
 
-\item{ellipse}{draw a normal data ellipse for each group?}
+\item{ellipse}{Logical; draw a normal data ellipse for each group?}
 
 \item{ellipse.prob}{Coverage size of the data ellipse in Normal probability}
 
@@ -69,23 +76,24 @@ If provided the points will be colored according to groups.}
 \item{labels}{Optional vector of labels for the observations. Often, this will be specified as the \code{row.names()}
 of the dataset.}
 
-\item{labels.size}{size of the text used for the labels}
+\item{labels.size}{Size of the text used for the point labels}
 
-\item{alpha}{alpha transparency value for the points (0 = transparent, 1 = opaque)}
+\item{alpha}{Alpha transparency value for the points (0 = transparent, 1 = opaque)}
 
-\item{var.axes}{draw arrows for the variables?}
+\item{var.axes}{logical; draw arrows for the variables?}
 
-\item{circle}{draw a correlation circle? (only applies when prcomp was called with scale = TRUE and when var.scale = 1)}
+\item{circle}{draw a correlation circle? (only applies when prcomp was called with 
+\code{scale = TRUE} and when \code{var.scale = 1})}
 
-\item{circle.prob}{size of circle}
+\item{circle.prob}{Size of the correlation circle}
 
-\item{varname.size}{size of the text for variable names}
+\item{varname.size}{Size of the text for variable names}
 
-\item{varname.adjust}{adjustment factor the placement of the variable names, >= 1 means farther from the arrow}
+\item{varname.adjust}{Adjustment factor the placement of the variable names, >= 1 means farther from the arrow}
 
-\item{varname.color}{color for the variable vectors and names}
+\item{varname.color}{Color for the variable vectors and names}
 
-\item{varname.abbrev}{whether or not to abbreviate the variable names}
+\item{varname.abbrev}{logical; whether or not to abbreviate the variable names, using \code{\link{abbreviate}}.}
 
 \item{...}{other arguments passed down}
 }
@@ -95,7 +103,52 @@ a ggplot2 plot object of class \code{c("gg", "ggplot")}
 \description{
 A biplot simultaneously displays information on the observations (as points)
 and the variables (as vectors) in a multidimensional dataset. The 2D biplot
-is typically based on the first two principal components of a dataset, giving a rank 2 approximation to the data.
+is typically based on the first two principal components of a dataset, giving a rank 2 approximation 
+to the data.
+
+The biplot method for principal component analysis was originally defined by Gabriel (1971, 1981).
+Gower & Hand (1996) give a more complete treatment. Gower et al. (2011) is the most up to date
+exposition of biplot methodology.
+}
+\details{
+The biplot is constructed by using the singular value decomposition (SVD) to obtain a low-rank 
+approximation to the data matrix \eqn{\mathbf{X}_{n \times p}} (centered, and optionally scaled to unit variances)
+whose \eqn{n} rows are the observations 
+and whose \eqn{p} columns are the variables. 
+
+Using the SVD, the matrix \eqn{\mathbf{X}}, of rank \eqn{r \le p}
+can be expressed \emph{exactly} as
+\deqn{\mathbf{X} = \mathbf{U} \mathbf{\Lambda} \mathbf{V}'
+                 = \Sigma_i^r \lambda_i \mathbf{u}_i \mathbf{v}_i' \; ,}
+
+where 
+\itemize{
+   \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores and also the eigenvectors
+         of \eqn{\mathbf{X} \mathbf{X}'},
+   \item \eqn{\mathbf{\Lambda}} is an \eqn{r \times r} diagonal matrix of singular values, 
+         \eqn{\lambda_1 \ge \lambda_2 \ge \cdots \lambda_r} 
+        % which are also the square roots
+        % of the eigenvalues of \eqn{\mathbf{X} \mathbf{X}'}. 
+   \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of observation scores and also the eigenvectors
+         of \eqn{\mathbf{X}' \mathbf{X}}.
+}
+
+Then, a rank 2 (or 3) PCA approximation \eqn{\widehat{\mathbf{X}}} to the data matrix used in the biplot
+can be obtained from the first 2 (or 3)
+singular values \eqn{\lambda_i}
+and the corresponding \eqn{\mathbf{u}_i, \mathbf{v}_i} as
+
+\deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2'}
+
+The biplot is then obtained by overlaying two scatterplots that share a common set of axes and have a between-set scalar 
+product interpretation. Typically, the observations (rows of \eqn{\mathbf{X}}) are represented as points
+and the variables (columns of \eqn{\mathbf{X}}) are represented as vectors from the origin.
+
+The \code{scale} factor, \eqn{\alpha} allows the variances of the components to be apportioned between the
+row points and column vectors, with different interpretations, by representing the approximation
+\eqn{\widehat{\mathbf{X}}} as the product of two matrices,
+
+\deqn{\widehat{\mathbf{X}} = (\mathbf{U} \mathbf{\Lambda}^\alpha) (\mathbf{\Lambda}^{1-\alpha} \mathbf{V}')}
 }
 \examples{
 data(wine)
@@ -129,8 +182,12 @@ Gabriel, K. R. (1971). The biplot graphical display of matrices with application
   Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. 
   In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. 
   
-  J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall
+  J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall.
+  
+  Gower, J. C., Lubbe, S. G., & Roux, N. J. L. (2011). \emph{Understanding Biplots}. Wiley.
 }
 \seealso{
-\code{link[stats]{biplot}}, \code{link[factoextra]{fviz_pca_biplot}}
+\code{\link{reflect}}, \code{\link{ggscreeplot}};
+  \code{link[stats]{biplot}} for the original stats package version;
+  \code{link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
 }
diff --git a/man/reflect.Rd b/man/reflect.Rd
index 38c6ca1..cd216a1 100644
--- a/man/reflect.Rd
+++ b/man/reflect.Rd
@@ -28,5 +28,14 @@ loadings (and corresponding observation scores). This is often
 useful for interpreting a biplot.
 }
 \examples{
-# none yet
+data(crime)
+crime.pca <- 
+  crime |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)
+  
+ biplot(crime.pca)
+ 
+ crime.pca <- reflect(crime.pca)
+ biplot(crime.pca)
 }

From 0ba237be215fe141475913ea214fb0a5f8157d84 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 19 Sep 2023 14:01:09 -0400
Subject: [PATCH 30/80] add interpretation for crime data to README

---
 README.Rmd | 26 ++++++++++++++++++++++++--
 README.md  | 30 +++++++++++++++++++++++++++++-
 2 files changed, 53 insertions(+), 3 deletions(-)

diff --git a/README.Rmd b/README.Rmd
index 3722136..b01138b 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -107,8 +107,9 @@ ggbiplot(crime.pca,
 The directions of the principal components are arbitrary; we are free to reflect
 the variable vectors and component scores to facilitate interpretation.
 Also, there seem to be differences among regions of the U.S., which can be
-visualized using data ellipses for the component scores.
-
+visualized using data ellipses for the component scores. The `groups` argument
+allows the observations to colored by group and to summarized by groups.
+ 
 ```{r crime-biplot1}
 crime.pca <- reflect(crime.pca)
 ggbiplot(crime.pca,
@@ -124,6 +125,27 @@ ggbiplot(crime.pca,
   theme(legend.direction = 'horizontal', legend.position = 'top')
 ```
 
+The interpretation of the data is now clear. 
+
+* The first dimension,
+accounting for 58.8% of variance, can be seen to represent **overall
+crime rate**, with Nevada (NV) at the high end and North Dakota (ND),
+South Dakota (SD) and West Virginia (WV) at the low end.
+
+* The second dimension, accounting for 17.7% of variance represents
+a contrast between
+**personal crime vs. property crime**. On this dimension, Massachusetts (MA),
+Rhode Island (RI) are opposed to Mississippi (MS), Alabama (AL), Louisiana (LA) and South
+Carolina (SC).
+
+* The regions are represented by the differences in the centers of the
+data ellipses for the scores. Southern states are highest on murder,
+assault and rape, while the Northeast states are highest on auto theft
+and larceny.
+
+* In this standardized view, the angles between variable vectors approximate
+the correlations among the variables, according to $\cos (\text{angle}) \approx r$.
+Thus, `murder` and `auto`, nearly $90^o$ reflect a near 0 correlation.
 
 ### Wine data
 
diff --git a/README.md b/README.md
index f2f7ece..7b39fff 100644
--- a/README.md
+++ b/README.md
@@ -68,6 +68,10 @@ crime |>
 
 ![](man/figures/README-crime-corrplot-1.png)
 
+The correlations are all positive. Note also that the variables in the
+dataset are ordered in seriousness or violence, ranging from murder to
+auto theft.
+
 Carry out a PCA:
 
 ``` r
@@ -108,7 +112,8 @@ The directions of the principal components are arbitrary; we are free to
 reflect the variable vectors and component scores to facilitate
 interpretation. Also, there seem to be differences among regions of the
 U.S., which can be visualized using data ellipses for the component
-scores.
+scores. The `groups` argument allows the observations to colored by
+group and to summarized by groups.
 
 ``` r
 crime.pca <- reflect(crime.pca)
@@ -127,6 +132,29 @@ ggbiplot(crime.pca,
 
 ![](man/figures/README-crime-biplot1-1.png)
 
+The interpretation of the data is now clear.
+
+- The first dimension, accounting for 58.8% of variance, can be seen to
+  represent **overall crime rate**, with Nevada (NV) at the high end and
+  North Dakota (ND), South Dakota (SD) and West Virginia (WV) at the low
+  end.
+
+- The second dimension, accounting for 17.7% of variance represents a
+  contrast between **personal crime vs. property crime**. On this
+  dimension, Massachusetts (MA), Rhode Island (RI) are opposed to
+  Mississippi (MS), Alabama (AL), Louisiana (LA) and South Carolina
+  (SC).
+
+- The regions are represented by the differences in the centers of the
+  data ellipses for the scores. Southern states are highest on murder,
+  assault and rape, while the Northeast states are highest on auto theft
+  and larceny.
+
+- In this standardized view, the angles between variable vectors
+  approximate the correlations among the variables, according to
+  $\cos (\text{angle}) \approx r$. Thus, `murder` and `auto`, nearly
+  $90^o$ reflect a near 0 correlation.
+
 ### Wine data
 
 The `wine` data contains results of a chemical analysis of wines grown

From 6dd5192463de398bc2cec1b8713e928186848c99 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Wed, 20 Sep 2023 11:00:53 -0400
Subject: [PATCH 31/80] more documentation of ggbiplot.R

---
 R/ggbiplot.r     | 26 +++++++++++++++++++++++---
 README.Rmd       |  2 +-
 extra/crime-ex.R |  2 +-
 extra/testing.R  |  2 +-
 man/ggbiplot.Rd  | 26 +++++++++++++++++++++++---
 5 files changed, 49 insertions(+), 9 deletions(-)

diff --git a/R/ggbiplot.r b/R/ggbiplot.r
index 5435486..b162836 100644
--- a/R/ggbiplot.r
+++ b/R/ggbiplot.r
@@ -24,10 +24,13 @@
 #' A biplot simultaneously displays information on the observations (as points)
 #' and the variables (as vectors) in a multidimensional dataset. The 2D biplot
 #' is typically based on the first two principal components of a dataset, giving a rank 2 approximation 
-#' to the data.
+#' to the data. The “bi” in biplot refers to the fact that two sets of points (i.e., the rows and
+#' columns of the data matrix) are visualized by scalar products, not the fact
+#' that the display is usually two-dimensional.
 #' 
 #' The biplot method for principal component analysis was originally defined by Gabriel (1971, 1981).
-#' Gower & Hand (1996) give a more complete treatment. Gower et al. (2011) is the most up to date
+#' Gower & Hand (1996) give a more complete treatment. Greenacre (2010) is a practical user-oriented guide to biplots.
+#' Gower et al. (2011) is the most up to date
 #' exposition of biplot methodology.
 #' 
 #' @details
@@ -58,8 +61,10 @@
 #' singular values \eqn{\lambda_i}
 #' and the corresponding \eqn{\mathbf{u}_i, \mathbf{v}_i} as
 #' 
-#' \deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2'}
+#' \deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2' \; .}
 #'
+#' The variance of \eqn{\mathbf{X}} accounted for by each term is \eqn{\lambda_i^2}.
+#' 
 #' The biplot is then obtained by overlaying two scatterplots that share a common set of axes and have a between-set scalar 
 #' product interpretation. Typically, the observations (rows of \eqn{\mathbf{X}}) are represented as points
 #' and the variables (columns of \eqn{\mathbf{X}}) are represented as vectors from the origin.
@@ -70,6 +75,18 @@
 #' 
 #' \deqn{\widehat{\mathbf{X}} = (\mathbf{U} \mathbf{\Lambda}^\alpha) (\mathbf{\Lambda}^{1-\alpha} \mathbf{V}')}
 #' 
+#' The choice \eqn{\alpha = 1}, assigning the singular values totally to the left factor,
+#'  gives a distance interpretation to the row display and 
+#' \eqn{\alpha = 0} gives a distance interpretation to the column display.
+#' \eqn{\alpha = 1/2} gives a symmetrically scaled biplot.
+#' 
+#' When the singular values are assigned totally to the left or to the right factor, the resultant 
+#' coordinates are called \emph{principal coordinates} and the sum of squared coordinates
+#' on each dimension equal the corresponding singular value.
+#' The other matrix, to which no part of the singular 
+#' values is assigned, contains the so-called \emph{standard coordinates} and have sum of squared
+#' values equal to 1.0. 
+#' 
 #' @param pcobj           an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, 
 #'                        \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}
 #' @param choices         Which components to plot? A vector of length 2.
@@ -129,6 +146,9 @@
 #'   Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. 
 #'   In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. 
 #'   
+#'   Greenacre, M. (2010). \emph{Biplots in Practice}. BBVA Foundation, Bilbao, Spain. 
+#'   Available for free at \url{https://www.multivariatestatistics.org}.
+#'   
 #'   J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall.
 #'   
 #'   Gower, J. C., Lubbe, S. G., & Roux, N. J. L. (2011). \emph{Understanding Biplots}. Wiley.
diff --git a/README.Rmd b/README.Rmd
index b01138b..25e93c7 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -76,7 +76,7 @@ data(crime)
 crime |> 
   dplyr::select(where(is.numeric)) |> 
   cor() |> 
-  corrplot(method = "ellipse")
+  corrplot(method = "ellipse", tl.srt = 0)
 ```
 
 The correlations are all positive.  Note also that the variables in the dataset
diff --git a/extra/crime-ex.R b/extra/crime-ex.R
index 171f23f..b1443b8 100644
--- a/extra/crime-ex.R
+++ b/extra/crime-ex.R
@@ -11,7 +11,7 @@ data(crime)
 crime |> 
   dplyr::select(where(is.numeric)) |> 
   cor() |> 
-  corrplot(method = "ellipse")
+  corrplot(method = "ellipse", tl.srt = 0)
 
 crime.pca <- 
   crime |> 
diff --git a/extra/testing.R b/extra/testing.R
index 968e6cf..b41c534 100644
--- a/extra/testing.R
+++ b/extra/testing.R
@@ -14,7 +14,7 @@ ggbiplot(wine.pca, groups=wine.class,
          circle = TRUE,
          varname.color = "darkred",
          varname.size = 4) +
-  theme_minimal() +
+  theme_minimal(base_size = 14) +
   theme(legend.direction = 'horizontal', legend.position = 'top')
 
 # unfilled
diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd
index 78ab3f1..9ae779d 100644
--- a/man/ggbiplot.Rd
+++ b/man/ggbiplot.Rd
@@ -104,10 +104,13 @@ a ggplot2 plot object of class \code{c("gg", "ggplot")}
 A biplot simultaneously displays information on the observations (as points)
 and the variables (as vectors) in a multidimensional dataset. The 2D biplot
 is typically based on the first two principal components of a dataset, giving a rank 2 approximation 
-to the data.
+to the data. The “bi” in biplot refers to the fact that two sets of points (i.e., the rows and
+columns of the data matrix) are visualized by scalar products, not the fact
+that the display is usually two-dimensional.
 
 The biplot method for principal component analysis was originally defined by Gabriel (1971, 1981).
-Gower & Hand (1996) give a more complete treatment. Gower et al. (2011) is the most up to date
+Gower & Hand (1996) give a more complete treatment. Greenacre (2010) is a practical user-oriented guide to biplots.
+Gower et al. (2011) is the most up to date
 exposition of biplot methodology.
 }
 \details{
@@ -138,7 +141,9 @@ can be obtained from the first 2 (or 3)
 singular values \eqn{\lambda_i}
 and the corresponding \eqn{\mathbf{u}_i, \mathbf{v}_i} as
 
-\deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2'}
+\deqn{\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2' \; .}
+
+The variance of \eqn{\mathbf{X}} accounted for by each term is \eqn{\lambda_i^2}.
 
 The biplot is then obtained by overlaying two scatterplots that share a common set of axes and have a between-set scalar 
 product interpretation. Typically, the observations (rows of \eqn{\mathbf{X}}) are represented as points
@@ -149,6 +154,18 @@ row points and column vectors, with different interpretations, by representing t
 \eqn{\widehat{\mathbf{X}}} as the product of two matrices,
 
 \deqn{\widehat{\mathbf{X}} = (\mathbf{U} \mathbf{\Lambda}^\alpha) (\mathbf{\Lambda}^{1-\alpha} \mathbf{V}')}
+
+The choice \eqn{\alpha = 1}, assigning the singular values totally to the left factor,
+ gives a distance interpretation to the row display and 
+\eqn{\alpha = 0} gives a distance interpretation to the column display.
+\eqn{\alpha = 1/2} gives a symmetrically scaled biplot.
+
+When the singular values are assigned totally to the left or to the right factor, the resultant 
+coordinates are called \emph{principal coordinates} and the sum of squared coordinates
+on each dimension equal the corresponding singular value.
+The other matrix, to which no part of the singular 
+values is assigned, contains the so-called \emph{standard coordinates} and have sum of squared
+values equal to 1.0.
 }
 \examples{
 data(wine)
@@ -182,6 +199,9 @@ Gabriel, K. R. (1971). The biplot graphical display of matrices with application
   Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. 
   In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. 
   
+  Greenacre, M. (2010). \emph{Biplots in Practice}. BBVA Foundation, Bilbao, Spain. 
+  Available for free at \url{https://www.multivariatestatistics.org}.
+  
   J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall.
   
   Gower, J. C., Lubbe, S. G., & Roux, N. J. L. (2011). \emph{Understanding Biplots}. Wiley.

From be43cdb56de53c52e493ec9a0d76f13dd821881c Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Wed, 20 Sep 2023 21:22:03 -0400
Subject: [PATCH 32/80] LazyData

---
 DESCRIPTION | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DESCRIPTION b/DESCRIPTION
index 73974e7..3495d9b 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -25,4 +25,4 @@ Encoding: UTF-8
 URL: https://github.com/friendly/ggbiplot
 BugReports: https://github.com/friendly/ggbiplot/issues
 RoxygenNote: 7.2.3
-
+LazyData: true

From 5c720f5556adb85a9c6a49419953d83a6fe67bb3 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 21 Sep 2023 18:44:12 -0400
Subject: [PATCH 33/80] extra/ -> examples; add discussion/

---
 .Rbuildignore                     |   3 ++-
 data/crime.rda                    | Bin 0 -> 1997 bytes
 {extra => examples}/crime-ex.R    |   0
 {extra => examples}/penguins-ex.R |   0
 {extra => examples}/test-iris.R   |   0
 {extra => examples}/testing.R     |   0
 6 files changed, 2 insertions(+), 1 deletion(-)
 create mode 100644 data/crime.rda
 rename {extra => examples}/crime-ex.R (100%)
 rename {extra => examples}/penguins-ex.R (100%)
 rename {extra => examples}/test-iris.R (100%)
 rename {extra => examples}/testing.R (100%)

diff --git a/.Rbuildignore b/.Rbuildignore
index 0b73413..6e2becd 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -2,5 +2,6 @@
 ^\.Rproj\.user$
 ^README\.Rmd$
 ^README-.*\.png$
-extra/
+examples/
+discussion/
 ^cran-comments\.md$
diff --git a/data/crime.rda b/data/crime.rda
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diff --git a/extra/crime-ex.R b/examples/crime-ex.R
similarity index 100%
rename from extra/crime-ex.R
rename to examples/crime-ex.R
diff --git a/extra/penguins-ex.R b/examples/penguins-ex.R
similarity index 100%
rename from extra/penguins-ex.R
rename to examples/penguins-ex.R
diff --git a/extra/test-iris.R b/examples/test-iris.R
similarity index 100%
rename from extra/test-iris.R
rename to examples/test-iris.R
diff --git a/extra/testing.R b/examples/testing.R
similarity index 100%
rename from extra/testing.R
rename to examples/testing.R

From 8ffcaed5dd7ad48d90a298d8927eda07a1038a55 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 21 Sep 2023 18:57:57 -0400
Subject: [PATCH 34/80] add topics/examples for discussion

---
 data/crime.RData        | Bin 1940 -> 0 bytes
 discussion/SO-biplot.md |  30 +++++++++++++++++++
 discussion/biplotR.md   |  48 ++++++++++++++++++++++++++++++
 discussion/tidy_pca.R   |  63 ++++++++++++++++++++++++++++++++++++++++
 4 files changed, 141 insertions(+)
 delete mode 100644 data/crime.RData
 create mode 100644 discussion/SO-biplot.md
 create mode 100644 discussion/biplotR.md
 create mode 100644 discussion/tidy_pca.R

diff --git a/data/crime.RData b/data/crime.RData
deleted file mode 100644
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GIT binary patch
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+  select(where(is.numeric)) %>% # retain only numeric columns
+  scale() %>% # scale data
+  prcomp() # do PCA
+
+# plot points
+pca_fit %>%
+  augment(biopsy) %>% # add original dataset back in
+  ggplot(aes(.fittedPC1, .fittedPC2, color = outcome)) + 
+  geom_point(size = 1.5) +
+  scale_color_manual(
+    values = c(malignant = "#D55E00", benign = "#0072B2")
+  ) +
+  theme_half_open(12) + background_grid()
+
+# extract rotation matrix (loadings)
+pca_fit %>%
+  tidy(matrix = "rotation")
+
+
+# define arrow style for plotting
+arrow_style <- arrow(
+  angle = 20, ends = "first", type = "closed", length = grid::unit(8, "pt")
+)
+# plot rotation matrix
+pca_fit %>%
+  tidy(matrix = "rotation") %>%
+  pivot_wider(names_from = "PC", names_prefix = "PC", values_from = "value") %>%
+  ggplot(aes(PC1, PC2)) +
+  geom_segment(xend = 0, yend = 0, arrow = arrow_style) +
+  geom_text(
+    aes(label = column),
+    hjust = 1, nudge_x = -0.02, 
+    color = "#904C2F"
+  ) +
+  xlim(-1.25, .5) + ylim(-.5, 1) +
+  coord_fixed() + # fix aspect ratio to 1:1
+  theme_minimal_grid(12)
+
+# scree plot
+pca_fit %>%
+  tidy(matrix = "eigenvalues") %>%
+  ggplot(aes(PC, percent)) +
+  geom_col(fill = "#56B4E9", alpha = 0.8) +
+  scale_x_continuous(breaks = 1:9) +
+  scale_y_continuous(
+    labels = scales::percent_format(),
+    expand = expansion(mult = c(0, 0.01))
+  ) +
+  theme_minimal_hgrid(12)

From 891b3fd3465987d602a860cc1cf75ddd9cc1feaa Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Fri, 22 Sep 2023 10:14:26 -0400
Subject: [PATCH 35/80] update crime docs

---
 R/crime.R    | 7 ++++++-
 man/crime.Rd | 7 ++++++-
 2 files changed, 12 insertions(+), 2 deletions(-)

diff --git a/R/crime.R b/R/crime.R
index 070c127..0f3e49f 100644
--- a/R/crime.R
+++ b/R/crime.R
@@ -1,7 +1,8 @@
 #' @title U. S. Crimes
 #' @name crime
 #' @description 
-#' This dataset gives rates of various serious crimes in each of the 50 U. S. states, 
+#' This dataset gives rates of occurrence (per 100,000 people)
+#' various serious crimes in each of the 50 U. S. states, 
 #' originally from the United States Statistical Abstracts (1970). The data
 #' were analyzed by John Hartigan (1975) in his book \emph{Clustering Algorithms} and 
 #' were later reanalyzed by Friendly (1991). 
@@ -25,6 +26,10 @@
 #' @keywords dataset
 #' @source 
 #' The data are originally from the United States Statistical Abstracts (1970).
+#' This dataset also appears in the SAS/Stat Sample library,
+#' \emph{Getting Started Example for PROC PRINCOMP}, 
+#' \url{https://support.sas.com/documentation/onlinedoc/stat/ex_code/131/princgs.html}, from which the
+#' current copy was derived.
 #' @references 
 #' Friendly, M. (1991). \emph{SAS System for Statistical Graphics}. SAS Institute.
 #'
diff --git a/man/crime.Rd b/man/crime.Rd
index fd6a1cb..199285a 100644
--- a/man/crime.Rd
+++ b/man/crime.Rd
@@ -21,12 +21,17 @@ A data frame with 50 observations on the following 10 variables.
 }
 \source{
 The data are originally from the United States Statistical Abstracts (1970).
+This dataset also appears in the SAS/Stat Sample library,
+\emph{Getting Started Example for PROC PRINCOMP}, 
+\url{https://support.sas.com/documentation/onlinedoc/stat/ex_code/131/princgs.html}, from which the
+current copy was derived.
 }
 \usage{
 data(crime)
 }
 \description{
-This dataset gives rates of various serious crimes in each of the 50 U. S. states, 
+This dataset gives rates of occurrence (per 100,000 people)
+various serious crimes in each of the 50 U. S. states, 
 originally from the United States Statistical Abstracts (1970). The data
 were analyzed by John Hartigan (1975) in his book \emph{Clustering Algorithms} and 
 were later reanalyzed by Friendly (1991).

From 086e5b35d135130a63194fa2329ee800dc6218d7 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Fri, 22 Sep 2023 13:12:10 -0400
Subject: [PATCH 36/80] add example to biplotR.Rmd

---
 discussion/{biplotR.md => biplotR.Rmd} |  16 +-
 discussion/peng-biplot.png             | Bin 0 -> 26361 bytes
 discussion/tidy_pca.R                  |  44 ++-
 discussion/tidy_pca.docx               | Bin 0 -> 27024 bytes
 discussion/tidy_pca.html               | 501 +++++++++++++++++++++++++
 examples/penguins-ex.R                 |   5 +-
 6 files changed, 543 insertions(+), 23 deletions(-)
 rename discussion/{biplotR.md => biplotR.Rmd} (88%)
 create mode 100644 discussion/peng-biplot.png
 create mode 100644 discussion/tidy_pca.docx
 create mode 100644 discussion/tidy_pca.html

diff --git a/discussion/biplotR.md b/discussion/biplotR.Rmd
similarity index 88%
rename from discussion/biplotR.md
rename to discussion/biplotR.Rmd
index 023987e..e6f5720 100644
--- a/discussion/biplotR.md
+++ b/discussion/biplotR.Rmd
@@ -1,8 +1,12 @@
-# biplots in R
+---
+title: Biplots in R
+author: Michael Friendly
+output: github_document
+---
+
 
 There are quite a few implementations of biplots in R, but IMHO, **none** are sufficiently general to become a
-current standard, with wide applicability, and easily used within modern R, encompasing the latest developments
-in the `tidyverse` and the `ggplot2` framework. 
+current standard, with wide applicability, and easily used within modern R, encompassing the latest developments in the `tidyverse` and the `ggplot2` framework. 
 
 Current implementation range from base R `biplot.princomp()`
 to `factoextra::fviz_pca()` extending the `FactoMineR` package, and
@@ -24,10 +28,14 @@ control for a given example.
   possibly direct labels for groups rather than a legend, etc.
 * show row/observation points as points or observation lables. Be able to control the
   point/character size easily. Be able to filter out some point labels to highlight
-  some more intersting ones.
+  some more interesting ones.
 * For variable vectors, control all graphical attributes: color, linewidth, font/sizes for
   variable names, etc.
 
+Here is a simple example showing the type of plot I'd like to produce:
+
+![](peng-biplot.png)
+
 Is it time for a new, more modern implementation that is easy to use and to understand?
 Any such implementation can't do everything, but if well-designed, it could be something
 many people could work with, contribute to and extend. 
diff --git a/discussion/peng-biplot.png b/discussion/peng-biplot.png
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zq6@2% 
-  select(where(is.numeric)) %>% # retain only numeric columns
-  scale() %>% # scale data
+#' ## Do the PCA
+pca_fit <- biopsy |> 
+  select(where(is.numeric)) |> # retain only numeric columns
+  scale() |> # scale data
   prcomp() # do PCA
 
-# plot points
-pca_fit %>%
-  augment(biopsy) %>% # add original dataset back in
+#' ## plot points
+pca_fit |>
+  augment(biopsy) |> # add original dataset back in
   ggplot(aes(.fittedPC1, .fittedPC2, color = outcome)) + 
   geom_point(size = 1.5) +
   scale_color_manual(
@@ -26,19 +35,20 @@ pca_fit %>%
   ) +
   theme_half_open(12) + background_grid()
 
-# extract rotation matrix (loadings)
-pca_fit %>%
+#' ## extract rotation matrix (loadings)
+pca_fit |>
   tidy(matrix = "rotation")
 
 
-# define arrow style for plotting
+#' define arrow style for plotting
 arrow_style <- arrow(
   angle = 20, ends = "first", type = "closed", length = grid::unit(8, "pt")
 )
-# plot rotation matrix
-pca_fit %>%
-  tidy(matrix = "rotation") %>%
-  pivot_wider(names_from = "PC", names_prefix = "PC", values_from = "value") %>%
+
+#' ## plot rotation matrix
+pca_fit |>
+  tidy(matrix = "rotation") |>
+  pivot_wider(names_from = "PC", names_prefix = "PC", values_from = "value") |>
   ggplot(aes(PC1, PC2)) +
   geom_segment(xend = 0, yend = 0, arrow = arrow_style) +
   geom_text(
@@ -51,8 +61,8 @@ pca_fit %>%
   theme_minimal_grid(12)
 
 # scree plot
-pca_fit %>%
-  tidy(matrix = "eigenvalues") %>%
+pca_fit |>
+  tidy(matrix = "eigenvalues") |>
   ggplot(aes(PC, percent)) +
   geom_col(fill = "#56B4E9", alpha = 0.8) +
   scale_x_continuous(breaks = 1:9) +
diff --git a/discussion/tidy_pca.docx b/discussion/tidy_pca.docx
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z@k(sDruEtTHDH0oqc^b0McPH0N~^PuV$Dydk8!4NyQ9oESz(i6N^D@V6kUz%A_wvya|E-yt>b3VEmO+XC;l+1v^(CJnua6`M{S_(xnR2&(2#G47a?pSt-(n`?Kr(a}G*d|Z5$opetPxg(g{iGIX1=?U0=m<>^{v&R
zg_!00!WYBL@kSu)c&Dslz~iIT!Y)V{*v|I8r!Cf!%WYw(wM^h$gcK&Fb{>_E-ah%c
ztToO%TjnE(5CsEr3(rSg^Mw&JcF$lDHgH<8G(GJZM
z%y*tZ+sC4;U!Qb?$WEa}FLwFl#zQKU@_);c)jy9$?=03e_A3v>DKAm7I;&gykkOw8mgKt
zA_y64??;Gdb#;khH_uL-FaaMp-<2YFVB1FZCj`pfR#Z1k#cA#iZ~@jdEPE3+KO|Q~
z2oTlkJM?Ozxn`H2Iq;hG15NpIiKIN>_m@^J
zTtSU0v3JQr)EiZN2Wh)#W{n~d5KTX`e)rsh{qC{-zbBRa?n(T|=YN@7@;2b@tc*W&
z=kLz!e@xDJ3%(sH@dq6Ly~6)7V&X0S*75rX_d)s_|38esZ
+
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+tidy_pca
+
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# from: https://clauswilke.com/blog/2020/09/07/pca-tidyverse-style/
+# see also: https://broom.tidymodels.org/reference/tidy.prcomp.html
+
+library(tidyverse)

+
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
+## ✔ dplyr     1.1.3     ✔ readr     2.1.4
+## ✔ forcats   1.0.0     ✔ stringr   1.5.0
+## ✔ ggplot2   3.4.3     ✔ tibble    3.2.1
+## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
+## ✔ purrr     1.0.2     
+## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
+## ✖ dplyr::filter() masks stats::filter()
+## ✖ dplyr::lag()    masks stats::lag()
+## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

+
library(broom)  # devtools::install_github("tidymodels/broom")
+library(cowplot)

+
## 
+## Attaching package: 'cowplot'
+## 
+## The following object is masked from 'package:lubridate':
+## 
+##     stamp

+
biopsy <- read_csv("https://wilkelab.org/classes/SDS348/data_sets/biopsy.csv")

+
## Rows: 683 Columns: 10
+## ── Column specification ────────────────────────────────────────────────────────
+## Delimiter: ","
+## chr (1): outcome
+## dbl (9): clump_thickness, uniform_cell_size, uniform_cell_shape, marg_adhesi...
+## 
+## ℹ Use `spec()` to retrieve the full column specification for this data.
+## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

+
pca_fit <- biopsy %>% 
+  select(where(is.numeric)) %>% # retain only numeric columns
+  scale() %>% # scale data
+  prcomp() # do PCA
+
+# plot points
+pca_fit %>%
+  augment(biopsy) %>% # add original dataset back in
+  ggplot(aes(.fittedPC1, .fittedPC2, color = outcome)) + 
+  geom_point(size = 1.5) +
+  scale_color_manual(
+    values = c(malignant = "#D55E00", benign = "#0072B2")
+  ) +
+  theme_half_open(12) + background_grid()

+

+
# extract rotation matrix (loadings)
+pca_fit %>%
+  tidy(matrix = "rotation")

+
## # A tibble: 81 × 3
+##    column               PC    value
+##    <chr>             <dbl>    <dbl>
+##  1 clump_thickness       1 -0.302  
+##  2 clump_thickness       2 -0.141  
+##  3 clump_thickness       3  0.866  
+##  4 clump_thickness       4  0.108  
+##  5 clump_thickness       5 -0.0803 
+##  6 clump_thickness       6 -0.243  
+##  7 clump_thickness       7 -0.00852
+##  8 clump_thickness       8 -0.248  
+##  9 clump_thickness       9  0.00275
+## 10 uniform_cell_size     1 -0.381  
+## # ℹ 71 more rows

+
# define arrow style for plotting
+arrow_style <- arrow(
+  angle = 20, ends = "first", type = "closed", length = grid::unit(8, "pt")
+)
+# plot rotation matrix
+pca_fit %>%
+  tidy(matrix = "rotation") %>%
+  pivot_wider(names_from = "PC", names_prefix = "PC", values_from = "value") %>%
+  ggplot(aes(PC1, PC2)) +
+  geom_segment(xend = 0, yend = 0, arrow = arrow_style) +
+  geom_text(
+    aes(label = column),
+    hjust = 1, nudge_x = -0.02, 
+    color = "#904C2F"
+  ) +
+  xlim(-1.25, .5) + ylim(-.5, 1) +
+  coord_fixed() + # fix aspect ratio to 1:1
+  theme_minimal_grid(12)

+

+
# scree plot
+pca_fit %>%
+  tidy(matrix = "eigenvalues") %>%
+  ggplot(aes(PC, percent)) +
+  geom_col(fill = "#56B4E9", alpha = 0.8) +
+  scale_x_continuous(breaks = 1:9) +
+  scale_y_continuous(
+    labels = scales::percent_format(),
+    expand = expansion(mult = c(0, 0.01))
+  ) +
+  theme_minimal_hgrid(12)

+

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+

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diff --git a/examples/penguins-ex.R b/examples/penguins-ex.R
index 5b200d1..1ff54f3 100644
--- a/examples/penguins-ex.R
+++ b/examples/penguins-ex.R
@@ -3,7 +3,8 @@
 #' ---
 #' 
 
-library(ggplot2) 
+library(ggplot2)
+library(ggbiplot)
 data(penguins, package = "palmerpenguins")
 peng <- penguins |>
   rename(
@@ -45,7 +46,7 @@ peng.gg + geom_label(data = group.labs,
 
 
 
-# try reflecting & scaline var vectors
+# try reflecting & scaling var vectors
 ggbiplot(peng.pca, obs.scale = 1, var.scale = 1,
          var.factor = -1,
          varname.adjust = 1,

From c81e6d13aa8cdb8999605fdde791c7d577679dc2 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 28 Sep 2023 13:16:12 -0400
Subject: [PATCH 37/80] add to discussion/

---
 discussion/biplot-packages.Rmd  |  57 ++++
 discussion/biplot-packages.html | 472 ++++++++++++++++++++++++++++++++
 discussion/biplot2d3d-ex.R      | 142 ++++++++++
 discussion/biplotEX-ex.R        |  11 +
 4 files changed, 682 insertions(+)
 create mode 100644 discussion/biplot-packages.Rmd
 create mode 100644 discussion/biplot-packages.html
 create mode 100644 discussion/biplot2d3d-ex.R
 create mode 100644 discussion/biplotEX-ex.R

diff --git a/discussion/biplot-packages.Rmd b/discussion/biplot-packages.Rmd
new file mode 100644
index 0000000..36c80d3
--- /dev/null
+++ b/discussion/biplot-packages.Rmd
@@ -0,0 +1,57 @@
+---
+title: "Biplot packages in R"
+author: "Michael Friendly"
+date: "`r Sys.Date()`"
+output: html_document
+---
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE)
+```
+
+## Why talk?
+
+There are quite a few implementations of biplots in R, but IMHO, **none** are sufficiently general to:
+
+* become a current standard, 
+* with wide applicability, and 
+* easily used within modern R, 
+* encompassing the latest developments in the `tidyverse` and the `ggplot2` framework. 
+
+Does anyone want to join me in making biplots more accessible and easy to use in modern R?
+
+### My problem
+
+My problem, as a **user** and **explainer** is that with none of these can I 
+
+* easily create and describe simple examples of biplot methods 
+* with all the graphical attributes I want to control for a given example.
+
+### What I'd like
+
+* Provide a **common interface** for PCA / LDA and **all** related methods: E.g., 
+
+> {`prcomp() / princomp() / MASS::lda(), ...} -> a common "biplot" class object.
+
+* Easily allow the different **scalings**, to show row/column variables in principal or
+  standard coordinates.
+* When there are groups, provide nice data ellipses or other bivariate summaries (convex hulls, ...)
+  for each group, with fine control over graphical attributes (color, fill, ...), 
+  possibly direct labels for groups rather than a legend, etc.
+* show row/observation points as points or observation labels. 
+* Be able to control the point/character size easily. Be able to filter out some point labels to highlight some more interesting ones.
+* For variable vectors, control all graphical attributes: color, linewidth, font/sizes for variable names, etc.
+
+
+## Current state: What packages exist?
+
+* **base R**: `prcomp()`, `princomp()` --> `biplot()`
+
+* **FactoMineR, factoextra**: `PCA()` --> `fviz_pca()`, `fviz_pca_ind()`, `fviz_pca_var()`
+
+* **adegraphics** Lattice-based. Development of `ade4`, "dudi" framework -> `biplot()`
+
+* **biplotEZ** based on _Understanding Biplots_, `UBbipl` package
+
+* **ggbiplot**: Original by Vincent Yu, devel now at https://github.com/friendly/ggbiplot 
+
diff --git a/discussion/biplot-packages.html b/discussion/biplot-packages.html
new file mode 100644
index 0000000..7886d2f
--- /dev/null
+++ b/discussion/biplot-packages.html
@@ -0,0 +1,472 @@
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+Biplot packages in R
+
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diff --git a/discussion/biplot2d3d-ex.R b/discussion/biplot2d3d-ex.R
new file mode 100644
index 0000000..21a2885
--- /dev/null
+++ b/discussion/biplot2d3d-ex.R
@@ -0,0 +1,142 @@
+
+library(biplot2d3d)
+# uses ade
+devtools::install_github("Andros-Spica/biplot2d3d")
+
+# Use iris data
+data("iris")
+
+# get an ordination object
+# ("PCA" is the default input of this function)
+pca <- princomp(iris[, 1:4])
+
+# Default plot using Species as the group factor
+biplot_2d(pca, groups = iris$Species)
+
+# Use the typical visualization,
+# placing scores and loadings around the same origin
+biplot_2d(pca, groups = iris$Species, detach_arrows = FALSE)
+
+
+# Compare different versions of the classical biplot
+# "default" vs. "pc.biplot"
+biplot_2d(pca,
+          output_type = "preview",
+          leave_device_open = TRUE,
+          x_title = 'biplot_type = "default"',
+          x_title_fig = c(0, 1, 0.9, 1),
+          fit_into_main = TRUE,
+          main_fig = c(0, 0.499, 0, 1))
+biplot_2d(pca,
+          output_type = "preview",
+          open_new_device = FALSE,
+          biplot_type = "pc.biplot",
+          x_title = 'biplot_type = "pc.biplot"',
+          x_title_fig = c(0, 1, 0.9, 1),
+          fit_into_main = TRUE,
+          main_fig = c(0.5099, 1, 0, 1))
+
+
+# ---------------------------------------------------------
+# Plot groups as different colors and point types (pch),
+# make group star, ellipsis, and label invisible and
+# add a group legend with a a custom title.
+biplot_2d(pca,
+          groups = iris$Species,
+          group_color = NULL,
+          point_pch = c(1, 3, 2),
+          group_star_cex = 0,
+          group_ellipse_cex = 0,
+          group_label_cex = 0,
+          show_group_legend = T,
+          group_legend_title = "Species")
+
+# ---------------------------------------------------------
+# Polish covariance arrows
+# Abbreviate variables names
+dimnames(pca$loadings)[[1]] <- c("SL", "SW", "PL", "PW")
+# Set a specific justification (adj) for each variable label
+arrow_label_adj_override <- rbind(c(-0.1, 0),
+                                  c(-0.1, 0.5),
+                                  c(0.5, 1.3),
+                                  c(0.5, 1.3))
+row.names(arrow_label_adj_override) <-
+  dimnames(pca$loadings)[[1]]
+# Plot: arrows with different colors and
+# without the background grid
+biplot_2d(pca,
+          groups = iris$Species,
+          point_pch = c(1, 3, 2),
+          group_star_cex = 0,
+          group_ellipse_cex = 0,
+          group_label_cex = 0,
+          show_group_legend = T,
+          group_legend_title = "Species",
+          arrow_color = c("orange",
+                          "blue",
+                          "red",
+                          "green"),
+          arrow_label_adj_override = arrow_label_adj_override,
+          show_grid = FALSE)
+
+# ---------------------------------------------------------
+# Get arbitrary Very Important Points
+irisVIP <- list(setosa = (1:nrow(iris) == 16 |
+                            1:nrow(iris) == 42),
+                versicolor=(1:nrow(iris) == 61),
+                virginica=(1:nrow(iris) == 107 |
+                             1:nrow(iris) == 118 |
+                             1:nrow(iris) == 132))
+
+# Plot observations using their names and group by Species using only color.
+# Mark the VIP and add the respective legend with custom characters.
+biplot_2d(pca,
+          groups = iris$Species,
+          point_type = "label",
+          point_label = row.names(iris),
+          group_color = c("red", "blue", "green"),
+          group_star_cex = 0,
+          group_ellipse_cex = 0,
+          group_label_cex = 0,
+          show_group_legend = TRUE,
+          group_legend_title = "",
+          vips = irisVIP,
+          vip_pch = c("X", "O", "+"),
+          vip_cex = c(2, 2, 3),
+          vip_legend_fig = c(0.01, 0.25, 0.7, 0.99),
+          show_axes = FALSE)
+
+# 3D biplots
+
+# Default plot using Species as the groups
+biplot_3d(pca, groups = iris$Species)
+
+biplot_3d(pca,
+          groups = iris$Species,
+          group_representation = "ellipsoids",
+          ellipsoid_label_alpha = 0,
+          show_group_legend = TRUE,
+          group_legend_title = "",
+          arrow_center_pos = c(.5, 0, .5),
+          arrow_body_length = 1,
+          arrow_body_width = 2,
+          view_theta = 0,
+          view_zoom = 0.9)
+
+# ---------------------------------------------------------
+# Plot observations using their names and groups as
+# stars but adding a legend instead of labels.
+# Modify the aspect to normalize the variability
+# of axes and do not show them. Zoom out a little.
+biplot_3d(pca, groups = iris$Species,
+          point_type = "label", 
+          point_label = row.names(iris),
+          star_label_alpha = 0,
+          show_group_legend = TRUE, 
+          group_legend_title = "",
+          arrow_center_pos = c(.5, 0, .5),
+          arrow_body_length = 2, 
+          arrow_body_width = 2,
+          show_axes = FALSE, view_zoom = 1)
+
+
diff --git a/discussion/biplotEX-ex.R b/discussion/biplotEX-ex.R
new file mode 100644
index 0000000..fce631b
--- /dev/null
+++ b/discussion/biplotEX-ex.R
@@ -0,0 +1,11 @@
+library(biplotEZ)
+
+
+biplot (iris[,1:4]) |> 
+  PCA(group.aes=iris[,5]) |> 
+  concentration.ellipse(kappa=2) |> 
+  plot()
+
+
+biplot(iris[,1:4],iris[,5]) |> 
+  CVA() |> plot()

From 85441f3c47ef8d0e453be2cbbbc37d7c07f9217a Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 28 Sep 2023 13:18:14 -0400
Subject: [PATCH 38/80] biplotEX -> biplotEZ

---
 discussion/{biplotEX-ex.R => biplotEZ-ex.R} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename discussion/{biplotEX-ex.R => biplotEZ-ex.R} (100%)

diff --git a/discussion/biplotEX-ex.R b/discussion/biplotEZ-ex.R
similarity index 100%
rename from discussion/biplotEX-ex.R
rename to discussion/biplotEZ-ex.R

From 5b5139fa6fbb647b0a5480469c42298fb6d141e6 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 28 Nov 2023 15:33:08 -0500
Subject: [PATCH 39/80] CARME discussion; doc for ggscreeplot

---
 R/ggscreeplot.r                 |  31 +++-----
 discussion/biplot-packages.Rmd  | 115 ++++++++++++++++++++++++++++--
 discussion/biplot-packages.html | 122 ++++++++++++++++++++++++++++----
 discussion/biplotEZ-ex.R        |   4 +-
 man/ggscreeplot.Rd              |   9 ++-
 5 files changed, 237 insertions(+), 44 deletions(-)

diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r
index 084bee6..b917d10 100644
--- a/R/ggscreeplot.r
+++ b/R/ggscreeplot.r
@@ -1,31 +1,17 @@
-# 
-#  ggscreeplot.r
-#
-#  Copyright 2011 Vincent Q. Vu.
-# 
-#  This program is free software; you can redistribute it and/or
-#  modify it under the terms of the GNU General Public License
-#  as published by the Free Software Foundation; either version 2
-#  of the License, or (at your option) any later version.
-#  
-#  This program is distributed in the hope that it will be useful,
-#  but WITHOUT ANY WARRANTY; without even the implied warranty of
-#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-#  GNU General Public License for more details.
-#  
-#  You should have received a copy of the GNU General Public License
-#  along with this program; if not, write to the Free Software
-#  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
-# 
-
 #' Screeplot for Principal Components
+#' 
+#' Produces scree plots (Cattell, 1966) of the variance proportions explained by each dimension against dimension number from 
+#' various dimension reduction techniques
 #'
-#' @param pcobj   an object returned by prcomp() or princomp()
+#' @param pcobj   an object representing a linear dimension technique, such a returned by \code{\link[stats]{prcomp}} 
+#'                or \code{\link[stats]{princomp}} or \code{\link[FactomineR]{PCA}} or \code{\link[MASS]{lda}}
 #' @param type    the type of scree plot.  
 #'                'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 
 #'                'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.
 #' @param size    point size
 #' @export
+#' @references 
+#' Cattell, R. B. (1966). The Scree Test For The Number Of Factors. \emph{Multivariate Behavioral Research}, 1, 245–276.
 #' @examples
 #'   data(wine)
 #'   wine.pca <- prcomp(wine, scale. = TRUE)
@@ -66,6 +52,7 @@ ggscreeplot <- function(pcobj,
   df <- data.frame(PC = 1:length(d), yvar = yvar)
 
   ggplot(data = df, aes(x = PC, y = yvar)) + 
-    xlab('Principal component number') + ylab(yvar.lab) +
+    xlab('Principal component number') + 
+    ylab(yvar.lab) +
     geom_point(size = size) + geom_path()
 }
diff --git a/discussion/biplot-packages.Rmd b/discussion/biplot-packages.Rmd
index 36c80d3..58be4a1 100644
--- a/discussion/biplot-packages.Rmd
+++ b/discussion/biplot-packages.Rmd
@@ -6,9 +6,14 @@ output: html_document
 ---
 
 ```{r setup, include=FALSE}
-knitr::opts_chunk$set(echo = TRUE)
+knitr::opts_chunk$set(echo = TRUE,
+                      message = FALSE,
+                      warning = FALSE)
 ```
 
+This document contains notes I initially prepared for a casual discussion session
+at the CARME23 meeting in Bonn, Sept. 24-28.
+
 ## Why talk?
 
 There are quite a few implementations of biplots in R, but IMHO, **none** are sufficiently general to:
@@ -45,13 +50,111 @@ My problem, as a **user** and **explainer** is that with none of these can I
 
 ## Current state: What packages exist?
 
-* **base R**: `prcomp()`, `princomp()` --> `biplot()`
+* **base R**: `prcomp()`, `princomp()` --> [`biplot()`](https://rdrr.io/r/stats/biplot.html)
+
+* [**FactoMineR**](https://cran.r-project.org/package=FactoMineR), [**factoextra**](https://rpkgs.datanovia.com/factoextra/): [`PCA()`](https://rdrr.io/cran/FactoMineR/man/PCA.html) --> [`fviz_pca()`](https://rpkgs.datanovia.com/factoextra/reference/fviz_pca.html), `fviz_pca_ind()`, `fviz_pca_var()`
+
+* [**adegraphics**](https://cran.r-project.org/package=adegraphics) Lattice-based. Development of `ade4`, "dudi" framework -> `biplot()`
+  + [**biplot2d3d**](https://github.com/Andros-Spica/biplot2d3d) By Andreas Angourakis. Uses **ade4*, **heplots** and **rgl**.
+
+* [**biplotEZ**](https://cran.r-project.org/package=biplotEZ) based on the _Understanding Biplots_, `UBbipl` package
+  
+
+* [**ggbiplot**](https://cran.r-project.org/package=ggbiplot): Original by Vincent Yu, development now at https://github.com/friendly/ggbiplot 
+
+* [**biplotGUI**](https://biplotgui.r-forge.r-project.org/): A Windows-only graphical interface to biplots using `tcktk`.
+
+* [**MultBiplot**](https://cran.r-project.org/package=MultBiplotR), by Jose Luis Vicente-Villardon. A wide variety of different biplot application types.
+
+## Discussion at CARME23
 
-* **FactoMineR, factoextra**: `PCA()` --> `fviz_pca()`, `fviz_pca_ind()`, `fviz_pca_var()`
+The following are some of the points raised by people at the _Biplot Software_
+session at CARME:
 
-* **adegraphics** Lattice-based. Development of `ade4`, "dudi" framework -> `biplot()`
+* Overplotting and labelling with auto / user defined shifting to avoid label overlap. 
+* Filtering what to plot and what to suppress 
+* Interactive plots and animation 
+* Simple default plot + possibilities to make it nice (decouple computations from representation)
+* Ability to show density of samples
+* Plot more than dim 1 & 2 - linked plots with same scales
+* Specific to CA: is it standard or principal points for rows or cols, symmetric or asymmetric
+* Needs to be a low level package to be used by other multivariate analysis packages 
 
-* **biplotEZ** based on _Understanding Biplots_, `UBbipl` package
+## Examples
 
-* **ggbiplot**: Original by Vincent Yu, devel now at https://github.com/friendly/ggbiplot 
+These examples show biplots produced by some of these packages.
+
+### Doing the PCA
+
+The default method for `prcomp()` takes a numeric or complex matrix or data frame argument. By default, it does **not** scale the observations to unit variance,
+so `scale. = TRUE` should usually be specified. You can control the number of
+components returned using the `rank. argument.`
+
+```{r}
+data(iris)
+iris.pca <- prcomp(iris[,1:4], scale. = TRUE)
+```
+
+There is also a formula method, which is more verbose, but more easily readable.
+
+```{r}
+iris.pca <- prcomp(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
+                   data=iris, scale. = TRUE)
+```
+
+You can also use tidy steps and pipes from **dplyr** to select variables, and
+perhaps filter out missing data.
+
+```{r}
+iris.pca <- 
+  iris |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)
+```
+
+### ggbiplot
+
+The default plot:
+
+```{r iris-ggbiplot-default}
+library(ggbiplot)
+library(ggplot2)
+library(dplyr)
+ggbiplot(iris.pca, groups = iris$Species)
+```
+
+Using more features:
+
+```{r iris-gg-features1}
+iris.gg <-
+  ggbiplot(iris.pca, obs.scale = 1, var.scale = 1,
+           groups = iris$Species, point.size=2,
+           varname.size = 5, 
+           varname.color = "darkred",
+           varname.adjust = 1.2,
+           ellipse = TRUE, 
+           circle = TRUE) +
+  labs(fill = "Species", color = "Species") +
+  theme_minimal(base_size = 14) +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
+iris.gg
+```
+
+Use direct labels for the groups rather than a legend.
+This makes use of the fact that the `gg` object contains the dataset used
+`iris.gg$data` used to construct the plot.
+
+```{r iris-gg-labels}
+# find means of the coordinates
+group.labs <-
+  iris.gg$data |>
+  summarise(xvar = mean(xvar),
+            yvar = mean(yvar), .by = groups)
+
+iris.gg + geom_label(data = group.labs,
+                     aes(x = xvar, y=yvar, label=groups),
+                     size = 5) +
+  theme(legend.position = "none")
+
+```
 
diff --git a/discussion/biplot-packages.html b/discussion/biplot-packages.html
index 7886d2f..40bc5c9 100644
--- a/discussion/biplot-packages.html
+++ b/discussion/biplot-packages.html
@@ -11,7 +11,7 @@
 
 
 
-
+
 
 Biplot packages in R
 
@@ -352,11 +352,13 @@
 
 
Biplot packages in R

 
Michael Friendly

-
2023-09-28

+
2023-10-01

 
 
 
 
+
This document contains notes I initially prepared for a casual
+discussion session at the CARME23 meeting in Bonn, Sept. 24-28.

 

 
Why talk?

 
There are quite a few implementations of biplots in R, but IMHO,
@@ -410,18 +412,114 @@ 
What I’d like

 
Current state: What packages exist?

 
    
 
  • base R: prcomp(),
-princomp() –> biplot()
    • 
-
  • FactoMineR, factoextra: PCA() –>
-fviz_pca(), fviz_pca_ind(),
-fviz_pca_var()
    • 
-
  • adegraphics Lattice-based. Development of
-ade4, “dudi” framework -> biplot()
    • 
-
  • biplotEZ based on Understanding
-Biplots, UBbipl package
    • 
-
  • ggbiplot: Original by Vincent Yu, devel now at
-https://github.com/friendly/ggbiplot
    • 
+princomp() –> biplot()
    
+
  • FactoMineR,
+factoextra:
+PCA()
+–> fviz_pca(),
+fviz_pca_ind(), fviz_pca_var()
    • 
+
  • adegraphics
+Lattice-based. Development of ade4, “dudi” framework ->
+biplot()
    
+
      
+
    • biplot2d3d
+By Andreas Angourakis. Uses **ade4*, heplots and
+rgl.
      • 
+
    • 
+
  • biplotEZ
+based on the Understanding Biplots, UBbipl
+package
    
+
      
+
    • Development version at []
      • 
+
    • 
+
  • ggbiplot:
+Original by Vincent Yu, development now at https://github.com/friendly/ggbiplot
    • 
+
  • biplotGUI:
+A Windows-only graphical interface to biplots using
+tcktk.
    • 
+

+

+

+
Discussion at CARME23

+
The following are some of the points raised by people at the
+Biplot Software session at CARME:

+
    
+
  • Overplotting and labelling with auto / user defined shifting to
+avoid label overlap.
    • 
+
  • Filtering what to plot and what to suppress
    • 
+
  • Interactive plots and animation
    • 
+
  • Simple default plot + possibilities to make it nice (decouple
+computations from representation)
    • 
+
  • Ability to show density of samples
    • 
+
  • Plot more than dim 1 & 2 - linked plots with same scales
    • 
+
  • Specific to CA: is it standard or principal points for rows or cols,
+symmetric or asymmetric
    • 
+
  • Needs to be a low level package to be used by other multivariate
+analysis packages
    • 
 

 

+

+
Examples

+
These examples show biplots produced by some of these packages.

+

+
Doing the PCA

+
The default method for prcomp() takes a numeric or
+complex matrix or data frame argument. By default, it does
+not scale the observations to unit variance, so
+scale. = TRUE should usually be specified. You can control
+the number of components returned using the
+rank. argument.

+
data(iris)
+iris.pca <- prcomp(iris[,1:4], scale. = TRUE)

+
There is also a formula method, which is more verbose, but more
+easily readable.

+
iris.pca <- prcomp(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
+                   data=iris, scale. = TRUE)

+
You can also use tidy steps and pipes from dplyr to
+select variables, and perhaps filter out missing data.

+
iris.pca <- 
+  iris |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)

+

+

+
ggbiplot

+
The default plot:

+
library(ggbiplot)
+library(ggplot2)
+library(dplyr)
+ggbiplot(iris.pca, groups = iris$Species)

+

+
Using more features:

+
iris.gg <-
+  ggbiplot(iris.pca, obs.scale = 1, var.scale = 1,
+           groups = iris$Species, point.size=2,
+           varname.size = 5, 
+           varname.color = "darkred",
+           varname.adjust = 1.2,
+           ellipse = TRUE, 
+           circle = TRUE) +
+  labs(fill = "Species", color = "Species") +
+  theme_minimal(base_size = 14) +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
+iris.gg

+

+
Use direct labels for the groups rather than a legend. This makes use
+of the fact that the gg object contains the dataset used
+iris.gg$data used to construct the plot.

+
# find means of the coordinates
+group.labs <-
+  iris.gg$data |>
+  summarise(xvar = mean(xvar),
+            yvar = mean(yvar), .by = groups)
+
+iris.gg + geom_label(data = group.labs,
+                     aes(x = xvar, y=yvar, label=groups),
+                     size = 5) +
+  theme(legend.position = "none")

+

+

+

 
 
 
diff --git a/discussion/biplotEZ-ex.R b/discussion/biplotEZ-ex.R
index fce631b..4ffc661 100644
--- a/discussion/biplotEZ-ex.R
+++ b/discussion/biplotEZ-ex.R
@@ -1,7 +1,7 @@
+if(!require(biplotEZ)) install.packages("biplotEZ")
 library(biplotEZ)
 
-
-biplot (iris[,1:4]) |> 
+biplot(iris[,1:4]) |> 
   PCA(group.aes=iris[,5]) |> 
   concentration.ellipse(kappa=2) |> 
   plot()
diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd
index e717218..0e21e17 100644
--- a/man/ggscreeplot.Rd
+++ b/man/ggscreeplot.Rd
@@ -7,7 +7,8 @@
 ggscreeplot(pcobj, type = c("pev", "cev"), size = 4)
 }
 \arguments{
-\item{pcobj}{an object returned by prcomp() or princomp()}
+\item{pcobj}{an object representing a linear dimension technique, such a returned by \code{\link[stats]{prcomp}} 
+or \code{\link[stats]{princomp}} or \code{\link[FactomineR]{PCA}} or \code{\link[MASS]{lda}}}
 
 \item{type}{the type of scree plot.
 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 
@@ -16,7 +17,8 @@ ggscreeplot(pcobj, type = c("pev", "cev"), size = 4)
 \item{size}{point size}
 }
 \description{
-Screeplot for Principal Components
+Produces scree plots (Cattell, 1966) of the variance proportions explained by each dimension against dimension number from 
+various dimension reduction techniques
 }
 \examples{
   data(wine)
@@ -24,3 +26,6 @@ Screeplot for Principal Components
   ggscreeplot(wine.pca)
 
 }
+\references{
+Cattell, R. B. (1966). The Scree Test For The Number Of Factors. \emph{Multivariate Behavioral Research}, 1, 245–276.
+}

From 3026f017d72200a5c10cc5c83bcf038d8dd12ecb Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 28 Nov 2023 16:51:54 -0500
Subject: [PATCH 40/80] edit Description: bump date and version

---
 DESCRIPTION | 17 ++++++++++-------
 1 file changed, 10 insertions(+), 7 deletions(-)

diff --git a/DESCRIPTION b/DESCRIPTION
index 3495d9b..086d316 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,18 +1,21 @@
 Package: ggbiplot
 Type: Package
-Title: A ggplot2 Based Biplot
-Version: 0.6.0
-Date: 2023-09-12
+Title: A ggplot2 Based Implementation of Biplots
+Version: 0.6.1
+Date: 2023-11-12
 Authors@R: c(
     person("Vincent", "Vu", , "vqv@stat.cmu.edu", role = c("aut")),
     person("Michael", "Friendly", , "friendly@yorku.ca", role = c("aut", "cre"),
            comment = c(ORCID = "0000-0002-3237-0941")),
     person("Aghasi", "Tavadyan", ,  "a.tavadyan@gmail.com", role = "ctb")
            )
-Description: A ggplot2 based biplot.  It provides a 
-    replacement for biplot.princomp(), but with many enhancements. It implements a
-    biplot and scree plot using ggplot2 which can be used with prcomp(), princomp(),
-    FactoMineR::PCA() or MASS::lda().
+Description: A ggplot2 based implementation of biplots, giving a representation of a dataset in
+    a two dimensional space accounting for the greatest variance, together with variable vectors
+    showing how the data variables relate to this space. It provides a 
+    replacement for stats::biplot(), but with many enhancements to control the analysis and
+    graphical display. It implements 
+    biplot and scree plot methods using ggplot2 which can be used with the results of prcomp(), princomp(),
+    FactoMineR::PCA() or MASS::lda() and can be customized using ggplot2 techniques.
 Depends: R (>= 3.5.0)
 Imports:
     ggplot2, scales

From 247126b6501a406a3959e03471fad4f06358f8c6 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 28 Nov 2023 17:47:31 -0500
Subject: [PATCH 41/80] update NEWS; spellcheck

---
 DESCRIPTION        |  1 +
 NEWS.md            |  7 ++++++-
 R/ggscreeplot.r    |  2 +-
 README.Rmd         |  2 +-
 cran-comments.md   | 12 +++++++++++-
 inst/WORDLIST      | 39 +++++++++++++++++++++++++++++++++++++++
 man/ggscreeplot.Rd |  2 +-
 7 files changed, 60 insertions(+), 5 deletions(-)
 create mode 100644 inst/WORDLIST

diff --git a/DESCRIPTION b/DESCRIPTION
index 086d316..ba6b1c1 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -25,6 +25,7 @@ Suggests:
     MASS
 License: GPL-2
 Encoding: UTF-8
+Language: en-US
 URL: https://github.com/friendly/ggbiplot
 BugReports: https://github.com/friendly/ggbiplot/issues
 RoxygenNote: 7.2.3
diff --git a/NEWS.md b/NEWS.md
index 36f08e5..5889dae 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,6 +1,11 @@
+## Version 0.6.1
+
+- Revise documentation for `ggscreeplot()`
+- `data(crime)` used in README
+
 ## Version 0.6.0
 
-- Use `geom_polygon()` rather than `geom_path()` for ellipses
+- Use `geom_polygon()` rather than `geom_path()` for ellipses to allow them to be filled.
 - Added `var.factor` argument to expand or reflect the variable vectors
 - Moved points/labels code earlier so ellipses and variable vectors are not obscured
 - Replaced internal calculation of ellipses with `stat_ellipse()`
diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r
index b917d10..71307a4 100644
--- a/R/ggscreeplot.r
+++ b/R/ggscreeplot.r
@@ -4,7 +4,7 @@
 #' various dimension reduction techniques
 #'
 #' @param pcobj   an object representing a linear dimension technique, such a returned by \code{\link[stats]{prcomp}} 
-#'                or \code{\link[stats]{princomp}} or \code{\link[FactomineR]{PCA}} or \code{\link[MASS]{lda}}
+#'                or \code{\link[stats]{princomp}} or \code{\link[FactoMineR]{PCA}} or \code{\link[MASS]{lda}}
 #' @param type    the type of scree plot.  
 #'                'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 
 #'                'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.
diff --git a/README.Rmd b/README.Rmd
index 25e93c7..ff5852f 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -180,7 +180,7 @@ ggbiplot(wine.pca,
 ```
 
 The three cultivars are arranged along the first dimension, in the order barolo < grignolino < barbera.
-These are distinguished largely by a conrtast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`).
+These are distinguished largely by a contrast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`).
 The second dimension is represented by the cluster of variables `Mg`, `Alcohol`, `Ash`, `Color`, which distinguishes
 grignolino from the other two.
 
diff --git a/cran-comments.md b/cran-comments.md
index 7a4afee..d8d6e17 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -7,4 +7,14 @@
 
 0 errors | 0 warnings | 1 note
 
-* This is a new release.
+* This is considered a new release, against the published CRAN version, 0.55,
+due to a change in maintainer
+
+* Possibly misspelled words in DESCRIPTION:
+  Biplots (3:42)
+  biplot (17:5)
+  biplots (12:48)
+  ggplot (3:10, 12:16, 17:41, 18:66)
+
+These are all spurious false alarms, owing to win-builder not recognizing the spelling WORDFILE
+
diff --git a/inst/WORDLIST b/inst/WORDLIST
new file mode 100644
index 0000000..91c2655
--- /dev/null
+++ b/inst/WORDLIST
@@ -0,0 +1,39 @@
+Alcalinity
+BBVA
+Biometrika
+Cattell
+FactoMineR
+Flavanoids
+Gower
+Greenacre
+Hartigan
+Lubbe
+Malic
+Nonflavanoid
+PRINCOMP
+PROC
+Proanthocyanins
+README
+UCI
+Yu
+al
+barbera
+barolo
+cev
+conrtast
+dplyr
+et
+factoextra
+ggplot
+grignolino
+lda
+loadings
+orthonormal
+pca
+pev
+phenols
+prcomp
+princomp
+purrr
+repo
+roxygen
diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd
index 0e21e17..03e1a35 100644
--- a/man/ggscreeplot.Rd
+++ b/man/ggscreeplot.Rd
@@ -8,7 +8,7 @@ ggscreeplot(pcobj, type = c("pev", "cev"), size = 4)
 }
 \arguments{
 \item{pcobj}{an object representing a linear dimension technique, such a returned by \code{\link[stats]{prcomp}} 
-or \code{\link[stats]{princomp}} or \code{\link[FactomineR]{PCA}} or \code{\link[MASS]{lda}}}
+or \code{\link[stats]{princomp}} or \code{\link[FactoMineR]{PCA}} or \code{\link[MASS]{lda}}}
 
 \item{type}{the type of scree plot.
 'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 

From 5b97ebc3212ed09e2479d37e5d9910744c7a3cf3 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 28 Nov 2023 18:12:45 -0500
Subject: [PATCH 42/80] fix 301 link in ggbiplot.Rd

---
 NEWS.md         | 5 +++--
 R/ggbiplot.r    | 2 +-
 man/ggbiplot.Rd | 2 +-
 3 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index 5889dae..f09a982 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,7 +1,8 @@
 ## Version 0.6.1
 
-- Revise documentation for `ggscreeplot()`
-- `data(crime)` used in README
+- Revised documentation for `ggscreeplot()`
+- `data(crime)` used in README giving a more complete example.
+- Fixed links reported as 301s
 
 ## Version 0.6.0
 
diff --git a/R/ggbiplot.r b/R/ggbiplot.r
index b162836..e096703 100644
--- a/R/ggbiplot.r
+++ b/R/ggbiplot.r
@@ -147,7 +147,7 @@
 #'   In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. 
 #'   
 #'   Greenacre, M. (2010). \emph{Biplots in Practice}. BBVA Foundation, Bilbao, Spain. 
-#'   Available for free at \url{https://www.multivariatestatistics.org}.
+#'   Available for free at \url{https://www.fbbva.es/microsite/multivariate-statistics/}.
 #'   
 #'   J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall.
 #'   
diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd
index 9ae779d..a0e528b 100644
--- a/man/ggbiplot.Rd
+++ b/man/ggbiplot.Rd
@@ -200,7 +200,7 @@ Gabriel, K. R. (1971). The biplot graphical display of matrices with application
   In V. Barnett (Ed.), \emph{Interpreting Multivariate Data}. London: Wiley. 
   
   Greenacre, M. (2010). \emph{Biplots in Practice}. BBVA Foundation, Bilbao, Spain. 
-  Available for free at \url{https://www.multivariatestatistics.org}.
+  Available for free at \url{https://www.fbbva.es/microsite/multivariate-statistics/}.
   
   J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman & Hall.
   

From 84d84dfaa0c2b6c43d4fdcc3a6bccd61f00e3fc0 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Sun, 3 Dec 2023 12:02:10 -0500
Subject: [PATCH 43/80] fix ggbiplot documentation

---
 R/ggbiplot.r    | 8 ++++----
 man/ggbiplot.Rd | 8 ++++----
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/R/ggbiplot.r b/R/ggbiplot.r
index e096703..7531b5d 100644
--- a/R/ggbiplot.r
+++ b/R/ggbiplot.r
@@ -46,13 +46,13 @@
 #' 
 #' where 
 #' \itemize{
-#'    \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores and also the eigenvectors
+#'    \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores; these are also the eigenvectors
 #'          of \eqn{\mathbf{X} \mathbf{X}'},
 #'    \item \eqn{\mathbf{\Lambda}} is an \eqn{r \times r} diagonal matrix of singular values, 
 #'          \eqn{\lambda_1 \ge \lambda_2 \ge \cdots \lambda_r} 
 #'         % which are also the square roots
 #'         % of the eigenvalues of \eqn{\mathbf{X} \mathbf{X}'}. 
-#'    \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of observation scores and also the eigenvectors
+#'    \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of variable weights and also the eigenvectors
 #'          of \eqn{\mathbf{X}' \mathbf{X}}.
 #' }
 #' 
@@ -136,8 +136,8 @@
 #' 
 #' @seealso 
 #'   \code{\link{reflect}}, \code{\link{ggscreeplot}};
-#'   \code{link[stats]{biplot}} for the original stats package version;
-#'   \code{link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
+#'   \code{\link[stats]{biplot}} for the original stats package version;
+#'   \code{\link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
 #' 
 #' @references 
 #'   Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. 
diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd
index a0e528b..cd2955a 100644
--- a/man/ggbiplot.Rd
+++ b/man/ggbiplot.Rd
@@ -126,13 +126,13 @@ can be expressed \emph{exactly} as
 
 where 
 \itemize{
-   \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores and also the eigenvectors
+   \item \eqn{\mathbf{U}} is an \eqn{n \times r} orthonormal matrix of observation scores; these are also the eigenvectors
          of \eqn{\mathbf{X} \mathbf{X}'},
    \item \eqn{\mathbf{\Lambda}} is an \eqn{r \times r} diagonal matrix of singular values, 
          \eqn{\lambda_1 \ge \lambda_2 \ge \cdots \lambda_r} 
         % which are also the square roots
         % of the eigenvalues of \eqn{\mathbf{X} \mathbf{X}'}. 
-   \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of observation scores and also the eigenvectors
+   \item \eqn{\mathbf{V}} is an \eqn{r \times p} orthonormal matrix of variable weights and also the eigenvectors
          of \eqn{\mathbf{X}' \mathbf{X}}.
 }
 
@@ -208,6 +208,6 @@ Gabriel, K. R. (1971). The biplot graphical display of matrices with application
 }
 \seealso{
 \code{\link{reflect}}, \code{\link{ggscreeplot}};
-  \code{link[stats]{biplot}} for the original stats package version;
-  \code{link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
+  \code{\link[stats]{biplot}} for the original stats package version;
+  \code{\link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
 }

From 58d83955686921972cfeda18c2f611ad5beb44df Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Mon, 4 Dec 2023 16:25:06 -0500
Subject: [PATCH 44/80] update README

---
 R/reflect.R                             |  15 +++++++++------
 README.Rmd                              |  12 ++++++++----
 README.md                               |  21 +++++++++++++--------
 man/figures/README-crime-corrplot-1.png | Bin 16394 -> 16205 bytes
 4 files changed, 30 insertions(+), 18 deletions(-)

diff --git a/R/reflect.R b/R/reflect.R
index fe106fa..2bea06f 100644
--- a/R/reflect.R
+++ b/R/reflect.R
@@ -1,13 +1,13 @@
 
-#' Reflect columns in a principal component-like object
+#' Reflect Columns in a Principal Component-like Object
 #' 
-#' Principle component like objects have variable loadings whose
-#' signs are arbitrary, in the sense that a given column can be 
+#' Principle component-like objects have variable loadings (the eigenvectors of the covariance/correlation matrix)
+#' whose signs are arbitrary, in the sense that a given column can be 
 #' reflected (multiplied by -1) without changing the fit.
 #' 
 #' This function allows one to reflect any columns of the variable
 #' loadings (and corresponding observation scores). This is often
-#' useful for interpreting a biplot.
+#' useful for interpreting a biplot, for example when a component (often the first) has all negative signs.
 #'
 #' @param pcobj     an object returned by \code{\link[stats]{prcomp}}, \code{\link[stats]{princomp}}, 
 #'                  \code{\link[FactoMineR]{PCA}}, or \code{\link[MASS]{lda}}
@@ -16,7 +16,10 @@
 #' @return    The pca-like object with specified columns of the 
 #'            variable loadings and observation scores multiplied
 #'            by -1.
+#' @author Michael Friendly
 #' @export
+#' @seealso \code{\link[stats]{prcomp}},  \code{\link[stats]{princomp}}, 
+#'          \code{\link[FactoMineR]{PCA}}, \code{\link[MASS]{lda}}
 #'
 #' @examples
 #' data(crime)
@@ -27,7 +30,7 @@
 #'   
 #'  biplot(crime.pca)
 #'  
-#'  crime.pca <- reflect(crime.pca)
+#'  crime.pca <- reflect(crime.pca)  # reflect columns 1:2
 #'  biplot(crime.pca)
 
 reflect <- function(pcobj, columns = 1:2){
@@ -53,7 +56,7 @@ reflect <- function(pcobj, columns = 1:2){
     pcobj$ind$coord[, columns]   <- -1 * pcobj$ind$coord[, columns]
   } 
   else if(inherits(pcobj, "lda")) {
-    warning("Can't reflect an 'lda' object")
+    warning("Can't reflect an 'lda' object")               # Why not???
   #   u <- predict(pcobj)$x
   #   check(u, columns)
   #   pcobj$scaling[, columns] <- -1 * pcobj$scaling[, columns]
diff --git a/README.Rmd b/README.Rmd
index ff5852f..efc4056 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -15,10 +15,12 @@ This repo for the [ggbiplot package](https://CRAN.R-project.org/package=ggbiplot
 was forked from [https://github.com/vqv/ggbiplot](https://github.com/vqv/ggbiplot) by Vince Yu, which has been dormant
 since 2015.  
 
-The goal is to complete that development and publish a new version on CRAN.
+The goal is to complete that development and publish a new version on CRAN with Vince Yu as the principal author.
 There is also an [experimental branch](https://github.com/friendly/ggbiplot/tree/experimental) which attempts to
 simplify the code, but this has some unresolved problems.
 
+
+
 ```{r, echo = FALSE}
 knitr::opts_chunk$set(
   collapse = TRUE,
@@ -35,9 +37,12 @@ options(digits = 3)
 
 # ggbiplot 
 
-An implementation of the biplot using `ggplot2`.  The package provides two functions: `ggscreeplot()` and `ggbiplot()`.
+This package provides a `ggplot2` implementation of the biplot, a simultaneous
+plot of scores for observations and vectors for variables for principal component-like analyses.  
+The package provides two main functions: `ggscreeplot()` and `ggbiplot()`.
+
 `ggbiplot` aims to be a drop-in replacement for the built-in R function `biplot.princomp()` with extended functionality 
-for labeling groups, drawing a correlation circle, and adding Normal probability ellipsoids.
+for labeling groups, drawing a correlation circle, and adding data ellipsoids.
 
 
 ## Installation
@@ -233,7 +238,6 @@ iris.gg + geom_label(data = group.labs,
                      aes(x = xvar, y=yvar, label=groups),
                      size = 5) +
   theme(legend.position = "none")
-
 ```
 
 
diff --git a/README.md b/README.md
index 7b39fff..958e2b5 100644
--- a/README.md
+++ b/README.md
@@ -14,17 +14,22 @@ package](https://CRAN.R-project.org/package=ggbiplot) was forked from
 since 2015.
 
 The goal is to complete that development and publish a new version on
-CRAN. There is also an [experimental
+CRAN with Vince Yu as the principal author. There is also an
+[experimental
 branch](https://github.com/friendly/ggbiplot/tree/experimental) which
 attempts to simplify the code, but this has some unresolved problems.
 
 # ggbiplot 
 
-An implementation of the biplot using `ggplot2`. The package provides
-two functions: `ggscreeplot()` and `ggbiplot()`. `ggbiplot` aims to be a
-drop-in replacement for the built-in R function `biplot.princomp()` with
-extended functionality for labeling groups, drawing a correlation
-circle, and adding Normal probability ellipsoids.
+This package provides a `ggplot2` implementation of the biplot, a
+simultaneous plot of scores for observations and vectors for variables
+for principal component-like analyses.  
+The package provides two main functions: `ggscreeplot()` and
+`ggbiplot()`.
+
+`ggbiplot` aims to be a drop-in replacement for the built-in R function
+`biplot.princomp()` with extended functionality for labeling groups,
+drawing a correlation circle, and adding data ellipsoids.
 
 ## Installation
 
@@ -63,7 +68,7 @@ data(crime)
 crime |> 
   dplyr::select(where(is.numeric)) |> 
   cor() |> 
-  corrplot(method = "ellipse")
+  corrplot(method = "ellipse", tl.srt = 0)
 ```
 
 ![](man/figures/README-crime-corrplot-1.png)
@@ -197,7 +202,7 @@ ggbiplot(wine.pca,
 
 The three cultivars are arranged along the first dimension, in the order
 barolo \< grignolino \< barbera. These are distinguished largely by a
-conrtast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`).
+contrast between (`Phenols`, `Flav`) vs. (`NonFlavPhenols`, `AlcAsh`).
 The second dimension is represented by the cluster of variables `Mg`,
 `Alcohol`, `Ash`, `Color`, which distinguishes grignolino from the other
 two.
diff --git a/man/figures/README-crime-corrplot-1.png b/man/figures/README-crime-corrplot-1.png
index 7e24421d783b7872f5ed791a18ddbca9fbe1b329..d324acc8d3fe31ae24e4319306e072f749fec96f 100644
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zKrLtgB<9d|pDUMbU6eDKm|HltcdR
Date: Mon, 4 Dec 2023 21:10:07 -0500
Subject: [PATCH 45/80] check @returns

---
 R/ggscreeplot.r |  2 ++
 man/reflect.Rd  | 17 ++++++++++++-----
 2 files changed, 14 insertions(+), 5 deletions(-)

diff --git a/R/ggscreeplot.r b/R/ggscreeplot.r
index 71307a4..dfb6ade 100644
--- a/R/ggscreeplot.r
+++ b/R/ggscreeplot.r
@@ -9,6 +9,8 @@
 #'                'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 
 #'                'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.
 #' @param size    point size
+#' 
+#' @returns A ggplot2 object
 #' @export
 #' @references 
 #' Cattell, R. B. (1966). The Scree Test For The Number Of Factors. \emph{Multivariate Behavioral Research}, 1, 245–276.
diff --git a/man/reflect.Rd b/man/reflect.Rd
index cd216a1..047f3de 100644
--- a/man/reflect.Rd
+++ b/man/reflect.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/reflect.R
 \name{reflect}
 \alias{reflect}
-\title{Reflect columns in a principal component-like object}
+\title{Reflect Columns in a Principal Component-like Object}
 \usage{
 reflect(pcobj, columns = 1:2)
 }
@@ -18,14 +18,14 @@ The pca-like object with specified columns of the
            by -1.
 }
 \description{
-Principle component like objects have variable loadings whose
-signs are arbitrary, in the sense that a given column can be 
+Principle component-like objects have variable loadings (the eigenvectors of the covariance/correlation matrix)
+whose signs are arbitrary, in the sense that a given column can be 
 reflected (multiplied by -1) without changing the fit.
 }
 \details{
 This function allows one to reflect any columns of the variable
 loadings (and corresponding observation scores). This is often
-useful for interpreting a biplot.
+useful for interpreting a biplot, for example when a component (often the first) has all negative signs.
 }
 \examples{
 data(crime)
@@ -36,6 +36,13 @@ crime.pca <-
   
  biplot(crime.pca)
  
- crime.pca <- reflect(crime.pca)
+ crime.pca <- reflect(crime.pca)  # reflect columns 1:2
  biplot(crime.pca)
 }
+\seealso{
+\code{\link[stats]{prcomp}},  \code{\link[stats]{princomp}}, 
+         \code{\link[FactoMineR]{PCA}}, \code{\link[MASS]{lda}}
+}
+\author{
+Michael Friendly
+}

From 94e58ed53366d249806afd35e4a4207175cc383f Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Mon, 4 Dec 2023 21:34:03 -0500
Subject: [PATCH 46/80] tweak README

---
 README.Rmd       | 3 ++-
 README.md        | 8 ++++----
 cran-comments.md | 3 +--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/README.Rmd b/README.Rmd
index efc4056..a2d0fc3 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -11,7 +11,8 @@ output: github_document
 
 
 
-This repo for the [ggbiplot package](https://CRAN.R-project.org/package=ggbiplot)
+This repo for the **ggbiplot** package
+
 was forked from [https://github.com/vqv/ggbiplot](https://github.com/vqv/ggbiplot) by Vince Yu, which has been dormant
 since 2015.  
 
diff --git a/README.md b/README.md
index 958e2b5..d1e4ad3 100644
--- a/README.md
+++ b/README.md
@@ -8,10 +8,10 @@ status](https://www.r-pkg.org/badges/version/ggbiplot)](https://CRAN.R-project.o
 Commit](https://img.shields.io/github/last-commit/friendly/ggbiplot)](https://github.com/friendly/ggbiplot)
 
 
-This repo for the [ggbiplot
-package](https://CRAN.R-project.org/package=ggbiplot) was forked from
- by Vince Yu, which has been dormant
-since 2015.
+This repo for the **ggbiplot** package
+
+was forked from  by Vince Yu, which has
+been dormant since 2015.
 
 The goal is to complete that development and publish a new version on
 CRAN with Vince Yu as the principal author. There is also an
diff --git a/cran-comments.md b/cran-comments.md
index d8d6e17..52cc416 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -7,8 +7,7 @@
 
 0 errors | 0 warnings | 1 note
 
-* This is considered a new release, against the published CRAN version, 0.55,
-due to a change in maintainer
+* This is considered a new release, against last the published CRAN version, 0.55, due to a change in maintainer.
 
 * Possibly misspelled words in DESCRIPTION:
   Biplots (3:42)

From aad9ffa790565074ff08f93440a7e70e66f7c86e Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 5 Dec 2023 15:48:22 -0500
Subject: [PATCH 47/80] fix point.size buglet in ggbiplot.R

---
 R/ggbiplot.r       | 17 ++---------------
 man/ggbiplot.Rd    |  3 +++
 man/ggscreeplot.Rd |  3 +++
 3 files changed, 8 insertions(+), 15 deletions(-)

diff --git a/R/ggbiplot.r b/R/ggbiplot.r
index 7531b5d..0f9fc47 100644
--- a/R/ggbiplot.r
+++ b/R/ggbiplot.r
@@ -3,20 +3,6 @@
 #  
 #  Copyright 2011 Vincent Q. Vu.
 # 
-#  This program is free software; you can redistribute it and/or
-#  modify it under the terms of the GNU General Public License
-#  as published by the Free Software Foundation; either version 2
-#  of the License, or (at your option) any later version.
-#  
-#  This program is distributed in the hope that it will be useful,
-#  but WITHOUT ANY WARRANTY; without even the implied warranty of
-#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-#  GNU General Public License for more details.
-#  
-#  You should have received a copy of the GNU General Public License
-#  along with this program; if not, write to the Free Software
-#  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
-# 
 
 #' Biplot for Principal Components using ggplot2
 #' 
@@ -139,6 +125,7 @@
 #'   \code{\link[stats]{biplot}} for the original stats package version;
 #'   \code{\link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
 #' 
+#' @author Vincent Q. Vu.
 #' @references 
 #'   Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. 
 #'   \emph{Biometrika}, \bold{58}, 453–467. \doi{10.2307/2334381}.
@@ -316,7 +303,7 @@ ggbiplot <- function(pcobj,
     if(!is.null(df.u$groups)) {
       g <- g + geom_point(aes(color = groups), alpha = alpha, size = point.size)
     } else {
-      g <- g + geom_point(alpha = alpha)      
+      g <- g + geom_point(alpha = alpha, size = point.size)      
     }
   }
   
diff --git a/man/ggbiplot.Rd b/man/ggbiplot.Rd
index cd2955a..6465a76 100644
--- a/man/ggbiplot.Rd
+++ b/man/ggbiplot.Rd
@@ -211,3 +211,6 @@ Gabriel, K. R. (1971). The biplot graphical display of matrices with application
   \code{\link[stats]{biplot}} for the original stats package version;
   \code{\link[factoextra]{fviz_pca_biplot}} for the factoextra package version.
 }
+\author{
+Vincent Q. Vu.
+}
diff --git a/man/ggscreeplot.Rd b/man/ggscreeplot.Rd
index 03e1a35..1680cb4 100644
--- a/man/ggscreeplot.Rd
+++ b/man/ggscreeplot.Rd
@@ -16,6 +16,9 @@ or \code{\link[stats]{princomp}} or \code{\link[FactoMineR]{PCA}} or \code{\link
 
 \item{size}{point size}
 }
+\value{
+A ggplot2 object
+}
 \description{
 Produces scree plots (Cattell, 1966) of the variance proportions explained by each dimension against dimension number from 
 various dimension reduction techniques

From 49556fad10aa4cd9f4a7150cade064c07b630ea7 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Tue, 5 Dec 2023 22:02:25 -0500
Subject: [PATCH 48/80] create pkgdown site

---
 _pkgdown.yaml.R                               |  21 +
 docs/404.html                                 | 110 +++++
 docs/apple-touch-icon-120x120.png             | Bin 0 -> 16585 bytes
 docs/apple-touch-icon-152x152.png             | Bin 0 -> 22082 bytes
 docs/apple-touch-icon-180x180.png             | Bin 0 -> 27723 bytes
 docs/apple-touch-icon-60x60.png               | Bin 0 -> 6409 bytes
 docs/apple-touch-icon-76x76.png               | Bin 0 -> 9083 bytes
 docs/apple-touch-icon.png                     | Bin 0 -> 27723 bytes
 docs/authors.html                             | 106 +++++
 docs/bootstrap-toc.css                        |  60 +++
 docs/bootstrap-toc.js                         | 159 ++++++++
 docs/docsearch.css                            | 148 +++++++
 docs/docsearch.js                             |  85 ++++
 docs/favicon-16x16.png                        | Bin 0 -> 1208 bytes
 docs/favicon-32x32.png                        | Bin 0 -> 2674 bytes
 docs/favicon.ico                              | Bin 0 -> 15086 bytes
 docs/index.html                               | 321 +++++++++++++++
 docs/link.svg                                 |  12 +
 docs/logo.png                                 | Bin 0 -> 35061 bytes
 docs/news/index.html                          | 105 +++++
 docs/pkgdown.css                              | 384 ++++++++++++++++++
 docs/pkgdown.js                               | 108 +++++
 docs/pkgdown.yml                              |   6 +
 docs/reference/Rplot001.png                   | Bin 0 -> 18707 bytes
 docs/reference/Rplot002.png                   | Bin 0 -> 55271 bytes
 docs/reference/crime-1.png                    | Bin 0 -> 95514 bytes
 docs/reference/crime.html                     | 156 +++++++
 .../figures/README-crime-biplot0-1.png        | Bin 0 -> 23888 bytes
 .../figures/README-crime-biplot1-1.png        | Bin 0 -> 41117 bytes
 .../figures/README-crime-corrplot-1.png       | Bin 0 -> 16205 bytes
 .../figures/README-iris-biplot0-1.png         | Bin 0 -> 26275 bytes
 .../figures/README-iris-biplot1-1.png         | Bin 0 -> 25467 bytes
 .../figures/README-wine-biplot-1.png          | Bin 0 -> 24302 bytes
 .../figures/README-wine-example-1.png         | Bin 0 -> 21502 bytes
 .../figures/README-wine-screeplot-1.png       | Bin 0 -> 7803 bytes
 docs/reference/figures/logo.png               | Bin 0 -> 35061 bytes
 docs/reference/ggbiplot-1.png                 | Bin 0 -> 177516 bytes
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diff --git a/_pkgdown.yaml.R b/_pkgdown.yaml.R
new file mode 100644
index 0000000..46da03d
--- /dev/null
+++ b/_pkgdown.yaml.R
@@ -0,0 +1,21 @@
+url: http://friendly.github.io/ggbiplot/
+
+template:
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+  bslib:
+    base_font: {google: "Roboto"}
+    heading_font: {google: "Roboto Slab"}
+    code_font: {google: "JetBrains Mono"}
+
+reference:
+  - title: "Biplot functions"
+    contents:
+      - ggbiplot
+      - ggscreeplot
+      - reflect
+  
+  - title: "Data sets"
+      - crime
+      - wine
+
+      
\ No newline at end of file
diff --git a/docs/404.html b/docs/404.html
new file mode 100644
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+++ b/docs/404.html
@@ -0,0 +1,110 @@
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+
+
+
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+
+
+
+
+
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+
+
+
+    
+
+    

+      

+
+
+      
+
+      

+  

+    

+      
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+    

+
+Content not found. Please use links in the navbar.
+
+  

+
+  
+
+

+
+
+
+      

+  

+
Developed by Vincent Vu, Michael Friendly.

+

+
+

+  

+
Site built with pkgdown 2.0.7.

+

+
+      

+

+
+  
+
+
+  
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+  
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+Authors and Citation • ggbiplot
+    
+
+    

+      

+
+      
+
+      

+  

+    

+      

+        
Authors

+      

+
+      
+      
  • 
+          
    Vincent Vu. Author. 
+          
    
+        
    • 
+        
  • 
+          
    Michael Friendly. Author, maintainer. 
+          
    
+        
    • 
+        
  • 
+          
    Aghasi Tavadyan. Contributor. 
+          
    
+        
    • 
+      

+    

+    

+      
Citation

+      Source: DESCRIPTION
+    

+    

+
+
+    
Vu V, Friendly M (2023).
+ggbiplot: A ggplot2 Based Implementation of Biplots.
+R package version 0.6.1, https://github.com/friendly/ggbiplot. 
+

+    
@Manual{,
+  title = {ggbiplot: A ggplot2 Based Implementation of Biplots},
+  author = {Vincent Vu and Michael Friendly},
+  year = {2023},
+  note = {R package version 0.6.1},
+  url = {https://github.com/friendly/ggbiplot},
+}

+
+  

+
+

+
+
+
+      

+  
Developed by Vincent Vu, Michael Friendly.

+

+
+

+  
Site built with pkgdown 2.0.7.

+

+
+      

+
+  
+
+
+  
+
+  
+
diff --git a/docs/bootstrap-toc.css b/docs/bootstrap-toc.css
new file mode 100644
index 0000000..5a85941
--- /dev/null
+++ b/docs/bootstrap-toc.css
@@ -0,0 +1,60 @@
+/*!
+ * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/)
+ * Copyright 2015 Aidan Feldman
+ * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */
+
+/* modified from https://github.com/twbs/bootstrap/blob/94b4076dd2efba9af71f0b18d4ee4b163aa9e0dd/docs/assets/css/src/docs.css#L548-L601 */
+
+/* All levels of nav */
+nav[data-toggle='toc'] .nav > li > a {
+  display: block;
+  padding: 4px 20px;
+  font-size: 13px;
+  font-weight: 500;
+  color: #767676;
+}
+nav[data-toggle='toc'] .nav > li > a:hover,
+nav[data-toggle='toc'] .nav > li > a:focus {
+  padding-left: 19px;
+  color: #563d7c;
+  text-decoration: none;
+  background-color: transparent;
+  border-left: 1px solid #563d7c;
+}
+nav[data-toggle='toc'] .nav > .active > a,
+nav[data-toggle='toc'] .nav > .active:hover > a,
+nav[data-toggle='toc'] .nav > .active:focus > a {
+  padding-left: 18px;
+  font-weight: bold;
+  color: #563d7c;
+  background-color: transparent;
+  border-left: 2px solid #563d7c;
+}
+
+/* Nav: second level (shown on .active) */
+nav[data-toggle='toc'] .nav .nav {
+  display: none; /* Hide by default, but at >768px, show it */
+  padding-bottom: 10px;
+}
+nav[data-toggle='toc'] .nav .nav > li > a {
+  padding-top: 1px;
+  padding-bottom: 1px;
+  padding-left: 30px;
+  font-size: 12px;
+  font-weight: normal;
+}
+nav[data-toggle='toc'] .nav .nav > li > a:hover,
+nav[data-toggle='toc'] .nav .nav > li > a:focus {
+  padding-left: 29px;
+}
+nav[data-toggle='toc'] .nav .nav > .active > a,
+nav[data-toggle='toc'] .nav .nav > .active:hover > a,
+nav[data-toggle='toc'] .nav .nav > .active:focus > a {
+  padding-left: 28px;
+  font-weight: 500;
+}
+
+/* from https://github.com/twbs/bootstrap/blob/e38f066d8c203c3e032da0ff23cd2d6098ee2dd6/docs/assets/css/src/docs.css#L631-L634 */
+nav[data-toggle='toc'] .nav > .active > ul {
+  display: block;
+}
diff --git a/docs/bootstrap-toc.js b/docs/bootstrap-toc.js
new file mode 100644
index 0000000..1cdd573
--- /dev/null
+++ b/docs/bootstrap-toc.js
@@ -0,0 +1,159 @@
+/*!
+ * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/)
+ * Copyright 2015 Aidan Feldman
+ * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */
+(function() {
+  'use strict';
+
+  window.Toc = {
+    helpers: {
+      // return all matching elements in the set, or their descendants
+      findOrFilter: function($el, selector) {
+        // http://danielnouri.org/notes/2011/03/14/a-jquery-find-that-also-finds-the-root-element/
+        // http://stackoverflow.com/a/12731439/358804
+        var $descendants = $el.find(selector);
+        return $el.filter(selector).add($descendants).filter(':not([data-toc-skip])');
+      },
+
+      generateUniqueIdBase: function(el) {
+        var text = $(el).text();
+        var anchor = text.trim().toLowerCase().replace(/[^A-Za-z0-9]+/g, '-');
+        return anchor || el.tagName.toLowerCase();
+      },
+
+      generateUniqueId: function(el) {
+        var anchorBase = this.generateUniqueIdBase(el);
+        for (var i = 0; ; i++) {
+          var anchor = anchorBase;
+          if (i > 0) {
+            // add suffix
+            anchor += '-' + i;
+          }
+          // check if ID already exists
+          if (!document.getElementById(anchor)) {
+            return anchor;
+          }
+        }
+      },
+
+      generateAnchor: function(el) {
+        if (el.id) {
+          return el.id;
+        } else {
+          var anchor = this.generateUniqueId(el);
+          el.id = anchor;
+          return anchor;
+        }
+      },
+
+      createNavList: function() {
+        return $('
    ');
+      },
+
+      createChildNavList: function($parent) {
+        var $childList = this.createNavList();
+        $parent.append($childList);
+        return $childList;
+      },
+
+      generateNavEl: function(anchor, text) {
+        var $a = $('');
+        $a.attr('href', '#' + anchor);
+        $a.text(text);
+        var $li = $('
  • ');
+        $li.append($a);
+        return $li;
+      },
+
+      generateNavItem: function(headingEl) {
+        var anchor = this.generateAnchor(headingEl);
+        var $heading = $(headingEl);
+        var text = $heading.data('toc-text') || $heading.text();
+        return this.generateNavEl(anchor, text);
+      },
+
+      // Find the first heading level (`
    `, then `
    `, etc.) that has more than one element. Defaults to 1 (for `
    `).
+      getTopLevel: function($scope) {
+        for (var i = 1; i <= 6; i++) {
+          var $headings = this.findOrFilter($scope, 'h' + i);
+          if ($headings.length > 1) {
+            return i;
+          }
+        }
+
+        return 1;
+      },
+
+      // returns the elements for the top level, and the next below it
+      getHeadings: function($scope, topLevel) {
+        var topSelector = 'h' + topLevel;
+
+        var secondaryLevel = topLevel + 1;
+        var secondarySelector = 'h' + secondaryLevel;
+
+        return this.findOrFilter($scope, topSelector + ',' + secondarySelector);
+      },
+
+      getNavLevel: function(el) {
+        return parseInt(el.tagName.charAt(1), 10);
+      },
+
+      populateNav: function($topContext, topLevel, $headings) {
+        var $context = $topContext;
+        var $prevNav;
+
+        var helpers = this;
+        $headings.each(function(i, el) {
+          var $newNav = helpers.generateNavItem(el);
+          var navLevel = helpers.getNavLevel(el);
+
+          // determine the proper $context
+          if (navLevel === topLevel) {
+            // use top level
+            $context = $topContext;
+          } else if ($prevNav && $context === $topContext) {
+            // create a new level of the tree and switch to it
+            $context = helpers.createChildNavList($prevNav);
+          } // else use the current $context
+
+          $context.append($newNav);
+
+          $prevNav = $newNav;
+        });
+      },
+
+      parseOps: function(arg) {
+        var opts;
+        if (arg.jquery) {
+          opts = {
+            $nav: arg
+          };
+        } else {
+          opts = arg;
+        }
+        opts.$scope = opts.$scope || $(document.body);
+        return opts;
+      }
+    },
+
+    // accepts a jQuery object, or an options object
+    init: function(opts) {
+      opts = this.helpers.parseOps(opts);
+
+      // ensure that the data attribute is in place for styling
+      opts.$nav.attr('data-toggle', 'toc');
+
+      var $topContext = this.helpers.createChildNavList(opts.$nav);
+      var topLevel = this.helpers.getTopLevel(opts.$scope);
+      var $headings = this.helpers.getHeadings(opts.$scope, topLevel);
+      this.helpers.populateNav($topContext, topLevel, $headings);
+    }
+  };
+
+  $(function() {
+    $('nav[data-toggle="toc"]').each(function(i, el) {
+      var $nav = $(el);
+      Toc.init($nav);
+    });
+  });
+})();
diff --git a/docs/docsearch.css b/docs/docsearch.css
new file mode 100644
index 0000000..e5f1fe1
--- /dev/null
+++ b/docs/docsearch.css
@@ -0,0 +1,148 @@
+/* Docsearch -------------------------------------------------------------- */
+/*
+  Source: https://github.com/algolia/docsearch/
+  License: MIT
+*/
+
+.algolia-autocomplete {
+  display: block;
+  -webkit-box-flex: 1;
+  -ms-flex: 1;
+  flex: 1
+}
+
+.algolia-autocomplete .ds-dropdown-menu {
+  width: 100%;
+  min-width: none;
+  max-width: none;
+  padding: .75rem 0;
+  background-color: #fff;
+  background-clip: padding-box;
+  border: 1px solid rgba(0, 0, 0, .1);
+  box-shadow: 0 .5rem 1rem rgba(0, 0, 0, .175);
+}
+
+@media (min-width:768px) {
+  .algolia-autocomplete .ds-dropdown-menu {
+      width: 175%
+  }
+}
+
+.algolia-autocomplete .ds-dropdown-menu::before {
+  display: none
+}
+
+.algolia-autocomplete .ds-dropdown-menu [class^=ds-dataset-] {
+  padding: 0;
+  background-color: rgb(255,255,255);
+  border: 0;
+  max-height: 80vh;
+}
+
+.algolia-autocomplete .ds-dropdown-menu .ds-suggestions {
+  margin-top: 0
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion {
+  padding: 0;
+  overflow: visible
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--category-header {
+  padding: .125rem 1rem;
+  margin-top: 0;
+  font-size: 1.3em;
+  font-weight: 500;
+  color: #00008B;
+  border-bottom: 0
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--wrapper {
+    float: none;
+    padding-top: 0
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--subcategory-column {
+  float: none;
+  width: auto;
+  padding: 0;
+  text-align: left
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--content {
+  float: none;
+  width: auto;
+  padding: 0
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--content::before {
+  display: none
+}
+
+.algolia-autocomplete .ds-suggestion:not(:first-child) .algolia-docsearch-suggestion--category-header {
+  padding-top: .75rem;
+  margin-top: .75rem;
+  border-top: 1px solid rgba(0, 0, 0, .1)
+}
+
+.algolia-autocomplete .ds-suggestion .algolia-docsearch-suggestion--subcategory-column {
+  display: block;
+  padding: .1rem 1rem;
+  margin-bottom: 0.1;
+  font-size: 1.0em;
+  font-weight: 400
+  /* display: none */
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--title {
+  display: block;
+  padding: .25rem 1rem;
+  margin-bottom: 0;
+  font-size: 0.9em;
+  font-weight: 400
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--text {
+  padding: 0 1rem .5rem;
+  margin-top: -.25rem;
+  font-size: 0.8em;
+  font-weight: 400;
+  line-height: 1.25
+}
+
+.algolia-autocomplete .algolia-docsearch-footer {
+  width: 110px;
+  height: 20px;
+  z-index: 3;
+  margin-top: 10.66667px;
+  float: right;
+  font-size: 0;
+  line-height: 0;
+}
+
+.algolia-autocomplete .algolia-docsearch-footer--logo {
+  background-image: url("data:image/svg+xml;utf8,");
+  background-repeat: no-repeat;
+  background-position: 50%;
+  background-size: 100%;
+  overflow: hidden;
+  text-indent: -9000px;
+  width: 100%;
+  height: 100%;
+  display: block;
+  transform: translate(-8px);
+}
+
+.algolia-autocomplete .algolia-docsearch-suggestion--highlight {
+  color: #FF8C00;
+  background: rgba(232, 189, 54, 0.1)
+}
+
+
+.algolia-autocomplete .algolia-docsearch-suggestion--text .algolia-docsearch-suggestion--highlight {
+  box-shadow: inset 0 -2px 0 0 rgba(105, 105, 105, .5)
+}
+
+.algolia-autocomplete .ds-suggestion.ds-cursor .algolia-docsearch-suggestion--content {
+  background-color: rgba(192, 192, 192, .15)
+}
diff --git a/docs/docsearch.js b/docs/docsearch.js
new file mode 100644
index 0000000..b35504c
--- /dev/null
+++ b/docs/docsearch.js
@@ -0,0 +1,85 @@
+$(function() {
+
+  // register a handler to move the focus to the search bar
+  // upon pressing shift + "/" (i.e. "?")
+  $(document).on('keydown', function(e) {
+    if (e.shiftKey && e.keyCode == 191) {
+      e.preventDefault();
+      $("#search-input").focus();
+    }
+  });
+
+  $(document).ready(function() {
+    // do keyword highlighting
+    /* modified from https://jsfiddle.net/julmot/bL6bb5oo/ */
+    var mark = function() {
+
+      var referrer = document.URL ;
+      var paramKey = "q" ;
+
+      if (referrer.indexOf("?") !== -1) {
+        var qs = referrer.substr(referrer.indexOf('?') + 1);
+        var qs_noanchor = qs.split('#')[0];
+        var qsa = qs_noanchor.split('&');
+        var keyword = "";
+
+        for (var i = 0; i < qsa.length; i++) {
+          var currentParam = qsa[i].split('=');
+
+          if (currentParam.length !== 2) {
+            continue;
+          }
+
+          if (currentParam[0] == paramKey) {
+            keyword = decodeURIComponent(currentParam[1].replace(/\+/g, "%20"));
+          }
+        }
+
+        if (keyword !== "") {
+          $(".contents").unmark({
+            done: function() {
+              $(".contents").mark(keyword);
+            }
+          });
+        }
+      }
+    };
+
+    mark();
+  });
+});
+
+/* Search term highlighting ------------------------------*/
+
+function matchedWords(hit) {
+  var words = [];
+
+  var hierarchy = hit._highlightResult.hierarchy;
+  // loop to fetch from lvl0, lvl1, etc.
+  for (var idx in hierarchy) {
+    words = words.concat(hierarchy[idx].matchedWords);
+  }
+
+  var content = hit._highlightResult.content;
+  if (content) {
+    words = words.concat(content.matchedWords);
+  }
+
+  // return unique words
+  var words_uniq = [...new Set(words)];
+  return words_uniq;
+}
+
+function updateHitURL(hit) {
+
+  var words = matchedWords(hit);
+  var url = "";
+
+  if (hit.anchor) {
+    url = hit.url_without_anchor + '?q=' + escape(words.join(" ")) + '#' + hit.anchor;
+  } else {
+    url = hit.url + '?q=' + escape(words.join(" "));
+  }
+
+  return url;
+}
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z@
+
+
+
+
+
+
+A ggplot2 Based Implementation of Biplots • ggbiplot
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+    
+
+    
    
+      
    
+
+
+      
+
+      
    
+  
    
+
+
+
    This repo for the ggbiplot package  was forked from https://github.com/vqv/ggbiplot by Vince Yu, which has been dormant since 2015.
    
+
    The goal is to complete that development and publish a new version on CRAN with Vince Yu as the principal author. There is also an experimental branch which attempts to simplify the code, but this has some unresolved problems.
    
+
    
+
    ggbiplot 
+
    
+
    This package provides a ggplot2 implementation of the biplot, a simultaneous plot of scores for observations and vectors for variables for principal component-like analyses.
    
+The package provides two main functions: ggscreeplot() and ggbiplot().
    
+
    ggbiplot aims to be a drop-in replacement for the built-in R function biplot.princomp() with extended functionality for labeling groups, drawing a correlation circle, and adding data ellipsoids.
    
+
    
+
    Installation
+
    
+
    Install the current master branch with:
    
+
    +remotes::install_github("friendly/ggbiplot")
    
+
    
+
    
+
    Examples
+
    
+
    Load packages:
    
+
    +library(ggplot2)
+library(ggbiplot)
+library(dplyr)
+library(corrplot)
+
+# set ggplot2 theme
+theme_set(theme_minimal(base_size = 14))
    
+
    
+
    Crime data
+
    
+
    The crime data gives rates of various serious crimes in each of the 50 U. S. states, originally from the United States Statistical Abstracts (1970).
    
+
    Let’s take a quick look at the correlations among these, using corrplot::corrplot() and showing each correlation by an ellipse whose eccentricity and shading represents the value of the correlation.
    
+
    +data(crime)
+crime |> 
+  dplyr::select(where(is.numeric)) |> 
+  cor() |> 
+  corrplot(method = "ellipse", tl.srt = 0)
    
+
    
+
    The correlations are all positive. Note also that the variables in the dataset are ordered in seriousness or violence, ranging from murder to auto theft.
    
+
    Carry out a PCA:
    
+
    +crime.pca <- 
+  crime |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)
+
+crime.pca
+#> Standard deviations (1, .., p=7):
+#> [1] 2.029 1.113 0.852 0.563 0.508 0.471 0.352
+#> 
+#> Rotation (n x k) = (7 x 7):
+#>             PC1     PC2     PC3     PC4     PC5     PC6     PC7
+#> murder   -0.300 -0.6292  0.1782 -0.2321  0.5381  0.2591  0.2676
+#> rape     -0.432 -0.1694 -0.2442  0.0622  0.1885 -0.7733 -0.2965
+#> robbery  -0.397  0.0422  0.4959 -0.5580 -0.5200 -0.1144 -0.0039
+#> assault  -0.397 -0.3435 -0.0695  0.6298 -0.5067  0.1724  0.1917
+#> burglary -0.440  0.2033 -0.2099 -0.0576  0.1010  0.5360 -0.6481
+#> larceny  -0.357  0.4023 -0.5392 -0.2349  0.0301  0.0394  0.6017
+#> auto     -0.295  0.5024  0.5684  0.4192  0.3698 -0.0573  0.1470
    
+
    The biplot, using default scaling (standardized components), and labeling the states by their state abbreviation:
    
+
    +ggbiplot(crime.pca,
+         labels = crime$st ,
+         circle = TRUE,
+         varname.size = 4,
+         varname.color = "red") 
    
+
    
+
    The directions of the principal components are arbitrary; we are free to reflect the variable vectors and component scores to facilitate interpretation. Also, there seem to be differences among regions of the U.S., which can be visualized using data ellipses for the component scores. The groups argument allows the observations to colored by group and to summarized by groups.
    
+
    +crime.pca <- reflect(crime.pca)
+ggbiplot(crime.pca,
+         groups = crime$region,
+         labels = crime$st,
+         labels.size = 4,
+         var.factor = 1.4,
+         ellipse = TRUE, ellipse.level = 0.5, ellipse.alpha = 0.1,
+         circle = TRUE,
+         varname.size = 4,
+         varname.color = "black") +
+  labs(fill = "Region", color = "Region") +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
    
+
    
+
    The interpretation of the data is now clear.
    
+
      
+
    • The first dimension, accounting for 58.8% of variance, can be seen to represent overall crime rate, with Nevada (NV) at the high end and North Dakota (ND), South Dakota (SD) and West Virginia (WV) at the low end.
      • 
+
    • The second dimension, accounting for 17.7% of variance represents a contrast between personal crime vs. property crime. On this dimension, Massachusetts (MA), Rhode Island (RI) are opposed to Mississippi (MS), Alabama (AL), Louisiana (LA) and South Carolina (SC).
      • 
+
    • The regions are represented by the differences in the centers of the data ellipses for the scores. Southern states are highest on murder, assault and rape, while the Northeast states are highest on auto theft and larceny.
      • 
+
    • In this standardized view, the angles between variable vectors approximate the correlations among the variables, according to cos (angle) ≈ r. Thus, murder and auto, nearly 90o reflect a near 0 correlation.
      • 
+
    
+
    
+
    
+
    Wine data
+
    
+
    The wine data contains results of a chemical analysis of wines grown in the same region in Italy, derived from three different cultivars. The analysis determined the quantities of 13 chemical constituents found in each of the three types of wines. The grape varieties (cultivars), barolo, barbera, and grignolino, are given in wine.class.
    
+
    What can we understand about the differences among these wines from a biplot?
    
+
    +library(ggbiplot)
+library(ggplot2)
+library(dplyr)
+
+data(wine)
+wine.pca <- prcomp(wine, scale. = TRUE)
+ggscreeplot(wine.pca) 
    
+
    
+
    Hmm. The screeplot shows that more than two dimensions are necessary to account for most of the variance.
    
+
    Plot the first two PCA dimensions, accounting for 55% of the variance.
    
+
    +ggbiplot(wine.pca, 
+  obs.scale = 1, var.scale = 1,
+  groups = wine.class, 
+  ellipse = TRUE, 
+  circle = TRUE) +
+  labs(fill = "Cultivar", color = "Cultivar") +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
    
+
    
+
    The three cultivars are arranged along the first dimension, in the order barolo < grignolino < barbera. These are distinguished largely by a contrast between (Phenols, Flav) vs. (NonFlavPhenols, AlcAsh). The second dimension is represented by the cluster of variables Mg, Alcohol, Ash, Color, which distinguishes grignolino from the other two.
    
+
    
+
    
+
    Iris data
+
    
+
    +data(iris)
+iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
+                    data=iris,
+                    scale. = TRUE)
+summary(iris.pca)
+#> Importance of components:
+#>                         PC1   PC2    PC3     PC4
+#> Standard deviation     1.71 0.956 0.3831 0.14393
+#> Proportion of Variance 0.73 0.229 0.0367 0.00518
+#> Cumulative Proportion  0.73 0.958 0.9948 1.00000
    
+
    Plot the first two dimensions:
    
+
    +iris.gg <-
+ggbiplot(iris.pca, obs.scale = 1, var.scale = 1,
+         groups = iris$Species, point.size=2,
+         varname.size = 5, 
+         varname.color = "black",
+         varname.adjust = 1.2,
+         ellipse = TRUE, 
+         circle = TRUE) +
+  labs(fill = "Species", color = "Species") +
+  theme_minimal(base_size = 14) +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
+
+iris.gg
    
+
    
+
    It is possible to add annotations to the biplot by making use of the fact that ggplot() returns a lot of information in the "gg" object. In particular, the $data component contains the scores on the principal components that are plotted as points here. Here we add direct labels for the groups and suppress the legend.
    
+
    +# get means of coordinates by group
+group.labs <-
+  iris.gg$data |>
+  summarise(xvar = mean(xvar),
+            yvar = mean(yvar), .by = groups)
+
+group.labs
+#>       groups   xvar   yvar
+#> 1     setosa -2.217 -0.288
+#> 2 versicolor  0.495  0.548
+#> 3  virginica  1.723 -0.260
    
+
    Now, just use geom_label to draw labels for the groups.
    
+
    +iris.gg + geom_label(data = group.labs,
+                     aes(x = xvar, y=yvar, label=groups),
+                     size = 5) +
+  theme(legend.position = "none")
    
+
    
+
    
+
    
+
    
+
+  
    
+
+  
+
    
+
+
+      
    
+  
    
+
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    
+
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
    
+
+  
+
+
+  
+
+  
+
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diff --git a/docs/news/index.html b/docs/news/index.html
new file mode 100644
index 0000000..e74410a
--- /dev/null
+++ b/docs/news/index.html
@@ -0,0 +1,105 @@
+
+Changelog • ggbiplot
+    
+
+    
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+      
    Changelog 
    
+      Source: NEWS.md
+    
    
+
+    
    
+
    Version 0.6.1
    
+
    • Revised documentation for ggscreeplot()
+
      • 
+
    • 
+data(crime) used in README giving a more complete example.
      • 
+
    • Fixed links reported as 301s
      • 
+
    
+    
    
+
    Version 0.6.0
    
+
    • Use geom_polygon() rather than geom_path() for ellipses to allow them to be filled.
      • 
+
    • Added var.factor argument to expand or reflect the variable vectors
      • 
+
    • Moved points/labels code earlier so ellipses and variable vectors are not obscured
      • 
+
    • Replaced internal calculation of ellipses with stat_ellipse()
+
      • 
+
    • Now allow ellipses to be filled (geom_polygon()) or unfilled (geom_path())
      • 
+
    • Added hex logo
      • 
+
    • Added iris example to README
      • 
+
    • Removed Imports: dplyr, purrr as no longer needed
      • 
+
    
+    
    
+
    Version 0.56
    
+
    • Fixed many documentation errors and warnings
      • 
+
    • Use roxygen2 for documentation
      • 
+
    • added varname.color to replace fixed muted("red")
+
      • 
+
    • tweaked arrow style
      • 
+
    • increased default thickness of variable vectors
      • 
+
    • add point.size argument
      • 
+
    
+  
    
+
+  
+
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
+  
+
+
+  
+
+  
+
diff --git a/docs/pkgdown.css b/docs/pkgdown.css
new file mode 100644
index 0000000..80ea5b8
--- /dev/null
+++ b/docs/pkgdown.css
@@ -0,0 +1,384 @@
+/* Sticky footer */
+
+/**
+ * Basic idea: https://philipwalton.github.io/solved-by-flexbox/demos/sticky-footer/
+ * Details: https://github.com/philipwalton/solved-by-flexbox/blob/master/assets/css/components/site.css
+ *
+ * .Site -> body > .container
+ * .Site-content -> body > .container .row
+ * .footer -> footer
+ *
+ * Key idea seems to be to ensure that .container and __all its parents__
+ * have height set to 100%
+ *
+ */
+
+html, body {
+  height: 100%;
+}
+
+body {
+  position: relative;
+}
+
+body > .container {
+  display: flex;
+  height: 100%;
+  flex-direction: column;
+}
+
+body > .container .row {
+  flex: 1 0 auto;
+}
+
+footer {
+  margin-top: 45px;
+  padding: 35px 0 36px;
+  border-top: 1px solid #e5e5e5;
+  color: #666;
+  display: flex;
+  flex-shrink: 0;
+}
+footer p {
+  margin-bottom: 0;
+}
+footer div {
+  flex: 1;
+}
+footer .pkgdown {
+  text-align: right;
+}
+footer p {
+  margin-bottom: 0;
+}
+
+img.icon {
+  float: right;
+}
+
+/* Ensure in-page images don't run outside their container */
+.contents img {
+  max-width: 100%;
+  height: auto;
+}
+
+/* Fix bug in bootstrap (only seen in firefox) */
+summary {
+  display: list-item;
+}
+
+/* Typographic tweaking ---------------------------------*/
+
+.contents .page-header {
+  margin-top: calc(-60px + 1em);
+}
+
+dd {
+  margin-left: 3em;
+}
+
+/* Section anchors ---------------------------------*/
+
+a.anchor {
+  display: none;
+  margin-left: 5px;
+  width: 20px;
+  height: 20px;
+
+  background-image: url(./link.svg);
+  background-repeat: no-repeat;
+  background-size: 20px 20px;
+  background-position: center center;
+}
+
+h1:hover .anchor,
+h2:hover .anchor,
+h3:hover .anchor,
+h4:hover .anchor,
+h5:hover .anchor,
+h6:hover .anchor {
+  display: inline-block;
+}
+
+/* Fixes for fixed navbar --------------------------*/
+
+.contents h1, .contents h2, .contents h3, .contents h4 {
+  padding-top: 60px;
+  margin-top: -40px;
+}
+
+/* Navbar submenu --------------------------*/
+
+.dropdown-submenu {
+  position: relative;
+}
+
+.dropdown-submenu>.dropdown-menu {
+  top: 0;
+  left: 100%;
+  margin-top: -6px;
+  margin-left: -1px;
+  border-radius: 0 6px 6px 6px;
+}
+
+.dropdown-submenu:hover>.dropdown-menu {
+  display: block;
+}
+
+.dropdown-submenu>a:after {
+  display: block;
+  content: " ";
+  float: right;
+  width: 0;
+  height: 0;
+  border-color: transparent;
+  border-style: solid;
+  border-width: 5px 0 5px 5px;
+  border-left-color: #cccccc;
+  margin-top: 5px;
+  margin-right: -10px;
+}
+
+.dropdown-submenu:hover>a:after {
+  border-left-color: #ffffff;
+}
+
+.dropdown-submenu.pull-left {
+  float: none;
+}
+
+.dropdown-submenu.pull-left>.dropdown-menu {
+  left: -100%;
+  margin-left: 10px;
+  border-radius: 6px 0 6px 6px;
+}
+
+/* Sidebar --------------------------*/
+
+#pkgdown-sidebar {
+  margin-top: 30px;
+  position: -webkit-sticky;
+  position: sticky;
+  top: 70px;
+}
+
+#pkgdown-sidebar h2 {
+  font-size: 1.5em;
+  margin-top: 1em;
+}
+
+#pkgdown-sidebar h2:first-child {
+  margin-top: 0;
+}
+
+#pkgdown-sidebar .list-unstyled li {
+  margin-bottom: 0.5em;
+}
+
+/* bootstrap-toc tweaks ------------------------------------------------------*/
+
+/* All levels of nav */
+
+nav[data-toggle='toc'] .nav > li > a {
+  padding: 4px 20px 4px 6px;
+  font-size: 1.5rem;
+  font-weight: 400;
+  color: inherit;
+}
+
+nav[data-toggle='toc'] .nav > li > a:hover,
+nav[data-toggle='toc'] .nav > li > a:focus {
+  padding-left: 5px;
+  color: inherit;
+  border-left: 1px solid #878787;
+}
+
+nav[data-toggle='toc'] .nav > .active > a,
+nav[data-toggle='toc'] .nav > .active:hover > a,
+nav[data-toggle='toc'] .nav > .active:focus > a {
+  padding-left: 5px;
+  font-size: 1.5rem;
+  font-weight: 400;
+  color: inherit;
+  border-left: 2px solid #878787;
+}
+
+/* Nav: second level (shown on .active) */
+
+nav[data-toggle='toc'] .nav .nav {
+  display: none; /* Hide by default, but at >768px, show it */
+  padding-bottom: 10px;
+}
+
+nav[data-toggle='toc'] .nav .nav > li > a {
+  padding-left: 16px;
+  font-size: 1.35rem;
+}
+
+nav[data-toggle='toc'] .nav .nav > li > a:hover,
+nav[data-toggle='toc'] .nav .nav > li > a:focus {
+  padding-left: 15px;
+}
+
+nav[data-toggle='toc'] .nav .nav > .active > a,
+nav[data-toggle='toc'] .nav .nav > .active:hover > a,
+nav[data-toggle='toc'] .nav .nav > .active:focus > a {
+  padding-left: 15px;
+  font-weight: 500;
+  font-size: 1.35rem;
+}
+
+/* orcid ------------------------------------------------------------------- */
+
+.orcid {
+  font-size: 16px;
+  color: #A6CE39;
+  /* margins are required by official ORCID trademark and display guidelines */
+  margin-left:4px;
+  margin-right:4px;
+  vertical-align: middle;
+}
+
+/* Reference index & topics ----------------------------------------------- */
+
+.ref-index th {font-weight: normal;}
+
+.ref-index td {vertical-align: top; min-width: 100px}
+.ref-index .icon {width: 40px;}
+.ref-index .alias {width: 40%;}
+.ref-index-icons .alias {width: calc(40% - 40px);}
+.ref-index .title {width: 60%;}
+
+.ref-arguments th {text-align: right; padding-right: 10px;}
+.ref-arguments th, .ref-arguments td {vertical-align: top; min-width: 100px}
+.ref-arguments .name {width: 20%;}
+.ref-arguments .desc {width: 80%;}
+
+/* Nice scrolling for wide elements --------------------------------------- */
+
+table {
+  display: block;
+  overflow: auto;
+}
+
+/* Syntax highlighting ---------------------------------------------------- */
+
+pre, code, pre code {
+  background-color: #f8f8f8;
+  color: #333;
+}
+pre, pre code {
+  white-space: pre-wrap;
+  word-break: break-all;
+  overflow-wrap: break-word;
+}
+
+pre {
+  border: 1px solid #eee;
+}
+
+pre .img, pre .r-plt {
+  margin: 5px 0;
+}
+
+pre .img img, pre .r-plt img {
+  background-color: #fff;
+}
+
+code a, pre a {
+  color: #375f84;
+}
+
+a.sourceLine:hover {
+  text-decoration: none;
+}
+
+.fl      {color: #1514b5;}
+.fu      {color: #000000;} /* function */
+.ch,.st  {color: #036a07;} /* string */
+.kw      {color: #264D66;} /* keyword */
+.co      {color: #888888;} /* comment */
+
+.error   {font-weight: bolder;}
+.warning {font-weight: bolder;}
+
+/* Clipboard --------------------------*/
+
+.hasCopyButton {
+  position: relative;
+}
+
+.btn-copy-ex {
+  position: absolute;
+  right: 0;
+  top: 0;
+  visibility: hidden;
+}
+
+.hasCopyButton:hover button.btn-copy-ex {
+  visibility: visible;
+}
+
+/* headroom.js ------------------------ */
+
+.headroom {
+  will-change: transform;
+  transition: transform 200ms linear;
+}
+.headroom--pinned {
+  transform: translateY(0%);
+}
+.headroom--unpinned {
+  transform: translateY(-100%);
+}
+
+/* mark.js ----------------------------*/
+
+mark {
+  background-color: rgba(255, 255, 51, 0.5);
+  border-bottom: 2px solid rgba(255, 153, 51, 0.3);
+  padding: 1px;
+}
+
+/* vertical spacing after htmlwidgets */
+.html-widget {
+  margin-bottom: 10px;
+}
+
+/* fontawesome ------------------------ */
+
+.fab {
+    font-family: "Font Awesome 5 Brands" !important;
+}
+
+/* don't display links in code chunks when printing */
+/* source: https://stackoverflow.com/a/10781533 */
+@media print {
+  code a:link:after, code a:visited:after {
+    content: "";
+  }
+}
+
+/* Section anchors ---------------------------------
+   Added in pandoc 2.11: https://github.com/jgm/pandoc-templates/commit/9904bf71
+*/
+
+div.csl-bib-body { }
+div.csl-entry {
+  clear: both;
+}
+.hanging-indent div.csl-entry {
+  margin-left:2em;
+  text-indent:-2em;
+}
+div.csl-left-margin {
+  min-width:2em;
+  float:left;
+}
+div.csl-right-inline {
+  margin-left:2em;
+  padding-left:1em;
+}
+div.csl-indent {
+  margin-left: 2em;
+}
diff --git a/docs/pkgdown.js b/docs/pkgdown.js
new file mode 100644
index 0000000..6f0eee4
--- /dev/null
+++ b/docs/pkgdown.js
@@ -0,0 +1,108 @@
+/* http://gregfranko.com/blog/jquery-best-practices/ */
+(function($) {
+  $(function() {
+
+    $('.navbar-fixed-top').headroom();
+
+    $('body').css('padding-top', $('.navbar').height() + 10);
+    $(window).resize(function(){
+      $('body').css('padding-top', $('.navbar').height() + 10);
+    });
+
+    $('[data-toggle="tooltip"]').tooltip();
+
+    var cur_path = paths(location.pathname);
+    var links = $("#navbar ul li a");
+    var max_length = -1;
+    var pos = -1;
+    for (var i = 0; i < links.length; i++) {
+      if (links[i].getAttribute("href") === "#")
+        continue;
+      // Ignore external links
+      if (links[i].host !== location.host)
+        continue;
+
+      var nav_path = paths(links[i].pathname);
+
+      var length = prefix_length(nav_path, cur_path);
+      if (length > max_length) {
+        max_length = length;
+        pos = i;
+      }
+    }
+
+    // Add class to parent 
  • , and enclosing 
  •  if in dropdown
+    if (pos >= 0) {
+      var menu_anchor = $(links[pos]);
+      menu_anchor.parent().addClass("active");
+      menu_anchor.closest("li.dropdown").addClass("active");
+    }
+  });
+
+  function paths(pathname) {
+    var pieces = pathname.split("/");
+    pieces.shift(); // always starts with /
+
+    var end = pieces[pieces.length - 1];
+    if (end === "index.html" || end === "")
+      pieces.pop();
+    return(pieces);
+  }
+
+  // Returns -1 if not found
+  function prefix_length(needle, haystack) {
+    if (needle.length > haystack.length)
+      return(-1);
+
+    // Special case for length-0 haystack, since for loop won't run
+    if (haystack.length === 0) {
+      return(needle.length === 0 ? 0 : -1);
+    }
+
+    for (var i = 0; i < haystack.length; i++) {
+      if (needle[i] != haystack[i])
+        return(i);
+    }
+
+    return(haystack.length);
+  }
+
+  /* Clipboard --------------------------*/
+
+  function changeTooltipMessage(element, msg) {
+    var tooltipOriginalTitle=element.getAttribute('data-original-title');
+    element.setAttribute('data-original-title', msg);
+    $(element).tooltip('show');
+    element.setAttribute('data-original-title', tooltipOriginalTitle);
+  }
+
+  if(ClipboardJS.isSupported()) {
+    $(document).ready(function() {
+      var copyButton = "";
+
+      $("div.sourceCode").addClass("hasCopyButton");
+
+      // Insert copy buttons:
+      $(copyButton).prependTo(".hasCopyButton");
+
+      // Initialize tooltips:
+      $('.btn-copy-ex').tooltip({container: 'body'});
+
+      // Initialize clipboard:
+      var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', {
+        text: function(trigger) {
+          return trigger.parentNode.textContent.replace(/\n#>[^\n]*/g, "");
+        }
+      });
+
+      clipboardBtnCopies.on('success', function(e) {
+        changeTooltipMessage(e.trigger, 'Copied!');
+        e.clearSelection();
+      });
+
+      clipboardBtnCopies.on('error', function() {
+        changeTooltipMessage(e.trigger,'Press Ctrl+C or Command+C to copy');
+      });
+    });
+  }
+})(window.jQuery || window.$)
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
new file mode 100644
index 0000000..4fb802c
--- /dev/null
+++ b/docs/pkgdown.yml
@@ -0,0 +1,6 @@
+pandoc: 3.1.2
+pkgdown: 2.0.7
+pkgdown_sha: ~
+articles: {}
+last_built: 2023-12-06T03:00Z
+
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diff --git a/docs/reference/crime.html b/docs/reference/crime.html
new file mode 100644
index 0000000..d8c1b30
--- /dev/null
+++ b/docs/reference/crime.html
@@ -0,0 +1,156 @@
+
+U. S. Crimes — crime • ggbiplot
+    
+
+    
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+    
    U. S. Crimes
    
+    Source: R/crime.R
+    
+    
    
+
+    
    
+    
    This dataset gives rates of occurrence (per 100,000 people)
+various serious crimes in each of the 50 U. S. states, 
+originally from the United States Statistical Abstracts (1970). The data
+were analyzed by John Hartigan (1975) in his book Clustering Algorithms and 
+were later reanalyzed by Friendly (1991).
    
+    
    
+
+    
    
+    
    data(crime)
    
+    
    
+
+    
    
+    
    Format
    
+    
    A data frame with 50 observations on the following 10 variables.
    state
    
+
    state name, a character vector
    
+
+  
    murder
    
+
    a numeric vector
    
+
+  
    rape
    
+
    a numeric vector
    
+
+  
    robbery
    
+
    a numeric vector
    
+
+  
    assault
    
+
    a numeric vector
    
+
+  
    burglary
    
+
    a numeric vector
    
+
+  
    larceny
    
+
    a numeric vector
    
+
+  
    auto
    
+
    auto thefts, a numeric vector
    
+
+  
    st
    
+
    state abbreviation, a character vector
    
+
+  
    region
    
+
    region of the U.S., a factor with levels Northeast South North Central West
    
+
+
+
    
+    
    
+    
    Source
    
+    
    The data are originally from the United States Statistical Abstracts (1970).
+This dataset also appears in the SAS/Stat Sample library,
+Getting Started Example for PROC PRINCOMP, 
+https://support.sas.com/documentation/onlinedoc/stat/ex_code/131/princgs.html, from which the
+current copy was derived.
    
+    
    
+    
    
+    
    References
    
+    
    Friendly, M. (1991). SAS System for Statistical Graphics. SAS Institute.
    
+
    Hartigan, J. A. (1975). Clustering Algorithms. John Wiley and Sons.
    
+    
    
+
+    
    
+    
    Examples
    
+    
    data(crime)
+library(ggplot2)
+crime.pca <- 
+  crime |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)
+
+ggbiplot(crime.pca,
+     labels = crime$st ,
+     circle = TRUE,
+     varname.size = 4,
+     varname.color = "red") +
+ theme_minimal(base_size = 14) 
+
+
    
+    
    
+  
    
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
+  
+
+
+  
+
+  
+
diff --git a/docs/reference/figures/README-crime-biplot0-1.png b/docs/reference/figures/README-crime-biplot0-1.png
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diff --git a/docs/reference/ggscreeplot.html b/docs/reference/ggscreeplot.html
new file mode 100644
index 0000000..f4a5461
--- /dev/null
+++ b/docs/reference/ggscreeplot.html
@@ -0,0 +1,121 @@
+
+Screeplot for Principal Components — ggscreeplot • ggbiplot
+    
+
+    
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+    
    Screeplot for Principal Components
    
+    Source: R/ggscreeplot.R
+    
+    
    
+
+    
    
+    
    Produces scree plots (Cattell, 1966) of the variance proportions explained by each dimension against dimension number from 
+various dimension reduction techniques
    
+    
    
+
+    
    
+    
    ggscreeplot(pcobj, type = c("pev", "cev"), size = 4)
    
+    
    
+
+    
    
+    
    Arguments
    
+    
    pcobj
    
+
    an object representing a linear dimension technique, such a returned by prcomp 
+or princomp or PCA or lda
    
+
+
+
    type
    
+
    the type of scree plot.
+'pev' corresponds proportion of explained variance, i.e. the eigenvalues divided by the trace. 
+'cev' corresponds to the cumulative proportion of explained variance, i.e. the partial sum of the first k eigenvalues divided by the trace.
    
+
+
+
    size
    
+
    point size
    
+
+
    
+    
    
+    
    Value
    
+    
+
+
    A ggplot2 object
    
+    
    
+    
    
+    
    References
    
+    
    Cattell, R. B. (1966). The Scree Test For The Number Of Factors. Multivariate Behavioral Research, 1, 245–276.
    
+    
    
+
+    
    
+    
    Examples
    
+    
      data(wine)
+  wine.pca <- prcomp(wine, scale. = TRUE)
+  ggscreeplot(wine.pca)
+
+
+
    
+    
    
+  
    
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
+  
+
+
+  
+
+  
+
diff --git a/docs/reference/index.html b/docs/reference/index.html
new file mode 100644
index 0000000..fcf7d48
--- /dev/null
+++ b/docs/reference/index.html
@@ -0,0 +1,97 @@
+
+Function reference • ggbiplot
+    
+
+    
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+      
    Reference
    
+    
    
+
+    
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
    
+          
    All functions 
    
+          
    
+        
    
+          
    crime 
    
+        
    U. S. Crimes
    
+          
    ggbiplot() 
    
+        
    Biplot for Principal Components using ggplot2
    
+          
    ggscreeplot() 
    
+        
    Screeplot for Principal Components
    
+          
    reflect() 
    
+        
    Reflect Columns in a Principal Component-like Object
    
+          
    wine 
    
+        
    Wine dataset
    
+
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
+  
+
+
+  
+
+  
+
diff --git a/docs/reference/reflect-1.png b/docs/reference/reflect-1.png
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diff --git a/docs/reference/reflect.html b/docs/reference/reflect.html
new file mode 100644
index 0000000..ddcefc7
--- /dev/null
+++ b/docs/reference/reflect.html
@@ -0,0 +1,137 @@
+
+Reflect Columns in a Principal Component-like Object — reflect • ggbiplot
+    
+
+    
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+    
    Reflect Columns in a Principal Component-like Object
    
+    Source: R/reflect.R
+    
+    
    
+
+    
    
+    
    Principle component-like objects have variable loadings (the eigenvectors of the covariance/correlation matrix)
+whose signs are arbitrary, in the sense that a given column can be 
+reflected (multiplied by -1) without changing the fit.
    
+    
    
+
+    
    
+    
    reflect(pcobj, columns = 1:2)
    
+    
    
+
+    
    
+    
    Arguments
    
+    
    pcobj
    
+
    an object returned by prcomp, princomp, 
+PCA, or lda
    
+
+
+
    columns
    
+
    a vector of indices of the columns to reflect
    
+
+
    
+    
    
+    
    Value
    
+    
+
+
    The pca-like object with specified columns of the 
+           variable loadings and observation scores multiplied
+           by -1.
    
+    
    
+    
    
+    
    Details
    
+    
    This function allows one to reflect any columns of the variable
+loadings (and corresponding observation scores). This is often
+useful for interpreting a biplot, for example when a component (often the first) has all negative signs.
    
+    
    
+    
    
+    
    See also
    
+    
    prcomp,  princomp, 
+         PCA, lda
    
+    
    
+    
    
+    
    Author
    
+    
    Michael Friendly
    
+    
    
+
+    
    
+    
    Examples
    
+    
    data(crime)
+crime.pca <- 
+  crime |> 
+  dplyr::select(where(is.numeric)) |>
+  prcomp(scale. = TRUE)
+  
+ biplot(crime.pca)
+
+ 
+ crime.pca <- reflect(crime.pca)  # reflect columns 1:2
+ biplot(crime.pca)
+
+
    
+    
    
+  
    
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+
+  
+
+
+  
+
+  
+
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z@
Date: Sun, 10 Dec 2023 22:48:56 -0500
Subject: [PATCH 49/80] biplot-packages.xlsx

---
 discussion/biplot-packages.xlsx | Bin 0 -> 10923 bytes
 examples/crime-ex.R             |   8 ++++++++
 2 files changed, 8 insertions(+)
 create mode 100644 discussion/biplot-packages.xlsx

diff --git a/discussion/biplot-packages.xlsx b/discussion/biplot-packages.xlsx
new file mode 100644
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zn?5J=f0~*Q{bBl?+CTU3oPYl5;r!+EG5AL|`rP4jw(_S#T+-hTpK+Cc 
+  dplyr::select(where(is.numeric)) |>
+  PCA()
+
+crime.PCA$var$cor

From 368b993875f034efa35b22bdb4957e640088c0b1 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Sun, 10 Dec 2023 22:50:14 -0500
Subject: [PATCH 50/80] update biplot-packages.Rmd

---
 discussion/biplot-packages.Rmd | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/discussion/biplot-packages.Rmd b/discussion/biplot-packages.Rmd
index 58be4a1..dc2fbd7 100644
--- a/discussion/biplot-packages.Rmd
+++ b/discussion/biplot-packages.Rmd
@@ -51,9 +51,12 @@ My problem, as a **user** and **explainer** is that with none of these can I
 ## Current state: What packages exist?
 
 * **base R**: `prcomp()`, `princomp()` --> [`biplot()`](https://rdrr.io/r/stats/biplot.html)
+Tutorial: https://www.benjaminbell.co.uk/2018/02/principal-components-analysis-pca-in-r.html
 
 * [**FactoMineR**](https://cran.r-project.org/package=FactoMineR), [**factoextra**](https://rpkgs.datanovia.com/factoextra/): [`PCA()`](https://rdrr.io/cran/FactoMineR/man/PCA.html) --> [`fviz_pca()`](https://rpkgs.datanovia.com/factoextra/reference/fviz_pca.html), `fviz_pca_ind()`, `fviz_pca_var()`
 
+Tutorials: https://medium.com/@RaharditoDP/principal-component-analysis-with-biplot-analysis-in-r-ee39d17096a1
+
 * [**adegraphics**](https://cran.r-project.org/package=adegraphics) Lattice-based. Development of `ade4`, "dudi" framework -> `biplot()`
   + [**biplot2d3d**](https://github.com/Andros-Spica/biplot2d3d) By Andreas Angourakis. Uses **ade4*, **heplots** and **rgl**.
 

From 8bad4d273296abb1859f1b8f55596bf41f04649c Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 14 Dec 2023 13:56:39 -0500
Subject: [PATCH 51/80] misc changes for submission

---
 .Rbuildignore                    |   3 +++
 R/reflect.R                      |   1 +
 _pkgdown.yaml.R => _pkgdown.yaml |   0
 cran-comments.md                 |   2 +-
 discussion/biplot-packages.xlsx  | Bin 10923 -> 11089 bytes
 5 files changed, 5 insertions(+), 1 deletion(-)
 rename _pkgdown.yaml.R => _pkgdown.yaml (100%)

diff --git a/.Rbuildignore b/.Rbuildignore
index 6e2becd..645733f 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -5,3 +5,6 @@
 examples/
 discussion/
 ^cran-comments\.md$
+docs/
+pkgdown/
+_pkgdown.yaml
diff --git a/R/reflect.R b/R/reflect.R
index 2bea06f..cf1eb19 100644
--- a/R/reflect.R
+++ b/R/reflect.R
@@ -51,6 +51,7 @@ reflect <- function(pcobj, columns = 1:2){
     pcobj$scores[, columns]   <- -1 * pcobj$scores[, columns]
   } 
   else if(inherits(pcobj, 'PCA')) {
+    # TODO: reflect quanti.sup$coords if that is present
     check(pcobj$var$coord, columns)
     pcobj$var$coord[, columns] <- -1 * pcobj$var$coord[, columns]
     pcobj$ind$coord[, columns]   <- -1 * pcobj$ind$coord[, columns]
diff --git a/_pkgdown.yaml.R b/_pkgdown.yaml
similarity index 100%
rename from _pkgdown.yaml.R
rename to _pkgdown.yaml
diff --git a/cran-comments.md b/cran-comments.md
index 52cc416..9375e6e 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -7,7 +7,7 @@
 
 0 errors | 0 warnings | 1 note
 
-* This is considered a new release, against last the published CRAN version, 0.55, due to a change in maintainer.
+* This is considered a new release, against the previously published CRAN version, 0.55, due to a change in maintainer.
 
 * Possibly misspelled words in DESCRIPTION:
   Biplots (3:42)
diff --git a/discussion/biplot-packages.xlsx b/discussion/biplot-packages.xlsx
index 93d5881f6405b26f0590cfda09f0f5f41638aa48..d2e4721d4534e1bf6ba395bd7e803a25a9afd8f8 100644
GIT binary patch
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From 87f0305be89ab4960e9c5dd6cbe930f07b10fe8d Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 14 Dec 2023 14:00:35 -0500
Subject: [PATCH 52/80] tweak NEWS.md

---
 NEWS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/NEWS.md b/NEWS.md
index f09a982..fb4ac4f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -3,6 +3,7 @@
 - Revised documentation for `ggscreeplot()`
 - `data(crime)` used in README giving a more complete example.
 - Fixed links reported as 301s
+- Published pkgdown site
 
 ## Version 0.6.0
 

From af4b362c830a1bb678677b66413107d8213b9065 Mon Sep 17 00:00:00 2001
From: Michael Friendly 
Date: Thu, 14 Dec 2023 14:23:32 -0500
Subject: [PATCH 53/80] tweak README/rebuild

---
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diff --git a/.Rbuildignore b/.Rbuildignore
index 645733f..ff134b2 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -8,3 +8,4 @@ discussion/
 docs/
 pkgdown/
 _pkgdown.yaml
+^CRAN-SUBMISSION$
diff --git a/CRAN-SUBMISSION b/CRAN-SUBMISSION
new file mode 100644
index 0000000..0c2af67
--- /dev/null
+++ b/CRAN-SUBMISSION
@@ -0,0 +1,3 @@
+Version: 0.6.1
+Date: 2023-12-14 19:02:05 UTC
+SHA: 87f0305be89ab4960e9c5dd6cbe930f07b10fe8d
diff --git a/README.Rmd b/README.Rmd
index a2d0fc3..e7aceec 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -179,6 +179,7 @@ Plot the first two PCA dimensions, accounting for 55% of the variance.
 ggbiplot(wine.pca, 
   obs.scale = 1, var.scale = 1,
   groups = wine.class, 
+  varname.size = 4,
   ellipse = TRUE, 
   circle = TRUE) +
   labs(fill = "Cultivar", color = "Cultivar") +
@@ -192,6 +193,8 @@ grignolino from the other two.
 
 ### Iris data
 
+The classic iris data is widely used for examples of multivariate analysis and biplots, so let's use it here.
+
 ```{r iris-pca}
 data(iris)
 iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
diff --git a/README.md b/README.md
index d1e4ad3..b86b596 100644
--- a/README.md
+++ b/README.md
@@ -192,6 +192,7 @@ Plot the first two PCA dimensions, accounting for 55% of the variance.
 ggbiplot(wine.pca, 
   obs.scale = 1, var.scale = 1,
   groups = wine.class, 
+  varname.size = 4,
   ellipse = TRUE, 
   circle = TRUE) +
   labs(fill = "Cultivar", color = "Cultivar") +
@@ -209,6 +210,9 @@ two.
 
 ### Iris data
 
+The classic iris data is widely used for examples of multivariate
+analysis and biplots, so let’s use it here.
+
 ``` r
 data(iris)
 iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
diff --git a/_pkgdown.yaml b/_pkgdown.yaml
index 46da03d..1f9133c 100644
--- a/_pkgdown.yaml
+++ b/_pkgdown.yaml
@@ -15,7 +15,6 @@ reference:
       - reflect
   
   - title: "Data sets"
+    contents:
       - crime
       - wine
-
-      
\ No newline at end of file
diff --git a/docs/404.html b/docs/404.html
index f0512b9..f491bcd 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -4,106 +4,96 @@
 
 
 
-
+
 Page not found (404) • ggbiplot
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
+
+
+
 
-
-
-
+
+
 
 
-
+
+    Skip to contents
     
 
-    
    
-      
    
-  
    
-    
    
-      
    Page not found (404)
    
     
    
 
 Content not found. Please use links in the navbar.
 
-  
    
-
-  
 
-
    
 
-
-
-      
    
+    
    
   
    
 
    Developed by Vincent Vu, Michael Friendly.
    
 
    
 
-
    
+
    
   
    
 
    Site built with pkgdown 2.0.7.
    
 
    
 
-      
    
+    
    
 
    
 
   
 
-
   
 
   
diff --git a/docs/authors.html b/docs/authors.html
index 51fd016..146ee60 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,52 +1,50 @@
 
-Authors and Citation • ggbiplotAuthors and Citation • ggbiplot
+
+    Skip to contents
     
 
-    
    
-      
    
-  
    
-    
    
-      
    
-        
    Authors
    
-      
    
+    
+  
    
+
    
+
    
+  
    
+      
    Authors and Citation
    
+    
    
 
+    
    
+      
    Authors
    
       
       
    • 
           
      Vincent Vu. Author. 
@@ -61,45 +59,39 @@ 
      Authors
      
           
      
         
      • 
       
    
-    
    
-    
    
-      
    Citation
    
-      Source: DESCRIPTION
-    
    
-    
    
 
+    
    
+      
    Citation
    
+      
    Source: DESCRIPTION
    
 
-    
    Vu V, Friendly M (2023).
+      
    Vu V, Friendly M (2023).
 ggbiplot: A ggplot2 Based Implementation of Biplots.
 R package version 0.6.1, https://github.com/friendly/ggbiplot. 
 
    
-    
    @Manual{,
+      
    @Manual{,
   title = {ggbiplot: A ggplot2 Based Implementation of Biplots},
   author = {Vincent Vu and Michael Friendly},
   year = {2023},
   note = {R package version 0.6.1},
   url = {https://github.com/friendly/ggbiplot},
 }
    
-
-  
    
-
-
    
-
+    
    
+  
    
 
 
-      
    
+    
    
   
    Developed by Vincent Vu, Michael Friendly.
    
 
    
 
-
    
+
    
   
    Site built with pkgdown 2.0.7.
    
 
    
 
-      
    
+    
    
 
   
 
-
   
 
   
diff --git a/docs/deps/JetBrains_Mono-0.4.8/font.css b/docs/deps/JetBrains_Mono-0.4.8/font.css
new file mode 100644
index 0000000..395dd07
--- /dev/null
+++ b/docs/deps/JetBrains_Mono-0.4.8/font.css
@@ -0,0 +1,7 @@
+@font-face {
+  font-family: 'JetBrains Mono';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url(tDbY2o-flEEny0FZhsfKu5WU4zr3E_BX0PnT8RD8yKxjPg.woff) format('woff');
+}
diff --git a/docs/deps/JetBrains_Mono-0.4.8/tDbY2o-flEEny0FZhsfKu5WU4zr3E_BX0PnT8RD8yKxjPg.woff b/docs/deps/JetBrains_Mono-0.4.8/tDbY2o-flEEny0FZhsfKu5WU4zr3E_BX0PnT8RD8yKxjPg.woff
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new file mode 100644
index 0000000..cddf76e
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+++ b/docs/deps/Roboto-0.4.8/font.css
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H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
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")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t 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object[0] : object\n  }\n\n  if (typeof object === 'string' && object.length > 0) {\n    return document.querySelector(parseSelector(object))\n  }\n\n  return null\n}\n\nconst isVisible = element => {\n  if (!isElement(element) || element.getClientRects().length === 0) {\n    return false\n  }\n\n  const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'\n  // Handle `details` element as its content may falsie appear visible when it is closed\n  const closedDetails = element.closest('details:not([open])')\n\n  if (!closedDetails) {\n    return elementIsVisible\n  }\n\n  if (closedDetails !== element) {\n    const summary = element.closest('summary')\n    if (summary && summary.parentNode !== closedDetails) {\n      return false\n    }\n\n    if (summary === null) {\n      return false\n    }\n  }\n\n  return elementIsVisible\n}\n\nconst isDisabled = element => {\n  if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n    return true\n  }\n\n  if (element.classList.contains('disabled')) {\n    return true\n  }\n\n  if (typeof element.disabled !== 'undefined') {\n    return element.disabled\n  }\n\n  return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false'\n}\n\nconst findShadowRoot = element => {\n  if (!document.documentElement.attachShadow) {\n    return null\n  }\n\n  // Can find the shadow root otherwise it'll return the document\n  if (typeof element.getRootNode === 'function') {\n    const root = element.getRootNode()\n    return root instanceof ShadowRoot ? root : null\n  }\n\n  if (element instanceof ShadowRoot) {\n    return element\n  }\n\n  // when we don't find a shadow root\n  if (!element.parentNode) {\n    return null\n  }\n\n  return findShadowRoot(element.parentNode)\n}\n\nconst noop = () => {}\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n  element.offsetHeight // eslint-disable-line no-unused-expressions\n}\n\nconst getjQuery = () => {\n  if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n    return window.jQuery\n  }\n\n  return null\n}\n\nconst DOMContentLoadedCallbacks = []\n\nconst onDOMContentLoaded = callback => {\n  if (document.readyState === 'loading') {\n    // add listener on the first call when the document is in loading state\n    if (!DOMContentLoadedCallbacks.length) {\n      document.addEventListener('DOMContentLoaded', () => {\n        for (const callback of DOMContentLoadedCallbacks) {\n          callback()\n        }\n      })\n    }\n\n    DOMContentLoadedCallbacks.push(callback)\n  } else {\n    callback()\n  }\n}\n\nconst isRTL = () => document.documentElement.dir === 'rtl'\n\nconst defineJQueryPlugin = plugin => {\n  onDOMContentLoaded(() => {\n    const $ = getjQuery()\n    /* istanbul ignore if */\n    if ($) {\n      const name = plugin.NAME\n      const JQUERY_NO_CONFLICT = $.fn[name]\n      $.fn[name] = plugin.jQueryInterface\n      $.fn[name].Constructor = plugin\n      $.fn[name].noConflict = () => {\n        $.fn[name] = JQUERY_NO_CONFLICT\n        return plugin.jQueryInterface\n      }\n    }\n  })\n}\n\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n  return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue\n}\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n  if (!waitForTransition) {\n    execute(callback)\n    return\n  }\n\n  const durationPadding = 5\n  const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding\n\n  let called = false\n\n  const handler = ({ target }) => {\n    if (target !== transitionElement) {\n      return\n    }\n\n    called = true\n    transitionElement.removeEventListener(TRANSITION_END, handler)\n    execute(callback)\n  }\n\n  transitionElement.addEventListener(TRANSITION_END, handler)\n  setTimeout(() => {\n    if (!called) {\n      triggerTransitionEnd(transitionElement)\n    }\n  }, emulatedDuration)\n}\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list    The list of elements\n * @param activeElement   The active element\n * @param shouldGetNext   Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n  const listLength = list.length\n  let index = list.indexOf(activeElement)\n\n  // if the element does not exist in the list return an element\n  // depending on the direction and if cycle is allowed\n  if (index === -1) {\n    return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0]\n  }\n\n  index += shouldGetNext ? 1 : -1\n\n  if (isCycleAllowed) {\n    index = (index + listLength) % listLength\n  }\n\n  return list[Math.max(0, Math.min(index, listLength - 1))]\n}\n\nexport {\n  defineJQueryPlugin,\n  execute,\n  executeAfterTransition,\n  findShadowRoot,\n  getElement,\n  getjQuery,\n  getNextActiveElement,\n  getTransitionDurationFromElement,\n  getUID,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop,\n  onDOMContentLoaded,\n  parseSelector,\n  reflow,\n  triggerTransitionEnd,\n  toType\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { getjQuery } from '../util/index.js'\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/\nconst stripNameRegex = /\\..*/\nconst stripUidRegex = /::\\d+$/\nconst eventRegistry = {} // Events storage\nlet uidEvent = 1\nconst customEvents = {\n  mouseenter: 'mouseover',\n  mouseleave: 'mouseout'\n}\n\nconst nativeEvents = new Set([\n  'click',\n  'dblclick',\n  'mouseup',\n  'mousedown',\n  'contextmenu',\n  'mousewheel',\n  'DOMMouseScroll',\n  'mouseover',\n  'mouseout',\n  'mousemove',\n  'selectstart',\n  'selectend',\n  'keydown',\n  'keypress',\n  'keyup',\n  'orientationchange',\n  'touchstart',\n  'touchmove',\n  'touchend',\n  'touchcancel',\n  'pointerdown',\n  'pointermove',\n  'pointerup',\n  'pointerleave',\n  'pointercancel',\n  'gesturestart',\n  'gesturechange',\n  'gestureend',\n  'focus',\n  'blur',\n  'change',\n  'reset',\n  'select',\n  'submit',\n  'focusin',\n  'focusout',\n  'load',\n  'unload',\n  'beforeunload',\n  'resize',\n  'move',\n  'DOMContentLoaded',\n  'readystatechange',\n  'error',\n  'abort',\n  'scroll'\n])\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n  return (uid && `${uid}::${uidEvent++}`) || element.uidEvent || uidEvent++\n}\n\nfunction getElementEvents(element) {\n  const uid = makeEventUid(element)\n\n  element.uidEvent = uid\n  eventRegistry[uid] = eventRegistry[uid] || {}\n\n  return eventRegistry[uid]\n}\n\nfunction bootstrapHandler(element, fn) {\n  return function handler(event) {\n    hydrateObj(event, { delegateTarget: element })\n\n    if (handler.oneOff) {\n      EventHandler.off(element, event.type, fn)\n    }\n\n    return fn.apply(element, [event])\n  }\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n  return function handler(event) {\n    const domElements = element.querySelectorAll(selector)\n\n    for (let { target } = event; target && target !== this; target = target.parentNode) {\n      for (const domElement of domElements) {\n        if (domElement !== target) {\n          continue\n        }\n\n        hydrateObj(event, { delegateTarget: target })\n\n        if (handler.oneOff) {\n          EventHandler.off(element, event.type, selector, fn)\n        }\n\n        return fn.apply(target, [event])\n      }\n    }\n  }\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n  return Object.values(events)\n    .find(event => event.callable === callable && event.delegationSelector === delegationSelector)\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n  const isDelegated = typeof handler === 'string'\n  // TODO: tooltip passes `false` instead of selector, so we need to check\n  const callable = isDelegated ? delegationFunction : (handler || delegationFunction)\n  let typeEvent = getTypeEvent(originalTypeEvent)\n\n  if (!nativeEvents.has(typeEvent)) {\n    typeEvent = originalTypeEvent\n  }\n\n  return [isDelegated, callable, typeEvent]\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n  if (typeof originalTypeEvent !== 'string' || !element) {\n    return\n  }\n\n  let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n\n  // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n  // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n  if (originalTypeEvent in customEvents) {\n    const wrapFunction = fn => {\n      return function (event) {\n        if (!event.relatedTarget || (event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget))) {\n          return fn.call(this, event)\n        }\n      }\n    }\n\n    callable = wrapFunction(callable)\n  }\n\n  const events = getElementEvents(element)\n  const handlers = events[typeEvent] || (events[typeEvent] = {})\n  const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null)\n\n  if (previousFunction) {\n    previousFunction.oneOff = previousFunction.oneOff && oneOff\n\n    return\n  }\n\n  const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''))\n  const fn = isDelegated ?\n    bootstrapDelegationHandler(element, handler, callable) :\n    bootstrapHandler(element, callable)\n\n  fn.delegationSelector = isDelegated ? handler : null\n  fn.callable = callable\n  fn.oneOff = oneOff\n  fn.uidEvent = uid\n  handlers[uid] = fn\n\n  element.addEventListener(typeEvent, fn, isDelegated)\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n  const fn = findHandler(events[typeEvent], handler, delegationSelector)\n\n  if (!fn) {\n    return\n  }\n\n  element.removeEventListener(typeEvent, fn, Boolean(delegationSelector))\n  delete events[typeEvent][fn.uidEvent]\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n  const storeElementEvent = events[typeEvent] || {}\n\n  for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n    if (handlerKey.includes(namespace)) {\n      removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n    }\n  }\n}\n\nfunction getTypeEvent(event) {\n  // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n  event = event.replace(stripNameRegex, '')\n  return customEvents[event] || event\n}\n\nconst EventHandler = {\n  on(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, false)\n  },\n\n  one(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, true)\n  },\n\n  off(element, originalTypeEvent, handler, delegationFunction) {\n    if (typeof originalTypeEvent !== 'string' || !element) {\n      return\n    }\n\n    const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n    const inNamespace = typeEvent !== originalTypeEvent\n    const events = getElementEvents(element)\n    const storeElementEvent = events[typeEvent] || {}\n    const isNamespace = originalTypeEvent.startsWith('.')\n\n    if (typeof callable !== 'undefined') {\n      // Simplest case: handler is passed, remove that listener ONLY.\n      if (!Object.keys(storeElementEvent).length) {\n        return\n      }\n\n      removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null)\n      return\n    }\n\n    if (isNamespace) {\n      for (const elementEvent of Object.keys(events)) {\n        removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1))\n      }\n    }\n\n    for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n      const handlerKey = keyHandlers.replace(stripUidRegex, '')\n\n      if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n        removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n      }\n    }\n  },\n\n  trigger(element, event, args) {\n    if (typeof event !== 'string' || !element) {\n      return null\n    }\n\n    const $ = getjQuery()\n    const typeEvent = getTypeEvent(event)\n    const inNamespace = event !== typeEvent\n\n    let jQueryEvent = null\n    let bubbles = true\n    let nativeDispatch = true\n    let defaultPrevented = false\n\n    if (inNamespace && $) {\n      jQueryEvent = $.Event(event, args)\n\n      $(element).trigger(jQueryEvent)\n      bubbles = !jQueryEvent.isPropagationStopped()\n      nativeDispatch = !jQueryEvent.isImmediatePropagationStopped()\n      defaultPrevented = jQueryEvent.isDefaultPrevented()\n    }\n\n    const evt = hydrateObj(new Event(event, { bubbles, cancelable: true }), args)\n\n    if (defaultPrevented) {\n      evt.preventDefault()\n    }\n\n    if (nativeDispatch) {\n      element.dispatchEvent(evt)\n    }\n\n    if (evt.defaultPrevented && jQueryEvent) {\n      jQueryEvent.preventDefault()\n    }\n\n    return evt\n  }\n}\n\nfunction hydrateObj(obj, meta = {}) {\n  for (const [key, value] of Object.entries(meta)) {\n    try {\n      obj[key] = value\n    } catch {\n      Object.defineProperty(obj, key, {\n        configurable: true,\n        get() {\n          return value\n        }\n      })\n    }\n  }\n\n  return obj\n}\n\nexport default EventHandler\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n  if (value === 'true') {\n    return true\n  }\n\n  if (value === 'false') {\n    return false\n  }\n\n  if (value === Number(value).toString()) {\n    return Number(value)\n  }\n\n  if (value === '' || value === 'null') {\n    return null\n  }\n\n  if (typeof value !== 'string') {\n    return value\n  }\n\n  try {\n    return JSON.parse(decodeURIComponent(value))\n  } catch {\n    return value\n  }\n}\n\nfunction normalizeDataKey(key) {\n  return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`)\n}\n\nconst Manipulator = {\n  setDataAttribute(element, key, value) {\n    element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value)\n  },\n\n  removeDataAttribute(element, key) {\n    element.removeAttribute(`data-bs-${normalizeDataKey(key)}`)\n  },\n\n  getDataAttributes(element) {\n    if (!element) {\n      return {}\n    }\n\n    const attributes = {}\n    const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'))\n\n    for (const key of bsKeys) {\n      let pureKey = key.replace(/^bs/, '')\n      pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length)\n      attributes[pureKey] = normalizeData(element.dataset[key])\n    }\n\n    return attributes\n  },\n\n  getDataAttribute(element, key) {\n    return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`))\n  }\n}\n\nexport default Manipulator\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport { isElement, toType } from './index.js'\n\n/**\n * Class definition\n */\n\nclass Config {\n  // Getters\n  static get Default() {\n    return {}\n  }\n\n  static get DefaultType() {\n    return {}\n  }\n\n  static get NAME() {\n    throw new Error('You have to implement the static method \"NAME\", for each component!')\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    return config\n  }\n\n  _mergeConfigObj(config, element) {\n    const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {} // try to parse\n\n    return {\n      ...this.constructor.Default,\n      ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n      ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n      ...(typeof config === 'object' ? config : {})\n    }\n  }\n\n  _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n    for (const [property, expectedTypes] of Object.entries(configTypes)) {\n      const value = config[property]\n      const valueType = isElement(value) ? 'element' : toType(value)\n\n      if (!new RegExp(expectedTypes).test(valueType)) {\n        throw new TypeError(\n          `${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`\n        )\n      }\n    }\n  }\n}\n\nexport default Config\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Data from './dom/data.js'\nimport EventHandler from './dom/event-handler.js'\nimport Config from './util/config.js'\nimport { executeAfterTransition, getElement } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.1'\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n  constructor(element, config) {\n    super()\n\n    element = getElement(element)\n    if (!element) {\n      return\n    }\n\n    this._element = element\n    this._config = this._getConfig(config)\n\n    Data.set(this._element, this.constructor.DATA_KEY, this)\n  }\n\n  // Public\n  dispose() {\n    Data.remove(this._element, this.constructor.DATA_KEY)\n    EventHandler.off(this._element, this.constructor.EVENT_KEY)\n\n    for (const propertyName of Object.getOwnPropertyNames(this)) {\n      this[propertyName] = null\n    }\n  }\n\n  _queueCallback(callback, element, isAnimated = true) {\n    executeAfterTransition(callback, element, isAnimated)\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config, this._element)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  // Static\n  static getInstance(element) {\n    return Data.get(getElement(element), this.DATA_KEY)\n  }\n\n  static getOrCreateInstance(element, config = {}) {\n    return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null)\n  }\n\n  static get VERSION() {\n    return VERSION\n  }\n\n  static get DATA_KEY() {\n    return `bs.${this.NAME}`\n  }\n\n  static get EVENT_KEY() {\n    return `.${this.DATA_KEY}`\n  }\n\n  static eventName(name) {\n    return `${name}${this.EVENT_KEY}`\n  }\n}\n\nexport default BaseComponent\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { isDisabled, isVisible, parseSelector } from '../util/index.js'\n\nconst getSelector = element => {\n  let selector = element.getAttribute('data-bs-target')\n\n  if (!selector || selector === '#') {\n    let hrefAttribute = element.getAttribute('href')\n\n    // The only valid content that could double as a selector are IDs or classes,\n    // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n    // `document.querySelector` will rightfully complain it is invalid.\n    // See https://github.com/twbs/bootstrap/issues/32273\n    if (!hrefAttribute || (!hrefAttribute.includes('#') && !hrefAttribute.startsWith('.'))) {\n      return null\n    }\n\n    // Just in case some CMS puts out a full URL with the anchor appended\n    if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n      hrefAttribute = `#${hrefAttribute.split('#')[1]}`\n    }\n\n    selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null\n  }\n\n  return parseSelector(selector)\n}\n\nconst SelectorEngine = {\n  find(selector, element = document.documentElement) {\n    return [].concat(...Element.prototype.querySelectorAll.call(element, selector))\n  },\n\n  findOne(selector, element = document.documentElement) {\n    return Element.prototype.querySelector.call(element, selector)\n  },\n\n  children(element, selector) {\n    return [].concat(...element.children).filter(child => child.matches(selector))\n  },\n\n  parents(element, selector) {\n    const parents = []\n    let ancestor = element.parentNode.closest(selector)\n\n    while (ancestor) {\n      parents.push(ancestor)\n      ancestor = ancestor.parentNode.closest(selector)\n    }\n\n    return parents\n  },\n\n  prev(element, selector) {\n    let previous = element.previousElementSibling\n\n    while (previous) {\n      if (previous.matches(selector)) {\n        return [previous]\n      }\n\n      previous = previous.previousElementSibling\n    }\n\n    return []\n  },\n  // TODO: this is now unused; remove later along with prev()\n  next(element, selector) {\n    let next = element.nextElementSibling\n\n    while (next) {\n      if (next.matches(selector)) {\n        return [next]\n      }\n\n      next = next.nextElementSibling\n    }\n\n    return []\n  },\n\n  focusableChildren(element) {\n    const focusables = [\n      'a',\n      'button',\n      'input',\n      'textarea',\n      'select',\n      'details',\n      '[tabindex]',\n      '[contenteditable=\"true\"]'\n    ].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',')\n\n    return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el))\n  },\n\n  getSelectorFromElement(element) {\n    const selector = getSelector(element)\n\n    if (selector) {\n      return SelectorEngine.findOne(selector) ? selector : null\n    }\n\n    return null\n  },\n\n  getElementFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.findOne(selector) : null\n  },\n\n  getMultipleElementsFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.find(selector) : []\n  }\n}\n\nexport default SelectorEngine\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isDisabled } from './index.js'\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n  const clickEvent = `click.dismiss${component.EVENT_KEY}`\n  const name = component.NAME\n\n  EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n    if (['A', 'AREA'].includes(this.tagName)) {\n      event.preventDefault()\n    }\n\n    if (isDisabled(this)) {\n      return\n    }\n\n    const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`)\n    const instance = component.getOrCreateInstance(target)\n\n    // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n    instance[method]()\n  })\n}\n\nexport {\n  enableDismissTrigger\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'alert'\nconst DATA_KEY = 'bs.alert'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_CLOSE = `close${EVENT_KEY}`\nconst EVENT_CLOSED = `closed${EVENT_KEY}`\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  close() {\n    const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE)\n\n    if (closeEvent.defaultPrevented) {\n      return\n    }\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    const isAnimated = this._element.classList.contains(CLASS_NAME_FADE)\n    this._queueCallback(() => this._destroyElement(), this._element, isAnimated)\n  }\n\n  // Private\n  _destroyElement() {\n    this._element.remove()\n    EventHandler.trigger(this._element, EVENT_CLOSED)\n    this.dispose()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Alert.getOrCreateInstance(this)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close')\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert)\n\nexport default Alert\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'button'\nconst DATA_KEY = 'bs.button'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"button\"]'\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n    this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE))\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Button.getOrCreateInstance(this)\n\n      if (config === 'toggle') {\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, event => {\n  event.preventDefault()\n\n  const button = event.target.closest(SELECTOR_DATA_TOGGLE)\n  const data = Button.getOrCreateInstance(button)\n\n  data.toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button)\n\nexport default Button\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'swipe'\nconst EVENT_KEY = '.bs.swipe'\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY}`\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY}`\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY}`\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY}`\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY}`\nconst POINTER_TYPE_TOUCH = 'touch'\nconst POINTER_TYPE_PEN = 'pen'\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event'\nconst SWIPE_THRESHOLD = 40\n\nconst Default = {\n  endCallback: null,\n  leftCallback: null,\n  rightCallback: null\n}\n\nconst DefaultType = {\n  endCallback: '(function|null)',\n  leftCallback: '(function|null)',\n  rightCallback: '(function|null)'\n}\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n  constructor(element, config) {\n    super()\n    this._element = element\n\n    if (!element || !Swipe.isSupported()) {\n      return\n    }\n\n    this._config = this._getConfig(config)\n    this._deltaX = 0\n    this._supportPointerEvents = Boolean(window.PointerEvent)\n    this._initEvents()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  dispose() {\n    EventHandler.off(this._element, EVENT_KEY)\n  }\n\n  // Private\n  _start(event) {\n    if (!this._supportPointerEvents) {\n      this._deltaX = event.touches[0].clientX\n\n      return\n    }\n\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX\n    }\n  }\n\n  _end(event) {\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX - this._deltaX\n    }\n\n    this._handleSwipe()\n    execute(this._config.endCallback)\n  }\n\n  _move(event) {\n    this._deltaX = event.touches && event.touches.length > 1 ?\n      0 :\n      event.touches[0].clientX - this._deltaX\n  }\n\n  _handleSwipe() {\n    const absDeltaX = Math.abs(this._deltaX)\n\n    if (absDeltaX <= SWIPE_THRESHOLD) {\n      return\n    }\n\n    const direction = absDeltaX / this._deltaX\n\n    this._deltaX = 0\n\n    if (!direction) {\n      return\n    }\n\n    execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback)\n  }\n\n  _initEvents() {\n    if (this._supportPointerEvents) {\n      EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event))\n      EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event))\n\n      this._element.classList.add(CLASS_NAME_POINTER_EVENT)\n    } else {\n      EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event))\n      EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event))\n      EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event))\n    }\n  }\n\n  _eventIsPointerPenTouch(event) {\n    return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH)\n  }\n\n  // Static\n  static isSupported() {\n    return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0\n  }\n}\n\nexport default Swipe\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getNextActiveElement,\n  isRTL,\n  isVisible,\n  reflow,\n  triggerTransitionEnd\n} from './util/index.js'\nimport Swipe from './util/swipe.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'carousel'\nconst DATA_KEY = 'bs.carousel'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst TOUCHEVENT_COMPAT_WAIT = 500 // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next'\nconst ORDER_PREV = 'prev'\nconst DIRECTION_LEFT = 'left'\nconst DIRECTION_RIGHT = 'right'\n\nconst EVENT_SLIDE = `slide${EVENT_KEY}`\nconst EVENT_SLID = `slid${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_MOUSEENTER = `mouseenter${EVENT_KEY}`\nconst EVENT_MOUSELEAVE = `mouseleave${EVENT_KEY}`\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_CAROUSEL = 'carousel'\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_SLIDE = 'slide'\nconst CLASS_NAME_END = 'carousel-item-end'\nconst CLASS_NAME_START = 'carousel-item-start'\nconst CLASS_NAME_NEXT = 'carousel-item-next'\nconst CLASS_NAME_PREV = 'carousel-item-prev'\n\nconst SELECTOR_ACTIVE = '.active'\nconst SELECTOR_ITEM = '.carousel-item'\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM\nconst SELECTOR_ITEM_IMG = '.carousel-item img'\nconst SELECTOR_INDICATORS = '.carousel-indicators'\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]'\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]'\n\nconst KEY_TO_DIRECTION = {\n  [ARROW_LEFT_KEY]: DIRECTION_RIGHT,\n  [ARROW_RIGHT_KEY]: DIRECTION_LEFT\n}\n\nconst Default = {\n  interval: 5000,\n  keyboard: true,\n  pause: 'hover',\n  ride: false,\n  touch: true,\n  wrap: true\n}\n\nconst DefaultType = {\n  interval: '(number|boolean)', // TODO:v6 remove boolean support\n  keyboard: 'boolean',\n  pause: '(string|boolean)',\n  ride: '(boolean|string)',\n  touch: 'boolean',\n  wrap: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._interval = null\n    this._activeElement = null\n    this._isSliding = false\n    this.touchTimeout = null\n    this._swipeHelper = null\n\n    this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element)\n    this._addEventListeners()\n\n    if (this._config.ride === CLASS_NAME_CAROUSEL) {\n      this.cycle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  next() {\n    this._slide(ORDER_NEXT)\n  }\n\n  nextWhenVisible() {\n    // FIXME TODO use `document.visibilityState`\n    // Don't call next when the page isn't visible\n    // or the carousel or its parent isn't visible\n    if (!document.hidden && isVisible(this._element)) {\n      this.next()\n    }\n  }\n\n  prev() {\n    this._slide(ORDER_PREV)\n  }\n\n  pause() {\n    if (this._isSliding) {\n      triggerTransitionEnd(this._element)\n    }\n\n    this._clearInterval()\n  }\n\n  cycle() {\n    this._clearInterval()\n    this._updateInterval()\n\n    this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval)\n  }\n\n  _maybeEnableCycle() {\n    if (!this._config.ride) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.cycle())\n      return\n    }\n\n    this.cycle()\n  }\n\n  to(index) {\n    const items = this._getItems()\n    if (index > items.length - 1 || index < 0) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.to(index))\n      return\n    }\n\n    const activeIndex = this._getItemIndex(this._getActive())\n    if (activeIndex === index) {\n      return\n    }\n\n    const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV\n\n    this._slide(order, items[index])\n  }\n\n  dispose() {\n    if (this._swipeHelper) {\n      this._swipeHelper.dispose()\n    }\n\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.defaultInterval = config.interval\n    return config\n  }\n\n  _addEventListeners() {\n    if (this._config.keyboard) {\n      EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n    }\n\n    if (this._config.pause === 'hover') {\n      EventHandler.on(this._element, EVENT_MOUSEENTER, () => this.pause())\n      EventHandler.on(this._element, EVENT_MOUSELEAVE, () => this._maybeEnableCycle())\n    }\n\n    if (this._config.touch && Swipe.isSupported()) {\n      this._addTouchEventListeners()\n    }\n  }\n\n  _addTouchEventListeners() {\n    for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n      EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault())\n    }\n\n    const endCallBack = () => {\n      if (this._config.pause !== 'hover') {\n        return\n      }\n\n      // If it's a touch-enabled device, mouseenter/leave are fired as\n      // part of the mouse compatibility events on first tap - the carousel\n      // would stop cycling until user tapped out of it;\n      // here, we listen for touchend, explicitly pause the carousel\n      // (as if it's the second time we tap on it, mouseenter compat event\n      // is NOT fired) and after a timeout (to allow for mouse compatibility\n      // events to fire) we explicitly restart cycling\n\n      this.pause()\n      if (this.touchTimeout) {\n        clearTimeout(this.touchTimeout)\n      }\n\n      this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval)\n    }\n\n    const swipeConfig = {\n      leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n      rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n      endCallback: endCallBack\n    }\n\n    this._swipeHelper = new Swipe(this._element, swipeConfig)\n  }\n\n  _keydown(event) {\n    if (/input|textarea/i.test(event.target.tagName)) {\n      return\n    }\n\n    const direction = KEY_TO_DIRECTION[event.key]\n    if (direction) {\n      event.preventDefault()\n      this._slide(this._directionToOrder(direction))\n    }\n  }\n\n  _getItemIndex(element) {\n    return this._getItems().indexOf(element)\n  }\n\n  _setActiveIndicatorElement(index) {\n    if (!this._indicatorsElement) {\n      return\n    }\n\n    const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement)\n\n    activeIndicator.classList.remove(CLASS_NAME_ACTIVE)\n    activeIndicator.removeAttribute('aria-current')\n\n    const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement)\n\n    if (newActiveIndicator) {\n      newActiveIndicator.classList.add(CLASS_NAME_ACTIVE)\n      newActiveIndicator.setAttribute('aria-current', 'true')\n    }\n  }\n\n  _updateInterval() {\n    const element = this._activeElement || this._getActive()\n\n    if (!element) {\n      return\n    }\n\n    const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10)\n\n    this._config.interval = elementInterval || this._config.defaultInterval\n  }\n\n  _slide(order, element = null) {\n    if (this._isSliding) {\n      return\n    }\n\n    const activeElement = this._getActive()\n    const isNext = order === ORDER_NEXT\n    const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap)\n\n    if (nextElement === activeElement) {\n      return\n    }\n\n    const nextElementIndex = this._getItemIndex(nextElement)\n\n    const triggerEvent = eventName => {\n      return EventHandler.trigger(this._element, eventName, {\n        relatedTarget: nextElement,\n        direction: this._orderToDirection(order),\n        from: this._getItemIndex(activeElement),\n        to: nextElementIndex\n      })\n    }\n\n    const slideEvent = triggerEvent(EVENT_SLIDE)\n\n    if (slideEvent.defaultPrevented) {\n      return\n    }\n\n    if (!activeElement || !nextElement) {\n      // Some weirdness is happening, so we bail\n      // TODO: change tests that use empty divs to avoid this check\n      return\n    }\n\n    const isCycling = Boolean(this._interval)\n    this.pause()\n\n    this._isSliding = true\n\n    this._setActiveIndicatorElement(nextElementIndex)\n    this._activeElement = nextElement\n\n    const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END\n    const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV\n\n    nextElement.classList.add(orderClassName)\n\n    reflow(nextElement)\n\n    activeElement.classList.add(directionalClassName)\n    nextElement.classList.add(directionalClassName)\n\n    const completeCallBack = () => {\n      nextElement.classList.remove(directionalClassName, orderClassName)\n      nextElement.classList.add(CLASS_NAME_ACTIVE)\n\n      activeElement.classList.remove(CLASS_NAME_ACTIVE, orderClassName, directionalClassName)\n\n      this._isSliding = false\n\n      triggerEvent(EVENT_SLID)\n    }\n\n    this._queueCallback(completeCallBack, activeElement, this._isAnimated())\n\n    if (isCycling) {\n      this.cycle()\n    }\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_SLIDE)\n  }\n\n  _getActive() {\n    return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element)\n  }\n\n  _getItems() {\n    return SelectorEngine.find(SELECTOR_ITEM, this._element)\n  }\n\n  _clearInterval() {\n    if (this._interval) {\n      clearInterval(this._interval)\n      this._interval = null\n    }\n  }\n\n  _directionToOrder(direction) {\n    if (isRTL()) {\n      return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT\n    }\n\n    return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV\n  }\n\n  _orderToDirection(order) {\n    if (isRTL()) {\n      return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT\n    }\n\n    return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Carousel.getOrCreateInstance(this, config)\n\n      if (typeof config === 'number') {\n        data.to(config)\n        return\n      }\n\n      if (typeof config === 'string') {\n        if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_SLIDE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n    return\n  }\n\n  event.preventDefault()\n\n  const carousel = Carousel.getOrCreateInstance(target)\n  const slideIndex = this.getAttribute('data-bs-slide-to')\n\n  if (slideIndex) {\n    carousel.to(slideIndex)\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n    carousel.next()\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  carousel.prev()\n  carousel._maybeEnableCycle()\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE)\n\n  for (const carousel of carousels) {\n    Carousel.getOrCreateInstance(carousel)\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel)\n\nexport default Carousel\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getElement,\n  reflow\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'collapse'\nconst DATA_KEY = 'bs.collapse'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_COLLAPSE = 'collapse'\nconst CLASS_NAME_COLLAPSING = 'collapsing'\nconst CLASS_NAME_COLLAPSED = 'collapsed'\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal'\n\nconst WIDTH = 'width'\nconst HEIGHT = 'height'\n\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"collapse\"]'\n\nconst Default = {\n  parent: null,\n  toggle: true\n}\n\nconst DefaultType = {\n  parent: '(null|element)',\n  toggle: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isTransitioning = false\n    this._triggerArray = []\n\n    const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE)\n\n    for (const elem of toggleList) {\n      const selector = SelectorEngine.getSelectorFromElement(elem)\n      const filterElement = SelectorEngine.find(selector)\n        .filter(foundElement => foundElement === this._element)\n\n      if (selector !== null && filterElement.length) {\n        this._triggerArray.push(elem)\n      }\n    }\n\n    this._initializeChildren()\n\n    if (!this._config.parent) {\n      this._addAriaAndCollapsedClass(this._triggerArray, this._isShown())\n    }\n\n    if (this._config.toggle) {\n      this.toggle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    if (this._isShown()) {\n      this.hide()\n    } else {\n      this.show()\n    }\n  }\n\n  show() {\n    if (this._isTransitioning || this._isShown()) {\n      return\n    }\n\n    let activeChildren = []\n\n    // find active children\n    if (this._config.parent) {\n      activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES)\n        .filter(element => element !== this._element)\n        .map(element => Collapse.getOrCreateInstance(element, { toggle: false }))\n    }\n\n    if (activeChildren.length && activeChildren[0]._isTransitioning) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    for (const activeInstance of activeChildren) {\n      activeInstance.hide()\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.classList.remove(CLASS_NAME_COLLAPSE)\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n\n    this._element.style[dimension] = 0\n\n    this._addAriaAndCollapsedClass(this._triggerArray, true)\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n      this._element.style[dimension] = ''\n\n      EventHandler.trigger(this._element, EVENT_SHOWN)\n    }\n\n    const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1)\n    const scrollSize = `scroll${capitalizedDimension}`\n\n    this._queueCallback(complete, this._element, true)\n    this._element.style[dimension] = `${this._element[scrollSize]}px`\n  }\n\n  hide() {\n    if (this._isTransitioning || !this._isShown()) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n    this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n    for (const trigger of this._triggerArray) {\n      const element = SelectorEngine.getElementFromSelector(trigger)\n\n      if (element && !this._isShown(element)) {\n        this._addAriaAndCollapsedClass([trigger], false)\n      }\n    }\n\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE)\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._element.style[dimension] = ''\n\n    this._queueCallback(complete, this._element, true)\n  }\n\n  _isShown(element = this._element) {\n    return element.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.toggle = Boolean(config.toggle) // Coerce string values\n    config.parent = getElement(config.parent)\n    return config\n  }\n\n  _getDimension() {\n    return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT\n  }\n\n  _initializeChildren() {\n    if (!this._config.parent) {\n      return\n    }\n\n    const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE)\n\n    for (const element of children) {\n      const selected = SelectorEngine.getElementFromSelector(element)\n\n      if (selected) {\n        this._addAriaAndCollapsedClass([element], this._isShown(selected))\n      }\n    }\n  }\n\n  _getFirstLevelChildren(selector) {\n    const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent)\n    // remove children if greater depth\n    return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element))\n  }\n\n  _addAriaAndCollapsedClass(triggerArray, isOpen) {\n    if (!triggerArray.length) {\n      return\n    }\n\n    for (const element of triggerArray) {\n      element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen)\n      element.setAttribute('aria-expanded', isOpen)\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    const _config = {}\n    if (typeof config === 'string' && /show|hide/.test(config)) {\n      _config.toggle = false\n    }\n\n    return this.each(function () {\n      const data = Collapse.getOrCreateInstance(this, _config)\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  // preventDefault only for  elements (which change the URL) not inside the collapsible element\n  if (event.target.tagName === 'A' || (event.delegateTarget && event.delegateTarget.tagName === 'A')) {\n    event.preventDefault()\n  }\n\n  for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n    Collapse.getOrCreateInstance(element, { toggle: false }).toggle()\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse)\n\nexport default Collapse\n","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n  return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n  return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n  return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n  if (node == null) {\n    return window;\n  }\n\n  if (node.toString() !== '[object Window]') {\n    var ownerDocument = node.ownerDocument;\n    return ownerDocument ? ownerDocument.defaultView || window : window;\n  }\n\n  return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n  var OwnElement = getWindow(node).Element;\n  return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n  var OwnElement = getWindow(node).HTMLElement;\n  return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n  // IE 11 has no ShadowRoot\n  if (typeof ShadowRoot === 'undefined') {\n    return false;\n  }\n\n  var OwnElement = getWindow(node).ShadowRoot;\n  return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n  var state = _ref.state;\n  Object.keys(state.elements).forEach(function (name) {\n    var style = state.styles[name] || {};\n    var attributes = state.attributes[name] || {};\n    var element = state.elements[name]; // arrow is optional + virtual elements\n\n    if (!isHTMLElement(element) || !getNodeName(element)) {\n      return;\n    } // Flow doesn't support to extend this property, but it's the most\n    // effective way to apply styles to an HTMLElement\n    // $FlowFixMe[cannot-write]\n\n\n    Object.assign(element.style, style);\n    Object.keys(attributes).forEach(function (name) {\n      var value = attributes[name];\n\n      if (value === false) {\n        element.removeAttribute(name);\n      } else {\n        element.setAttribute(name, value === true ? '' : value);\n      }\n    });\n  });\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state;\n  var initialStyles = {\n    popper: {\n      position: state.options.strategy,\n      left: '0',\n      top: '0',\n      margin: '0'\n    },\n    arrow: {\n      position: 'absolute'\n    },\n    reference: {}\n  };\n  Object.assign(state.elements.popper.style, initialStyles.popper);\n  state.styles = initialStyles;\n\n  if (state.elements.arrow) {\n    Object.assign(state.elements.arrow.style, initialStyles.arrow);\n  }\n\n  return function () {\n    Object.keys(state.elements).forEach(function (name) {\n      var element = state.elements[name];\n      var attributes = state.attributes[name] || {};\n      var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n      var style = styleProperties.reduce(function (style, property) {\n        style[property] = '';\n        return style;\n      }, {}); // arrow is optional + virtual elements\n\n      if (!isHTMLElement(element) || !getNodeName(element)) {\n        return;\n      }\n\n      Object.assign(element.style, style);\n      Object.keys(attributes).forEach(function (attribute) {\n        element.removeAttribute(attribute);\n      });\n    });\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'applyStyles',\n  enabled: true,\n  phase: 'write',\n  fn: applyStyles,\n  effect: effect,\n  requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n  return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n  var uaData = navigator.userAgentData;\n\n  if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n    return uaData.brands.map(function (item) {\n      return item.brand + \"/\" + item.version;\n    }).join(' ');\n  }\n\n  return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n  return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n  if (includeScale === void 0) {\n    includeScale = false;\n  }\n\n  if (isFixedStrategy === void 0) {\n    isFixedStrategy = false;\n  }\n\n  var clientRect = element.getBoundingClientRect();\n  var scaleX = 1;\n  var scaleY = 1;\n\n  if (includeScale && isHTMLElement(element)) {\n    scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n    scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n  }\n\n  var _ref = isElement(element) ? getWindow(element) : window,\n      visualViewport = _ref.visualViewport;\n\n  var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n  var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n  var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n  var width = clientRect.width / scaleX;\n  var height = clientRect.height / scaleY;\n  return {\n    width: width,\n    height: height,\n    top: y,\n    right: x + width,\n    bottom: y + height,\n    left: x,\n    x: x,\n    y: y\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n  var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n  // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n  var width = element.offsetWidth;\n  var height = element.offsetHeight;\n\n  if (Math.abs(clientRect.width - width) <= 1) {\n    width = clientRect.width;\n  }\n\n  if (Math.abs(clientRect.height - height) <= 1) {\n    height = clientRect.height;\n  }\n\n  return {\n    x: element.offsetLeft,\n    y: element.offsetTop,\n    width: width,\n    height: height\n  };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n  var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n  if (parent.contains(child)) {\n    return true;\n  } // then fallback to custom implementation with Shadow DOM support\n  else if (rootNode && isShadowRoot(rootNode)) {\n      var next = child;\n\n      do {\n        if (next && parent.isSameNode(next)) {\n          return true;\n        } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n        next = next.parentNode || next.host;\n      } while (next);\n    } // Give up, the result is false\n\n\n  return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n  return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n  return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n  // $FlowFixMe[incompatible-return]: assume body is always available\n  return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n  element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n  if (getNodeName(element) === 'html') {\n    return element;\n  }\n\n  return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n    // $FlowFixMe[incompatible-return]\n    // $FlowFixMe[prop-missing]\n    element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n    element.parentNode || ( // DOM Element detected\n    isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n    // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n    getDocumentElement(element) // fallback\n\n  );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n  if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n  getComputedStyle(element).position === 'fixed') {\n    return null;\n  }\n\n  return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n  var isFirefox = /firefox/i.test(getUAString());\n  var isIE = /Trident/i.test(getUAString());\n\n  if (isIE && isHTMLElement(element)) {\n    // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n    var elementCss = getComputedStyle(element);\n\n    if (elementCss.position === 'fixed') {\n      return null;\n    }\n  }\n\n  var currentNode = getParentNode(element);\n\n  if (isShadowRoot(currentNode)) {\n    currentNode = currentNode.host;\n  }\n\n  while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n    var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n    // create a containing block.\n    // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n    if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n      return currentNode;\n    } else {\n      currentNode = currentNode.parentNode;\n    }\n  }\n\n  return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n  var window = getWindow(element);\n  var offsetParent = getTrueOffsetParent(element);\n\n  while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n    offsetParent = getTrueOffsetParent(offsetParent);\n  }\n\n  if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n    return window;\n  }\n\n  return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n  return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n  return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n  var v = within(min, value, max);\n  return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n  return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n  return {\n    top: 0,\n    right: 0,\n    bottom: 0,\n    left: 0\n  };\n}","export default function expandToHashMap(value, keys) {\n  return keys.reduce(function (hashMap, key) {\n    hashMap[key] = value;\n    return hashMap;\n  }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n  padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : padding;\n  return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n  var _state$modifiersData$;\n\n  var state = _ref.state,\n      name = _ref.name,\n      options = _ref.options;\n  var arrowElement = state.elements.arrow;\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var basePlacement = getBasePlacement(state.placement);\n  var axis = getMainAxisFromPlacement(basePlacement);\n  var isVertical = [left, right].indexOf(basePlacement) >= 0;\n  var len = isVertical ? 'height' : 'width';\n\n  if (!arrowElement || !popperOffsets) {\n    return;\n  }\n\n  var paddingObject = toPaddingObject(options.padding, state);\n  var arrowRect = getLayoutRect(arrowElement);\n  var minProp = axis === 'y' ? top : left;\n  var maxProp = axis === 'y' ? bottom : right;\n  var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n  var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n  var arrowOffsetParent = getOffsetParent(arrowElement);\n  var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n  var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n  // outside of the popper bounds\n\n  var min = paddingObject[minProp];\n  var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n  var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n  var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n  var axisProp = axis;\n  state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options;\n  var _options$element = options.element,\n      arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n  if (arrowElement == null) {\n    return;\n  } // CSS selector\n\n\n  if (typeof arrowElement === 'string') {\n    arrowElement = state.elements.popper.querySelector(arrowElement);\n\n    if (!arrowElement) {\n      return;\n    }\n  }\n\n  if (!contains(state.elements.popper, arrowElement)) {\n    return;\n  }\n\n  state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'arrow',\n  enabled: true,\n  phase: 'main',\n  fn: arrow,\n  effect: effect,\n  requires: ['popperOffsets'],\n  requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n  return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n  top: 'auto',\n  right: 'auto',\n  bottom: 'auto',\n  left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n  var x = _ref.x,\n      y = _ref.y;\n  var dpr = win.devicePixelRatio || 1;\n  return {\n    x: round(x * dpr) / dpr || 0,\n    y: round(y * dpr) / dpr || 0\n  };\n}\n\nexport function mapToStyles(_ref2) {\n  var _Object$assign2;\n\n  var popper = _ref2.popper,\n      popperRect = _ref2.popperRect,\n      placement = _ref2.placement,\n      variation = _ref2.variation,\n      offsets = _ref2.offsets,\n      position = _ref2.position,\n      gpuAcceleration = _ref2.gpuAcceleration,\n      adaptive = _ref2.adaptive,\n      roundOffsets = _ref2.roundOffsets,\n      isFixed = _ref2.isFixed;\n  var _offsets$x = offsets.x,\n      x = _offsets$x === void 0 ? 0 : _offsets$x,\n      _offsets$y = offsets.y,\n      y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n  var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n    x: x,\n    y: y\n  }) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref3.x;\n  y = _ref3.y;\n  var hasX = offsets.hasOwnProperty('x');\n  var hasY = offsets.hasOwnProperty('y');\n  var sideX = left;\n  var sideY = top;\n  var win = window;\n\n  if (adaptive) {\n    var offsetParent = getOffsetParent(popper);\n    var heightProp = 'clientHeight';\n    var widthProp = 'clientWidth';\n\n    if (offsetParent === getWindow(popper)) {\n      offsetParent = getDocumentElement(popper);\n\n      if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n        heightProp = 'scrollHeight';\n        widthProp = 'scrollWidth';\n      }\n    } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n    offsetParent = offsetParent;\n\n    if (placement === top || (placement === left || placement === right) && variation === end) {\n      sideY = bottom;\n      var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n      offsetParent[heightProp];\n      y -= offsetY - popperRect.height;\n      y *= gpuAcceleration ? 1 : -1;\n    }\n\n    if (placement === left || (placement === top || placement === bottom) && variation === end) {\n      sideX = right;\n      var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n      offsetParent[widthProp];\n      x -= offsetX - popperRect.width;\n      x *= gpuAcceleration ? 1 : -1;\n    }\n  }\n\n  var commonStyles = Object.assign({\n    position: position\n  }, adaptive && unsetSides);\n\n  var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n    x: x,\n    y: y\n  }, getWindow(popper)) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref4.x;\n  y = _ref4.y;\n\n  if (gpuAcceleration) {\n    var _Object$assign;\n\n    return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n  }\n\n  return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n  var state = _ref5.state,\n      options = _ref5.options;\n  var _options$gpuAccelerat = options.gpuAcceleration,\n      gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n      _options$adaptive = options.adaptive,\n      adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n      _options$roundOffsets = options.roundOffsets,\n      roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n  var commonStyles = {\n    placement: getBasePlacement(state.placement),\n    variation: getVariation(state.placement),\n    popper: state.elements.popper,\n    popperRect: state.rects.popper,\n    gpuAcceleration: gpuAcceleration,\n    isFixed: state.options.strategy === 'fixed'\n  };\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.popperOffsets,\n      position: state.options.strategy,\n      adaptive: adaptive,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  if (state.modifiersData.arrow != null) {\n    state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.arrow,\n      position: 'absolute',\n      adaptive: false,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-placement': state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'computeStyles',\n  enabled: true,\n  phase: 'beforeWrite',\n  fn: computeStyles,\n  data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n  passive: true\n};\n\nfunction effect(_ref) {\n  var state = _ref.state,\n      instance = _ref.instance,\n      options = _ref.options;\n  var _options$scroll = options.scroll,\n      scroll = _options$scroll === void 0 ? true : _options$scroll,\n      _options$resize = options.resize,\n      resize = _options$resize === void 0 ? true : _options$resize;\n  var window = getWindow(state.elements.popper);\n  var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n  if (scroll) {\n    scrollParents.forEach(function (scrollParent) {\n      scrollParent.addEventListener('scroll', instance.update, passive);\n    });\n  }\n\n  if (resize) {\n    window.addEventListener('resize', instance.update, passive);\n  }\n\n  return function () {\n    if (scroll) {\n      scrollParents.forEach(function (scrollParent) {\n        scrollParent.removeEventListener('scroll', instance.update, passive);\n      });\n    }\n\n    if (resize) {\n      window.removeEventListener('resize', instance.update, passive);\n    }\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'eventListeners',\n  enabled: true,\n  phase: 'write',\n  fn: function fn() {},\n  effect: effect,\n  data: {}\n};","var hash = {\n  left: 'right',\n  right: 'left',\n  bottom: 'top',\n  top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n  return placement.replace(/left|right|bottom|top/g, function (matched) {\n    return hash[matched];\n  });\n}","var hash = {\n  start: 'end',\n  end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n  return placement.replace(/start|end/g, function (matched) {\n    return hash[matched];\n  });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n  var win = getWindow(node);\n  var scrollLeft = win.pageXOffset;\n  var scrollTop = win.pageYOffset;\n  return {\n    scrollLeft: scrollLeft,\n    scrollTop: scrollTop\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n  // If  has a CSS width greater than the viewport, then this will be\n  // incorrect for RTL.\n  // Popper 1 is broken in this case and never had a bug report so let's assume\n  // it's not an issue. I don't think anyone ever specifies width on \n  // anyway.\n  // Browsers where the left scrollbar doesn't cause an issue report `0` for\n  // this (e.g. Edge 2019, IE11, Safari)\n  return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n  // Firefox wants us to check `-x` and `-y` variations as well\n  var _getComputedStyle = getComputedStyle(element),\n      overflow = _getComputedStyle.overflow,\n      overflowX = _getComputedStyle.overflowX,\n      overflowY = _getComputedStyle.overflowY;\n\n  return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n  if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n    // $FlowFixMe[incompatible-return]: assume body is always available\n    return node.ownerDocument.body;\n  }\n\n  if (isHTMLElement(node) && isScrollParent(node)) {\n    return node;\n  }\n\n  return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n  var _element$ownerDocumen;\n\n  if (list === void 0) {\n    list = [];\n  }\n\n  var scrollParent = getScrollParent(element);\n  var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n  var win = getWindow(scrollParent);\n  var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n  var updatedList = list.concat(target);\n  return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n  updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n  return Object.assign({}, rect, {\n    left: rect.x,\n    top: rect.y,\n    right: rect.x + rect.width,\n    bottom: rect.y + rect.height\n  });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n  var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n  rect.top = rect.top + element.clientTop;\n  rect.left = rect.left + element.clientLeft;\n  rect.bottom = rect.top + element.clientHeight;\n  rect.right = rect.left + element.clientWidth;\n  rect.width = element.clientWidth;\n  rect.height = element.clientHeight;\n  rect.x = rect.left;\n  rect.y = rect.top;\n  return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n  return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n  var clippingParents = listScrollParents(getParentNode(element));\n  var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n  var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n  if (!isElement(clipperElement)) {\n    return [];\n  } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n  return clippingParents.filter(function (clippingParent) {\n    return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n  });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n  var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n  var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n  var firstClippingParent = clippingParents[0];\n  var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n    var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n    accRect.top = max(rect.top, accRect.top);\n    accRect.right = min(rect.right, accRect.right);\n    accRect.bottom = min(rect.bottom, accRect.bottom);\n    accRect.left = max(rect.left, accRect.left);\n    return accRect;\n  }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n  clippingRect.width = clippingRect.right - clippingRect.left;\n  clippingRect.height = clippingRect.bottom - clippingRect.top;\n  clippingRect.x = clippingRect.left;\n  clippingRect.y = clippingRect.top;\n  return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n  var win = getWindow(element);\n  var html = getDocumentElement(element);\n  var visualViewport = win.visualViewport;\n  var width = html.clientWidth;\n  var height = html.clientHeight;\n  var x = 0;\n  var y = 0;\n\n  if (visualViewport) {\n    width = visualViewport.width;\n    height = visualViewport.height;\n    var layoutViewport = isLayoutViewport();\n\n    if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n      x = visualViewport.offsetLeft;\n      y = visualViewport.offsetTop;\n    }\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x + getWindowScrollBarX(element),\n    y: y\n  };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n  var _element$ownerDocumen;\n\n  var html = getDocumentElement(element);\n  var winScroll = getWindowScroll(element);\n  var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n  var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n  var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n  var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n  var y = -winScroll.scrollTop;\n\n  if (getComputedStyle(body || html).direction === 'rtl') {\n    x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x,\n    y: y\n  };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n  var reference = _ref.reference,\n      element = _ref.element,\n      placement = _ref.placement;\n  var basePlacement = placement ? getBasePlacement(placement) : null;\n  var variation = placement ? getVariation(placement) : null;\n  var commonX = reference.x + reference.width / 2 - element.width / 2;\n  var commonY = reference.y + reference.height / 2 - element.height / 2;\n  var offsets;\n\n  switch (basePlacement) {\n    case top:\n      offsets = {\n        x: commonX,\n        y: reference.y - element.height\n      };\n      break;\n\n    case bottom:\n      offsets = {\n        x: commonX,\n        y: reference.y + reference.height\n      };\n      break;\n\n    case right:\n      offsets = {\n        x: reference.x + reference.width,\n        y: commonY\n      };\n      break;\n\n    case left:\n      offsets = {\n        x: reference.x - element.width,\n        y: commonY\n      };\n      break;\n\n    default:\n      offsets = {\n        x: reference.x,\n        y: reference.y\n      };\n  }\n\n  var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n  if (mainAxis != null) {\n    var len = mainAxis === 'y' ? 'height' : 'width';\n\n    switch (variation) {\n      case start:\n        offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n        break;\n\n      case end:\n        offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n        break;\n\n      default:\n    }\n  }\n\n  return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      _options$placement = _options.placement,\n      placement = _options$placement === void 0 ? state.placement : _options$placement,\n      _options$strategy = _options.strategy,\n      strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n      _options$boundary = _options.boundary,\n      boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n      _options$rootBoundary = _options.rootBoundary,\n      rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n      _options$elementConte = _options.elementContext,\n      elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n      _options$altBoundary = _options.altBoundary,\n      altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n      _options$padding = _options.padding,\n      padding = _options$padding === void 0 ? 0 : _options$padding;\n  var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n  var altContext = elementContext === popper ? reference : popper;\n  var popperRect = state.rects.popper;\n  var element = state.elements[altBoundary ? altContext : elementContext];\n  var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n  var referenceClientRect = getBoundingClientRect(state.elements.reference);\n  var popperOffsets = computeOffsets({\n    reference: referenceClientRect,\n    element: popperRect,\n    strategy: 'absolute',\n    placement: placement\n  });\n  var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n  var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n  // 0 or negative = within the clipping rect\n\n  var overflowOffsets = {\n    top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n    bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n    left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n    right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n  };\n  var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n  if (elementContext === popper && offsetData) {\n    var offset = offsetData[placement];\n    Object.keys(overflowOffsets).forEach(function (key) {\n      var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n      var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n      overflowOffsets[key] += offset[axis] * multiply;\n    });\n  }\n\n  return overflowOffsets;\n}","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      placement = _options.placement,\n      boundary = _options.boundary,\n      rootBoundary = _options.rootBoundary,\n      padding = _options.padding,\n      flipVariations = _options.flipVariations,\n      _options$allowedAutoP = _options.allowedAutoPlacements,\n      allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n  var variation = getVariation(placement);\n  var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n    return getVariation(placement) === variation;\n  }) : basePlacements;\n  var allowedPlacements = placements.filter(function (placement) {\n    return allowedAutoPlacements.indexOf(placement) >= 0;\n  });\n\n  if (allowedPlacements.length === 0) {\n    allowedPlacements = placements;\n  } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n  var overflows = allowedPlacements.reduce(function (acc, placement) {\n    acc[placement] = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding\n    })[getBasePlacement(placement)];\n    return acc;\n  }, {});\n  return Object.keys(overflows).sort(function (a, b) {\n    return overflows[a] - overflows[b];\n  });\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n  if (getBasePlacement(placement) === auto) {\n    return [];\n  }\n\n  var oppositePlacement = getOppositePlacement(placement);\n  return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n\n  if (state.modifiersData[name]._skip) {\n    return;\n  }\n\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n      specifiedFallbackPlacements = options.fallbackPlacements,\n      padding = options.padding,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      _options$flipVariatio = options.flipVariations,\n      flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n      allowedAutoPlacements = options.allowedAutoPlacements;\n  var preferredPlacement = state.options.placement;\n  var basePlacement = getBasePlacement(preferredPlacement);\n  var isBasePlacement = basePlacement === preferredPlacement;\n  var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n  var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n    return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding,\n      flipVariations: flipVariations,\n      allowedAutoPlacements: allowedAutoPlacements\n    }) : placement);\n  }, []);\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var checksMap = new Map();\n  var makeFallbackChecks = true;\n  var firstFittingPlacement = placements[0];\n\n  for (var i = 0; i < placements.length; i++) {\n    var placement = placements[i];\n\n    var _basePlacement = getBasePlacement(placement);\n\n    var isStartVariation = getVariation(placement) === start;\n    var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n    var len = isVertical ? 'width' : 'height';\n    var overflow = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      altBoundary: altBoundary,\n      padding: padding\n    });\n    var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n    if (referenceRect[len] > popperRect[len]) {\n      mainVariationSide = getOppositePlacement(mainVariationSide);\n    }\n\n    var altVariationSide = getOppositePlacement(mainVariationSide);\n    var checks = [];\n\n    if (checkMainAxis) {\n      checks.push(overflow[_basePlacement] <= 0);\n    }\n\n    if (checkAltAxis) {\n      checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n    }\n\n    if (checks.every(function (check) {\n      return check;\n    })) {\n      firstFittingPlacement = placement;\n      makeFallbackChecks = false;\n      break;\n    }\n\n    checksMap.set(placement, checks);\n  }\n\n  if (makeFallbackChecks) {\n    // `2` may be desired in some cases – research later\n    var numberOfChecks = flipVariations ? 3 : 1;\n\n    var _loop = function _loop(_i) {\n      var fittingPlacement = placements.find(function (placement) {\n        var checks = checksMap.get(placement);\n\n        if (checks) {\n          return checks.slice(0, _i).every(function (check) {\n            return check;\n          });\n        }\n      });\n\n      if (fittingPlacement) {\n        firstFittingPlacement = fittingPlacement;\n        return \"break\";\n      }\n    };\n\n    for (var _i = numberOfChecks; _i > 0; _i--) {\n      var _ret = _loop(_i);\n\n      if (_ret === \"break\") break;\n    }\n  }\n\n  if (state.placement !== firstFittingPlacement) {\n    state.modifiersData[name]._skip = true;\n    state.placement = firstFittingPlacement;\n    state.reset = true;\n  }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'flip',\n  enabled: true,\n  phase: 'main',\n  fn: flip,\n  requiresIfExists: ['offset'],\n  data: {\n    _skip: false\n  }\n};","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n  if (preventedOffsets === void 0) {\n    preventedOffsets = {\n      x: 0,\n      y: 0\n    };\n  }\n\n  return {\n    top: overflow.top - rect.height - preventedOffsets.y,\n    right: overflow.right - rect.width + preventedOffsets.x,\n    bottom: overflow.bottom - rect.height + preventedOffsets.y,\n    left: overflow.left - rect.width - preventedOffsets.x\n  };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n  return [top, right, bottom, left].some(function (side) {\n    return overflow[side] >= 0;\n  });\n}\n\nfunction hide(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var preventedOffsets = state.modifiersData.preventOverflow;\n  var referenceOverflow = detectOverflow(state, {\n    elementContext: 'reference'\n  });\n  var popperAltOverflow = detectOverflow(state, {\n    altBoundary: true\n  });\n  var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n  var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n  var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n  var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n  state.modifiersData[name] = {\n    referenceClippingOffsets: referenceClippingOffsets,\n    popperEscapeOffsets: popperEscapeOffsets,\n    isReferenceHidden: isReferenceHidden,\n    hasPopperEscaped: hasPopperEscaped\n  };\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-reference-hidden': isReferenceHidden,\n    'data-popper-escaped': hasPopperEscaped\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'hide',\n  enabled: true,\n  phase: 'main',\n  requiresIfExists: ['preventOverflow'],\n  fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n  var basePlacement = getBasePlacement(placement);\n  var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n  var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n    placement: placement\n  })) : offset,\n      skidding = _ref[0],\n      distance = _ref[1];\n\n  skidding = skidding || 0;\n  distance = (distance || 0) * invertDistance;\n  return [left, right].indexOf(basePlacement) >= 0 ? {\n    x: distance,\n    y: skidding\n  } : {\n    x: skidding,\n    y: distance\n  };\n}\n\nfunction offset(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options,\n      name = _ref2.name;\n  var _options$offset = options.offset,\n      offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n  var data = placements.reduce(function (acc, placement) {\n    acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n    return acc;\n  }, {});\n  var _data$state$placement = data[state.placement],\n      x = _data$state$placement.x,\n      y = _data$state$placement.y;\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.modifiersData.popperOffsets.x += x;\n    state.modifiersData.popperOffsets.y += y;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'offset',\n  enabled: true,\n  phase: 'main',\n  requires: ['popperOffsets'],\n  fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  // Offsets are the actual position the popper needs to have to be\n  // properly positioned near its reference element\n  // This is the most basic placement, and will be adjusted by\n  // the modifiers in the next step\n  state.modifiersData[name] = computeOffsets({\n    reference: state.rects.reference,\n    element: state.rects.popper,\n    strategy: 'absolute',\n    placement: state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'popperOffsets',\n  enabled: true,\n  phase: 'read',\n  fn: popperOffsets,\n  data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      padding = options.padding,\n      _options$tether = options.tether,\n      tether = _options$tether === void 0 ? true : _options$tether,\n      _options$tetherOffset = options.tetherOffset,\n      tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n  var overflow = detectOverflow(state, {\n    boundary: boundary,\n    rootBoundary: rootBoundary,\n    padding: padding,\n    altBoundary: altBoundary\n  });\n  var basePlacement = getBasePlacement(state.placement);\n  var variation = getVariation(state.placement);\n  var isBasePlacement = !variation;\n  var mainAxis = getMainAxisFromPlacement(basePlacement);\n  var altAxis = getAltAxis(mainAxis);\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : tetherOffset;\n  var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n    mainAxis: tetherOffsetValue,\n    altAxis: tetherOffsetValue\n  } : Object.assign({\n    mainAxis: 0,\n    altAxis: 0\n  }, tetherOffsetValue);\n  var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n  var data = {\n    x: 0,\n    y: 0\n  };\n\n  if (!popperOffsets) {\n    return;\n  }\n\n  if (checkMainAxis) {\n    var _offsetModifierState$;\n\n    var mainSide = mainAxis === 'y' ? top : left;\n    var altSide = mainAxis === 'y' ? bottom : right;\n    var len = mainAxis === 'y' ? 'height' : 'width';\n    var offset = popperOffsets[mainAxis];\n    var min = offset + overflow[mainSide];\n    var max = offset - overflow[altSide];\n    var additive = tether ? -popperRect[len] / 2 : 0;\n    var minLen = variation === start ? referenceRect[len] : popperRect[len];\n    var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n    // outside the reference bounds\n\n    var arrowElement = state.elements.arrow;\n    var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n      width: 0,\n      height: 0\n    };\n    var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n    var arrowPaddingMin = arrowPaddingObject[mainSide];\n    var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n    // to include its full size in the calculation. If the reference is small\n    // and near the edge of a boundary, the popper can overflow even if the\n    // reference is not overflowing as well (e.g. virtual elements with no\n    // width or height)\n\n    var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n    var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n    var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n    var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n    var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n    var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n    var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n    var tetherMax = offset + maxOffset - offsetModifierValue;\n    var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n    popperOffsets[mainAxis] = preventedOffset;\n    data[mainAxis] = preventedOffset - offset;\n  }\n\n  if (checkAltAxis) {\n    var _offsetModifierState$2;\n\n    var _mainSide = mainAxis === 'x' ? top : left;\n\n    var _altSide = mainAxis === 'x' ? bottom : right;\n\n    var _offset = popperOffsets[altAxis];\n\n    var _len = altAxis === 'y' ? 'height' : 'width';\n\n    var _min = _offset + overflow[_mainSide];\n\n    var _max = _offset - overflow[_altSide];\n\n    var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n    var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n    var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n    var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n    var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n    popperOffsets[altAxis] = _preventedOffset;\n    data[altAxis] = _preventedOffset - _offset;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'preventOverflow',\n  enabled: true,\n  phase: 'main',\n  fn: preventOverflow,\n  requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n  return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n  var rect = element.getBoundingClientRect();\n  var scaleX = round(rect.width) / element.offsetWidth || 1;\n  var scaleY = round(rect.height) / element.offsetHeight || 1;\n  return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n  if (isFixed === void 0) {\n    isFixed = false;\n  }\n\n  var isOffsetParentAnElement = isHTMLElement(offsetParent);\n  var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n  var documentElement = getDocumentElement(offsetParent);\n  var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n  var scroll = {\n    scrollLeft: 0,\n    scrollTop: 0\n  };\n  var offsets = {\n    x: 0,\n    y: 0\n  };\n\n  if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n    if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n    isScrollParent(documentElement)) {\n      scroll = getNodeScroll(offsetParent);\n    }\n\n    if (isHTMLElement(offsetParent)) {\n      offsets = getBoundingClientRect(offsetParent, true);\n      offsets.x += offsetParent.clientLeft;\n      offsets.y += offsetParent.clientTop;\n    } else if (documentElement) {\n      offsets.x = getWindowScrollBarX(documentElement);\n    }\n  }\n\n  return {\n    x: rect.left + scroll.scrollLeft - offsets.x,\n    y: rect.top + scroll.scrollTop - offsets.y,\n    width: rect.width,\n    height: rect.height\n  };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n  if (node === getWindow(node) || !isHTMLElement(node)) {\n    return getWindowScroll(node);\n  } else {\n    return getHTMLElementScroll(node);\n  }\n}","export default function getHTMLElementScroll(element) {\n  return {\n    scrollLeft: element.scrollLeft,\n    scrollTop: element.scrollTop\n  };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n  var map = new Map();\n  var visited = new Set();\n  var result = [];\n  modifiers.forEach(function (modifier) {\n    map.set(modifier.name, modifier);\n  }); // On visiting object, check for its dependencies and visit them recursively\n\n  function sort(modifier) {\n    visited.add(modifier.name);\n    var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n    requires.forEach(function (dep) {\n      if (!visited.has(dep)) {\n        var depModifier = map.get(dep);\n\n        if (depModifier) {\n          sort(depModifier);\n        }\n      }\n    });\n    result.push(modifier);\n  }\n\n  modifiers.forEach(function (modifier) {\n    if (!visited.has(modifier.name)) {\n      // check for visited object\n      sort(modifier);\n    }\n  });\n  return result;\n}\n\nexport default function orderModifiers(modifiers) {\n  // order based on dependencies\n  var orderedModifiers = order(modifiers); // order based on phase\n\n  return modifierPhases.reduce(function (acc, phase) {\n    return acc.concat(orderedModifiers.filter(function (modifier) {\n      return modifier.phase === phase;\n    }));\n  }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n  placement: 'bottom',\n  modifiers: [],\n  strategy: 'absolute'\n};\n\nfunction areValidElements() {\n  for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n    args[_key] = arguments[_key];\n  }\n\n  return !args.some(function (element) {\n    return !(element && typeof element.getBoundingClientRect === 'function');\n  });\n}\n\nexport function popperGenerator(generatorOptions) {\n  if (generatorOptions === void 0) {\n    generatorOptions = {};\n  }\n\n  var _generatorOptions = generatorOptions,\n      _generatorOptions$def = _generatorOptions.defaultModifiers,\n      defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n      _generatorOptions$def2 = _generatorOptions.defaultOptions,\n      defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n  return function createPopper(reference, popper, options) {\n    if (options === void 0) {\n      options = defaultOptions;\n    }\n\n    var state = {\n      placement: 'bottom',\n      orderedModifiers: [],\n      options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n      modifiersData: {},\n      elements: {\n        reference: reference,\n        popper: popper\n      },\n      attributes: {},\n      styles: {}\n    };\n    var effectCleanupFns = [];\n    var isDestroyed = false;\n    var instance = {\n      state: state,\n      setOptions: function setOptions(setOptionsAction) {\n        var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n        cleanupModifierEffects();\n        state.options = Object.assign({}, defaultOptions, state.options, options);\n        state.scrollParents = {\n          reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n          popper: listScrollParents(popper)\n        }; // Orders the modifiers based on their dependencies and `phase`\n        // properties\n\n        var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n        state.orderedModifiers = orderedModifiers.filter(function (m) {\n          return m.enabled;\n        });\n        runModifierEffects();\n        return instance.update();\n      },\n      // Sync update – it will always be executed, even if not necessary. This\n      // is useful for low frequency updates where sync behavior simplifies the\n      // logic.\n      // For high frequency updates (e.g. `resize` and `scroll` events), always\n      // prefer the async Popper#update method\n      forceUpdate: function forceUpdate() {\n        if (isDestroyed) {\n          return;\n        }\n\n        var _state$elements = state.elements,\n            reference = _state$elements.reference,\n            popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n        // anymore\n\n        if (!areValidElements(reference, popper)) {\n          return;\n        } // Store the reference and popper rects to be read by modifiers\n\n\n        state.rects = {\n          reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n          popper: getLayoutRect(popper)\n        }; // Modifiers have the ability to reset the current update cycle. The\n        // most common use case for this is the `flip` modifier changing the\n        // placement, which then needs to re-run all the modifiers, because the\n        // logic was previously ran for the previous placement and is therefore\n        // stale/incorrect\n\n        state.reset = false;\n        state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n        // is filled with the initial data specified by the modifier. This means\n        // it doesn't persist and is fresh on each update.\n        // To ensure persistent data, use `${name}#persistent`\n\n        state.orderedModifiers.forEach(function (modifier) {\n          return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n        });\n\n        for (var index = 0; index < state.orderedModifiers.length; index++) {\n          if (state.reset === true) {\n            state.reset = false;\n            index = -1;\n            continue;\n          }\n\n          var _state$orderedModifie = state.orderedModifiers[index],\n              fn = _state$orderedModifie.fn,\n              _state$orderedModifie2 = _state$orderedModifie.options,\n              _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n              name = _state$orderedModifie.name;\n\n          if (typeof fn === 'function') {\n            state = fn({\n              state: state,\n              options: _options,\n              name: name,\n              instance: instance\n            }) || state;\n          }\n        }\n      },\n      // Async and optimistically optimized update – it will not be executed if\n      // not necessary (debounced to run at most once-per-tick)\n      update: debounce(function () {\n        return new Promise(function (resolve) {\n          instance.forceUpdate();\n          resolve(state);\n        });\n      }),\n      destroy: function destroy() {\n        cleanupModifierEffects();\n        isDestroyed = true;\n      }\n    };\n\n    if (!areValidElements(reference, popper)) {\n      return instance;\n    }\n\n    instance.setOptions(options).then(function (state) {\n      if (!isDestroyed && options.onFirstUpdate) {\n        options.onFirstUpdate(state);\n      }\n    }); // Modifiers have the ability to execute arbitrary code before the first\n    // update cycle runs. They will be executed in the same order as the update\n    // cycle. This is useful when a modifier adds some persistent data that\n    // other modifiers need to use, but the modifier is run after the dependent\n    // one.\n\n    function runModifierEffects() {\n      state.orderedModifiers.forEach(function (_ref) {\n        var name = _ref.name,\n            _ref$options = _ref.options,\n            options = _ref$options === void 0 ? {} : _ref$options,\n            effect = _ref.effect;\n\n        if (typeof effect === 'function') {\n          var cleanupFn = effect({\n            state: state,\n            name: name,\n            instance: instance,\n            options: options\n          });\n\n          var noopFn = function noopFn() {};\n\n          effectCleanupFns.push(cleanupFn || noopFn);\n        }\n      });\n    }\n\n    function cleanupModifierEffects() {\n      effectCleanupFns.forEach(function (fn) {\n        return fn();\n      });\n      effectCleanupFns = [];\n    }\n\n    return instance;\n  };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n  var pending;\n  return function () {\n    if (!pending) {\n      pending = new Promise(function (resolve) {\n        Promise.resolve().then(function () {\n          pending = undefined;\n          resolve(fn());\n        });\n      });\n    }\n\n    return pending;\n  };\n}","export default function mergeByName(modifiers) {\n  var merged = modifiers.reduce(function (merged, current) {\n    var existing = merged[current.name];\n    merged[current.name] = existing ? Object.assign({}, existing, current, {\n      options: Object.assign({}, existing.options, current.options),\n      data: Object.assign({}, existing.data, current.data)\n    }) : current;\n    return merged;\n  }, {}); // IE11 does not support Object.values\n\n  return Object.keys(merged).map(function (key) {\n    return merged[key];\n  });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  execute,\n  getElement,\n  getNextActiveElement,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'dropdown'\nconst DATA_KEY = 'bs.dropdown'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ESCAPE_KEY = 'Escape'\nconst TAB_KEY = 'Tab'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst RIGHT_MOUSE_BUTTON = 2 // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_DROPUP = 'dropup'\nconst CLASS_NAME_DROPEND = 'dropend'\nconst CLASS_NAME_DROPSTART = 'dropstart'\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center'\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center'\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)'\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE}.${CLASS_NAME_SHOW}`\nconst SELECTOR_MENU = '.dropdown-menu'\nconst SELECTOR_NAVBAR = '.navbar'\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav'\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)'\n\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start'\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end'\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start'\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end'\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start'\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start'\nconst PLACEMENT_TOPCENTER = 'top'\nconst PLACEMENT_BOTTOMCENTER = 'bottom'\n\nconst Default = {\n  autoClose: true,\n  boundary: 'clippingParents',\n  display: 'dynamic',\n  offset: [0, 2],\n  popperConfig: null,\n  reference: 'toggle'\n}\n\nconst DefaultType = {\n  autoClose: '(boolean|string)',\n  boundary: '(string|element)',\n  display: 'string',\n  offset: '(array|string|function)',\n  popperConfig: '(null|object|function)',\n  reference: '(string|element|object)'\n}\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._popper = null\n    this._parent = this._element.parentNode // dropdown wrapper\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.prev(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.findOne(SELECTOR_MENU, this._parent)\n    this._inNavbar = this._detectNavbar()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    return this._isShown() ? this.hide() : this.show()\n  }\n\n  show() {\n    if (isDisabled(this._element) || this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, relatedTarget)\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._createPopper()\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    this._element.focus()\n    this._element.setAttribute('aria-expanded', true)\n\n    this._menu.classList.add(CLASS_NAME_SHOW)\n    this._element.classList.add(CLASS_NAME_SHOW)\n    EventHandler.trigger(this._element, EVENT_SHOWN, relatedTarget)\n  }\n\n  hide() {\n    if (isDisabled(this._element) || !this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    this._completeHide(relatedTarget)\n  }\n\n  dispose() {\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    super.dispose()\n  }\n\n  update() {\n    this._inNavbar = this._detectNavbar()\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Private\n  _completeHide(relatedTarget) {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE, relatedTarget)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    this._menu.classList.remove(CLASS_NAME_SHOW)\n    this._element.classList.remove(CLASS_NAME_SHOW)\n    this._element.setAttribute('aria-expanded', 'false')\n    Manipulator.removeDataAttribute(this._menu, 'popper')\n    EventHandler.trigger(this._element, EVENT_HIDDEN, relatedTarget)\n  }\n\n  _getConfig(config) {\n    config = super._getConfig(config)\n\n    if (typeof config.reference === 'object' && !isElement(config.reference) &&\n      typeof config.reference.getBoundingClientRect !== 'function'\n    ) {\n      // Popper virtual elements require a getBoundingClientRect method\n      throw new TypeError(`${NAME.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`)\n    }\n\n    return config\n  }\n\n  _createPopper() {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)')\n    }\n\n    let referenceElement = this._element\n\n    if (this._config.reference === 'parent') {\n      referenceElement = this._parent\n    } else if (isElement(this._config.reference)) {\n      referenceElement = getElement(this._config.reference)\n    } else if (typeof this._config.reference === 'object') {\n      referenceElement = this._config.reference\n    }\n\n    const popperConfig = this._getPopperConfig()\n    this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig)\n  }\n\n  _isShown() {\n    return this._menu.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _getPlacement() {\n    const parentDropdown = this._parent\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n      return PLACEMENT_RIGHT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n      return PLACEMENT_LEFT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n      return PLACEMENT_TOPCENTER\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n      return PLACEMENT_BOTTOMCENTER\n    }\n\n    // We need to trim the value because custom properties can also include spaces\n    const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end'\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n      return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP\n    }\n\n    return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM\n  }\n\n  _detectNavbar() {\n    return this._element.closest(SELECTOR_NAVBAR) !== null\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _getPopperConfig() {\n    const defaultBsPopperConfig = {\n      placement: this._getPlacement(),\n      modifiers: [{\n        name: 'preventOverflow',\n        options: {\n          boundary: this._config.boundary\n        }\n      },\n      {\n        name: 'offset',\n        options: {\n          offset: this._getOffset()\n        }\n      }]\n    }\n\n    // Disable Popper if we have a static display or Dropdown is in Navbar\n    if (this._inNavbar || this._config.display === 'static') {\n      Manipulator.setDataAttribute(this._menu, 'popper', 'static') // TODO: v6 remove\n      defaultBsPopperConfig.modifiers = [{\n        name: 'applyStyles',\n        enabled: false\n      }]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _selectMenuItem({ key, target }) {\n    const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element))\n\n    if (!items.length) {\n      return\n    }\n\n    // if target isn't included in items (e.g. when expanding the dropdown)\n    // allow cycling to get the last item in case key equals ARROW_UP_KEY\n    getNextActiveElement(items, target, key === ARROW_DOWN_KEY, !items.includes(target)).focus()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Dropdown.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n\n  static clearMenus(event) {\n    if (event.button === RIGHT_MOUSE_BUTTON || (event.type === 'keyup' && event.key !== TAB_KEY)) {\n      return\n    }\n\n    const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN)\n\n    for (const toggle of openToggles) {\n      const context = Dropdown.getInstance(toggle)\n      if (!context || context._config.autoClose === false) {\n        continue\n      }\n\n      const composedPath = event.composedPath()\n      const isMenuTarget = composedPath.includes(context._menu)\n      if (\n        composedPath.includes(context._element) ||\n        (context._config.autoClose === 'inside' && !isMenuTarget) ||\n        (context._config.autoClose === 'outside' && isMenuTarget)\n      ) {\n        continue\n      }\n\n      // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n      if (context._menu.contains(event.target) && ((event.type === 'keyup' && event.key === TAB_KEY) || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n        continue\n      }\n\n      const relatedTarget = { relatedTarget: context._element }\n\n      if (event.type === 'click') {\n        relatedTarget.clickEvent = event\n      }\n\n      context._completeHide(relatedTarget)\n    }\n  }\n\n  static dataApiKeydownHandler(event) {\n    // If not an UP | DOWN | ESCAPE key => not a dropdown command\n    // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n    const isInput = /input|textarea/i.test(event.target.tagName)\n    const isEscapeEvent = event.key === ESCAPE_KEY\n    const isUpOrDownEvent = [ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)\n\n    if (!isUpOrDownEvent && !isEscapeEvent) {\n      return\n    }\n\n    if (isInput && !isEscapeEvent) {\n      return\n    }\n\n    event.preventDefault()\n\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE) ?\n      this :\n      (SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.next(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.findOne(SELECTOR_DATA_TOGGLE, event.delegateTarget.parentNode))\n\n    const instance = Dropdown.getOrCreateInstance(getToggleButton)\n\n    if (isUpOrDownEvent) {\n      event.stopPropagation()\n      instance.show()\n      instance._selectMenuItem(event)\n      return\n    }\n\n    if (instance._isShown()) { // else is escape and we check if it is shown\n      event.stopPropagation()\n      instance.hide()\n      getToggleButton.focus()\n    }\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_CLICK_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  event.preventDefault()\n  Dropdown.getOrCreateInstance(this).toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown)\n\nexport default Dropdown\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute, executeAfterTransition, getElement, reflow } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'backdrop'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME}`\n\nconst Default = {\n  className: 'modal-backdrop',\n  clickCallback: null,\n  isAnimated: false,\n  isVisible: true, // if false, we use the backdrop helper without adding any element to the dom\n  rootElement: 'body' // give the choice to place backdrop under different elements\n}\n\nconst DefaultType = {\n  className: 'string',\n  clickCallback: '(function|null)',\n  isAnimated: 'boolean',\n  isVisible: 'boolean',\n  rootElement: '(element|string)'\n}\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isAppended = false\n    this._element = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  show(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._append()\n\n    const element = this._getElement()\n    if (this._config.isAnimated) {\n      reflow(element)\n    }\n\n    element.classList.add(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      execute(callback)\n    })\n  }\n\n  hide(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._getElement().classList.remove(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      this.dispose()\n      execute(callback)\n    })\n  }\n\n  dispose() {\n    if (!this._isAppended) {\n      return\n    }\n\n    EventHandler.off(this._element, EVENT_MOUSEDOWN)\n\n    this._element.remove()\n    this._isAppended = false\n  }\n\n  // Private\n  _getElement() {\n    if (!this._element) {\n      const backdrop = document.createElement('div')\n      backdrop.className = this._config.className\n      if (this._config.isAnimated) {\n        backdrop.classList.add(CLASS_NAME_FADE)\n      }\n\n      this._element = backdrop\n    }\n\n    return this._element\n  }\n\n  _configAfterMerge(config) {\n    // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n    config.rootElement = getElement(config.rootElement)\n    return config\n  }\n\n  _append() {\n    if (this._isAppended) {\n      return\n    }\n\n    const element = this._getElement()\n    this._config.rootElement.append(element)\n\n    EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n      execute(this._config.clickCallback)\n    })\n\n    this._isAppended = true\n  }\n\n  _emulateAnimation(callback) {\n    executeAfterTransition(callback, this._getElement(), this._config.isAnimated)\n  }\n}\n\nexport default Backdrop\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'focustrap'\nconst DATA_KEY = 'bs.focustrap'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY}`\n\nconst TAB_KEY = 'Tab'\nconst TAB_NAV_FORWARD = 'forward'\nconst TAB_NAV_BACKWARD = 'backward'\n\nconst Default = {\n  autofocus: true,\n  trapElement: null // The element to trap focus inside of\n}\n\nconst DefaultType = {\n  autofocus: 'boolean',\n  trapElement: 'element'\n}\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isActive = false\n    this._lastTabNavDirection = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  activate() {\n    if (this._isActive) {\n      return\n    }\n\n    if (this._config.autofocus) {\n      this._config.trapElement.focus()\n    }\n\n    EventHandler.off(document, EVENT_KEY) // guard against infinite focus loop\n    EventHandler.on(document, EVENT_FOCUSIN, event => this._handleFocusin(event))\n    EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event))\n\n    this._isActive = true\n  }\n\n  deactivate() {\n    if (!this._isActive) {\n      return\n    }\n\n    this._isActive = false\n    EventHandler.off(document, EVENT_KEY)\n  }\n\n  // Private\n  _handleFocusin(event) {\n    const { trapElement } = this._config\n\n    if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n      return\n    }\n\n    const elements = SelectorEngine.focusableChildren(trapElement)\n\n    if (elements.length === 0) {\n      trapElement.focus()\n    } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n      elements[elements.length - 1].focus()\n    } else {\n      elements[0].focus()\n    }\n  }\n\n  _handleKeydown(event) {\n    if (event.key !== TAB_KEY) {\n      return\n    }\n\n    this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD\n  }\n}\n\nexport default FocusTrap\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top'\nconst SELECTOR_STICKY_CONTENT = '.sticky-top'\nconst PROPERTY_PADDING = 'padding-right'\nconst PROPERTY_MARGIN = 'margin-right'\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n  constructor() {\n    this._element = document.body\n  }\n\n  // Public\n  getWidth() {\n    // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n    const documentWidth = document.documentElement.clientWidth\n    return Math.abs(window.innerWidth - documentWidth)\n  }\n\n  hide() {\n    const width = this.getWidth()\n    this._disableOverFlow()\n    // give padding to element to balance the hidden scrollbar width\n    this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n    this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width)\n  }\n\n  reset() {\n    this._resetElementAttributes(this._element, 'overflow')\n    this._resetElementAttributes(this._element, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN)\n  }\n\n  isOverflowing() {\n    return this.getWidth() > 0\n  }\n\n  // Private\n  _disableOverFlow() {\n    this._saveInitialAttribute(this._element, 'overflow')\n    this._element.style.overflow = 'hidden'\n  }\n\n  _setElementAttributes(selector, styleProperty, callback) {\n    const scrollbarWidth = this.getWidth()\n    const manipulationCallBack = element => {\n      if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n        return\n      }\n\n      this._saveInitialAttribute(element, styleProperty)\n      const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty)\n      element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _saveInitialAttribute(element, styleProperty) {\n    const actualValue = element.style.getPropertyValue(styleProperty)\n    if (actualValue) {\n      Manipulator.setDataAttribute(element, styleProperty, actualValue)\n    }\n  }\n\n  _resetElementAttributes(selector, styleProperty) {\n    const manipulationCallBack = element => {\n      const value = Manipulator.getDataAttribute(element, styleProperty)\n      // We only want to remove the property if the value is `null`; the value can also be zero\n      if (value === null) {\n        element.style.removeProperty(styleProperty)\n        return\n      }\n\n      Manipulator.removeDataAttribute(element, styleProperty)\n      element.style.setProperty(styleProperty, value)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _applyManipulationCallback(selector, callBack) {\n    if (isElement(selector)) {\n      callBack(selector)\n      return\n    }\n\n    for (const sel of SelectorEngine.find(selector, this._element)) {\n      callBack(sel)\n    }\n  }\n}\n\nexport default ScrollBarHelper\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport { defineJQueryPlugin, isRTL, isVisible, reflow } from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'modal'\nconst DATA_KEY = 'bs.modal'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst ESCAPE_KEY = 'Escape'\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY}`\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_OPEN = 'modal-open'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_STATIC = 'modal-static'\n\nconst OPEN_SELECTOR = '.modal.show'\nconst SELECTOR_DIALOG = '.modal-dialog'\nconst SELECTOR_MODAL_BODY = '.modal-body'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"modal\"]'\n\nconst Default = {\n  backdrop: true,\n  focus: true,\n  keyboard: true\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  focus: 'boolean',\n  keyboard: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element)\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._isShown = false\n    this._isTransitioning = false\n    this._scrollBar = new ScrollBarHelper()\n\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, {\n      relatedTarget\n    })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._isTransitioning = true\n\n    this._scrollBar.hide()\n\n    document.body.classList.add(CLASS_NAME_OPEN)\n\n    this._adjustDialog()\n\n    this._backdrop.show(() => this._showElement(relatedTarget))\n  }\n\n  hide() {\n    if (!this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = false\n    this._isTransitioning = true\n    this._focustrap.deactivate()\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    this._queueCallback(() => this._hideModal(), this._element, this._isAnimated())\n  }\n\n  dispose() {\n    EventHandler.off(window, EVENT_KEY)\n    EventHandler.off(this._dialog, EVENT_KEY)\n\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n\n    super.dispose()\n  }\n\n  handleUpdate() {\n    this._adjustDialog()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    return new Backdrop({\n      isVisible: Boolean(this._config.backdrop), // 'static' option will be translated to true, and booleans will keep their value,\n      isAnimated: this._isAnimated()\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _showElement(relatedTarget) {\n    // try to append dynamic modal\n    if (!document.body.contains(this._element)) {\n      document.body.append(this._element)\n    }\n\n    this._element.style.display = 'block'\n    this._element.removeAttribute('aria-hidden')\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.scrollTop = 0\n\n    const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog)\n    if (modalBody) {\n      modalBody.scrollTop = 0\n    }\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_SHOW)\n\n    const transitionComplete = () => {\n      if (this._config.focus) {\n        this._focustrap.activate()\n      }\n\n      this._isTransitioning = false\n      EventHandler.trigger(this._element, EVENT_SHOWN, {\n        relatedTarget\n      })\n    }\n\n    this._queueCallback(transitionComplete, this._dialog, this._isAnimated())\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      this._triggerBackdropTransition()\n    })\n\n    EventHandler.on(window, EVENT_RESIZE, () => {\n      if (this._isShown && !this._isTransitioning) {\n        this._adjustDialog()\n      }\n    })\n\n    EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n      // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n      EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n        if (this._element !== event.target || this._element !== event2.target) {\n          return\n        }\n\n        if (this._config.backdrop === 'static') {\n          this._triggerBackdropTransition()\n          return\n        }\n\n        if (this._config.backdrop) {\n          this.hide()\n        }\n      })\n    })\n  }\n\n  _hideModal() {\n    this._element.style.display = 'none'\n    this._element.setAttribute('aria-hidden', true)\n    this._element.removeAttribute('aria-modal')\n    this._element.removeAttribute('role')\n    this._isTransitioning = false\n\n    this._backdrop.hide(() => {\n      document.body.classList.remove(CLASS_NAME_OPEN)\n      this._resetAdjustments()\n      this._scrollBar.reset()\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    })\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_FADE)\n  }\n\n  _triggerBackdropTransition() {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const initialOverflowY = this._element.style.overflowY\n    // return if the following background transition hasn't yet completed\n    if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n      return\n    }\n\n    if (!isModalOverflowing) {\n      this._element.style.overflowY = 'hidden'\n    }\n\n    this._element.classList.add(CLASS_NAME_STATIC)\n    this._queueCallback(() => {\n      this._element.classList.remove(CLASS_NAME_STATIC)\n      this._queueCallback(() => {\n        this._element.style.overflowY = initialOverflowY\n      }, this._dialog)\n    }, this._dialog)\n\n    this._element.focus()\n  }\n\n  /**\n   * The following methods are used to handle overflowing modals\n   */\n\n  _adjustDialog() {\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const scrollbarWidth = this._scrollBar.getWidth()\n    const isBodyOverflowing = scrollbarWidth > 0\n\n    if (isBodyOverflowing && !isModalOverflowing) {\n      const property = isRTL() ? 'paddingLeft' : 'paddingRight'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n\n    if (!isBodyOverflowing && isModalOverflowing) {\n      const property = isRTL() ? 'paddingRight' : 'paddingLeft'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n  }\n\n  _resetAdjustments() {\n    this._element.style.paddingLeft = ''\n    this._element.style.paddingRight = ''\n  }\n\n  // Static\n  static jQueryInterface(config, relatedTarget) {\n    return this.each(function () {\n      const data = Modal.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](relatedTarget)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  EventHandler.one(target, EVENT_SHOW, showEvent => {\n    if (showEvent.defaultPrevented) {\n      // only register focus restorer if modal will actually get shown\n      return\n    }\n\n    EventHandler.one(target, EVENT_HIDDEN, () => {\n      if (isVisible(this)) {\n        this.focus()\n      }\n    })\n  })\n\n  // avoid conflict when clicking modal toggler while another one is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen) {\n    Modal.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Modal.getOrCreateInstance(target)\n\n  data.toggle(this)\n})\n\nenableDismissTrigger(Modal)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal)\n\nexport default Modal\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport {\n  defineJQueryPlugin,\n  isDisabled,\n  isVisible\n} from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'offcanvas'\nconst DATA_KEY = 'bs.offcanvas'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst ESCAPE_KEY = 'Escape'\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\nconst CLASS_NAME_HIDING = 'hiding'\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop'\nconst OPEN_SELECTOR = '.offcanvas.show'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"offcanvas\"]'\n\nconst Default = {\n  backdrop: true,\n  keyboard: true,\n  scroll: false\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  keyboard: 'boolean',\n  scroll: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isShown = false\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, { relatedTarget })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._backdrop.show()\n\n    if (!this._config.scroll) {\n      new ScrollBarHelper().hide()\n    }\n\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.classList.add(CLASS_NAME_SHOWING)\n\n    const completeCallBack = () => {\n      if (!this._config.scroll || this._config.backdrop) {\n        this._focustrap.activate()\n      }\n\n      this._element.classList.add(CLASS_NAME_SHOW)\n      this._element.classList.remove(CLASS_NAME_SHOWING)\n      EventHandler.trigger(this._element, EVENT_SHOWN, { relatedTarget })\n    }\n\n    this._queueCallback(completeCallBack, this._element, true)\n  }\n\n  hide() {\n    if (!this._isShown) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._focustrap.deactivate()\n    this._element.blur()\n    this._isShown = false\n    this._element.classList.add(CLASS_NAME_HIDING)\n    this._backdrop.hide()\n\n    const completeCallback = () => {\n      this._element.classList.remove(CLASS_NAME_SHOW, CLASS_NAME_HIDING)\n      this._element.removeAttribute('aria-modal')\n      this._element.removeAttribute('role')\n\n      if (!this._config.scroll) {\n        new ScrollBarHelper().reset()\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._queueCallback(completeCallback, this._element, true)\n  }\n\n  dispose() {\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n    super.dispose()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    const clickCallback = () => {\n      if (this._config.backdrop === 'static') {\n        EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n        return\n      }\n\n      this.hide()\n    }\n\n    // 'static' option will be translated to true, and booleans will keep their value\n    const isVisible = Boolean(this._config.backdrop)\n\n    return new Backdrop({\n      className: CLASS_NAME_BACKDROP,\n      isVisible,\n      isAnimated: true,\n      rootElement: this._element.parentNode,\n      clickCallback: isVisible ? clickCallback : null\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    })\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Offcanvas.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  if (isDisabled(this)) {\n    return\n  }\n\n  EventHandler.one(target, EVENT_HIDDEN, () => {\n    // focus on trigger when it is closed\n    if (isVisible(this)) {\n      this.focus()\n    }\n  })\n\n  // avoid conflict when clicking a toggler of an offcanvas, while another is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen && alreadyOpen !== target) {\n    Offcanvas.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Offcanvas.getOrCreateInstance(target)\n  data.toggle(this)\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n    Offcanvas.getOrCreateInstance(selector).show()\n  }\n})\n\nEventHandler.on(window, EVENT_RESIZE, () => {\n  for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n    if (getComputedStyle(element).position !== 'fixed') {\n      Offcanvas.getOrCreateInstance(element).hide()\n    }\n  }\n})\n\nenableDismissTrigger(Offcanvas)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas)\n\nexport default Offcanvas\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i\n\nexport const DefaultAllowlist = {\n  // Global attributes allowed on any supplied element below.\n  '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n  a: ['target', 'href', 'title', 'rel'],\n  area: [],\n  b: [],\n  br: [],\n  col: [],\n  code: [],\n  div: [],\n  em: [],\n  hr: [],\n  h1: [],\n  h2: [],\n  h3: [],\n  h4: [],\n  h5: [],\n  h6: [],\n  i: [],\n  img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n  li: [],\n  ol: [],\n  p: [],\n  pre: [],\n  s: [],\n  small: [],\n  span: [],\n  sub: [],\n  sup: [],\n  strong: [],\n  u: [],\n  ul: []\n}\n// js-docs-end allow-list\n\nconst uriAttributes = new Set([\n  'background',\n  'cite',\n  'href',\n  'itemtype',\n  'longdesc',\n  'poster',\n  'src',\n  'xlink:href'\n])\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n  const attributeName = attribute.nodeName.toLowerCase()\n\n  if (allowedAttributeList.includes(attributeName)) {\n    if (uriAttributes.has(attributeName)) {\n      return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue))\n    }\n\n    return true\n  }\n\n  // Check if a regular expression validates the attribute.\n  return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp)\n    .some(regex => regex.test(attributeName))\n}\n\nexport function sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n  if (!unsafeHtml.length) {\n    return unsafeHtml\n  }\n\n  if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n    return sanitizeFunction(unsafeHtml)\n  }\n\n  const domParser = new window.DOMParser()\n  const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html')\n  const elements = [].concat(...createdDocument.body.querySelectorAll('*'))\n\n  for (const element of elements) {\n    const elementName = element.nodeName.toLowerCase()\n\n    if (!Object.keys(allowList).includes(elementName)) {\n      element.remove()\n      continue\n    }\n\n    const attributeList = [].concat(...element.attributes)\n    const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || [])\n\n    for (const attribute of attributeList) {\n      if (!allowedAttribute(attribute, allowedAttributes)) {\n        element.removeAttribute(attribute.nodeName)\n      }\n    }\n  }\n\n  return createdDocument.body.innerHTML\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\nimport { DefaultAllowlist, sanitizeHtml } from './sanitizer.js'\nimport { execute, getElement, isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'TemplateFactory'\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  content: {}, // { selector : text ,  selector2 : text2 , }\n  extraClass: '',\n  html: false,\n  sanitize: true,\n  sanitizeFn: null,\n  template: '
    '\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  content: 'object',\n  extraClass: '(string|function)',\n  html: 'boolean',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  template: 'string'\n}\n\nconst DefaultContentType = {\n  entry: '(string|element|function|null)',\n  selector: '(string|element)'\n}\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  getContent() {\n    return Object.values(this._config.content)\n      .map(config => this._resolvePossibleFunction(config))\n      .filter(Boolean)\n  }\n\n  hasContent() {\n    return this.getContent().length > 0\n  }\n\n  changeContent(content) {\n    this._checkContent(content)\n    this._config.content = { ...this._config.content, ...content }\n    return this\n  }\n\n  toHtml() {\n    const templateWrapper = document.createElement('div')\n    templateWrapper.innerHTML = this._maybeSanitize(this._config.template)\n\n    for (const [selector, text] of Object.entries(this._config.content)) {\n      this._setContent(templateWrapper, text, selector)\n    }\n\n    const template = templateWrapper.children[0]\n    const extraClass = this._resolvePossibleFunction(this._config.extraClass)\n\n    if (extraClass) {\n      template.classList.add(...extraClass.split(' '))\n    }\n\n    return template\n  }\n\n  // Private\n  _typeCheckConfig(config) {\n    super._typeCheckConfig(config)\n    this._checkContent(config.content)\n  }\n\n  _checkContent(arg) {\n    for (const [selector, content] of Object.entries(arg)) {\n      super._typeCheckConfig({ selector, entry: content }, DefaultContentType)\n    }\n  }\n\n  _setContent(template, content, selector) {\n    const templateElement = SelectorEngine.findOne(selector, template)\n\n    if (!templateElement) {\n      return\n    }\n\n    content = this._resolvePossibleFunction(content)\n\n    if (!content) {\n      templateElement.remove()\n      return\n    }\n\n    if (isElement(content)) {\n      this._putElementInTemplate(getElement(content), templateElement)\n      return\n    }\n\n    if (this._config.html) {\n      templateElement.innerHTML = this._maybeSanitize(content)\n      return\n    }\n\n    templateElement.textContent = content\n  }\n\n  _maybeSanitize(arg) {\n    return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this])\n  }\n\n  _putElementInTemplate(element, templateElement) {\n    if (this._config.html) {\n      templateElement.innerHTML = ''\n      templateElement.append(element)\n      return\n    }\n\n    templateElement.textContent = element.textContent\n  }\n}\n\nexport default TemplateFactory\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport { defineJQueryPlugin, execute, findShadowRoot, getElement, getUID, isRTL, noop } from './util/index.js'\nimport { DefaultAllowlist } from './util/sanitizer.js'\nimport TemplateFactory from './util/template-factory.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tooltip'\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn'])\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_MODAL = 'modal'\nconst CLASS_NAME_SHOW = 'show'\n\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner'\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`\n\nconst EVENT_MODAL_HIDE = 'hide.bs.modal'\n\nconst TRIGGER_HOVER = 'hover'\nconst TRIGGER_FOCUS = 'focus'\nconst TRIGGER_CLICK = 'click'\nconst TRIGGER_MANUAL = 'manual'\n\nconst EVENT_HIDE = 'hide'\nconst EVENT_HIDDEN = 'hidden'\nconst EVENT_SHOW = 'show'\nconst EVENT_SHOWN = 'shown'\nconst EVENT_INSERTED = 'inserted'\nconst EVENT_CLICK = 'click'\nconst EVENT_FOCUSIN = 'focusin'\nconst EVENT_FOCUSOUT = 'focusout'\nconst EVENT_MOUSEENTER = 'mouseenter'\nconst EVENT_MOUSELEAVE = 'mouseleave'\n\nconst AttachmentMap = {\n  AUTO: 'auto',\n  TOP: 'top',\n  RIGHT: isRTL() ? 'left' : 'right',\n  BOTTOM: 'bottom',\n  LEFT: isRTL() ? 'right' : 'left'\n}\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  animation: true,\n  boundary: 'clippingParents',\n  container: false,\n  customClass: '',\n  delay: 0,\n  fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n  html: false,\n  offset: [0, 6],\n  placement: 'top',\n  popperConfig: null,\n  sanitize: true,\n  sanitizeFn: null,\n  selector: false,\n  template: '
    ' +\n            '
    ' +\n            '
    ' +\n            '
    ',\n  title: '',\n  trigger: 'hover focus'\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  animation: 'boolean',\n  boundary: '(string|element)',\n  container: '(string|element|boolean)',\n  customClass: '(string|function)',\n  delay: '(number|object)',\n  fallbackPlacements: 'array',\n  html: 'boolean',\n  offset: '(array|string|function)',\n  placement: '(string|function)',\n  popperConfig: '(null|object|function)',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  selector: '(string|boolean)',\n  template: 'string',\n  title: '(string|element|function)',\n  trigger: 'string'\n}\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n  constructor(element, config) {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)')\n    }\n\n    super(element, config)\n\n    // Private\n    this._isEnabled = true\n    this._timeout = 0\n    this._isHovered = null\n    this._activeTrigger = {}\n    this._popper = null\n    this._templateFactory = null\n    this._newContent = null\n\n    // Protected\n    this.tip = null\n\n    this._setListeners()\n\n    if (!this._config.selector) {\n      this._fixTitle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  enable() {\n    this._isEnabled = true\n  }\n\n  disable() {\n    this._isEnabled = false\n  }\n\n  toggleEnabled() {\n    this._isEnabled = !this._isEnabled\n  }\n\n  toggle() {\n    if (!this._isEnabled) {\n      return\n    }\n\n    this._activeTrigger.click = !this._activeTrigger.click\n    if (this._isShown()) {\n      this._leave()\n      return\n    }\n\n    this._enter()\n  }\n\n  dispose() {\n    clearTimeout(this._timeout)\n\n    EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n\n    if (this._element.getAttribute('data-bs-original-title')) {\n      this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'))\n    }\n\n    this._disposePopper()\n    super.dispose()\n  }\n\n  show() {\n    if (this._element.style.display === 'none') {\n      throw new Error('Please use show on visible elements')\n    }\n\n    if (!(this._isWithContent() && this._isEnabled)) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW))\n    const shadowRoot = findShadowRoot(this._element)\n    const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element)\n\n    if (showEvent.defaultPrevented || !isInTheDom) {\n      return\n    }\n\n    // TODO: v6 remove this or make it optional\n    this._disposePopper()\n\n    const tip = this._getTipElement()\n\n    this._element.setAttribute('aria-describedby', tip.getAttribute('id'))\n\n    const { container } = this._config\n\n    if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n      container.append(tip)\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED))\n    }\n\n    this._popper = this._createPopper(tip)\n\n    tip.classList.add(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    const complete = () => {\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN))\n\n      if (this._isHovered === false) {\n        this._leave()\n      }\n\n      this._isHovered = false\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  hide() {\n    if (!this._isShown()) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE))\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const tip = this._getTipElement()\n    tip.classList.remove(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    this._activeTrigger[TRIGGER_CLICK] = false\n    this._activeTrigger[TRIGGER_FOCUS] = false\n    this._activeTrigger[TRIGGER_HOVER] = false\n    this._isHovered = null // it is a trick to support manual triggering\n\n    const complete = () => {\n      if (this._isWithActiveTrigger()) {\n        return\n      }\n\n      if (!this._isHovered) {\n        this._disposePopper()\n      }\n\n      this._element.removeAttribute('aria-describedby')\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN))\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  update() {\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Protected\n  _isWithContent() {\n    return Boolean(this._getTitle())\n  }\n\n  _getTipElement() {\n    if (!this.tip) {\n      this.tip = this._createTipElement(this._newContent || this._getContentForTemplate())\n    }\n\n    return this.tip\n  }\n\n  _createTipElement(content) {\n    const tip = this._getTemplateFactory(content).toHtml()\n\n    // TODO: remove this check in v6\n    if (!tip) {\n      return null\n    }\n\n    tip.classList.remove(CLASS_NAME_FADE, CLASS_NAME_SHOW)\n    // TODO: v6 the following can be achieved with CSS only\n    tip.classList.add(`bs-${this.constructor.NAME}-auto`)\n\n    const tipId = getUID(this.constructor.NAME).toString()\n\n    tip.setAttribute('id', tipId)\n\n    if (this._isAnimated()) {\n      tip.classList.add(CLASS_NAME_FADE)\n    }\n\n    return tip\n  }\n\n  setContent(content) {\n    this._newContent = content\n    if (this._isShown()) {\n      this._disposePopper()\n      this.show()\n    }\n  }\n\n  _getTemplateFactory(content) {\n    if (this._templateFactory) {\n      this._templateFactory.changeContent(content)\n    } else {\n      this._templateFactory = new TemplateFactory({\n        ...this._config,\n        // the `content` var has to be after `this._config`\n        // to override config.content in case of popover\n        content,\n        extraClass: this._resolvePossibleFunction(this._config.customClass)\n      })\n    }\n\n    return this._templateFactory\n  }\n\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n    }\n  }\n\n  _getTitle() {\n    return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title')\n  }\n\n  // Private\n  _initializeOnDelegatedTarget(event) {\n    return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig())\n  }\n\n  _isAnimated() {\n    return this._config.animation || (this.tip && this.tip.classList.contains(CLASS_NAME_FADE))\n  }\n\n  _isShown() {\n    return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _createPopper(tip) {\n    const placement = execute(this._config.placement, [this, tip, this._element])\n    const attachment = AttachmentMap[placement.toUpperCase()]\n    return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment))\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this._element])\n  }\n\n  _getPopperConfig(attachment) {\n    const defaultBsPopperConfig = {\n      placement: attachment,\n      modifiers: [\n        {\n          name: 'flip',\n          options: {\n            fallbackPlacements: this._config.fallbackPlacements\n          }\n        },\n        {\n          name: 'offset',\n          options: {\n            offset: this._getOffset()\n          }\n        },\n        {\n          name: 'preventOverflow',\n          options: {\n            boundary: this._config.boundary\n          }\n        },\n        {\n          name: 'arrow',\n          options: {\n            element: `.${this.constructor.NAME}-arrow`\n          }\n        },\n        {\n          name: 'preSetPlacement',\n          enabled: true,\n          phase: 'beforeMain',\n          fn: data => {\n            // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n            // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n            this._getTipElement().setAttribute('data-popper-placement', data.state.placement)\n          }\n        }\n      ]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _setListeners() {\n    const triggers = this._config.trigger.split(' ')\n\n    for (const trigger of triggers) {\n      if (trigger === 'click') {\n        EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK), this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context.toggle()\n        })\n      } else if (trigger !== TRIGGER_MANUAL) {\n        const eventIn = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSEENTER) :\n          this.constructor.eventName(EVENT_FOCUSIN)\n        const eventOut = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSELEAVE) :\n          this.constructor.eventName(EVENT_FOCUSOUT)\n\n        EventHandler.on(this._element, eventIn, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true\n          context._enter()\n        })\n        EventHandler.on(this._element, eventOut, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] =\n            context._element.contains(event.relatedTarget)\n\n          context._leave()\n        })\n      }\n    }\n\n    this._hideModalHandler = () => {\n      if (this._element) {\n        this.hide()\n      }\n    }\n\n    EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n  }\n\n  _fixTitle() {\n    const title = this._element.getAttribute('title')\n\n    if (!title) {\n      return\n    }\n\n    if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n      this._element.setAttribute('aria-label', title)\n    }\n\n    this._element.setAttribute('data-bs-original-title', title) // DO NOT USE IT. Is only for backwards compatibility\n    this._element.removeAttribute('title')\n  }\n\n  _enter() {\n    if (this._isShown() || this._isHovered) {\n      this._isHovered = true\n      return\n    }\n\n    this._isHovered = true\n\n    this._setTimeout(() => {\n      if (this._isHovered) {\n        this.show()\n      }\n    }, this._config.delay.show)\n  }\n\n  _leave() {\n    if (this._isWithActiveTrigger()) {\n      return\n    }\n\n    this._isHovered = false\n\n    this._setTimeout(() => {\n      if (!this._isHovered) {\n        this.hide()\n      }\n    }, this._config.delay.hide)\n  }\n\n  _setTimeout(handler, timeout) {\n    clearTimeout(this._timeout)\n    this._timeout = setTimeout(handler, timeout)\n  }\n\n  _isWithActiveTrigger() {\n    return Object.values(this._activeTrigger).includes(true)\n  }\n\n  _getConfig(config) {\n    const dataAttributes = Manipulator.getDataAttributes(this._element)\n\n    for (const dataAttribute of Object.keys(dataAttributes)) {\n      if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n        delete dataAttributes[dataAttribute]\n      }\n    }\n\n    config = {\n      ...dataAttributes,\n      ...(typeof config === 'object' && config ? config : {})\n    }\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    config.container = config.container === false ? document.body : getElement(config.container)\n\n    if (typeof config.delay === 'number') {\n      config.delay = {\n        show: config.delay,\n        hide: config.delay\n      }\n    }\n\n    if (typeof config.title === 'number') {\n      config.title = config.title.toString()\n    }\n\n    if (typeof config.content === 'number') {\n      config.content = config.content.toString()\n    }\n\n    return config\n  }\n\n  _getDelegateConfig() {\n    const config = {}\n\n    for (const [key, value] of Object.entries(this._config)) {\n      if (this.constructor.Default[key] !== value) {\n        config[key] = value\n      }\n    }\n\n    config.selector = false\n    config.trigger = 'manual'\n\n    // In the future can be replaced with:\n    // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n    // `Object.fromEntries(keysWithDifferentValues)`\n    return config\n  }\n\n  _disposePopper() {\n    if (this._popper) {\n      this._popper.destroy()\n      this._popper = null\n    }\n\n    if (this.tip) {\n      this.tip.remove()\n      this.tip = null\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tooltip.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip)\n\nexport default Tooltip\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Tooltip from './tooltip.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'popover'\n\nconst SELECTOR_TITLE = '.popover-header'\nconst SELECTOR_CONTENT = '.popover-body'\n\nconst Default = {\n  ...Tooltip.Default,\n  content: '',\n  offset: [0, 8],\n  placement: 'right',\n  template: '
    ' +\n    '
    ' +\n    '
    ' +\n    '
    ' +\n    '
    ',\n  trigger: 'click'\n}\n\nconst DefaultType = {\n  ...Tooltip.DefaultType,\n  content: '(null|string|element|function)'\n}\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Overrides\n  _isWithContent() {\n    return this._getTitle() || this._getContent()\n  }\n\n  // Private\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TITLE]: this._getTitle(),\n      [SELECTOR_CONTENT]: this._getContent()\n    }\n  }\n\n  _getContent() {\n    return this._resolvePossibleFunction(this._config.content)\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Popover.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover)\n\nexport default Popover\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getElement, isDisabled, isVisible } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'scrollspy'\nconst DATA_KEY = 'bs.scrollspy'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_ACTIVATE = `activate${EVENT_KEY}`\nconst EVENT_CLICK = `click${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item'\nconst CLASS_NAME_ACTIVE = 'active'\n\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]'\nconst SELECTOR_TARGET_LINKS = '[href]'\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group'\nconst SELECTOR_NAV_LINKS = '.nav-link'\nconst SELECTOR_NAV_ITEMS = '.nav-item'\nconst SELECTOR_LIST_ITEMS = '.list-group-item'\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`\nconst SELECTOR_DROPDOWN = '.dropdown'\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\n\nconst Default = {\n  offset: null, // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: '0px 0px -25%',\n  smoothScroll: false,\n  target: null,\n  threshold: [0.1, 0.5, 1]\n}\n\nconst DefaultType = {\n  offset: '(number|null)', // TODO v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: 'string',\n  smoothScroll: 'boolean',\n  target: 'element',\n  threshold: 'array'\n}\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    // this._element is the observablesContainer and config.target the menu links wrapper\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n    this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element\n    this._activeTarget = null\n    this._observer = null\n    this._previousScrollData = {\n      visibleEntryTop: 0,\n      parentScrollTop: 0\n    }\n    this.refresh() // initialize\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  refresh() {\n    this._initializeTargetsAndObservables()\n    this._maybeEnableSmoothScroll()\n\n    if (this._observer) {\n      this._observer.disconnect()\n    } else {\n      this._observer = this._getNewObserver()\n    }\n\n    for (const section of this._observableSections.values()) {\n      this._observer.observe(section)\n    }\n  }\n\n  dispose() {\n    this._observer.disconnect()\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n    config.target = getElement(config.target) || document.body\n\n    // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n    config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin\n\n    if (typeof config.threshold === 'string') {\n      config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value))\n    }\n\n    return config\n  }\n\n  _maybeEnableSmoothScroll() {\n    if (!this._config.smoothScroll) {\n      return\n    }\n\n    // unregister any previous listeners\n    EventHandler.off(this._config.target, EVENT_CLICK)\n\n    EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n      const observableSection = this._observableSections.get(event.target.hash)\n      if (observableSection) {\n        event.preventDefault()\n        const root = this._rootElement || window\n        const height = observableSection.offsetTop - this._element.offsetTop\n        if (root.scrollTo) {\n          root.scrollTo({ top: height, behavior: 'smooth' })\n          return\n        }\n\n        // Chrome 60 doesn't support `scrollTo`\n        root.scrollTop = height\n      }\n    })\n  }\n\n  _getNewObserver() {\n    const options = {\n      root: this._rootElement,\n      threshold: this._config.threshold,\n      rootMargin: this._config.rootMargin\n    }\n\n    return new IntersectionObserver(entries => this._observerCallback(entries), options)\n  }\n\n  // The logic of selection\n  _observerCallback(entries) {\n    const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`)\n    const activate = entry => {\n      this._previousScrollData.visibleEntryTop = entry.target.offsetTop\n      this._process(targetElement(entry))\n    }\n\n    const parentScrollTop = (this._rootElement || document.documentElement).scrollTop\n    const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop\n    this._previousScrollData.parentScrollTop = parentScrollTop\n\n    for (const entry of entries) {\n      if (!entry.isIntersecting) {\n        this._activeTarget = null\n        this._clearActiveClass(targetElement(entry))\n\n        continue\n      }\n\n      const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop\n      // if we are scrolling down, pick the bigger offsetTop\n      if (userScrollsDown && entryIsLowerThanPrevious) {\n        activate(entry)\n        // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n        if (!parentScrollTop) {\n          return\n        }\n\n        continue\n      }\n\n      // if we are scrolling up, pick the smallest offsetTop\n      if (!userScrollsDown && !entryIsLowerThanPrevious) {\n        activate(entry)\n      }\n    }\n  }\n\n  _initializeTargetsAndObservables() {\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n\n    const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target)\n\n    for (const anchor of targetLinks) {\n      // ensure that the anchor has an id and is not disabled\n      if (!anchor.hash || isDisabled(anchor)) {\n        continue\n      }\n\n      const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element)\n\n      // ensure that the observableSection exists & is visible\n      if (isVisible(observableSection)) {\n        this._targetLinks.set(decodeURI(anchor.hash), anchor)\n        this._observableSections.set(anchor.hash, observableSection)\n      }\n    }\n  }\n\n  _process(target) {\n    if (this._activeTarget === target) {\n      return\n    }\n\n    this._clearActiveClass(this._config.target)\n    this._activeTarget = target\n    target.classList.add(CLASS_NAME_ACTIVE)\n    this._activateParents(target)\n\n    EventHandler.trigger(this._element, EVENT_ACTIVATE, { relatedTarget: target })\n  }\n\n  _activateParents(target) {\n    // Activate dropdown parents\n    if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n      SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE, target.closest(SELECTOR_DROPDOWN))\n        .classList.add(CLASS_NAME_ACTIVE)\n      return\n    }\n\n    for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n      // Set triggered links parents as active\n      // With both 
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+    
    Wine dataset
    
+    Source: R/wine.R
+    
+    
    
+
+    
    
+    
    Results of a chemical analysis of wines grown in the same region in Italy,
+   derived from three different cultivars. The analysis determined the 
+   quantities of 13 chemical constituents found in each of the three types of wines.
       
+
    The grape varieties (cultivars), 'barolo', 'barbera', and 'grignolino', are indicated in wine.class.
    
+    
    
+
+    
    
+    
    data(wine)
    
+    
    
+
+    
    
+    
    Format
    
+    
    A wine data frame consisting of 178 observations (rows) and
+13 columns and vector wine.class of factors indicating the cultivars.
+The variables are:
    Alcohol
    
+
    a numeric vector
    
+
+     
    MalicAcid
    
+
    Malic acid, a numeric vector
    
+
+     
    Ash
    
+
    Ash, a numeric vector
    
+
+     
    AlcAsh
    
+
    Alcalinity of ash, a numeric vector
    
+
+     
    Mg
    
+
    Magnesium, a numeric vector
    
+
+     
    Phenols
    
+
    total phenols, a numeric vector
    
+
+     
    Flav
    
+
    Flavanoids, a numeric vector
    
+
+     
    NonFlavPhenols
    
+
    Nonflavanoid phenols, a numeric vector
    
+
+     
    Proa
    
+
    Proanthocyanins, a numeric vector
    
+
+     
    Color
    
+
    Color intensity, a numeric vector
    
+
+     
    Hue
    
+
    a numeric vector
    
+
+     
    OD
    
+
    D280/OD315 of diluted wines, a numeric vector
    
+
+     
    Proline
    
+
    a numeric vector
    
+
+     
+
    
+    
    
+    
    Source
    
+    
    UCI Machine Learning Repository (http://archive.ics.uci.edu/ml/datasets/Wine)
    
+    
    
+
+    
    
+    
    Examples
    
+    
    data(wine)
+table(wine.class)
+#> wine.class
+#>     barolo grignolino    barbera 
+#>         59         71         48 
+
+wine.pca <- prcomp(wine, scale. = TRUE)
+ggscreeplot(wine.pca)                                               
+
+ggbiplot(wine.pca, 
+         obs.scale = 1, var.scale = 1, 
+         groups = wine.class, ellipse = TRUE, circle = TRUE)
+
+
    
+    
    
+  
    
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    
+      
    
+
+      
+
+      
    
+  
    
+    
    
+    
    Biplot for Principal Components using ggplot2
    
+    Source: R/ggbiplot.R
+    
+    
    
+
+    
    
+    
    A biplot simultaneously displays information on the observations (as points)
+and the variables (as vectors) in a multidimensional dataset. The 2D biplot
+is typically based on the first two principal components of a dataset, giving a rank 2 approximation 
+to the data. The “bi” in biplot refers to the fact that two sets of points (i.e., the rows and
+columns of the data matrix) are visualized by scalar products, not the fact
+that the display is usually two-dimensional.
    
+
    The biplot method for principal component analysis was originally defined by Gabriel (1971, 1981).
+Gower & Hand (1996) give a more complete treatment. Greenacre (2010) is a practical user-oriented guide to biplots.
+Gower et al. (2011) is the most up to date
+exposition of biplot methodology.
    
+    
    
+
+    
    
+    
    ggbiplot(
+  pcobj,
+  choices = 1:2,
+  scale = 1,
+  pc.biplot = TRUE,
+  obs.scale = 1 - scale,
+  var.scale = scale,
+  var.factor = 1,
+  groups = NULL,
+  point.size = 1.5,
+  ellipse = FALSE,
+  ellipse.prob = 0.68,
+  ellipse.linewidth = 1.3,
+  ellipse.fill = TRUE,
+  ellipse.alpha = 0.25,
+  labels = NULL,
+  labels.size = 3,
+  alpha = 1,
+  var.axes = TRUE,
+  circle = FALSE,
+  circle.prob = 0.68,
+  varname.size = 3,
+  varname.adjust = 1.25,
+  varname.color = "black",
+  varname.abbrev = FALSE,
+  ...
+)
    
+    
    
+
+    
    
+    
    Arguments
    
+    
    pcobj
    
+
    an object returned by prcomp, princomp, 
+PCA, or lda
    
+
+
+
    choices
    
+
    Which components to plot? A vector of length 2.
    
+
+
+
    scale
    
+
    Covariance biplot (scale = 1), form biplot (scale = 0). 
+When scale = 1 (the default), the inner product 
+between the variables approximates the covariance and the distance between the points 
+approximates the Mahalanobis distance.
    
+
+
+
    pc.biplot
    
+
    Logical, for compatibility with biplot.princomp(). If TRUE, use what Gabriel (1971) 
+refers to as a "principal component biplot", with \(\alpha = 1\) and observations scaled 
+up by sqrt(n) and variables scaled down by sqrt(n). Then inner products between 
+variables approximate covariances and distances between observations approximate 
+Mahalanobis distance.
    
+
+
+
    obs.scale
    
+
    Scale factor to apply to observations
    
+
+
+
    var.scale
    
+
    Scale factor to apply to variables
    
+
+
+
    var.factor
    
+
    Factor to be applied to variable vectors after scaling. This allows the variable vectors to be reflected
+(var.factor = -1) or expanded in length (var.factor > 1) for greater visibility.
+reflect provides a simpler way to reflect the variables.
    
+
+
+
    groups
    
+
    Optional factor variable indicating the groups that the observations belong to. 
+If provided the points will be colored according to groups and this allows data ellipses also
+to be drawn when ellipse = TRUE.
    
+
+
+
    point.size
    
+
    Size of observation points.
    
+
+
+
    ellipse
    
+
    Logical; draw a normal data ellipse for each group?
    
+
+
+
    ellipse.prob
    
+
    Coverage size of the data ellipse in Normal probability
    
+
+
+
    ellipse.linewidth
    
+
    Thickness of the line outlining the ellipses
    
+
+
+
    ellipse.fill
    
+
    Logical; should the ellipses be filled?
    
+
+
+
    ellipse.alpha
    
+
    Transparency value (0 - 1) for filled ellipses
    
+
+
+
    labels
    
+
    Optional vector of labels for the observations. Often, this will be specified as the row.names()
+of the dataset.
    
+
+
+
    labels.size
    
+
    Size of the text used for the point labels
    
+
+
+
    alpha
    
+
    Alpha transparency value for the points (0 = transparent, 1 = opaque)
    
+
+
+
    var.axes
    
+
    logical; draw arrows for the variables?
    
+
+
+
    circle
    
+
    draw a correlation circle? (only applies when prcomp was called with 
+scale = TRUE and when var.scale = 1)
    
+
+
+
    circle.prob
    
+
    Size of the correlation circle
    
+
+
+
    varname.size
    
+
    Size of the text for variable names
    
+
+
+
    varname.adjust
    
+
    Adjustment factor the placement of the variable names, >= 1 means farther from the arrow
    
+
+
+
    varname.color
    
+
    Color for the variable vectors and names
    
+
+
+
    varname.abbrev
    
+
    logical; whether or not to abbreviate the variable names, using abbreviate.
    
+
+
+
    ...
    
+
    other arguments passed down
    
+
+
    
+    
    
+    
    Value
    
+    
+
+
    a ggplot2 plot object of class c("gg", "ggplot")
    
+
+
+    
    
+    
    
+    
    Details
    
+    
    The biplot is constructed by using the singular value decomposition (SVD) to obtain a low-rank 
+approximation to the data matrix \(\mathbf{X}_{n \times p}\) (centered, and optionally scaled to unit variances)
+whose \(n\) rows are the observations 
+and whose \(p\) columns are the variables.
    
+
    Using the SVD, the matrix \(\mathbf{X}\), of rank \(r \le p\)
+can be expressed exactly as
+$$\mathbf{X} = \mathbf{U} \mathbf{\Lambda} \mathbf{V}'
+                 = \Sigma_i^r \lambda_i \mathbf{u}_i \mathbf{v}_i' \; ,$$
    
+
    where
    • \(\mathbf{U}\) is an \(n \times r\) orthonormal matrix of observation scores; these are also the eigenvectors
+         of \(\mathbf{X} \mathbf{X}'\),
      • 
+
    • \(\mathbf{\Lambda}\) is an \(r \times r\) diagonal matrix of singular values, 
+         \(\lambda_1 \ge \lambda_2 \ge \cdots \lambda_r\) 
+        
+        
      • 
+
    • \(\mathbf{V}\) is an \(r \times p\) orthonormal matrix of variable weights and also the eigenvectors
+         of \(\mathbf{X}' \mathbf{X}\).
      • 
+
    Then, a rank 2 (or 3) PCA approximation \(\widehat{\mathbf{X}}\) to the data matrix used in the biplot
+can be obtained from the first 2 (or 3)
+singular values \(\lambda_i\)
+and the corresponding \(\mathbf{u}_i, \mathbf{v}_i\) as
    
+
    $$\mathbf{X} \approx \widehat{\mathbf{X}} = \lambda_1 \mathbf{u}_1 \mathbf{v}_1' + \lambda_2 \mathbf{u}_2 \mathbf{v}_2' \; .$$
    
+
    The variance of \(\mathbf{X}\) accounted for by each term is \(\lambda_i^2\).
    
+
    The biplot is then obtained by overlaying two scatterplots that share a common set of axes and have a between-set scalar 
+product interpretation. Typically, the observations (rows of \(\mathbf{X}\)) are represented as points
+and the variables (columns of \(\mathbf{X}\)) are represented as vectors from the origin.
    
+
    The scale factor, \(\alpha\) allows the variances of the components to be apportioned between the
+row points and column vectors, with different interpretations, by representing the approximation
+\(\widehat{\mathbf{X}}\) as the product of two matrices,
    
+
    $$\widehat{\mathbf{X}} = (\mathbf{U} \mathbf{\Lambda}^\alpha) (\mathbf{\Lambda}^{1-\alpha} \mathbf{V}')$$
    
+
    The choice \(\alpha = 1\), assigning the singular values totally to the left factor,
+ gives a distance interpretation to the row display and 
+\(\alpha = 0\) gives a distance interpretation to the column display.
+\(\alpha = 1/2\) gives a symmetrically scaled biplot.
    
+
    When the singular values are assigned totally to the left or to the right factor, the resultant 
+coordinates are called principal coordinates and the sum of squared coordinates
+on each dimension equal the corresponding singular value.
+The other matrix, to which no part of the singular 
+values is assigned, contains the so-called standard coordinates and have sum of squared
+values equal to 1.0.
    
+    
    
+    
    
+    
    References
    
+    
    Gabriel, K. R. (1971). The biplot graphical display of matrices with application to principal component analysis. 
+  Biometrika, 58, 453–467. doi:10.2307/2334381
+.
      
+
    Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspection of data and diagnosis. 
+  In V. Barnett (Ed.), Interpreting Multivariate Data. London: Wiley.
      
+
    Greenacre, M. (2010). Biplots in Practice. BBVA Foundation, Bilbao, Spain. 
+  Available for free at https://www.fbbva.es/microsite/multivariate-statistics/.
      
+
    J.C. Gower and D. J. Hand (1996). Biplots. Chapman & Hall.
      
+
    Gower, J. C., Lubbe, S. G., & Roux, N. J. L. (2011). Understanding Biplots. Wiley.
    
+    
    
+    
    
+    
    See also
    
+    
    reflect, ggscreeplot;
+  biplot for the original stats package version;
+  fviz_pca_biplot for the factoextra package version.
    
+    
    
+    
    
+    
    Author
    
+    
    Vincent Q. Vu.
    
+    
    
+
+    
    
+    
    Examples
    
+    
    data(wine)
+library(ggplot2)
+wine.pca <- prcomp(wine, scale. = TRUE)
+ggbiplot(wine.pca, 
+         obs.scale = 1, var.scale = 1, 
+         varname.size = 4,
+         groups = wine.class, 
+         ellipse = TRUE, circle = TRUE)
+
+
+data(iris)
+iris.pca <- prcomp (~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
+                    data=iris,
+                    scale. = TRUE)
+ggbiplot(iris.pca, obs.scale = 1, var.scale = 1,
+         groups = iris$Species, point.size=2,
+         varname.size = 5, 
+         varname.color = "black",
+         varname.adjust = 1.2,
+         ellipse = TRUE, 
+         circle = TRUE) +
+  labs(fill = "Species", color = "Species") +
+  theme_minimal(base_size = 14) +
+  theme(legend.direction = 'horizontal', legend.position = 'top')
+
+
    
+    
    
+  
    
+  
+
    
+
+
+      
    
+  
    Developed by Vincent Vu, Michael Friendly.
    
+
    
+
+
    
+  
    Site built with pkgdown 2.0.7.
    
+
    
+
+      
    • 
+
+
+
+
+
+
+
+
    
+
    Why talk?
    
+
    There are quite a few implementations of biplots in R, but IMHO,
+none are sufficiently general to:
    
+
      
+
    • become a current standard,
      • 
+
    • with wide applicability, and
      • 
+
    • easily used within modern R,
      • 
+
    • encompassing the latest developments in the tidyverse
+and the ggplot2 framework.
      • 
+
    
+
    Does anyone want to join me in making biplots more accessible and
+easy to use in modern R?
    
+
    
+
    My problem
    
+
    My problem, as a user and explainer
+is that with none of these can I
    
+
      
+
    • easily create and describe simple examples of biplot methods
      • 
+
    • with all the graphical attributes I want to control for a given
+example.
      • 
+
    
+
    
+
    
+
    What I’d like
    
+
      
+
    • Provide a common interface for PCA / LDA and
+all related methods: E.g.,
      • 
+
    
+
    
+
    {`prcomp() / princomp() / MASS::lda(), …} -> a common “biplot”
+class object.
    
+
    
+
      
+
    • Easily allow the different scalings, to show
+row/column variables in principal or standard coordinates.
      • 
+
    • When there are groups, provide nice data ellipses or other bivariate
+summaries (convex hulls, …) for each group, with fine control over
+graphical attributes (color, fill, …), possibly direct labels for groups
+rather than a legend, etc.
      • 
+
    • show row/observation points as points or observation labels.
      • 
+
    • Be able to control the point/character size easily. Be able to
+filter out some point labels to highlight some more interesting
+ones.
      • 
+
    • For variable vectors, control all graphical attributes: color,
+linewidth, font/sizes for variable names, etc.
      • 
+
    
+
    
+
    
+    
+
+
+
+
+