# bpca-Ex.R — exemplos agregados dos arquivos man/*.Rd
# Gerado com tools:::Rd2ex() a partir de cada .Rd com secao \examples.
# Antes em \dontrun (prefixo ##D) — descomentado para execucao manual.

library(bpca)


# ---- bpca-package.Rd ----

### Name: bpca-package
### Title: Biplot of Multivariate Data Based on Principal Component
###   Analysis
### Aliases: bpca-package
### Keywords: package multivariate

### ** Examples

##
## Grouping objects with different symbols and colors (2D and 3D)
##

dev.new(w = 6, h = 6)
oask <- devAskNewPage(dev.interactive(orNone = TRUE))

# 2D
plot(bpca(iris[-5]),
  var.pos = c(4, 2, 3, 1),
  var.offset = .3,
  var.cex = .7,
  obj.names = FALSE,
  obj.cex = 1.5,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D static
plot(
  bpca(iris[-5],
    d = 1:3
  ),
  var.color = c("blue", "red"),
  var.cex = 1,
  obj.names = FALSE,
  obj.cex = 1,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D dynamic
plot(
  bpca(iris[-5],
    method = "hj",
    d = 1:3
  ),
  rgl.use = TRUE,
  var.col = c("blue", "red"),
  var.cex = 1.2,
  obj.names = FALSE,
  obj.cex = .8,
  obj.col = c("red", "green3", "orange")[as.numeric(iris$Species)],
  simple.axes = FALSE,
  box = TRUE
)

##
## New plotting options
##
plot(bpca(ontario))

# Labels for all objects
(obj.lab <- paste("g",
  1:18,
  sep = ""
))

# Set obj.labels
plot(bpca(ontario),
  obj.labels = obj.lab
)

# Evaluate an object (1 is the default)
plot(bpca(ontario),
  type = "eo",
  obj.cex = 1
)

plot(bpca(ontario),
  type = "eo",
  obj.id = 7,
  obj.cex = 1
)

# Set obj.labels
plot(bpca(ontario),
  type = "eo",
  obj.labels = obj.lab,
  obj.id = 7,
  obj.cex = 1
)

# The same as above
plot(bpca(ontario),
  type = "eo",
  obj.labels = obj.lab,
  obj.id = "g7",
  obj.cex = 1
)

# Evaluate a variable (1 is the default)
plot(bpca(ontario),
  type = "ev",
  var.cex = 1
)

plot(bpca(ontario),
  type = "ev",
  var.id = "E7",
  obj.labels = obj.lab,
  var.cex = 1
)

# A complete plot
cl <- 1:3
plot(bpca(iris[-5]),
  type = "ev",
  var.id = 1,
  obj.names = FALSE,
  obj.col = cl[as.numeric(iris$Species)],
  obj.cex = 1
)

legend("topleft",
  legend = levels(iris$Species),
  text.col = cl,
  pch = 19,
  col = cl,
  cex = .9,
  box.lty = 0
)

# Compare two objects (1 and 2 are the default)
plot(bpca(ontario),
  type = "co"
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab,
  obj.id = 13:14
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab,
  obj.id = c("g7", "g13")
)

# Compare two variables
plot(bpca(ontario),
  type = "cv"
)

# Which won where/what
plot(bpca(ontario),
  type = "ww"
)

# Discriminativeness vs. representativeness
plot(bpca(ontario),
  type = "dv"
)

# Means vs. stability
plot(bpca(ontario),
  type = "ms"
)

# Rank objects with reference to the ideal variable
plot(bpca(ontario),
  type = "ro"
)

# Rank variables with reference to the ideal object
plot(bpca(ontario),
  type = "rv"
)

plot(bpca(iris[-5]),
  type = "eo",
  obj.id = 42,
  obj.cex = 1
)

plot(bpca(iris[-5]),
  type = "ev",
  var.id = "Sepal.Width"
)

plot(bpca(iris[-5]),
  type = "ev",
  var.id = "Sepal.Length"
)

devAskNewPage(oask)


# ---- bpca.Rd ----

### Name: bpca
### Title: Biplot of Multivariate Data Based on Principal Component
###   Analysis
### Aliases: bpca bpca.default bpca.prcomp
### Keywords: multivariate

### ** Examples

##
## Example 1
## Compute and plot a bpca object with base graphics (2D)
##

bp <- bpca(gabriel1971)

dev.new(w = 6, h = 6)
oask <- devAskNewPage(dev.interactive(orNone = TRUE))
plot(bp)

# Explore the object created by bpca()
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd

##
## Example 2
## Compute and plot a bpca object with scatterplot3d (3D)
##

bp <- bpca(gabriel1971,
  d = 2:4
)

plot(bp)

# Explore the object created by bpca()
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd

##
## Example 3
## Compute and plot a bpca object with rgl (3D)
##

plot(
  bpca(gabriel1971,
    d = 1:3
  ),
  rgl.use = TRUE
)

# Tip: interact with the graphic using the mouse
# left button: click and drag to rotate;
# right button: click and drag to zoom.

##
## Example 4
## Group objects using different symbols and colors (2D and 3D)
##

# 2D
plot(bpca(iris[-5]),
  var.cex = .7,
  obj.names = FALSE,
  obj.cex = 1.5,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D static
plot(
  bpca(iris[-5],
    d = 1:3
  ),
  var.color = c("blue", "red"),
  var.cex = 1,
  obj.names = FALSE,
  obj.cex = 1,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D dynamic
plot(
  bpca(iris[-5],
    method = "hj",
    d = 1:3
  ),
  rgl.use = TRUE,
  var.col = c("blue", "red"),
  var.cex = 1.2,
  obj.names = FALSE,
  obj.cex = .8,
  obj.col = c("red", "green3", "orange")[as.numeric(iris$Species)],
  simple.axes = FALSE,
  box = TRUE
)

devAskNewPage(oask)


# ---- dt.tools.Rd ----

### Name: dt.tools
### Title: Data Tools for Multivariate Analysis
### Aliases: dt.tools
### Keywords: multivariate

### ** Examples

##
## Computes vector lengths, angles between variable vectors,
## and variable correlations from data.frame or matrix objects (n x p)
## n = rows (objects)
## p = columns (variables)
##

dt <- dt.tools(
  iris,
  2
) # Non-numeric columns are ignored internally.

# Explore the object created by dt.tools()
class(dt)
names(dt)
str(dt)

dt$length
dt$angle
dt$r
dt

# Checking the determinations
(iris.tools <- round(
  dt.tools(iris,
    center = 2
  )$r,
  5
))

(iris.obsv <- round(
  cor(iris[-5]),
  5
))

all(iris.tools == iris.obsv)


# ---- gabriel1971.Rd ----

### Name: gabriel1971
### Title: Percentages of households having various facilities and
###   appliances in East Jerusalem Arab areas, by quarters of the town
### Aliases: gabriel1971
### Keywords: datasets

### ** Examples

##
## A simple example
##
data(gabriel1971)
bp <- bpca(gabriel1971)

dev.new(w = 6, h = 6)
plot(bp)

# Explore the object created by bpca()
class(bp)
names(bp)
str(bp)

summary(bp)
bp$call
bp$eigenval
bp$eigenvec
bp$numb
bp$import
bp$coord
bp$coord$obj
bp$coord$var
bp$var.rb
bp$var.rd


# ---- gge2003.Rd ----

### Name: gge2003
### Title: A didactic matrix of genotypes (rows) and environments (columns)
### Aliases: gge2003
### Keywords: datasets

### ** Examples

##
## Example from Yan and Kang (2003), GGE biplot analysis
## for breeders, geneticists, and agronomists
##

data(gge2003)
bp <- bpca(t(gge2003),
  var.rb = TRUE
)

as.dist(bp$var.rb)

dev.new(w = 8, h = 4)
op <- par(no.readonly = TRUE)
par(mfrow = c(1, 2))

plot(bpca(gge2003),
  main = "Columns as variables",
  var.col = 1,
  obj.col = 2:4,
  obj.cex = .8
)

plot(bpca(t(gge2003)),
  main = "Rows as variables",
  var.col = 1,
  obj.col = c(2:4, 2),
  obj.cex = .8
)

par(op)


# ---- ontario.Rd ----

### Name: ontario
### Title: Ontario winter wheat (1993)
### Aliases: ontario
### Keywords: datasets

### ** Examples

data(ontario)

# 2D
plot(bpca(ontario,
  d = 1:2
))

# 3D
plot(
  bpca(ontario,
    d = 1:3
  ),
  rgl.use = TRUE
)


# ---- plot.Rd ----

### Name: plot
### Title: Biplot of Multivariate Data Based on Principal Component
###   Analysis
### Aliases: plot.bpca.2d plot.bpca.3d plot.qbpca
### Keywords: multivariate

### ** Examples


# To avoid overlap in a 2D biplot by manually positioning labels:
# Suppose we have 4 variables and want to position them differently
plot(bpca(ontario),
  var.pos = c(1, 3, 4, 2),
  var.offset = 0.5
)

# For 3D dynamic plots with custom offsets:
if (interactive()) {
  plot(bpca(ontario, d = 1:3),
    rgl.use = TRUE,
    var.pos = 3,
    var.offset = 0.8
  )
}

##
## Example 1
## Computing and plotting a bpca object with base graphics (2D)
##

bp <- bpca(gabriel1971)

dev.new(w = 6, h = 6)
oask <- devAskNewPage(dev.interactive(orNone = TRUE))
plot(bp)

# To avoid overlap in a 2D biplot by manually positioning labels
plot(bp,
  var.pos = c(
    1,
    3,
    rep(4, 7)
  ),
  var.offset = .3
)

# Additional graphical parameters (nonsense)
plot(
  bpca(gabriel1971,
    meth = "sqrt"
  ),
  main = "gabriel1971 - sqrt",
  sub = "The graphical parameters are working fine!",
  var.cex = .6,
  var.col = rainbow(9),
  var.pch = "v",
  obj.pch = "o",
  obj.cex = .5,
  obj.col = rainbow(8),
  obj.pos = 1,
  obj.offset = .5
)

##
## Example 2
## Computing and plotting a bpca object with scatterplot3d (3D)
##

bp <- bpca(gabriel1971,
  d = 1:3
)

plot(bp,
  var.col = rainbow(9)
)

# Additional graphical parameters (nonsense)
plot(
  bpca(gabriel1971,
    d = 1:3,
    meth = "jk"
  ),
  main = "gabriel1971 - jk",
  sub = "The graphical parameters are working fine!",
  var.pch = "+",
  var.cex = .6,
  var.col = rainbow(ncol(gabriel1971)),
  obj.pch = "*",
  obj.cex = .8,
  obj.col = rainbow(nrow(gabriel1971)),
  ref.lty = "dotted",
  ref.col = gray(.6),
  angle = 70
)

##
## Example 3
## Computing and plotting a bpca object with rgl (3D)
##

plot(
  bpca(gabriel1971,
    d = 1:3
  ),
  rgl.use = TRUE
)

# Tip: interact with the graphic using the mouse
# left button: click and drag to rotate;
# right button: click and drag to zoom.

##
## Example 4
## Grouping objects with different symbols and colors (2D and 3D)
##

# 2D
plot(bpca(iris[-5]),
  var.cex = .7,
  obj.names = FALSE,
  obj.cex = 1.5,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

plot(bpca(iris[-5]),
  var.cex = .7,
  var.pos = c(4, 2, 3, 1),
  var.offset = .3,
  obj.names = FALSE,
  obj.cex = 1.5,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D static
plot(
  bpca(iris[-5],
    d = 1:3
  ),
  var.color = c("blue", "red"),
  var.cex = 1,
  obj.names = FALSE,
  obj.cex = 1,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.pch = c("+", "*", "-")[as.numeric(iris$Species)]
)

# 3D dynamic
plot(
  bpca(iris[-5],
    method = "hj",
    d = 1:3
  ),
  rgl.use = TRUE,
  var.col = c("blue", "red"),
  var.cex = 1.2,
  obj.names = FALSE,
  obj.cex = .8,
  obj.col = c("red", "green3", "orange")[as.numeric(iris$Species)]
)

##
## Example 5
## Computing and plotting a bpca object with `obj.identify=TRUE` (2D)
##

bp <- bpca(gabriel1971)

# Normal labels
if (interactive()) {
  plot(bp,
    obj.names = FALSE,
    obj.identify = TRUE
  )
}

# Alternative labels
if (interactive()) {
  plot(bp,
    obj.names = FALSE,
    obj.labels = c("toi", "kit", "bat", "ele", "wat", "rad", "tv", "ref"),
    obj.identify = TRUE
  )
}

##
## Example 6
## Computing and plotting a bpca object with `obj.identify=TRUE` (3D)
##

bp <- bpca(gabriel1971,
  d = 1:3
)

# Normal labels
if (interactive()) {
  plot(bp,
    obj.names = FALSE,
    obj.identify = TRUE
  )
}

# Alternative labels
if (interactive()) {
  plot(bp,
    obj.names = FALSE,
    obj.labels = c("toi", "kit", "bat", "ele", "wat", "rad", "tv", "ref"),
    obj.identify = TRUE
  )
}

##
## New plotting options
##
plot(bpca(ontario))

# Labels for all objects
(obj.lab <- paste("g",
  1:18,
  sep = ""
))

# Set obj.labels
plot(bpca(ontario),
  obj.labels = obj.lab
)

# Evaluate an object (1 is the default)
plot(bpca(ontario),
  type = "eo",
  obj.cex = 1
)

plot(bpca(ontario),
  type = "eo",
  obj.cex = 1
)

plot(bpca(ontario),
  type = "eo",
  obj.id = 7,
  obj.cex = 1
)

# Set obj.labels
plot(bpca(ontario),
  type = "eo",
  obj.labels = obj.lab,
  obj.id = 7,
  obj.cex = 1
)

# The same as above
plot(bpca(ontario),
  type = "eo",
  obj.labels = obj.lab,
  obj.id = "g7",
  obj.cex = 1
)

# Evaluate a variable (1 is the default)
plot(bpca(ontario),
  type = "ev",
  var.cex = 1
)

plot(bpca(ontario),
  type = "ev",
  var.id = "E7",
  obj.labels = obj.lab,
  var.cex = 1
)

# A complete plot
cl <- 1:3
plot(bpca(iris[-5]),
  type = "ev",
  var.id = 1,
  var.fac = .3,
  obj.names = FALSE,
  obj.cex = .9,
  obj.col = cl[as.numeric(iris$Species)]
)

legend("topleft",
  legend = levels(iris$Species),
  text.col = cl,
  pch = 19,
  col = cl,
  cex = .9,
  box.lty = 0
)

# Compare two objects (1 and 2 are the default)
plot(bpca(ontario),
  type = "co",
  c.radio = .4,
  c.color = "blue",
  c.lwd = 2
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab,
  c.radio = .5,
  c.color = "blue",
  c.lwd = 2
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab,
  obj.id = 13:14
)

plot(bpca(ontario),
  type = "co",
  obj.labels = obj.lab,
  obj.id = c(
    "g7",
    "g13"
  )
)

# Compare two variables
plot(bpca(ontario),
  type = "cv",
  c.number = 3,
  c.radio = 1.5
)

# Which won where/what
plot(bpca(ontario),
  type = "ww"
)

# Discriminativeness vs. representativeness
plot(bpca(ontario),
  type = "dv"
)

plot(bpca(ontario),
  type = "dv",
  c.number = 4,
  c.radio = 1
)

# Means vs. stability
plot(bpca(ontario),
  type = "ms"
)

plot(bpca(ontario),
  type = "ms",
  c.number = 3
)

# Rank objects with reference to the ideal variable
plot(bpca(ontario),
  type = "ro"
)

plot(bpca(ontario),
  type = "ro",
  c.number = 6,
  c.radio = .5
)

# Rank variables with reference to the ideal object
plot(bpca(ontario),
  type = "rv"
)

plot(bpca(ontario),
  type = "rv",
  c.number = 6,
  c.radio = .5
)

plot(bpca(iris[-5]),
  type = "eo",
  obj.id = 42,
  obj.cex = 1
)

plot(bpca(iris[-5]),
  type = "ev",
  var.id = "Sepal.Width"
)

plot(bpca(iris[-5]),
  type = "ev",
  var.id = "Sepal.Width",
  var.factor = .3
)

devAskNewPage(oask)


# ---- print.xtable.Rd ----

### Name: print.xtable
### Title: Print Method for xtable.bpca Objects
### Aliases: print.xtable print.xtable.bpca print.xtable.default
### Keywords: multivariate

### ** Examples


## Example 1: Principal labels in Portuguese
library(xtable)

bp2 <- bpca(gabriel1971)
tbl <- xtable(bp2)
rownames(tbl) <- gsub("Eigenvectors", "Autovetores", rownames(tbl))
rownames(tbl) <- c(rownames(tbl)[1:9], "Autovalores", "Variância retida", "Variância acumulada")
dimnames(tbl)[[2]] <- c("CP 1", "CP 2")

print(tbl)

## Example 2: With bold in the column
tbl1 <- xtable(bp2)
bold <- function(x) {
  paste(
    "\textbf{",
    x,
    "}"
  )
}

print(tbl1,
  sanitize.colnames.function = bold
)

# Example 3: With italic row labels
tbl2 <- xtable(bp2)
italic <- function(x) {
  paste(
    "& \textit{",
    x,
    "}"
  )
} # The "&" keeps the correct number of table columns.

print(tbl2,
  sanitize.rownames.function = italic
)

## HTML table (e.g. R Markdown HTML): pass type via print()
print(tbl,
  type = "html"
)


# ---- qbpca.Rd ----

### Name: qbpca
### Title: Quality of the Representation of Variables by Biplot
### Aliases: qbpca
### Keywords: multivariate

### ** Examples

##
## Example 1
## Example of the `var.rb=TRUE` parameter as a quality measure (2D)
##

oask <- devAskNewPage(dev.interactive(orNone = TRUE))

## Differences between methods of factorization
# SQRT
bp1 <- bpca(gabriel1971,
  meth = "sqrt",
  var.rb = TRUE
)

qbp1 <- qbpca(
  gabriel1971,
  bp1
)

plot(qbp1,
  main = "sqrt - 2D \n (poor)"
)


# JK
bp2 <- bpca(gabriel1971,
  meth = "jk",
  var.rb = TRUE
)

qbp2 <- qbpca(
  gabriel1971,
  bp2
)

plot(qbp2,
  main = "jk - 2D \n (very poor)"
)


# GH
bp3 <- bpca(gabriel1971,
  meth = "gh",
  var.rb = TRUE
)

qbp3 <- qbpca(
  gabriel1971,
  bp3
)

plot(qbp3,
  main = "gh - 2D \n (good)"
)


# HJ
bp4 <- bpca(gabriel1971,
  meth = "hj",
  var.rb = TRUE
)

qbp4 <- qbpca(
  gabriel1971,
  bp4
)

plot(qbp4,
  main = "hj - 2D \n (good)"
)

##
## Example 2
## Example of the `var.rb=TRUE` parameter as a quality measure (3D)
##

## Differences between methods of factorization
# SQRT
bp1 <- bpca(gabriel1971,
  meth = "sqrt",
  d = 1:3,
  var.rb = TRUE
)

qbp1 <- qbpca(
  gabriel1971,
  bp1
)

plot(qbp1,
  main = "sqrt - 3D \n (poor)"
)


# JK
bp2 <- bpca(gabriel1971,
  meth = "jk",
  d = 1:3,
  var.rb = TRUE
)

qbp2 <- qbpca(
  gabriel1971,
  bp2
)

plot(qbp2,
  main = "jk - 3D \n (very poor)"
)


# GH
bp3 <- bpca(gabriel1971,
  meth = "gh",
  d = 1:3,
  var.rb = TRUE
)

qbp3 <- qbpca(
  gabriel1971,
  bp3
)

plot(qbp3,
  main = "gh - 3D \n (wow!)"
)


# HJ
bp4 <- bpca(gabriel1971,
  meth = "hj",
  d = 1:3,
  var.rb = TRUE
)

qbp4 <- qbpca(
  gabriel1971,
  bp4
)

plot(qbp4,
  main = "hj - 3D \n (wow!)"
)

devAskNewPage(oask)


# ---- summary.bpca.Rd ----

### Name: summary.bpca
### Title: Summary Method for bpca Objects
### Aliases: summary.bpca
### Keywords: bpca summary multivariate

### ** Examples

##
## Example 1
## bpca - 2D
##
# bpca
bp <- bpca(gabriel1971)
summary(bp)
summary(bp,
  presentation = TRUE
)

##
## Example 2
## bpca - 3D
##
bp <- bpca(gabriel1971,
  d = 1:3
)

# bpca
sm <- summary(bp)
str(sm)
sm
summary(bp,
  presentation = TRUE
)


# ---- var.rbf.Rd ----

### Name: var.rbf
### Title: Projected Correlations by BPCA
### Aliases: var.rbf
### Keywords: multivariate

### ** Examples

##
## Direct use
##

bp1 <- bpca(gabriel1971)
bp1$var.rb # NA

# Compute correlations of all variables under the biplot projection
(res <- var.rbf(bp1$coord$var))

##
## Typical use
##

bp2 <- bpca(gabriel1971,
  var.rb = TRUE
)

bp2$var.rb


# ---- var.rdf.Rd ----

### Name: var.rdf
### Title: Diagnostic of Projected Correlations
### Aliases: var.rdf
### Keywords: multivariate

### ** Examples

##
## Example 1
## Diagnostic of representation quality for the gabriel1971 dataset
##

oask <- devAskNewPage(dev.interactive(orNone = TRUE))

bp1 <- bpca(gabriel1971,
  meth = "hj",
  var.rb = TRUE
)

(res <- var.rdf(gabriel1971,
  bp1$var.rb,
  lim = 3
))
class(res)

##
## Example 2
## Diagnostic of representation quality using `var.rd`
##

bp2 <- bpca(gabriel1971,
  meth = "hj",
  var.rb = TRUE,
  var.rd = TRUE,
  limit = 3
)

plot(bp2,
  var.factor = 2
)

bp2$var.rd

bp2$eigenvectors

# Graphical visualization of variable importance not represented
# in the selected reduction
plot(
  bpca(gabriel1971,
    meth = "hj",
    d = 3:4
  ),
  main = "hj"
)

# Interpretation:
# RUR followed by CRISTIAN contains information in dimensions not captured
# by the 2D biplot reduction (mainly PC3).
# Among all variables, RUR and CRISTIAN are the most poorly represented
# in a 2D biplot.

##
## Example 3
## Diagnostic of iris representation quality using `var.rd`
##

bp3 <- bpca(iris[-5],
  var.rb = TRUE,
  var.rd = TRUE,
  limit = 3
)

plot(bp3,
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  var.factor = .3
)

bp3$var.rd
bp3$eigenvectors

# Graphical diagnostic
plot(
  bpca(iris[-5],
    d = 3:4
  ),
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.names = FALSE
)

# Interpretation:
# Sepal.Length followed by Petal.Width contains information in dimensions
# (mainly PC3) that is not fully captured by the PC1-PC2 reduction.
# Therefore, among all variables, these are the most poorly represented
# by a 2D biplot.

bp4 <- bpca(iris[-5],
  d = 1:3,
  var.rb = TRUE,
  var.rd = TRUE,
  limit = 2
)

plot(bp4,
  obj.names = FALSE,
  obj.pch = c("+", "-", "*")[as.numeric(iris$Species)],
  obj.col = c("red", "green3", "blue")[as.numeric(iris$Species)],
  obj.cex = 1
)

bp4$var.rd
bp4$eigenvectors

round(bp3$var.rb, 2)

round(cor(iris[-5]), 2)

# Good representation of all variables with a 3D biplot.

devAskNewPage(oask)


# ---- xtable.bpca.Rd ----

### Name: xtable.bpca
### Title: LaTeX Table for Biplot Results
### Aliases: xtable.bpca
### Keywords: multivariate table latex bpca

### ** Examples

## Example 1: Simplest use
library(xtable)

bp <- bpca(iris[-5],
  d = 1:3
)

xtable::xtable(bp)

## Example 2: With caption and label
bp2 <- bpca(gabriel1971)

xtable::xtable(bp2,
  caption = "Biplot gabriel1971",
  label = "example_2"
)