---
title: "Comparison with other R packages"
output: rmarkdown::html_vignette
description: |
  Speed and result comparison with other R packages.
vignette: >
  %\VignetteIndexEntry{Comparison with other R packages}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE, comment = "#>", eval = TRUE, cache = FALSE,
  warning = FALSE, fig.width = 8, fig.height = 5
)
```

All `mosum` code is commented out due to
[[#4](https://github.com/doccstat/fastcpd/issues/4)].

All `mcp` code is commented out due to
[link 1](https://github.com/doccstat/fastcpd/actions/runs/7272426093/job/19814531091)
and
[link 2](https://github.com/doccstat/fastcpd/actions/runs/7272426093/job/19814531284).

All `bcp` code is commented out due to
[[#5](https://github.com/doccstat/fastcpd/issues/5)]

```{r package_installation}
for (
  package in c(
    # "bcp",
    "ggplot2", "mvtnorm",
    "breakfast", "changepoint", "cpm", "CptNonPar", "ecp", "fpop", "gfpop",
    "InspectChangepoint", "jointseg", "mcp", "mosum", "not", "Rbeast",
    "segmented", "stepR", "strucchange", "VARDetect", "wbs"
  )
) {
  if (!requireNamespace(package, quietly = TRUE)) utils::install.packages(
    package, repos = "https://cloud.r-project.org", quiet = TRUE
  )
}
```

# Data setup

## Univariate mean change

```{r data-setup-univariate-mean-change}
# Univariate mean change
set.seed(1)
p <- 1
mean_data_1 <- rbind(
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(100, p)),
  mvtnorm::rmvnorm(400, mean = rep(50, p), sigma = diag(100, p)),
  mvtnorm::rmvnorm(300, mean = rep(2, p), sigma = diag(100, p))
)

plot.ts(mean_data_1)
```

## Univariate mean and/or variance change

```{r data-setup-univariate-mean-and-or-variance-change}
# Univariate mean and/or variance change
set.seed(1)
p <- 1
mv_data_1 <- rbind(
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(400, mean = rep(10, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(50, p)),
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(400, mean = rep(10, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(300, mean = rep(10, p), sigma = diag(50, p))
)

plot.ts(mv_data_1)
```

## Multivariate mean change

```{r data-setup-multivariate-mean-change}
# Multivariate mean change
set.seed(1)
p <- 3
mean_data_3 <- rbind(
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(100, p)),
  mvtnorm::rmvnorm(400, mean = rep(50, p), sigma = diag(100, p)),
  mvtnorm::rmvnorm(300, mean = rep(2, p), sigma = diag(100, p))
)

plot.ts(mean_data_3)
```

## Multivariate mean and/or variance change

```{r data-setup-multivariate-mean-and-or-variance-change}
# Multivariate mean and/or variance change
set.seed(1)
p <- 3
mv_data_3 <- rbind(
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(400, mean = rep(10, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(50, p)),
  mvtnorm::rmvnorm(300, mean = rep(0, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(400, mean = rep(10, p), sigma = diag(1, p)),
  mvtnorm::rmvnorm(300, mean = rep(10, p), sigma = diag(50, p))
)

plot.ts(mv_data_3)
```

## Linear regression

```{r data-setup-linear-regression}
# Linear regression
set.seed(1)
n <- 300
p <- 4
x <- mvtnorm::rmvnorm(n, rep(0, p), diag(p))
theta_0 <- rbind(c(1, 3.2, -1, 0), c(-1, -0.5, 2.5, -2), c(0.8, 0, 1, 2))
y <- c(
  x[1:100, ] %*% theta_0[1, ] + rnorm(100, 0, 3),
  x[101:200, ] %*% theta_0[2, ] + rnorm(100, 0, 3),
  x[201:n, ] %*% theta_0[3, ] + rnorm(100, 0, 3)
)
lm_data <- data.frame(y = y, x = x)

plot.ts(lm_data)
```

## Logistic regression

```{r data-setup-logistic-regression}
# Logistic regression
set.seed(1)
n <- 500
p <- 4
x <- mvtnorm::rmvnorm(n, rep(0, p), diag(p))
theta <- rbind(rnorm(p, 0, 1), rnorm(p, 2, 1))
y <- c(
  rbinom(300, 1, 1 / (1 + exp(-x[1:300, ] %*% theta[1, ]))),
  rbinom(200, 1, 1 / (1 + exp(-x[301:n, ] %*% theta[2, ])))
)
binomial_data <- data.frame(y = y, x = x)

plot.ts(binomial_data)
```

## Poisson regression

```{r data-setup-poisson-regression}
# Poisson regression
set.seed(1)
n <- 1100
p <- 3
x <- mvtnorm::rmvnorm(n, rep(0, p), diag(p))
delta <- rnorm(p)
theta_0 <- c(1, 0.3, -1)
y <- c(
  rpois(500, exp(x[1:500, ] %*% theta_0)),
  rpois(300, exp(x[501:800, ] %*% (theta_0 + delta))),
  rpois(200, exp(x[801:1000, ] %*% theta_0)),
  rpois(100, exp(x[1001:1100, ] %*% (theta_0 - delta)))
)
poisson_data <- data.frame(y = y, x = x)

plot.ts(log(poisson_data$y))
plot.ts(poisson_data[, -1])
```

## Lasso

```{r data-setup-lasso}
# Lasso
set.seed(1)
n <- 480
p_true <- 6
p <- 50
x <- mvtnorm::rmvnorm(n, rep(0, p), diag(p))
theta_0 <- rbind(
  runif(p_true, -5, -2),
  runif(p_true, -3, 3),
  runif(p_true, 2, 5),
  runif(p_true, -5, 5)
)
theta_0 <- cbind(theta_0, matrix(0, ncol = p - p_true, nrow = 4))
y <- c(
  x[1:80, ] %*% theta_0[1, ] + rnorm(80, 0, 1),
  x[81:200, ] %*% theta_0[2, ] + rnorm(120, 0, 1),
  x[201:320, ] %*% theta_0[3, ] + rnorm(120, 0, 1),
  x[321:n, ] %*% theta_0[4, ] + rnorm(160, 0, 1)
)
lasso_data <- data.frame(y = y, x = x)

plot.ts(lasso_data[, seq_len(p_true + 1)])
```

## AR(3)

```{r data-setup-ar3}
# AR(3)
set.seed(1)
n <- 1000
x <- rep(0, n + 3)
for (i in 1:600) {
  x[i + 3] <- 0.6 * x[i + 2] - 0.2 * x[i + 1] + 0.1 * x[i] + rnorm(1, 0, 3)
}
for (i in 601:1000) {
  x[i + 3] <- 0.3 * x[i + 2] + 0.4 * x[i + 1] + 0.2 * x[i] + rnorm(1, 0, 3)
}
ar_data <- x[-seq_len(3)]

plot.ts(ar_data)
```

## GARCH(1, 1)

```{r data-setup-garch11}
# GARCH(1, 1)
set.seed(1)
n <- 400
sigma_2 <- rep(1, n + 1)
x <- rep(0, n + 1)
for (i in seq_len(200)) {
  sigma_2[i + 1] <- 20 + 0.5 * x[i]^2 + 0.1 * sigma_2[i]
  x[i + 1] <- rnorm(1, 0, sqrt(sigma_2[i + 1]))
}
for (i in 201:400) {
  sigma_2[i + 1] <- 1 + 0.1 * x[i]^2 + 0.5 * sigma_2[i]
  x[i + 1] <- rnorm(1, 0, sqrt(sigma_2[i + 1]))
}
garch_data <- x[-1]

plot.ts(garch_data)
```

## VAR(2)

```{r data-setup-var2}
# VAR(2)
set.seed(1)
n <- 800
p <- 2
theta_1 <- matrix(c(-0.3, 0.6, -0.5, 0.4, 0.2, 0.2, 0.2, -0.2), nrow = p)
theta_2 <- matrix(c(0.3, -0.4, 0.1, -0.5, -0.5, -0.2, -0.5, 0.2), nrow = p)
x <- matrix(0, n + 2, p)
for (i in 1:500) {
  x[i + 2, ] <- theta_1 %*% c(x[i + 1, ], x[i, ]) + rnorm(p, 0, 1)
}
for (i in 501:n) {
  x[i + 2, ] <- theta_2 %*% c(x[i + 1, ], x[i, ]) + rnorm(p, 0, 1)
}
var_data <- x[-seq_len(2), ]

plot.ts(var_data)
```

# Univariate mean change

The true change points are 300 and 700.
Some methods are plotted due to the un-retrievable change points.

```{r univariate-mean-change-fastcpd}
fastcpd::fastcpd.mean(mean_data_1, r.progress = FALSE)@cp_set
```

```{r univariate-mean-change-CptNonPar}
CptNonPar::np.mojo(mean_data_1, G = floor(length(mean_data_1) / 6))$cpts
```

```{r univariate-mean-change-strucchange, eval = FALSE}
strucchange::breakpoints(y ~ 1, data = data.frame(y = mean_data_1))$breakpoints
#> [1] 300 700
```

```{r univariate-mean-change-ecp, eval = FALSE}
ecp::e.divisive(mean_data_1)$estimates
#> [1]    1  301  701 1001
```

```{r univariate-mean-change-changepoint}
# Data need to be processed
changepoint::cpt.mean(c(mean_data_1))@cpts
```

```{r univariate-mean-change-breakfast}
breakfast::breakfast(mean_data_1)$cptmodel.list[[6]]$cpts
```

```{r univariate-mean-change-wbs}
wbs::wbs(mean_data_1)$cpt$cpt.ic$mbic.penalty
```

```{r univariate-mean-change-mosum}
# Data need to be processed. `G` is selected based on the example
if (interactive()) {
  mosum::mosum(c(mean_data_1), G = 40)$cpts.info$cpts
}
```

```{r univariate-mean-change-fpop}
fpop::Fpop(mean_data_1, nrow(mean_data_1))$t.est
```

```{r univariate-mean-change-gfpop}
gfpop::gfpop(
  data = mean_data_1,
  mygraph = gfpop::graph(
    penalty = 2 * log(nrow(mean_data_1)) * gfpop::sdDiff(mean_data_1) ^ 2,
    type = "updown"
  ),
  type = "mean"
)$changepoints
```

```{r univariate-mean-change-InspectChangepoint}
invisible(
  suppressMessages(
    capture.output(
      result_InspectChangepoint <- InspectChangepoint::inspect(
        t(mean_data_1),
        threshold = InspectChangepoint::compute.threshold(
          nrow(mean_data_1), ncol(mean_data_1)
        )
      )
    )
  )
)
result_InspectChangepoint$changepoints[, "location"]
```

```{r univariate-mean-change-jointseg}
jointseg::jointSeg(mean_data_1, K = 2)$bestBkp
```

```{r univariate-mean-change-Rbeast}
# Rbeast::beast(
#   mean_data_1, season = "none", print.progress = FALSE, quiet = TRUE
# )$trend$cp
```

```{r univariate-mean-change-stepR}
stepR::stepFit(mean_data_1, alpha = 0.5)$rightEnd
```

```{r univariate-mean-change-cpm}
cpm::processStream(mean_data_1, cpmType = "Student")$changePoints
```

```{r univariate-mean-change-segmented}
segmented::segmented(
  lm(y ~ 1 + x, data.frame(y = mean_data_1, x = seq_len(nrow(mean_data_1)))),
  seg.Z = ~ x
)$psi[, "Est."]
```

```{r univariate-mean-change-mcp}
if (interactive()) {
  plot(
    mcp::mcp(
      list(y ~ 1, ~ 1, ~ 1),
      data = data.frame(y = mean_data_1, x = seq_len(nrow(mean_data_1))),
      par_x = "x"
    )
  )
}
```

```{r univariate-mean-change-not}
plot(not::not(mean_data_1, contrast = "pcwsConstMean"))
```

```{r univariate-mean-change-bcp}
# plot(bcp::bcp(mean_data_1))
```

# Univariate mean and/or variance change

The true change points are 300, 700, 1000, 1300 and 1700.
Some methods are plotted due to the un-retrievable change points.

```{r univariate-mean-and-or-variance-change-fastcpd}
fastcpd::fastcpd.mv(mv_data_1, r.progress = FALSE)@cp_set
```

```{r univariate-mean-and-or-variance-change-ecp, eval = FALSE}
ecp::e.divisive(mv_data_1)$estimates
#> [1]    1  301  701 1001 1301 1701 2001
```

```{r univariate-mean-and-or-variance-change-changepoint}
# Data need to be processed
changepoint::cpt.meanvar(c(mv_data_1))@cpts
```

```{r univariate-mean-and-or-variance-change-CptNonPar}
CptNonPar::np.mojo(mv_data_1, G = floor(length(mv_data_1) / 6))$cpts
```

```{r univariate-mean-and-or-variance-change-cpm}
cpm::processStream(mv_data_1, cpmType = "GLR")$changePoints
```

```{r univariate-mean-and-or-variance-change-InspectChangepoint}
invisible(
  suppressMessages(
    capture.output(
      result_InspectChangepoint <- InspectChangepoint::inspect(
        t(mv_data_1),
        threshold = InspectChangepoint::compute.threshold(
          nrow(mv_data_1), ncol(mv_data_1)
        )
      )
    )
  )
)
result_InspectChangepoint$changepoints[, "location"]
```

```{r univariate-mean-and-or-variance-change-Rbeast}
# Rbeast::beast(
#   mv_data_1, season = "none", print.progress = FALSE, quiet = TRUE
# )$trend$cp
```

```{r univariate-mean-and-or-variance-change-mcp}
if (interactive()) {
  plot(
    mcp::mcp(
      list(y ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1),
      data = data.frame(y = mv_data_1, x = seq_len(nrow(mv_data_1))),
      par_x = "x"
    )
  )
}
```

```{r univariate-mean-and-or-variance-change-not}
plot(not::not(mv_data_1, contrast = "pcwsConstMeanVar"))
```

# Multivariate mean change

The true change points are 300 and 700.
Some methods are plotted due to the un-retrievable change points.

```{r multivariate-mean-change-fastcpd}
fastcpd::fastcpd.mean(mean_data_3, r.progress = FALSE)@cp_set
```

```{r multivariate-mean-change-CptNonPar}
CptNonPar::np.mojo(mean_data_3, G = floor(nrow(mean_data_3) / 6))$cpts
```

```{r multivariate-mean-change-InspectChangepoint}
invisible(
  suppressMessages(
    capture.output(
      result_InspectChangepoint <- InspectChangepoint::inspect(
        t(mean_data_3),
        threshold = InspectChangepoint::compute.threshold(
          nrow(mean_data_3), ncol(mean_data_3)
        )
      )
    )
  )
)
result_InspectChangepoint$changepoints[, "location"]
```

```{r multivariate-mean-change-jointseg}
jointseg::jointSeg(mean_data_3, K = 2)$bestBkp
```

```{r multivariate-mean-change-Rbeast}
# invisible(
#   capture.output(
#     result_Rbeast <- Rbeast::beast123(
#       mean_data_3,
#       metadata = list(whichDimIsTime = 1),
#       season = "none"
#     )
#   )
# )
# result_Rbeast$trend$cp
```

```{r multivariate-mean-change-strucchange, eval = FALSE}
strucchange::breakpoints(
  cbind(y.1, y.2, y.3) ~ 1, data = data.frame(y = mean_data_3)
)$breakpoints
#> [1] 300 700
```

```{r multivariate-mean-change-ecp, eval = FALSE}
ecp::e.divisive(mean_data_3)$estimates
#> [1]    1  301  701 1001
```

```{r multivariate-mean-change-bcp}
# plot(bcp::bcp(mean_data_3))
```

# Multivariate mean and/or variance change

The true change points are 300, 700, 1000, 1300 and 1700.
Some methods are plotted due to the un-retrievable change points.

```{r multivariate-mean-and-or-variance-change-fastcpd}
fastcpd::fastcpd.mv(mv_data_3, r.progress = FALSE)@cp_set
```

```{r multivariate-mean-and-or-variance-change-ecp, eval = FALSE}
ecp::e.divisive(mv_data_3)$estimates
#> [1]    1  301  701 1001 1301 1701 2001
```

```{r multivariate-mean-and-or-variance-change-InspectChangepoint}
invisible(
  suppressMessages(
    capture.output(
      result_InspectChangepoint <- InspectChangepoint::inspect(
        t(mv_data_3),
        threshold = InspectChangepoint::compute.threshold(
          nrow(mv_data_3), ncol(mv_data_3)
        )
      )
    )
  )
)
result_InspectChangepoint$changepoints[, "location"]
```

```{r multivariate-mean-and-or-variance-change-Rbeast}
# invisible(
#   capture.output(
#     result_Rbeast <- Rbeast::beast123(
#       mv_data_3,
#       metadata = list(whichDimIsTime = 1),
#       season = "none"
#     )
#   )
# )
# result_Rbeast$trend$cp
```

# Linear regression

The true change points are 100 and 200.

```{r linear-regression-fastcpd}
fastcpd::fastcpd.lm(lm_data, r.progress = FALSE)@cp_set
```

```{r linear-regression-strucchange, eval = FALSE}
strucchange::breakpoints(y ~ . - 1, data = lm_data)$breakpoints
#> [1] 100 201
```

```{r linear-regression-segmented}
segmented::segmented(
  lm(
    y ~ . - 1,
    data.frame(y = lm_data$y, x = lm_data[, -1], index = seq_len(nrow(lm_data)))
  ),
  seg.Z = ~ index
)$psi[, "Est."]
```

# Logistic regression

The true change point is 300.

```{r logistic-regression-fastcpd}
fastcpd::fastcpd.binomial(binomial_data, r.progress = FALSE)@cp_set
```

```{r logistic-regression-strucchange, eval = FALSE}
strucchange::breakpoints(y ~ . - 1, data = binomial_data)$breakpoints
#> [1] 297
```

# Poisson regression

The true change points are 500, 800 and 1000.

```{r poisson-regression-fastcpd}
fastcpd::fastcpd.poisson(poisson_data, r.progress = FALSE)@cp_set
```

```{r poisson-regression-strucchange, eval = FALSE}
strucchange::breakpoints(y ~ . - 1, data = poisson_data)$breakpoints
#> [1] 935
```

# Lasso

The true change points are 80, 200 and 320.

```{r lasso-fastcpd}
fastcpd::fastcpd.lasso(lasso_data, r.progress = FALSE)@cp_set
```

```{r lasso-strucchange, eval = FALSE}
strucchange::breakpoints(y ~ . - 1, data = lasso_data)$breakpoints,
#> [1]  80 200 321
```

# AR(3)

The true change point is 600.
Some methods are plotted due to the un-retrievable change points.

```{r ar3-fastcpd}
fastcpd::fastcpd.ar(ar_data, 3, r.progress = FALSE)@cp_set
```

```{r ar3-CptNonPar}
CptNonPar::np.mojo(ar_data, G = floor(length(ar_data) / 6))$cpts
```

```{r ar3-segmented}
segmented::segmented(
  lm(
    y ~ x + 1, data.frame(y = ar_data, x = seq_along(ar_data))
  ),
  seg.Z = ~ x
)$psi[, "Est."]
```

```{r ar3-mcp}
if (interactive()) {
  plot(
    mcp::mcp(
      list(y ~ 1 + ar(3), ~ 0 + ar(3)),
      data = data.frame(y = ar_data, x = seq_along(ar_data)),
      par_x = "x"
    )
  )
}
```

# GARCH(1, 1)

The true change point is 200.

```{r garch11-fastcpd}
fastcpd::fastcpd.garch(garch_data, c(1, 1), r.progress = FALSE)@cp_set
```

```{r garch11-CptNonPar}
CptNonPar::np.mojo(garch_data, G = floor(length(garch_data) / 6))$cpts
```

```{r garch11-strucchange, eval = FALSE}
strucchange::breakpoints(x ~ 1, data = data.frame(x = garch_data))$breakpoints
#> [1] NA
```

# VAR(2)

The true change points is 500.

```{r var2-fastcpd}
fastcpd::fastcpd.var(
  var_data, 2, cost_adjustment = NULL, r.progress = FALSE
)@cp_set
```

```{r var2-VARDetect}
VARDetect::tbss(var_data)
```

# Detection comparison using `well_log`

```{r detection-comparison-well-log, eval = FALSE}
result <- list(
  fastcpd = fastcpd.mean(well_log, trim = 0.003)@cp_set,
  changepoint = changepoint::cpt.mean(well_log)@cpts,
  CptNonPar =
    CptNonPar::np.mojo(well_log, G = floor(length(well_log) / 6))$cpts,
  strucchange = strucchange::breakpoints(
    y ~ 1, data = data.frame(y = well_log)
  )$breakpoints,
  ecp = ecp::e.divisive(matrix(well_log))$estimates,
  breakfast = breakfast::breakfast(well_log)$cptmodel.list[[6]]$cpts,
  wbs = wbs::wbs(well_log)$cpt$cpt.ic$mbic.penalty,
  mosum = mosum::mosum(c(well_log), G = 40)$cpts.info$cpts,
  # fpop = fpop::Fpop(well_log, length(well_log))$t.est,  # meaningless
  gfpop = gfpop::gfpop(
    data = well_log,
    mygraph = gfpop::graph(
      penalty = 2 * log(length(well_log)) * gfpop::sdDiff(well_log) ^ 2,
      type = "updown"
    ),
    type = "mean"
  )$changepoints,
  InspectChangepoint = InspectChangepoint::inspect(
    well_log,
    threshold = InspectChangepoint::compute.threshold(length(well_log), 1)
  )$changepoints[, "location"],
  jointseg = jointseg::jointSeg(well_log, K = 12)$bestBkp,
  Rbeast = Rbeast::beast(
    well_log, season = "none", print.progress = FALSE, quiet = TRUE
  )$trend$cp,
  stepR = stepR::stepFit(well_log, alpha = 0.5)$rightEnd
)

package_list <- sort(names(result), decreasing = TRUE)
comparison_table <- NULL
for (package_index in seq_along(package_list)) {
  package <- package_list[[package_index]]
  comparison_table <- rbind(
    comparison_table,
    data.frame(
      change_point = result[[package]],
      package = package,
      y_offset = (package_index - 1) * 400
    )
  )
}

most_selected <- sort(table(comparison_table$change_point), decreasing = TRUE)
most_selected <- sort(as.numeric(names(most_selected[most_selected >= 4])))
for (i in seq_len(length(most_selected) - 1)) {
  if (most_selected[i + 1] - most_selected[i] < 2) {
    most_selected[i] <- NA
    most_selected[i + 1] <- most_selected[i + 1] - 0.5
  }
}
(most_selected <- most_selected[!is.na(most_selected)])
#>  [1]    6.0  314.0  434.0  704.0  776.0 1021.0 1057.0 1347.0 1405.0 1502.0 1661.0 1842.0 2023.0 2202.0
#> [15] 2384.5 2445.0 2507.0 2567.5 2738.0 2921.0 3094.0 3251.0 3464.0 3499.0 3622.0 3709.0 3820.0 3976.0
```

```{r detection-comparison-well-log-plot, eval = FALSE}
ggplot2::ggplot() +
  ggplot2::geom_point(
    data = data.frame(x = seq_along(well_log), y = c(well_log)),
    ggplot2::aes(x = x, y = y)
  ) +
  ggplot2::geom_vline(
    xintercept = most_selected,
    color = "black",
    linetype = "dashed",
    alpha = 0.2
  ) +
  ggplot2::geom_point(
    data = comparison_table,
    ggplot2::aes(x = change_point, y = 95000 + y_offset, color = package),
    shape = 17,
    size = 1.75
  ) +
  ggplot2::geom_hline(
    data = comparison_table,
    ggplot2::aes(yintercept = 95000 + y_offset, color = package),
    linetype = "dashed",
    alpha = 0.1
  ) +
  ggplot2::coord_cartesian(
    ylim = c(95000 - 500, max(well_log) + 1000),
    xlim = c(-200, length(well_log) + 200),
    expand = FALSE
  ) +
  ggplot2::theme(
    panel.background = ggplot2::element_blank(),
    panel.border = ggplot2::element_rect(colour = "black", fill = NA),
    panel.grid.major = ggplot2::element_blank(),
    panel.grid.minor = ggplot2::element_blank()
  ) +
  ggplot2::xlab(NULL) + ggplot2::ylab(NULL)
```

![Plot of the detection using `well_log` data](comparison-packages-well_log-cpts.svg)

# Time comparison using `well_log`

```{r time-comparison-well-log, eval = FALSE}
microbenchmark_result <- microbenchmark::microbenchmark(
  fastcpd = fastcpd::fastcpd.mean(well_log, trim = 0.003, r.progress = FALSE),
  changepoint = changepoint::cpt.mean(well_log, method = "PELT"),
  CptNonPar = CptNonPar::np.mojo(well_log, G = floor(length(well_log) / 6)),
  strucchange =
    strucchange::breakpoints(y ~ 1, data = data.frame(y = well_log)),
  ecp = ecp::e.divisive(matrix(well_log)),
  breakfast = breakfast::breakfast(well_log),
  wbs = wbs::wbs(well_log),
  mosum = mosum::mosum(c(well_log), G = 40),
  fpop = fpop::Fpop(well_log, nrow(well_log)),
  gfpop = gfpop::gfpop(
    data = well_log,
    mygraph = gfpop::graph(
      penalty = 2 * log(length(well_log)) * gfpop::sdDiff(well_log) ^ 2,
      type = "updown"
    ),
    type = "mean"
  ),
  InspectChangepoint = InspectChangepoint::inspect(
    well_log,
    threshold = InspectChangepoint::compute.threshold(length(well_log), 1)
  ),
  jointseg = jointseg::jointSeg(well_log, K = 12),
  Rbeast = Rbeast::beast(
    well_log, season = "none", print.progress = FALSE, quiet = TRUE
  ),
  stepR = stepR::stepFit(well_log, alpha = 0.5),
  # mcp = mcp::mcp(
  #   list(y ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1, ~ 1),
  #   data = data.frame(y = well_log, x = seq_along(well_log)),
  #   par_x = "x"
  # ),
  not = not::not(well_log, contrast = "pcwsConstMean"),
  times = 10
)
#> Unit: milliseconds
#>                expr          min           lq         mean       median           uq          max neval
#>             fastcpd 4.010279e+02 4.129134e+02 4.171979e+02 4.148564e+02 4.196057e+02 4.350300e+02    10
#>         changepoint 3.195488e+01 3.230887e+01 3.743290e+01 3.352390e+01 4.418598e+01 4.980063e+01    10
#>           CptNonPar 1.809139e+04 1.867986e+04 1.904000e+04 1.876936e+04 1.947816e+04 2.076009e+04    10
#>         strucchange 5.813672e+04 5.831023e+04 5.963604e+04 5.952739e+04 6.139957e+04 6.173251e+04    10
#>                 ecp 7.534981e+05 7.642983e+05 7.742041e+05 7.661485e+05 7.880130e+05 8.003981e+05    10
#>           breakfast 9.231426e+03 9.261763e+03 9.514283e+03 9.492325e+03 9.630395e+03 1.001344e+04    10
#>                 wbs 1.133042e+02 1.168601e+02 1.189637e+02 1.187244e+02 1.201765e+02 1.281057e+02    10
#>               mosum 1.082397e+00 1.167387e+00 1.213233e+00 1.209105e+00 1.286479e+00 1.320333e+00    10
#>                fpop 2.407630e+00 2.481348e+00 2.641625e+00 2.551970e+00 2.618455e+00 3.328585e+00    10
#>               gfpop 5.918783e+01 5.959448e+01 6.081621e+01 6.006626e+01 6.048699e+01 6.725864e+01    10
#>  InspectChangepoint 1.550181e+02 1.885944e+02 2.103973e+02 2.030795e+02 2.262247e+02 3.025476e+02    10
#>            jointseg 1.082510e+01 1.082948e+01 1.174498e+01 1.110779e+01 1.221183e+01 1.424236e+01    10
#>              Rbeast 6.311987e+02 6.634019e+02 6.702594e+02 6.680217e+02 6.846772e+02 7.048629e+02    10
#>               stepR 2.812109e+01 2.836331e+01 2.864408e+01 2.862293e+01 2.897236e+01 2.933441e+01    10
#>                 not 9.350182e+01 9.469137e+01 9.684097e+01 9.647117e+01 9.763828e+01 1.031233e+02    10
```

```{r time-comparison-well-log-plot, eval = FALSE}
ggplot2::autoplot(microbenchmark_result)
```

![Plot of the running time using `well_log` data](comparison-packages-well_log-time.svg)

# Appendix: all code snippets

```{r ref.label = knitr::all_labels(), echo = TRUE, eval = FALSE}
```
