\donttest{
if (!requireNamespace("ggplot2", quietly = TRUE)) utils::install.packages(
  "ggplot2", repos = "https://cloud.r-project.org", quiet = TRUE
)

### linear regression with one-dimensional covariate
library(fastcpd)
set.seed(1)
p <- 1
x <- mvtnorm::rmvnorm(300, rep(0, p), diag(p))
theta_0 <- matrix(c(1, -1, 0.5))
y <- c(
  x[1:100, ] * theta_0[1, ] + rnorm(100, 0, 1),
  x[101:200, ] * theta_0[2, ] + rnorm(100, 0, 1),
  x[201:300, ] * theta_0[3, ] + rnorm(100, 0, 1)
)
result <- fastcpd(
  formula = y ~ . - 1,
  data = data.frame(y = y, x = x),
  family = "lm"
)
plot(result)
summary(result)

### custom logistic regression
library(fastcpd)
set.seed(1)
p <- 5
x <- matrix(rnorm(375 * p, 0, 1), ncol = p)
theta <- rbind(rnorm(p, 0, 1), rnorm(p, 2, 1))
y <- c(
  rbinom(200, 1, 1 / (1 + exp(-x[1:200, ] %*% theta[1, ]))),
  rbinom(175, 1, 1 / (1 + exp(-x[201:375, ] %*% theta[2, ])))
)
data <- data.frame(y = y, x = x)
result_builtin <- suppressWarnings(fastcpd(
  formula = y ~ . - 1,
  data = data,
  family = "binomial"
))
logistic_loss <- function(data, theta) {
  x <- data[, -1]
  y <- data[, 1]
  u <- x %*% theta
  nll <- -y * u + log(1 + exp(u))
  nll[u > 10] <- -y[u > 10] * u[u > 10] + u[u > 10]
  sum(nll)
}
logistic_loss_gradient <- function(data, theta) {
  x <- data[nrow(data), -1]
  y <- data[nrow(data), 1]
  c(-(y - 1 / (1 + exp(-x %*% theta)))) * x
}
logistic_loss_hessian <- function(data, theta) {
  x <- data[nrow(data), -1]
  prob <- 1 / (1 + exp(-x %*% theta))
  (x %o% x) * c((1 - prob) * prob)
}
result_custom <- fastcpd(
  formula = y ~ . - 1,
  data = data,
  epsilon = 1e-5,
  cost = logistic_loss,
  cost_gradient = logistic_loss_gradient,
  cost_hessian = logistic_loss_hessian
)
cat(
  "Change points detected by built-in logistic regression model: ",
  result_builtin@cp_set, "\n",
  "Change points detected by custom logistic regression model: ",
  result_custom@cp_set, "\n",
  sep = ""
)
result_custom_two_epochs <- fastcpd(
  formula = y ~ . - 1,
  data = data,
  k = function(x) 1,
  epsilon = 1e-5,
  cost = logistic_loss,
  cost_gradient = logistic_loss_gradient,
  cost_hessian = logistic_loss_hessian
)
summary(result_custom_two_epochs)

### custom cost function huber regression
library(fastcpd)
set.seed(1)
n <- 400 + 300 + 500
p <- 5
x <- mvtnorm::rmvnorm(n, mean = rep(0, p), sigma = diag(p))
theta <- rbind(
  mvtnorm::rmvnorm(1, mean = rep(0, p - 3), sigma = diag(p - 3)),
  mvtnorm::rmvnorm(1, mean = rep(5, p - 3), sigma = diag(p - 3)),
  mvtnorm::rmvnorm(1, mean = rep(9, p - 3), sigma = diag(p - 3))
)
theta <- cbind(theta, matrix(0, 3, 3))
theta <- theta[rep(seq_len(3), c(400, 300, 500)), ]
y_true <- rowSums(x * theta)
factor <- c(
  2 * stats::rbinom(400, size = 1, prob = 0.95) - 1,
  2 * stats::rbinom(300, size = 1, prob = 0.95) - 1,
  2 * stats::rbinom(500, size = 1, prob = 0.95) - 1
)
y <- factor * y_true + stats::rnorm(n)
data <- cbind.data.frame(y, x)
huber_threshold <- 1
huber_loss <- function(data, theta) {
  residual <- data[, 1] - data[, -1, drop = FALSE] %*% theta
  indicator <- abs(residual) <= huber_threshold
  sum(
    residual^2 / 2 * indicator +
      huber_threshold * (
        abs(residual) - huber_threshold / 2
      ) * (1 - indicator)
  )
}
huber_loss_gradient <- function(data, theta) {
  residual <- c(data[nrow(data), 1] - data[nrow(data), -1] %*% theta)
  if (abs(residual) <= huber_threshold) {
    -residual * data[nrow(data), -1]
  } else {
    -huber_threshold * sign(residual) * data[nrow(data), -1]
  }
}
huber_loss_hessian <- function(data, theta) {
  residual <- c(data[nrow(data), 1] - data[nrow(data), -1] %*% theta)
  if (abs(residual) <= huber_threshold) {
    outer(data[nrow(data), -1], data[nrow(data), -1])
  } else {
    0.01 * diag(length(theta))
  }
}
huber_regression_result <- fastcpd(
  formula = y ~ . - 1,
  data = data,
  beta = (p + 1) * log(n) / 2,
  cost = huber_loss,
  cost_gradient = huber_loss_gradient,
  cost_hessian = huber_loss_hessian
)
summary(huber_regression_result)
}