set.seed(313)
x1 <- sort(rnorm(10))
y1 <- c(rep(1, 3), rep(2, 3), rep(3, 4)) + rbinom(10, 10, 0.1)
x2 <- c(rep(1, 2), rep(2, 2), runif(4, 3, 4), rep(5, 2))
y2 <- c(rep(1, 3), rep(2, 3), rep(3, 4)) + rbinom(10, 10, 0.1)
x3 <- c(rep(1, 2), rep(2, 3), c(3, 4, 5, 5, 5))
y3 <- c(rep(1, 3), rep(2, 3), rep(3, 4))
x4 <- c(rep(1, 3), rep(2, 3), c(3, 4, 5, 5))
y4 <- c(rep(1, 3), rep(2, 3), rep(3, 4))
x5 <- c(rep(1, 3), rep(2, 3), c(3, 4, 4, 4))
y5 <- c(rep(1, 3), c(2, 3, 3), c(3, 4, 4, 5))
x6 <- c(rep(1, 3), rep(2, 3), c(5, 5, 5, 5))
y6 <- c(rep(1, 3), rep(2, 3), c(3, 4, 5, 6))
x7 <- c(rep(1, 3), rep(2, 3), rep(3, 3))
y7 <- c(1, 2, 3, 3, 2, 1, 2, 1, 3)
plot(x1, y1)
plot(x2, y2)
plot(x3, y3)
plot(x4, y4) # y = f(x) is weakly monotone.
plot(x4, x4**2) # y =
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