Nothing
library(mcmc)
x <- seq(0, 10, length = 10001)
### sub-exponentially light transformation
b <- 0.5
fsub <- morph(b = b)
y <- unlist(Map(fsub$inverse, x))
myfsub <- function(x) ifelse(x > 1 / b, exp(b * x) - exp(1) / 3,
(x * b)^3 * exp(1) / 6 + x * b * exp(1) / 2)
y2 <- myfsub(x)
all.equal(y, y2, tolerance = 1e-14)
z <- unlist(Map(fsub$transform, y))
all.equal(z, x, tolerance = 1e-14)
### exponentially light transformation
r <- 5
p <- 3
fp3 <- morph(r = r)
y <- unlist(Map(fp3$inverse, x))
myfp3 <- function(x) ifelse(x < r, x, x + (x - r)^p)
y2 <- myfp3(x)
all.equal(y, y2, tolerance = 1e-14)
z <- unlist(Map(fp3$transform, y))
all.equal(z, x, tolerance = 1e-12)
### both together
fboth <- morph(b = b, r = r)
y <- unlist(Map(fboth$inverse, x))
y2 <- myfsub(myfp3(x))
all.equal(y, y2, tolerance = 1e-14)
z <- unlist(Map(fboth$transform, y))
all.equal(z, x, tolerance = 1e-12)
### exponentially light transformation with p != 3
r <- 5
p <- 2.2
fpo <- morph(r = r, p = p)
y <- unlist(Map(fpo$inverse, x))
myfpo <- function(x) ifelse(x < r, x, x + (x - r)^p)
y2 <- myfpo(x)
all.equal(y, y2, tolerance = 1e-14)
z <- unlist(Map(fpo$transform, y))
all.equal(z, x, tolerance = 1e-14)
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