# [SOLVED] How can a make the sum of two step functions (R-stepfun) of class "stepfun"?

## Issue

From the example here I tried to make the sum as class "stepfun". I thought, `as.stepfun` is the right choice, but my ideas don’t work. What is wrong?

``````y1 <- c(0, 1, 2, 0)
x1 <- c(1, 2, 3)
f1 <- stepfun(x = x1, y = y1)
print(class(f1))
#  "stepfun"  "function" #  OK!!!
plot(f1)

y2 <- c(0, 1, 0)
x2 <- c(1.5, 2.5)
f2 <- stepfun(x = x2, y = y2)
plot(f2)

fs <- function(x, f1, f2) {
# y <- f1(x) + f2(x) #  OK
# y <- as.stepfun(x = x, y = y, ties = "ordered", right = FALSE) # does not work
# return(y) #           does not work
return(f1(x) + f2(x))
}
print(class(fs)) #  "function"
# attributes(fs) # no new information...

fm <- function(x, f1, f2) {
return(f1(x) * f2(x))
}
print(class(fm)) #  "function"
``````

Example `as.` for ` data.frame` which works as expected:

``````z <- c(1, 2)
class(z) #     "numeric"
class(as.data.frame(z)) #     "data.frame"
``````

About internals of `stepfun`

``````function (x, y, f = as.numeric(right), ties = "ordered", right = FALSE)
{
if (is.unsorted(x))
stop("stepfun: 'x' must be ordered increasingly")
n <- length(x)
if (n < 1)
stop("'x' must have length >= 1")
n1 <- n + 1L
if (length(y) != n1)
stop("'y' must be one longer than 'x'")
rval <- approxfun(x, y[-if (right)
n1
else 1], method = "constant", yleft = y[1L], yright = y[n1],
f = f, ties = ties)
class(rval) <- c("stepfun", class(rval))
attr(rval, "call") <- sys.call()
rval
}
``````

## Solution

Thanks to the answers from @jblood94, @user2554330 and @rbm here I found an elegant way which I plan to use in my case. I hope that also helps others:

``````par(mfrow = c(2, 2))
y1 <- c(0, 1, 2, 0)
x1 <- c(1, 2, 3)
f1 <- stepfun(x = x1, y = y1)

y2 <- c(0, 1, 0)
x2 <- c(1.5, 2.5)
f2 <- stepfun(x = x2, y = y2)

plot(f1)
plot(f2)

'+.stepfun' <- function(f1, f2) {
xs1 <- get("x", envir = environment(f1))
xs2 <- get("x", envir = environment(f2))
xs <- sort(unique(c(x1, x2)))
ys <- f1(c(xs - 1, xs)) + f2(c(xs - 1, xs))
return(stepfun(x = xs, y = ys))
}
f1 + f2
print(class(f1 + f2))
plot(f1 + f2, main = "Sum f1+f2")

'*.stepfun' <- function(f1, f2) {
xs1 <- get("x", envir = environment(f1))
xs2 <- get("x", envir = environment(f2))
xs <- sort(unique(c(x1, x2)))
ys <- f1(c(xs - 1, xs)) * f2(c(xs - 1, xs))
return(stepfun(x = xs, y = ys))
}
f1 * f2
print(class(f1 * f2))
plot(f1 * f2, main = "Sum f1*f2")

par(mfrow = c(1, 1))
``````