How to define a flexible 'function expression' in R - r

Question

Is it possible to write a flexible function expression?
I want to use input arguments to control the expression of function.
For example
input arg -> function
c(1,1) -> func1 = function(x) x+1
c(1,3,2) -> func2 = function(x) x^2+3*x+2
c(6,8,-1) -> func3 = function(x) 6*x^2+8*x-1

Answer 1

makepoly <- function(b)
{
p <- rev(seq_along(b) - 1)
function(x)
{
xp <- outer(x, p, '^')
rowSums(xp * rep(b, each=length(x)))
}
}
# x^2 + 2x + 3
f <- makepoly(1:3)
f(0:4)
[1] 3 6 11 18 27

Answer 2

Here is my take on this task
create_poly <- function(coef)
paste(rev(coef),
paste("x", seq_along(coef) - 1, sep = "^"),
sep = "*", collapse = " + ")
make_polyfun <- function(input) {
myfun <- paste("function(x)", create_poly(input))
eval(parse(text = myfun))
}
With the example the OP gave we have :
make_polyfun(c(1, 1))
## function(x) 1*x^0 + 1*x^1
## <environment: 0x243a540>
make_polyfun(c(1, 3, 2))
## function(x) 2*x^0 + 3*x^1 + 1*x^2
## <environment: 0x1bd46e0>
make_polyfun(c(6, 8, 1))
## function(x) 1*x^0 + 8*x^1 + 6*x^2
## <environment: 0x22a59c0>

Answer 3

You can use polynom
library(polynom)
as.polynomial(c(2,3,1))
2 + 3*x + x^2
as.polynomial(c(6,8,1)
1 + 8*x + 6*x^2
EDIT you can of course coerce the result to a function using the genericas.function.polynomial. better here you can use ,as.polylist` to create many polynomials given a list of coefficients lists. For example:
lapply(as.polylist(list(c(2,3,1),c(6,8,1),c(6,8,-1))),
as.function)
[[1]]
function (x)
{
w <- 0
w <- 1 + x * w
w <- 3 + x * w
w <- 2 + x * w
w
}
<environment: 0x00000000113bd778>
[[2]]
function (x)
{
w <- 0
w <- 1 + x * w
w <- 8 + x * w
w <- 6 + x * w
w
}
<environment: 0x0000000011524168>
[[3]]
function (x)
{
w <- 0
w <- -1 + x * w
w <- 8 + x * w
w <- 6 + x * w
w
}
<environment: 0x0000000011527f28>

Answer 4

It's not clear how general you want to be from OP. For the particular case of polynomials, you can do:
f = function(x, coeffs) {
sum(outer(x, seq_along(coeffs) - 1, `^`) * coeffs)
}
f(2, c(1,2,3)) # 1 + 2*x + 3*x^2, with x = 2
#[1] 17

Answer 5

I read this as the desire to make functions and I think the agstudy/eddi responses would probably do this, but I thought trying it from scratch might be instructive:
poly.maker <- function(coefs) { func <- function(x){} #empty func in x
body(func) <- parse(text= paste( seq_along(coefs),"*x^",
(length(coefs)-1):0,collapse="+" ) )
return(func) }
func2 <- poly.maker(c(1,2,3)) # return a function
func2(3) # now test it out
#[1] 18
Note I needed to swap the order to agree with the OP request, which I only noticed after getting different results than #dickoa. This seems less clunky:
poly.make2 <- function(coefs) { func <- function(x){}
body(func) <- bquote(sum(.(coefs)*x^.( (length(coefs)-1):0 ) ) )
return(func) }
func <- poly.make2(c(1,2,5))
func
#function (x)
#sum(c(1, 2, 5) * x^c(2L, 1L, 0L))
#<environment: 0x29023d508>
func(3)
#[1] 20

Answer 6

One liner:
polymaker2 <- function(coefs)
{
eval(parse(text=paste0( "function(x) sum(x^(",length(coefs)-1,":0) * ",capture.output(dput(coefs)),")" )))
}
Vectorized form:
polymaker3 <- function(coefs)
{
eval(parse(text=paste0( "function(x) colSums(t(outer(x, ",length(coefs)-1,":0, `^`))*",capture.output(dput(coefs)),")" )))
}