R: Converting expression to function for integral-CodePudding

My goal is to integrate the square of the derivative of a differentiable function between 0 and 1: I've tried 2 codes: Attempt 1:

expToFunc <- function(f) {
  #input as an expression in terms of x
  function(x) eval(f)
}

int <- function(f) {
  Df2 <- substitute(expression(y^2), list(y = D(f,'x')))
  integrate(expToFunc(Df2),0,1)
}

int(expression(x*(x-1)))

Returns Error in integrate(expToFunc(Df2), 0, 1) : evaluation of function gave a result of wrong length., I think my first function isn't acting as intended expToFunc(expression(x*(x-1))) returns function(x) eval(f), and so the code interpreted the f as that letter and not the input?

Attempt 2 is similar, with a change in attempting to convert from expression to function by using the expression string

expToFunc <- function(str) {
  #input as a string in terms of x
  function(x) str
}

int <- function(f) {
  Df2 <- substitute(expression(y^2), list(y = D(f,'x')))
  integrate(expToFunc(Df2[[1]]),0,1)
}

int(expression(x*(x-1)))

which return the same thing as Attempt 1, as well as with Df2[[2]] in the place of Df2[[1]] as confusingly

Df2 <- substitute(expression(y^2), list(y = D(expression(x * (x-1)),'x')))
Df2[[1]]
% expression
Df2[[2]]
% ((x - 1)   x)^2

I'm clearly missing something with the expression class or integrate function, but I'm not sure what. Any help is greatly appreciated.

CodePudding user response：

1) Evaluate the expression and assign it to the body of a function f. Then integrate f.

int <- function(expr) {
  f <- function(x) {}
  body(f) <- eval(substitute(expression(y^2), list(y = D(expr,'x'))))
  integrate(f, 0, 1)
}

int(expression(x*(x-1)))
## .3333333 with absolute error < 3.7e-15

2) This variation also works.

int2 <- function(expr) {
  f <- function(x) {}
  body(f) <- eval(substitute(D(expr, "x")))
  integrate(function(x) f(x)^2, 0, 1)
}

int2(expression(x * (x - 1)))
## .3333333 with absolute error < 3.7e-15

3) as.function.formula in the gsubfn package can turn a formula into a function.

library(gsubfn)
int3 <- function(fo) {
  integrate(function(x) as.function(fo)(x)^2, 0, 1)
}

int3(~ x*(x-1))
## .3333333 with absolute error < 3.7e-15