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Integrating a function that contains for loop or vectorization for for loop

2 messages · Shaami, Rui Barradas

Original
Shaami
# 
Hi Everyone

It has been a long time I am facing a problem with integrating a function
that contains for-loop or even vectorization of for loop. Could you please
guide for the following MWE that how I could get rid of the error or
warning messages?

My MWE code is here:

myfun <- function(X, a, b){
  k <- 1:10
  term <- a * b * X^k
  fx <- exp(X) * sum(term)
  print(X)
  print(term)
  return(fx)
}

a <- 5
b <- 4
integrate(myfun, lower = 0, upper = 10, a = a, b = b)

If I use the following version of my code, it does not give any error.
However, I am not sure that it is correct.

myfun <- function(X, a, b){
  term <- list()
  for(k in 1:10){
    term[[k]] <- a * b * X^k
  }
  fx <- exp(X) * sum(unlist(term))
  print(X)
  print(term)
  return(fx)
}

a <- 5
b <- 4
integrate(myfun, lower = 0, upper = 10, a = a, b = b)



Thank you

Regrads
1 day later
Rui Barradas
# 
Hello,

The functions are not equivalent.
integrate subdivides the interval lower = 0, upper = 10 in into a 
maximum subdivisions = 100L. If you print length(X) you will see that 
it's 21.
X is a vector of 21 values and to compute X^(1:10) this expands to

X[1]^1, X[2]^2, ..., X[10]^10, X[11]^1, X[12]^2, ..., X[20]^10, X[21]^1

Each of these values is multiplied by a*b and then added.
A total different computation is performed by the second function:

X[1:21]^1, X[1:21]^2, etc.

I have rewrote the functions a bit, without the print statements and in 
myfun2 creating the list term beforehand.



myfun <- function(X, a, b){
 ? k <- 1:10
 ? term <- a * b * X^k
 ? fx <- exp(X) * sum(term)
 ? fx
}

myfun2 <- function(X, a, b){
 ? term <- vector("list", length = 10)
 ? for(k in 1:10){
 ??? term[[k]] <- a * b * X^k
 ? }
 ? fx <- exp(X) * sum(unlist(term))
 ? fx
}

a <- 5
b <- 4

integrate(myfun, lower = 0, upper = 10, a = a, b = b)
integrate(myfun2, lower = 0, upper = 10, a = a, b = b)

curve(myfun(x, a = a, b = b), 0, 10)
curve(myfun2(x, a = a, b = b), 0, 10, col = "blue", add = TRUE)

Hope this helps,

Rui Barradas

?s 04:14 de 18/07/2020, Shaami escreveu: