R中的ifelse（）语句出现问题

Question

I have a homework assignment where I have to write a Bessel function and compare it to the built in Bessel function in r. I have to plot the curve on the interval (0.01:10). The function has several parts and for the interval 0<=x<=3 I have to find x using equation 1. On the interval 3 < x <= infinity I have to use equation 2. I've tried the if and else but I kept having the "length >1 so first element is used" message. I found out that for vectors I need the ifelse statement but how do I actually use it? I played with it and found that it only does true/false type stuff. ie ifelse(x<=3, y, z) where all the numbers below and equal to x are y and all numbers greater than x are z. How would I go about writing a function where it does equation 1 if x <=3 and equation 2 for all other numbers?

The code I provided is the wrong one and it may be sloppy but I've been playing around with r for one week now and this is about as go

x <- seq(.01,10, .01) #sequence of numbers 0.01 - 10 in 0.01 intervals.

#Bessel function for a set of numbers
bess.J = function(x){  
  if(x<=3){
    #
    less3 =  1-2.249997*(x/3)^2+1.2656208*(x/3)^4-0.31638*(x/3)^6+0.044479*  (x/3)^8-0.0039444*(x/3)^10+0.00021*(x/3)^12
    return(less3)
  }
  #
  else{
    Tgreater3 = x - 0.78539816 - 0.04166397*(3/x) - (0.00003954*(3/x)^2) + (0.00262573*(3/x)^3) - (0.00054125*(x/3)^4) - (0.00029333*(3/x)^5) + (0.00013558*(3/x)^6)
    Fgreater3 = 0.79788456 - 0.0000077*(3/x) - (0.00552740*(3/x)^2) - (0.00009512*(3/x)^3) + (0.00137237*(3/x)^4) - (0.00072805*(3/x)^5) + (0.00014476*(3/x)^6)
    Jgreater3 = x^(-1/2)*Fgreater3*cos(Tgreater3)
    return(Jgreater3)
  }
}

plot(x,bess.J(x))

Answer 1

As you said, you can use ifelse() instead of if and else. I create 2 functions (equation1 and equation2) to make the code more readable.

equation1 <- function(x){
   1-2.249997*(x/3)^2+1.2656208*(x/3)^4-0.31638*(x/3)^6+0.044479*  (x/3)^8-0.0039444*(x/3)^10+0.00021*(x/3)^12
}

equation2 <- function(x){
  Tgreater3 = x - 0.78539816 - 0.04166397*(3/x) - (0.00003954*(3/x)^2) + (0.00262573*(3/x)^3) - (0.00054125*(x/3)^4) - (0.00029333*(3/x)^5) + (0.00013558*(3/x)^6)
  Fgreater3 = 0.79788456 - 0.0000077*(3/x) - (0.00552740*(3/x)^2) - (0.00009512*(3/x)^3) + (0.00137237*(3/x)^4) - (0.00072805*(3/x)^5) + (0.00014476*(3/x)^6)
  Jgreater3 = x^(-1/2)*Fgreater3*cos(Tgreater3)
  return(Jgreater3)
}

bess.J <- function(x){
  ifelse(x <= 3, equation1(x), equation2(x))
} 

plot(x, bess.J(x))

Answer 2

A possible solution is to write two functions, one for each equation and then use the ifelse to pass the x variable to appropriate equation.
Below I defined the function "eq1" when x<=3 and defined "eq2" for x>3.

x <- seq(.01,10, .01) #sequence of numbers 0.01 - 10 in 0.01 intervals.

#Bessel function for a set of number
eq1<- function(x) {
  less3 =  1-2.249997*(x/3)^2+1.2656208*(x/3)^4-0.31638*(x/3)^6+0.044479*  (x/3)^8-0.0039444*(x/3)^10+0.00021*(x/3)^12
  return(less3)
}

eq2<- function(x){
  Tgreater3 = x - 0.78539816 - 0.04166397*(3/x) - (0.00003954*(3/x)^2) + (0.00262573*(3/x)^3) - (0.00054125*(x/3)^4) - (0.00029333*(3/x)^5) + (0.00013558*(3/x)^6)
  Fgreater3 = 0.79788456 - 0.0000077*(3/x) - (0.00552740*(3/x)^2) - (0.00009512*(3/x)^3) + (0.00137237*(3/x)^4) - (0.00072805*(3/x)^5) + (0.00014476*(3/x)^6)
  Jgreater3 = x^(-1/2)*Fgreater3*cos(Tgreater3)
  return(Jgreater3)
}


bess.jx<-ifelse(x<=3, eq1(x), eq2(x))
plot(x,bess.jx)