Misunderstanding of functions in R

Question

I have a vector

p <- seq(0,1,length=11)

That I want to use as the independent variable in the summation

If I craft a function that codes the summation by hand

f <- function(a){
a^0*(1-a)^5+a^1*(1-a)^4+...
}

and pass it p, then I get the correct output and no errors are thrown

results <- f(p)

I can plot it, results is the right length, everything's kosher. It just looks really ugly so I wanted to use sum() instead and tried

i <- 0:5    
g <- function(a,i){
    sum(a^i*(1-a)^(5-i))
}

but when I attempt g(p,i) it throws the error

longer object length is not a multiple of shorter object length

I believe the reason I'm getting this error is answered over here quite nicely, especially the part about recycling. sum cycles through the i vector as well as p at the same time, then starts over with p[7] and i[1] when it runs into the end of i. My question, however, is what is the CORRECT way to simplify f into g?

baptiste · Answer 1 · 2017-10-04T20:59:07.843

3

I'd do something like this,

p <- seq(0,1,length=11)
i <- 0:5
g <- function(a,i){
  a^i*(1-a)^(5-i)
}

plot(p, rowSums(outer(X = p, Y = i, FUN = g)))

To answer your question, I don't think there is one correct way to do this; a more functional approach might be

Reduce(function(s, x) s + g(p, x), x = 0:5, init=0)

but it's likely to be less efficient, and arguably less readable.

edited Oct 04 '17 at 20:59

answered Oct 04 '17 at 20:51

baptiste

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You're absolutely right, there isn't one correct way. Perhaps I should have said 'a correct' since my solution was clearly broken. – Pentaquark Oct 05 '17 at 20:11
note that if `p` is a large vector the proposed sapply solutions will be less efficient – baptiste Oct 05 '17 at 21:17
How large? It presently only has ~100 elements and I don't intend to make it larger. – Pentaquark Oct 06 '17 at 15:05
in that case it won't make any difference and you can go with whichever solution feels most natural to you – baptiste Oct 06 '17 at 20:17

score 2 · Answer 2 · answered Oct 04 '17 at 20:44

2

Maybe try this:

g <- function(a, i){
  sum(sapply(i, function(x)a ^ x * (1 - a) ^ (5 - x)))
}


p <- seq(0, 1, length = 11)
i <- 0:5
g(p, i)
# [1] 5.3999

answered Oct 04 '17 at 20:44

zx8754

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1

Thanks so much for responding! I think perhaps I wasn't clear which vector I need to map but `sapply` is definitely what I needed. – Pentaquark Oct 05 '17 at 15:34

John Coleman · Accepted Answer · 2017-10-04T20:52:20.390

2

The function that you want to compute isn't naturally vectorized with respect to p. sapply is a natural choice for mapping non-vectorized functions over a vector:

f <- function(x){
  i <- 0:5
  sum(x^i*(1-x)^(5-i))
}

p <- seq(0,1,length=11)

sums <- sapply(p,f)
> sums
 [1] 1.0000 0.6643 0.4368 0.2923 0.2128 0.1875 0.2128
 [8] 0.2923 0.4368 0.6643 1.0000

edited Oct 04 '17 at 20:52

answered Oct 04 '17 at 20:47

John Coleman

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Thanks so much! This is exactly the answer I needed. – Pentaquark Oct 05 '17 at 15:34
If I wanted to pass my function additional vectors, how would I go about that with `sapply`? For example, if I wanted to set the length of the `i` vector outside of the `function` and pass it as `function(x,i)`, what would be the proper way to do that? Trying `sapply(p,f(p,i))` would put me right back in the same boat. – Pentaquark Oct 05 '17 at 20:35

Misunderstanding of functions in R

3 Answers3