Sum together different subsets in a vector without a for loop in R-CodePudding

Suppose I have the vector

v = 0:12

Is it possible to create a new vector which sums different subsets of that vector v together without using a for loop? For example:

Suppose I wanted to sum the first 1 elements together, then the next 2 elements, then the next 3 elements, then the next 4 elements. Then you would end up with vector:

0 3 12 21 42

Can this be done without a for loop? I am not sure.

CodePudding user response：

You can try by to make vector values grouped and summed

> n <- ceiling(sqrt(2 * length(v)))

> c(by(v, head(rep(1:n, 1:n), length(v)), sum))
 1  2  3  4  5
 0  3 12 30 33

CodePudding user response：

> n=4;l=n*(n 1)/2;v=0:(l-1)
> sapply(split(v,rep(1:n,1:n)),sum)
 1  2  3  4
 0  3 12 30

Or if the length of the vector is not n*(n 1)/2:

> v=0:12
> l=length(v)
> n=ceiling((sqrt(8*l 1)-1)/2)
> r=head(rep(1:n,1:n),l)
> sapply(split(v,r),sum)
 1  2  3  4  5
 0  3 12 30 33
> tapply(v,r,sum)
 1  2  3  4  5
 0  3 12 30 33

The second argument for tapply is automatically converted to a factor:

tapply                  package:base                   R Documentation

Apply a Function Over a Ragged Array

Description:

     Apply a function to each cell of a ragged array, that is to each
     (non-empty) group of values given by a unique combination of the
     levels of certain factors.

Usage:

     tapply(X, INDEX, FUN = NULL, ..., default = NA, simplify = TRUE)

Arguments:

       X: an R object for which a split method exists.  Typically
          vector-like, allowing subsetting with [.

   INDEX: a list of one or more factors, each of same length as
          ‘X’.  The elements are coerced to factors by as.factor.

I derived the value of n by using the quadratic formula:

l=n*(n-1)/2
2*l=n^2 n
n^2 n-2*l=0
n=(-1±sqrt(1^2-4*1*-2*l))/2*1
n=(-1±sqrt(1 8*l))/2

n*(n-1)/2 is the same as sum(1:(n-1)) and choose(n,2) and length(which(lower.tri(matrix(,n,n)))).