# [R] summation coding

Berend Hasselman bhh at xs4all.nl
Fri Oct 19 10:38:18 CEST 2012

```On 18-10-2012, at 21:33, djbanana wrote:

> I would like to code the following in R: a1(b1+b2+b3) + a2(b1+b3+b4) +
> a3(b1+b2+b4) + a4(b1+b2+b3)
>
> or in summation notation: sum_{i=1, j\neq i}^{4} a_i * b_i
>
> I realise this is the same as: sum_{i=1, j=1}^{4} a_i * b_i - sum_{i=j} a_i
> * b_i
>

This is partly TeX notation not summation notation, whatever that may be.
And these "sums" make no sense: where is index j used in the first? where is it used in the second?

Solutions starting from you explicit formula, from slowest to fastest

sum( outer(a,b,"*") ) - sum(a*b)
sum(sapply(1:length(a),function(k) a[k]*sum(b[-k])))
sum(convolve(a,b)) - sum(a*b)   # sum(convolve(a,rev(b), type="o")) - sum(a*b)

Berend

> would appreciate some help.
>
> Thank you.
>
>
>
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