R help - Sep 2015 - writing an equation with multiple summation

Dear All,

I'm trying to write and evaluate an equation which involves multiple
summations but can't figure out how to do it.

I've an numeric vector r
r<-vector(mode = "numeric", length = m)
 and I have multiple summations (for ex.) of the form:

[(sum from r[1]=0 to g(r[1])) (sum from r[2] =0 to g(r[2]))......(sum from
r[m] to g(r[m]))] {the sum is over some complicated expression in
r[1],r[2],.....,r[m]},

where g(r[i]) = m- (r[1] +r[2]+...+r[i-1])
Any suggestions for some function or a package that can help me with this?

Many Thanks,
Maram

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The brute force answer involves for loops or apply functions, with or without
defining your own functions for calculating terms. More optimized methods
usually require understanding the specific structure of the summations and
unwinding them with functions like expand.grid. For more specific help, read the
Posting Guide (which among other things warns you to post in plain text) and
post a specific example of the type of problem that you want to solve.
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On September 28, 2015 8:26:56 AM PDT, Maram SAlem <marammagdysalem at
gmail.com> wrote:
>Dear All,
>
>I'm trying to write and evaluate an equation which involves multiple
>summations but can't figure out how to do it.
>
>I've an numeric vector r
>r<-vector(mode = "numeric", length = m)
> and I have multiple summations (for ex.) of the form:
>
>[(sum from r[1]=0 to g(r[1])) (sum from r[2] =0 to g(r[2]))......(sum
>from
>r[m] to g(r[m]))] {the sum is over some complicated expression in
>r[1],r[2],.....,r[m]},
>
>where g(r[i]) = m- (r[1] +r[2]+...+r[i-1])
>Any suggestions for some function or a package that can help me with
>this?
>
>Many Thanks,
>Maram
>
>	[[alternative HTML version deleted]]
>
>______________________________________________
>R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

My first problem is that the counters involved in the summation are
dependent, For instance for each r[i], 0<r[i]< m-(r[1] +r[2]+...+r[i-1])
 so I tried using seq() and for loops to express all the possible
combinations but I couldn't.


On 28 September 2015 at 17:26, Maram SAlem <marammagdysalem at gmail.com>
wrote:
> Dear All,
>
> I'm trying to write and evaluate an equation which involves multiple
> summations but can't figure out how to do it.
>
> I've an numeric vector r
> r<-vector(mode = "numeric", length = m)
>  and I have multiple summations (for ex.) of the form:
>
> [(sum from r[1]=0 to g(r[1])) (sum from r[2] =0 to g(r[2]))......(sum from
> r[m] to g(r[m]))] {the sum is over some complicated expression in
> r[1],r[2],.....,r[m]},
>
> where g(r[i]) = m- (r[1] +r[2]+...+r[i-1])
> Any suggestions for some function or a package that can help me with this?
>
> Many Thanks,
> Maram
>
>
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