On Aug 24, 2013, at 2:13 PM, Sebastian Hersberger wrote:
> Thanks. I restate my problem/question and hope its better understandable now.
>
> Let us define A and B as kxk matrices. C is the output (matrix), which I try
> to calculate for differnt i values.
>
> So for example: I want to caluclate the matrix C for the value i=10:
>
> Therefore, I set:
>
> i <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
>
> Finally, I have to define the summation formula in R. My question is how this
> following summation formula has to be applied to R.
>
> The arithmetic form of the formula equals:
>
> C = (Σ(from i=0 to i) A^i ) x B x (Σ(from i=0 to i) A^i )’
>
> Which means:
> matrix C equals the sum from i=0 to i times matrix A to the power of i
That first term might be (untested in absence of test data by questioner) :
require(expm)
res1 <- Reduce("+", lapply(1:i, function(i) powm(A, i) ) )
> times matrix B
res2 <- res1 %*% B
> times the transposed/invers of the sum from i=0 to i times matrix A to the
> power of i
>
Well, the transpose was not generally the inverse when I took linear algebra,
but as I said I didn't make it to all the sessions. (I'm assuming it is the
transpose.)
res3 <- res2 %*% t(res1)
You could probably do it all in one line, but I like to check my itermediates.
--
David.
> I hope I were able to specify my problem in an understandable way. If not,
> please let me know.
>
> Thanks and regards
> Sebastian
>
> ________________________________________
> From: David Winsemius [dwinsem...@comcast.net]
> Sent: Saturday, August 24, 2013 8:35 PM
> To: Sebastian Hersberger
> Cc: r-help@r-project.org
> Subject: Re: [R] how to apply summation sign formula to R
>
> On Aug 24, 2013, at 6:37 AM, Sebastian Hersberger wrote:
>
>> Hi all
>>
>> I have a short question relating to the usage of the summation sign in R.
>>
>> Let's define A and B as two kxk matrice.
>> My goal is to calculate the matrix C for the periods from 1 to 200 (n=1-200).
>>
>> C^(n) = Σ_(j=1)^n [(Σ_(i=1)^(j-1) A^i ) B (Σ_(i=1)^(j-1) A^i)’ ]
>>
>> How has that to be implemented in R (lets say for example for period = n =
>> 150)?
>
> I don't follow all this notation but you might want to look at the expm
> package that has a powm function. It's possible that the expm function may do
> what you want, but as I said I was unclear what the equation was attempting
> to do. Perhaps if you explained the steps in mathematical language, then
> other viewers who actually woke up to attend their linear algebra course
> might have a better chance of offering assistance.
>
> ( When I saw the earlier copy yesterday, I had hopes that such wiser viewers
> might chime in and still have such hopes.)
>
> --
>
> David Winsemius
> Alameda, CA, USA
>
David Winsemius
Alameda, CA, USA
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