Hi David
Thanks for your help.
I tried it for a simplified example with vectors instead of matrices.
Once again the formula:
C = (Σ(from i=0 to i) A^i ) x B x (Σ(from i=0 to i) A^i )’
I applied it at follows – but couldn’t figure out what’s missing:
library(expm)
i <- c(0,1,2,3,4,5,6,7,8,9,10)
A <- c(1,2,3)
B <- 5
res1 <- Reduce("+", lapply(1:i, function(i) A ^ i) )
res2 <- res1 * B
> res3 <- res2 * t(res1)
> res3
[,1] [,2] [,3]
[1,] 20 45 80
My expected result must be in this case a single number, which is the sum of
i=0 to i=10:
i=0 ⇒ 5
i=1 ⇒ 1*5*1 + 1*5*2+1*5*3 + 2*5*1+2*5*2 + 2*5*3+3*5*1+3*5*2+3*5*3 = 180
i = 2 ⇒ ........... (=985)
i=3 ⇒ ....
...
i=10 ⇒ =............
After having adjusted the above provided „R-code“: what is necessary to get
from the „vector-solution“ to the matrix-solution“: would it be enough to:
- define A and B as matrices
- and replace * by %*% ?
Or what else is required?
Thanks and regards
Sebastian
________________________________________
From: David Winsemius [[email protected]]
Sent: Sunday, August 25, 2013 3:51 AM
To: David Winsemius
Cc: Sebastian Hersberger; [email protected]
Subject: Re: [R] how to apply summation sign formula to R
On Aug 24, 2013, at 6:43 PM, David Winsemius wrote:
>
> 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) ) )
I did test it and both my memory about the functions name and its operation
were wrong. Try:
res1 <- Reduce("+", lapply(1:i, function(i) 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 [[email protected]]
>> Sent: Saturday, August 24, 2013 8:35 PM
>> To: Sebastian Hersberger
>> Cc: [email protected]
>> 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
>
> ______________________________________________
> [email protected] mailing list
> 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.
David Winsemius
Alameda, CA, USA
______________________________________________
[email protected] mailing list
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.
