On Aug 26, 2013, at 11:59 AM, Sebastian Hersberger wrote:
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) )
I thought I suggested the use of the %^% operator? Doing A^i is only
going to give you the element-wise values to the i-th power, not the
matrix to the i-th power. (But perhaps that is what you actually
wanted, which was never expalined in the portions of the thread which
I read. And I would have expected A %^% 0 to be I, so it shouldn't
really matter whether the iteration limit was from 0 to 10 or from 1
to 10.)
And you might need to use a final sum( around that Reduce()-ed value
if you were not planning on using matrix multiplication. I thought
this was supposed to be using matrix math. Please explain the purpose
of this effort.
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 %*% ?
Perhaps also replacing ^ with %^%. Just a guess. I'm unable to
decipher from your still sketchy description what the mathematical
operations are supposed to be or do.
--
David.
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
David Winsemius, MD
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.
