R help - May 2008 - How do I write a sum of matrixes??

Hello best helpers,

I am a new user and I have been struggling for hours. So finally I decide to ask
you:
If I have a matrix P, and P.2 = P%*%P, and P.3=P.2%*%P
is there a function to calculate the power of a matrix?? if not how can i do:
for (i in 1:10)  {P.i=P^i} 
after this I need to sum them up and my problem is to combine P and i to P.i 
can anyone help me please???

Thanks and have a nice day, 

Pascal.
 

_________________________________________________________________
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> I am a new user and I have been struggling for hours. So finally I 
> decide to ask you:
> If I have a matrix P, and P.2 = P%*%P, and P.3=P.2%*%P
> is there a function to calculate the power of a matrix?? if not how can 
i do:
> for (i in 1:10)  {P.i=P^i} 
> after this I need to sum them up and my problem is to combine P and 
> i to P.i  can anyone help me please???
Take a look at FAQ on R 7.21 ("How can I turn a string into a
variable?").

This code will do what you ask (though the first matrix is named P.1, 
rather than P for convenience):

paste0 <- function(x) paste("P.", x, sep="")
P.1 <- matrix(rnorm(25), nrow=5)
varnames <- paste0(1:10)
for(i in 2:10) assign(paste0(i), get(paste0(i-1)) %*% P.1)

Regards,
Richie.

Mathematical Sciences Unit
HSL


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pascal vrolijk <pascalvrolijk at hotmail.com> wrote in
news:BAY120-W47837F2A708683682EB44AACD60 at phx.gbl: 
> Hello best helpers,
> 
> I am a new user and I have been struggling for hours. So finally I
> decide to ask you: If I have a matrix P, and P.2 = P%*%P, and
> P.3=P.2%*%P is there a function to calculate the power of a matrix??
> if not how can i do: for (i in 1:10)  {P.i=P^i} 
Three methods show up in a search "r-help power of a matrix":

1) Use a pre-built function:
library(msm)
?MatrixExp 

2) 
<https://stat.ethz.ch/pipermail/r-help/2007-May/131330.html>

3) Bill Venables offered this about a week ago in this list:
--------------
This is probably as good a way as any way for this kind of problem.
First define a binary operator:
> "%^%" <- function(x, n)
        with(eigen(x), vectors %*% (values^n * t(vectors)))

Your toy example then becomes
> m <- matrix(c(1, 0.4, 0.4, 1), nrow = 2)
> m
     [,1] [,2]
[1,]  1.0  0.4
[2,]  0.4  1.0
> m %^% (-0.5)
           [,1]       [,2]
[1,]  1.0680744 -0.2229201
[2,] -0.2229201  1.0680744 
-------------

-- 
David Winsemius

> after this I need to sum them up and my problem is to combine P and
> i to P.i  can anyone help me please??? 
> 
> Thanks and have a nice day, 
> 
> Pascal.

> 3) Bill Venables offered this about a week ago in this list:
> --------------
> This is probably as good a way as any way for this kind of problem.
> First define a binary operator:
> 
> > "%^%" <- function(x, n)
>         with(eigen(x), vectors %*% (values^n * t(vectors)))
> 
This example only works for _diagonalizable_ matrices. It
crashes, for example, in cases like:

m <-  rbind(c(1,1,0), c(0,1,1), c(0,0,1))
m %^% 2
m %*% m

Alberto Monteiro

Hi Pascal,

I think the function could be better but try this:

# Function: M is your matrix and n MUST be an integer>0
mat.pow<-function(M,n) {
  result<-M
    if(n>1){
       for ( iter in 2:n) result<-M%*%result
       result
           }
    else {result}
  result
 }

# The matrix
m <-  rbind(c(1,1,0), c(0,1,1), c(0,0,1))

# Goal m^2 = m x m
goal=m%*%m

# matpow
res=mat.pow(m,2)

# Check point
all.equal(goal,res)

See RSiteSearch('nth step transition matrices')


HTH,

Jorge


On Tue, May 6, 2008 at 1:37 AM, pascal vrolijk <pascalvrolijk@hotmail.com>
wrote:
> Hello best helpers,
>
> I am a new user and I have been struggling for hours. So finally I decide
> to ask you:
> If I have a matrix P, and P.2 = P%*%P, and P.3=P.2%*%P
> is there a function to calculate the power of a matrix?? if not how can i
> do:
> for (i in 1:10)  {P.i=P^i}
> after this I need to sum them up and my problem is to combine P and i to
> P.i  can anyone help me please???
>
> Thanks and have a nice day,
>
> Pascal.
>
>
> _________________________________________________________________
> [[elided Hotmail spam]]
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@r-project.org mailing list
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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Jorge Ivan Velez wrote:
> 
> I think the function could be better but try this:
> 
> # Function: M is your matrix and n MUST be an integer>0
> mat.pow<-function(M,n) {
>   result<-M
>     if(n>1){
>        for ( iter in 2:n) result<-M%*%result
>        result
>            }
>     else {result}
>   result
>  }
> 
There are much more efficient ways to compute a power,
just check:
http://en.wikipedia.org/wiki/Exponentiation_by_squaring

Or, translating the pseudo-code to R:

mat.pow <- function(M, n) {
  result <- diag(1, ncol(M))
  while (n > 0) {
    if (n %% 2 == 1) {  
      result <- result %*% M
      n <- n - 1
    }
    M <- M %*% M
    n <- n / 2
  }
  return(result)
}

# The matrix
m <-  rbind(c(1,1,0), c(0,1,1), c(0,0,1))
 
# Goal m^6 = m x m x m x m x m x m
goal=  m %*% m %*% m %*% m %*% m %*% m
 
# matpow
res=mat.pow(m,6)
 
# Check point
all.equal(goal,res)

This algorithm would be fast, unless n is a _very_ big number.

Alberto Monteiro