R help - May 2012 - How to apply a function to a multidimensional array based on its indices

Hello. I have a 4 dimensional array and I want to fill in the slots with
values which are a function of the inputs. Through searching the forums here
I found that the function "outer" is helpful for 2x2 matrices but
cannot be
applied to general multidimensional arrays. Is there anything which can
achieve, more efficiently than the following code, the job I want?

K <- array(0,dim=c(2,2,2,2)) #dimensions will be much larger
for(x1 in 1:2)
{
  for(y1 in 1:2)
  {
    for(x2 in 1:2)
    {
      for(y2 in 1:2)
      {
        K[x1,y1,x2,y2] <- x1*y2 - sin(x2*y1) #this is just a dummy function.
      }   
    }
  }
}

Thank you in advance for any help.


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Hello,

Try

K <- array(0,dim=c(2,2,2,2)) #dimensions will be much larger
for(x1 in 1:2){
  for(y1 in 1:2)  {
    for(x2 in 1:2)    {
      for(y2 in 1:2)      {
        K[x1,y1,x2,y2] <-  x1*y2 - sin(x2*y1) #this is just a dummy
function.
      }  
    }
  }
}


fun <- function(x){
	x1 <- x[1]  # these are
	x2 <- x[2]  # not
	y1 <- x[3]  # really
	y2 <- x[4]  # needed
	x1*y2 - sin(x2*y1) # could have used x[1], etc
}


res <- apply(expand.grid(1:2, 1:2, 1:2, 1:2), 1, fun)
dim(res) <- c(2, 2, 2, 2)
res

all.equal(K, res)
[1] TRUE

See the help pages
?expand.grid
?apply


Hope this helps,

Rui Barradas

math_daddy wrote
> 
> Hello. I have a 4 dimensional array and I want to fill in the slots with
> values which are a function of the inputs. Through searching the forums
> here I found that the function "outer" is helpful for 2x2
matrices but
> cannot be applied to general multidimensional arrays. Is there anything
> which can achieve, more efficiently than the following code, the job I
> want?
> 
> K <- array(0,dim=c(2,2,2,2)) #dimensions will be much larger
> for(x1 in 1:2)
> {
>   for(y1 in 1:2)
>   {
>     for(x2 in 1:2)
>     {
>       for(y2 in 1:2)
>       {
>         K[x1,y1,x2,y2] <- x1*y2 - sin(x2*y1) #this is just a dummy
> function.
>       }   
>     }
>   }
> }
> 
> Thank you in advance for any help.
> 

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On May 14, 2012, at 10:09 AM, math_daddy wrote:
> Hello. I have a 4 dimensional array and I want to fill in the slots  
> with
> values which are a function of the inputs. Through searching the  
> forums here
> I found that the function "outer" is helpful for 2x2 matrices but
> cannot be
> applied to general multidimensional arrays. Is there anything which  
> can
> achieve, more efficiently than the following code, the job I want?
>
> K <- array(0,dim=c(2,2,2,2)) #dimensions will be much larger
> for(x1 in 1:2)
> {
>  for(y1 in 1:2)
>  {
>    for(x2 in 1:2)
>    {
>      for(y2 in 1:2)
>      {
>        K[x1,y1,x2,y2] <- x1*y2 - sin(x2*y1) #this is just a dummy  
> function.
>      }
>    }
>  }
> }
>
If you can create a data.frame or matrix that has the indices  
x1,x2,y1,y2 and the values you can use the:  K[cbind(index-vectors)]  
<- values construction:

mtx<- data.matrix( expand.grid(x1=1:2,x2=1:2,y1=1:2,y2=1:2) )
K[mtx] <- apply(mtx, 1, function(x) x["x1"]*x["y2"] -  
sin(x['x2']*x['y1']) )
#----------------
 > K
, , 1, 1

          [,1]       [,2]
[1,] 0.158529 0.09070257
[2,] 1.158529 1.09070257

, , 2, 1

            [,1]     [,2]
[1,] 0.09070257 1.756802
[2,] 1.09070257 2.756802

, , 1, 2

          [,1]     [,2]
[1,] 1.158529 1.090703
[2,] 3.158529 3.090703

, , 2, 2

          [,1]     [,2]
[1,] 1.090703 2.756802
[2,] 3.090703 4.756802

> Thank you in advance for any help.
>
>
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> View this message in context:
http://r.789695.n4.nabble.com/How-to-apply-a-function-to-a-multidimensional-array-based-on-its-indices-tp4629940.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org 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, MD
West Hartford, CT

Thanks for the help, this worked great! Much appreciated.

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