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Help with applying a function to all possible 2x2 submatrices

6 messages · Sarah Goslee, Rui Barradas, CMB123 +2 more

CMB123
# 
Hi all,

I'm working with a large data set (on the order of 300X300) and trying to
apply a function which compares the elements of all possible 2x2
submatrices. There are rc(r-1)(c-1) such submatrices, so obviously the naive
method of looping through the rows and columns is computationally unfeasible
for my data set:

  for(i in 1:(nrow(data)-1)) {
    for(j in (i+1):nrow(data)) {
      for (m in 1:(ncol(data)-1)) {
        for (n in (m+1):ncol(data)) {

I have tried using the outer and apply functions to vectorize the task, but
I can't seem to figure out the best method (or any method, for that matter)
to help with what I'm trying to do. 

Any and all help is much appreciated! Thanks in advance,

C



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Sarah Goslee
# 
300x300 isn't terribly large; looping should work just fine. But I'm
confused about a 2x2 submatrix:
I would have thought that a submatrix would be adjacent elements, like
x[1:2, 1:2]
or
x[13:14, 296:297]
but your loop compares all possible sets of four elements, so the
matrix position doesn't matter except for avoiding duplication.

Maybe a bit more about what you're trying to accomplish (including the
function you want to perform with those four elements) would be
helpful.

Sarah
On Mon, Oct 22, 2012 at 1:10 PM, CMB123 <craig.bielski at gmail.com> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Rui Barradas
    

    

      
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Hello,

If your matrix is in the order of 300x300, the problem of extracting all 
possible submatrices and applying a function will allways be a large 
one, but the use of ?combn may reduce it a bit if the order of 
rows/columns in the submatrices doesn't matter. It can reduce it from 
300^4 = 8.1e+09 to 2.0e+09 submatrices, a factor of 4.
See the example below.

# Make up some data.
nr <- nc <- 10
x <- matrix(rnorm(nr*nc), nrow = nr)

cr <- combn(nr, 2)
cc <- combn(nc, 2)

fun <- function(rr, cc, xx, FUN) FUN(xx[rr, cc])

apply(cr, 2, function(i)
     apply(cc, 2, function(j)
         fun(cr[, i], cc[, j], x, sum)
     )
)


Note that this hides away the quartic nature of the algorithm.

Hope this helps,

Rui Barradas
Em 22-10-2012 18:10, CMB123 escreveu:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      CMB123
    

    

      
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I apologize if the term "submatrix" was confusing - I am basically 2 rows and
2 columns from a r x c matrix to construct 2x2 matricies. Thus, the
choose(r,2) * choose(c,2) possible combinations.

For each matrix [(a,b), (c,d)], I am testing a > b, b > d, d > c, and c > a.
For the sake of simplicity I have combined these tests into a single
function (with the intent of applying it to the matrix, ideally).

I hope this is clearer...



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      Bert Gunter
    

    

      
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Inline.

        
On Mon, Oct 22, 2012 at 1:10 PM, CMB123 <craig.bielski at gmail.com> wrote:

            

      
      
      
    

        
What does that mean? -- it ain't R syntax. Is (a,b) a row or column?

Also, please don't post through Nabble, as R-help is a separate
mailing list and we lose context here (and don't wish to mess with
Nabble).

-- Bert

-- Bert


I am testing a > b, b > d, d > c, and c > a.

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Michael Friendly
    

    

      
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On 10/22/2012 1:10 PM, CMB123 wrote:

            

      
      
      
    

        
See the function vcdExtra::loddsratio for something similar