[R] Find pattern in matrix

[Q]

Hello all,

I'm trying to find all combinations of 4 numbers that satisfy 4 criteria,
inside of a matrix (62 x 25).  I've found a way to do this using for loops,
but it is extremely slow because it involves checking every possible
combination of numbers (567300) to see if the criteria are satisfied.  Do
you think there is a faster method of doing this?  Or some functions that
might help me out?

The matrix is of species abundances, with each row representing a species
(A,B,C...) and each column representing a site (1,2,3...).  The numbers in
the matrix tell the abundance of the species at that site:



>     1  2  3...
> A  0  5  6...
> B  7  8  2...
> C  4  1  3...
> ...
> 

I'm trying to find combinations of species/sites such that
A1>B1,A1>A2,B2>B1,B2>A2

I have used expand.grid to get all combinations of species pairs and site
pairs, and then checked to see if the inequalities are satisfied.  However,
as I said, it takes forever.

I tried to write a function that would take vectors and trick R into
searching for my pattern:



> count <- function(i,j,k,l){
> length(matrix[matrix[i,k] > matrix[i,l] &&
> matrix[i,k] > matrix[j,k] &&
> matrix[j,l] > matrix[j,k] &&
> matrix[j,l] > matrix[i,l]])
> }
> 

That didn't work.  So I wonder if anyone has any ideas of another way to
proceed or functions I could look up that would head me in the right
direction.  Something fully fleshed out isn't necessary.  

Thanks!

Q

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