  Hello R-list.

I have three vectors a, b, c with different lengths and I want to count 
the number of differences between a[i], b[j], c[k] where a[i], b[j], 
c[k] distinct. That is, the number of pairs (i, j) with a[i]-b[j] =u or 
the numbers of triples (i, j, k) with a[i]-b[j] =u  and a[i]-c[k] =v.

For the first case I use the following commands:

    dif.ab <- matrix(0, nrow=length(b), ncol=length(a))
    for (i in 1:length(b)    {   dif.ab[i,] <- a-b[i]  }
    dif.ab <- as.vector(dif.ab)
    dif.ab <- dif.ab[dif.ab !=0]
    
    Cab <- vector(mode="integer", length=nu)
    for ( u in 1:nu )   {      Cab[u] <- sum( abs(dif.ab-u)<h )      }


or

    dif.ab <- matrix(0, nrow=length(b), ncol=length(a))
    for (i in 1:lengt(a))    {  
        for (j in 1:length(b))   {
            if (a[i] != b[j])   dif[j,i] <- a[i]-b[j]    }}
    
    Cab <- vector(mode="numeric", length=nu)
    for (u in 1:nu)    {      Cab[u] <- sum(abs(dif-u)<h)    }



Notice that I use large data sets (length a, b, c= from 300 to 1500) and 
seek the fastest way to do it especially for the 3D case.
I am waiting for your suggestions.
Thank you in advance.

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