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r - Sort one matrix based on another matrix

I'm trying to put the rows of one matrix in the same order as the rows of another matrix of the same dimension. However I can't quite figure out how to do this without an explicit loop. It seems I should be able to do this with subsetting and an apply or Map function, but I can't figure out how to do it.

Here's a toy example:

sortMe <- matrix(rnorm(6), ncol=2)
sortBy <- matrix(c(2,1,3, 1,3,2), ncol=2)

sorted <- sortMe 
for (i in 1:ncol(sortMe)) {
  sorted[,i] <- sortMe[,i][sortBy[,i]]
}

Using this method, the resulting sorted matrix contains the values from sortMe sorted in the same order as the sortBy matrix. Any idea how I'd do this without the loop?

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This (using a two-column integer matrix to index the matrix's two dimensions) should do the trick:

sorted <- sortMe
sorted[] <- sortMe[cbind(as.vector(sortBy), as.vector(col(sortBy)))]

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