efficiently update matrix element with a matrix of indices

Question

I have a matrix of indices I where some of the indices are repeated. I put an example below. I have another matrix A with dimensions compatible with the indices and initiated to 0 everywhere. I would like to do something like ``` A[I] += 1 ``` I face two issues: - `A[I] = A[I] + 1` is too inefficient - matrix `I` has redundant indices. For example rows 2 & 6 are identical and I would like to obtain `A[1,2] = 2` A partial answer would be to create a 3 columns matrix with the two first columns being the product of `unique(I)` and the third column with the counts, but I don't see any solution for that either. Any pointer or help would be greatly appreciated! ``` > I is: [,1] [,2] [1,] 1 1 [2,] 1 2 [3,] 1 3 [4,] 1 4 [5,] 1 1 [6,] 1 2 [7,] 1 3 ```

Accepted Answer

This may be quickest using sparse matrix methods (see the Matrix package and others).

Using standard matricies you could collapse the identical rows using the `xtabs` function then matrix assignment (edited based on comment):

```
I <- cbind(1, c(1:4,1:3))

tmp <- as.data.frame(xtabs( ~I[,1]+I[,2] ))

A <- matrix(0, nrow=5, ncol=5)
tmp2 <- as.matrix(tmp[,1:2])
tmp3 <- as.numeric(tmp2)
dim(tmp3) <- dim(tmp2)
A[ tmp3 ] <- tmp[,3]
A
```

You could probably make it a little quicker by pulling the core functionality out of `as.data.frame.table` rather than converting to data frame and back again.

Here is another version that may be more efficient. It will overwrite some 0's with other 0's computed by `xtabs`:

```
I <- cbind(1:5,1:5)
A <- matrix(0, 5, 5)

tmp <- xtabs( ~I[,2]+I[,1] )

A[ as.numeric(rownames(tmp)), as.numeric(colnames(tmp)) ] <- c(tmp)
A
```

If the A matrix has dimnames and the I matrix has the names instead of the indexes, then this later one will also work (just remove the `as.numeric`s.

efficiently update matrix element with a matrix of indices

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