Chunked version of covariance

cov_chunked.R

cov_chunked = function(x, nchunks = 2L)
{

    p = ncol(x)
    indices = parallel::splitIndices(p, nchunks)

    diagonal_blocks = lapply(indices, function(idx) cov(x[, idx, drop = FALSE]))

    upper_right_indices = combn(indices, 2, simplify = FALSE)

    upper_right_blocks = lapply(upper_right_indices, function(index){
            cov(x[, index[[1]]], x[, index[[2]]])
    })

    # All computation is done, just assemble the results in the right way
    output = matrix(numeric(p*p), nrow = p)
    for(i in seq_along(indices)){
        idx = indices[[i]]
        output[idx, idx] = diagonal_blocks[[i]]
    }
    for(i in seq_along(upper_right_indices)){
        index = upper_right_indices[[i]]
        output[index[[1]], index[[2]]] = upper_right_blocks[[i]]
        output[index[[2]], index[[1]]] = t(upper_right_blocks[[i]])
    }
    output
}