# Automatic grouping (partitioning) of locations Take in an array of nearest neighbors, and automatically partition the array into groups that share neighbors. This is helpful to speed the computations and improve their accuracy. The function returns a list, with each list element containing one or several rows of NNarray. The algorithm attempts to find groupings such that observations within a group share many common neighbors. ```r group_obs(NNarray, exponent = 2) ``` ## Arguments - `NNarray`: Matrix of nearest neighbor indices, usually the result of `find_ordered_nn`. - `exponent`: Within the algorithm, two groups are merged if the number of unique neighbors raised to the `exponent` power is less than the sum of the unique numbers raised to the `exponent` power from the two groups. ## Returns A list with elements defining the grouping. The list entries are: * `all_inds`: vector of all indices of all blocks. * `last_ind_of_block`: The `i`th entry tells us the location in `all_inds` of the last index of the `i`th block. Thus the length of `last_ind_of_block` is the number of blocks, and `last_ind_of_block` can be used to chop `all_inds` up into blocks. * `global_resp_inds`: The `i`th entry tells us the index of the `i`th response, as ordered in `all_inds`. * `local_resp_inds`: The `i`th entry tells us the location within the block of the response index. * `last_resp_of_block`: The `i`th entry tells us the location within `local_resp_inds` and `global_resp_inds` of the last index of the `i`th block. `last_resp_of_block` is to `global_resp_inds` and `local_resp_inds` as `last_ind_of_block` is to `all_inds`. ## Examples ```r locs <- matrix( runif(200), 100, 2 ) # generate random locations ord <- order_maxmin(locs) # calculate an ordering locsord <- locs[ord,] # reorder locations m <- 10 NNarray <- find_ordered_nn(locsord,m) # m nearest neighbor indices NNlist2 <- group_obs(NNarray) # join blocks if joining reduces squares NNlist3 <- group_obs(NNarray,3) # join blocks if joining reduces cubes object.size(NNarray) object.size(NNlist2) object.size(NNlist3) mean( NNlist2[["local_resp_inds"]] - 1 ) # average number of neighbors (exponent 2) mean( NNlist3[["local_resp_inds"]] - 1 ) # average number of neighbors (exponent 3) all_inds <- NNlist2$all_inds last_ind_of_block <- NNlist2$last_ind_of_block inds_of_block_2 <- all_inds[ (last_ind_of_block[1] + 1):last_ind_of_block[2] ] local_resp_inds <- NNlist2$local_resp_inds global_resp_inds <- NNlist2$global_resp_inds last_resp_of_block <- NNlist2$last_resp_of_block local_resp_of_block_2 <- local_resp_inds[(last_resp_of_block[1]+1):last_resp_of_block[2]] global_resp_of_block_2 <- global_resp_inds[(last_resp_of_block[1]+1):last_resp_of_block[2]] inds_of_block_2[local_resp_of_block_2] # these last two should be the same ```

group_obs function