Split a correlation matrix in blocks as independent as possible. This will find the splitting in blocks that minimize the sum of squared correlation between these blocks (i.e. everything outside these blocks).

snp_ldsplit(corr, thr_r2, min_size, max_size, max_K)

## Arguments

corr Sparse correlation matrix. Usually, the output of snp_cor(). Threshold under which squared correlations are ignored. This is useful to avoid counting noise, which should give clearer patterns of costs vs. number of blocks. It is therefore possible to have a splitting cost of 0. If this parameter is used, then corr can be computed using the same parameter in snp_cor() (to increase the sparsity of the resulting matrix). Minimum number of variants in each block. This is used not to have a disproportionate number of small blocks. Maximum number of variants in each block. This is used not to have blocks that are too large, e.g. to limit computational and memory requirements of applications that would use these blocks. For some long-range LD regions, it may be needed to allow for large blocks. Maximum number of blocks to consider. All optimal solutions for K from 1 to max_K will be returned. Some of these K might not have any corresponding solution due to the limitations in size of the blocks. For example, splitting 10,000 variants in blocks with at least 500 and at most 2000 variants implies that there are at least 5 and at most 20 blocks. Then, the choice of K depends on the application, but a simple solution is to choose the largest K for which the cost is lower than some threshold.

## Value

A tibble with five columns:

• $n_block: Number of blocks. • $cost: The sum of squared correlations outside the blocks.

• $perc_kept: Percentage of initial non-zero values kept within the blocks defined. • $block_num: Resulting block numbers for each variant.

• $all_last: Last index of each block. • $all_size: Sizes of the blocks.

## Examples

if (FALSE) {

THR_R2 <- 0.01

(res <- snp_ldsplit(corr, thr_r2 = THR_R2, min_size = 10, max_size = 50, max_K = 50))

library(ggplot2)
qplot(n_block, cost, data = res) + theme_bw(16) + scale_y_log10()

all_ind <- head(res$all_last[[6]], -1) ## Transform sparse representation into (i,j,x) triplets corrT <- as(corr, "dgTMatrix") upper <- (corrT@i <= corrT@j & corrT@x^2 >= THR_R2) df <- data.frame( i = corrT@i[upper] + 1L, j = corrT@j[upper] + 1L, r2 = corrT@x[upper]^2 ) df$y <- (df$j - df$i) / 2

ggplot(df) +
geom_point(aes(i + y, y, color = r2), size = rel(0.5)) +
coord_fixed() +