Calculate Qi (inverse of Q) and log determinant of Q

calc_qi(eval, D_l, X)

Arguments

eval	vector of eigenvalues from decomposition of relatedness matrix
D_l	vector of length d_size
X	design matrix

Value

a list of length two. First entry in the list is a symmetric numeric matrix, Qi, the inverse of the Q matrix. The second entry in the outputted list is the log determinant of the matrix Q for use in likelihood calculations.

Examples

as.matrix(readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100]) -> kinship
#> 
#> ── Column specification ────────────────────────────────────────────────────────
#> cols(
#>   .default = col_double(),
#>   X101 = col_logical()
#> )
#> ℹ Use `spec()` for the full column specifications.
eigen2(kinship) -> e2_out
e2_out$values -> eval
e2_out$vectors -> U
eigen_proc(V_g = diag(c(1.91352, 0.530827)),
V_e = diag(c(0.320028, 0.561589))) -> ep_out

calc_qi(eval = eval,
D_l = ep_out[[4]],
X = t(rep(1, 100)) %*% U)
#> [[1]]
#>      [,1] [,2]
#> [1,] 0.01 0.00
#> [2,] 0.00 0.01
#> 
#> [[2]]
#> [1] 9.21034
#>