Lazy genomic relationship matrix

Describes the genomic relationship matrix of VanRaden (2008), $$G = \frac{Z Z^\top}{2 \sum_j f_j (1 - f_j)},$$ where $Z$ holds the marker genotypes centred by twice the allele frequencies $f_j$, without forming it. A product with $G$ costs two products with $Z$, and rows are computed on demand, so the functions in this package can work with $G$ while only the $n \times p$ genotypes are held in memory.

Usage

grm_matrix(M, freq = NULL)

Arguments

M: Genotype matrix with one row per individual and one column per marker, coded as allele counts between 0 and 2. Missing genotypes must be imputed first.
freq: Allele frequencies used for centring. Defaults to the observed frequencies, colMeans(M) / 2.

Value

An object of class matsketch_grm, accepted wherever matsketch expects a matrix. as.matrix() forms the full matrix.

Details

This matters once $n$ is large: for 50,000 individuals the full matrix takes 20 GB, while the genotypes on a 10,000-marker panel take 4 GB.

References

VanRaden, P. M. (2008) Efficient methods to compute genomic predictions. Journal of Dairy Science 91, 4414-4423. doi:10.3168/jds.2007-0980

Examples

set.seed(1)
M <- matrix(rbinom(200 * 500, 2, 0.3), 200)
G <- grm_matrix(M)
G
#> <matsketch_grm> relationships among 200 individuals from 500 markers
#>   full matrix would hold 40,000 entries; only genotypes are stored
G$block(1:3, 1:3)
#>             [,1]        [,2]         [,3]
#> [1,]  0.98263803 0.090872547 -0.040163453
#> [2,]  0.09087255 1.003208604  0.008303878
#> [3,] -0.04016345 0.008303878  1.051365706