Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently

Table 5 Computational costs for different matrices and for the software used for the field dataset

Model	Method^a	Galerkin matrix (E⁻¹)			Dense matrix^d	\({\mathbf{G}}^{ - 1} - {\mathbf{A}}_{{\varvec{gg}}}^{ - 1}\)	Software peak memory^e
Model	Method^a	Size^b	GB	Time^c (s)	GB	GB	GB
ssGBLUP	PCG	–	–	–	–	63.1	70.2
ssSNPBLUP	PCG	–	–	–	26.4	–	34.0
	DPCG (200)	764	0.004	2199	26.4	–	43.8
	DPCG (50)	3044	0.071	2959	26.4	–	43.9
	DPCG (5)	30,400	7.1	9131	26.4	–	51.0
ssPCBLUP	PCG	–	–	–	9.6	–	16.6
	DPCG (200)	284	< 0.001	430	9.6	–	16.8
	DPCG (50)	1112	0.009	663	9.6	–	16.8
	DPCG(5)	11,048	0.9	1965	9.6	–	17.7
	DPCG (1)	55,216	23.3	9630	9.6	–	40.6

^aNumber of SNP (PC) effects per subdomain is within brackets
^bThe size of the Galerkin matrix is equal to the rank of the deflation-subspace matrix
^cWall clock time required for the computation of the Galerkin matrix following a naive implementation, and computation of its inverse
^dThe dense matrix is the centered genotype matrix \({\mathbf{Z}}\) for ssSNPBLUP and the matrix with principal components \({\mathbf{T}}\) for ssPCBLUP
^eThe software peak memory is defined as the peak resident set size (VmHWM) obtained from the Linux/proc virtual file system

ISSN: 1297-9686