Advantage of supernodal methods in restricted maximum likelihood when dense matrices are involved in a coefficient matrix of mixed model equations

Abstract Text: The objective of this study was to determine speed-up of an average-information (AI) REML algorithm with a supernodal sparse-matrix package. Comparisons included twenty-three models with data sets from broiler, swine, beef and dairy cattle. Models included single-trait, multiple-trait, maternal, and random regression models with phenotypic data; selected models used genomic information as a genomic relationship matrix in single-step GBLUP. The AIREMLF90 program was used to compare two sparse-matrix packages: FSPAK and YAMS; the latter package used supernodal methods for faster computing when sparse matrices contain large dense blocks. The program was compiled with the Intel Fortran Compiler 13.1 using the Intel Math Kernel Library and ran on a computer with 16-core CPUs. Computations with YAMS were on average over 10 times faster than with FSPAK and had greater advantages for large data and more complicated models including multiple traits and random regressions and with genomic effects. The highest speed-up with YAMS over FSPAK was over 20 times in AI REML iteration and over 80 times faster in sparse inversion. In a model with 213,297 pedigreed and 15,723 genotyped animals, a single-trait analysis with FSPAK took about 5 h and multiple-trait analyses did not converge in one day. With YAMS, a single-trait analysis took about 20 min and a 4-trait analysis took about 5 h. Supernodal methods dramatically improve the computing cost if the AI REML for larger and more complex analyses, especially when genomic information is included in the single-step GBLUP models.

Keywords: AIREML, supernodal methods, sparse-matrix package