Premium
Application of supernodal sparse factorization and inversion to the estimation of (co)variance components by residual maximum likelihood
Author(s) -
Masuda Y.,
Baba T.,
Suzuki M.
Publication year - 2014
Publication title -
journal of animal breeding and genetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.689
H-Index - 51
eISSN - 1439-0388
pISSN - 0931-2668
DOI - 10.1111/jbg.12058
Subject(s) - residual , restricted maximum likelihood , sire , inversion (geology) , mixed model , factorization , computer science , inverse , sparse matrix , algorithm , mathematics , maximum likelihood , statistics , zoology , paleontology , physics , geometry , structural basin , quantum mechanics , gaussian , biology
Summary We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations ( MME ), which are often required in residual maximum likelihood ( REML ). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver ( yams ), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak , respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams . The yams package is freely available on request by contacting the corresponding author.