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Stochastic Lanczos REML algorithms

SL_REML v0.1a

Code accompanying Stochastic Lanczos estimation of genomic variance components for linear mixed-effects models.

  • L_Seed constructs bases for Krylov subspaces: B, (A+σI)B, (A+σI)²B, ...

  • L_Solve solves (A + σI)X = B using results from L_Seed

  • SLQ_LDet returns approximate log det (A + σI) given spectal decompositions of Jacobi matrices from Lanczos decompositions of seed Krylov subspaces for probe vectors

  • L_FOMC_REML extension of BOLT-LMM algorithm to recycle Krylov subspace bases involved in solving linear systems

  • SLDF_REML zero order REML estimation using (shifted) block Lanczos conjugate gradients and (shifted) stochastic Lanczos quadrature

SL_REML v0.1b

High performance variant of Stochastic First-order Derivative-Free REML algorithm (SLDF_REML) as employed in Assortative mating biases marker-based heritability estimators.

  • L_Seed_numba compiled variant of L_Seed above

  • L_Solve_numba compiled variant of L_Seed above

  • SLQ_LDet see above

  • SLDF_REML_numba compiled variant of SLDF_REML above

In contrast to SLDF_REML, SLDF_REML_numba assumes all covariates have been projected out of the genotype and phenotype data. See the SL_REML_v0.1b directory for installation instructions and a toy example.

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Stochastic Lanczos REML algorithms for genomic variance component estimation

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