Chunk #24 — Findings — Improvements in PLINK 1.9 — Other noteworthy algorithms — Partial sum lookup

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Second-generation PLINK: rising to the challenge of larger and richer datasets.

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For example, the GCTA genomic relationship matrix is defined by the following per-marker increments, where q is the minor allele frequency: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(2-2q)(2-2q)}{2q(1-q)}$ \end{document}(2−2q)(2−2q)2q(1−q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(2-2q)(1-2q)}{2q(1-q)}$ \end{document}(2−2q)(1−2q)2q(1−q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(2-2q)(0-2q)}{2q(1-q)}$ \end{document}(2−2q)(0−2q)2q(1−q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(1-2q)(1-2q)}{2q(1-q)}$ \end{document}(1−2q)(1−2q)2q(1−q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(1-2q)(0-2q)}{2q(1-q)}$ \end{document}(1−2q)(0−2q)2q(1−q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\frac {(0-2q)(0-2q)}{2q(1-q)}$ \end{document}(0−2q)(0−2q)2q(1−q)0; subtract 1 from the final denominator instead, in another loop