We note that when computing a matrix of correlation coefficients between all pairs of variants, if no genotype data is absent, then |Ix,y| is invariant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\overline {v}$ \end{document}v¯ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\overline {v^{2}}$ \end{document}v2¯ do not depend on y, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\overline {w}$ \end{document}w¯ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\overline {w^{2}}$ \end{document}w2¯ do not depend on x. Thus, these five values would not need to be recomputed for each variant pair at O(m2n) total time cost; they could instead be precomputed outside the main loop at a total cost of O(mn) time and O(m) space. PLINK 1.9 optimizes this common case.
