{ "_id": "6a1ed4f0b401979e7340e40e", "Package": "qfratio", "Type": "Package", "Title": "Moments and Distributions of Ratios of Quadratic Forms Using\nRecursion", "Version": "1.1.1.9000", "Date": "2026-05-20", "Authors@R": "c(person(\"Junya\", \"Watanabe\",\nemail = \"Junya.Watanabe@vetmeduni.ac.at\",\nrole = c(\"aut\", \"cre\", \"cph\"),\ncomment = c(ORCID = \"0000-0002-9810-5286\")),\nperson(\"Patrick\", \"Alken\", role = \"cph\",\ncomment = \"Author of bundled C codes from GSL\"),\nperson(\"Brian\", \"Gough\", role = \"cph\",\ncomment = \"Author of bundled C codes from GSL\"),\nperson(\"Pavel\", \"Holoborodko\", role = \"cph\",\ncomment = \"Author of bundled C codes from GSL\"),\nperson(\"Gerard\", \"Jungman\", role = \"cph\",\ncomment = \"Author of bundled C codes from GSL\"),\nperson(\"Reid\", \"Priedhorsky\", role = \"cph\",\ncomment = \"Author of bundled C codes from GSL\"),\nperson(\"Free Software Foundation, Inc.\", role = \"cph\",\ncomment = \"Copyright holder of some bundled scripts\"))", "Description": "Evaluates moments of ratios (and products) of quadratic\nforms in normal variables, specifically using recursive\nalgorithms developed by Bao and Kan (2013)\n and Hillier et al. (2014)\n. Also provides distribution,\nquantile, and probability density functions of simple ratios of\nquadratic forms in normal variables with several algorithms.\nOriginally developed as a supplement to Watanabe (2023)\n for evaluating average\nevolvability measures in evolutionary quantitative genetics,\nbut can be used for a broader class of statistics. Generating\nfunctions for these moments are also closely related to the\ntop-order zonal and invariant polynomials of matrix arguments.", "License": "GPL (>= 3)", "URL": "https://github.com/watanabe-j/qfratio", "BugReports": "https://github.com/watanabe-j/qfratio/issues", "Encoding": "UTF-8", "Roxygen": "list(markdown = TRUE)", "RoxygenNote": "7.3.3", "Config/testthat/edition": "3", "VignetteBuilder": "knitr, rmarkdown", "Repository": "https://watanabe-j.r-universe.dev", "Date/Publication": "2026-05-20 08:10:37 UTC", "RemoteUrl": "https://github.com/watanabe-j/qfratio", "RemoteRef": "HEAD", "RemoteSha": "4c906aadb6717c9e8fd1c885ae36c5c47e98513b", "NeedsCompilation": "yes", "Packaged": { "Date": "2026-05-20 11:16:08 UTC", "User": "root" }, "Author": "Junya Watanabe [aut, cre, cph] (ORCID:\n),\nPatrick Alken [cph] (Author of bundled C codes from GSL),\nBrian Gough [cph] (Author of bundled C codes from GSL),\nPavel Holoborodko [cph] (Author of bundled C codes from GSL),\nGerard Jungman [cph] (Author of bundled C codes from GSL),\nReid Priedhorsky [cph] (Author of bundled C codes from GSL),\nFree Software Foundation, Inc. [cph] (Copyright holder of some bundled\nscripts)", "Maintainer": "Junya Watanabe ", "MD5sum": "af169ddc1ee3589e7ef4ba585f2be48f", "_user": "watanabe-j", "_type": "src", "_file": "qfratio_1.1.1.9000.tar.gz", "_fileid": "393e0ac3052a9138fbb226009b4ec25f39ec8dca32ba6eb865c30115279df09e", "_filesize": 1390510, "_sha256": "393e0ac3052a9138fbb226009b4ec25f39ec8dca32ba6eb865c30115279df09e", "_created": "2026-05-20T11:16:08.000Z", "_published": "2026-06-02T13:04:48.854Z", "_distro": "noble", "_jobs": [ { "job": 79076728301, "time": 284, "config": "linux-devel-arm64", "r": "4.7.0", "check": "OK", "artifact": "7108588430" }, { "job": 79076728082, "time": 282, "config": "linux-devel-x86_64", "r": "4.7.0", "check": "OK", "artifact": "7108587860" }, { "job": 79076729004, "time": 268, "config": "linux-release-arm64", "r": "4.6.0", "check": "OK", "artifact": "7108583242" }, { "job": 79076729003, "time": 365, "config": "linux-release-x86_64", "r": "4.6.0", "check": "OK", "artifact": "7108615506" }, { 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"config": "windows-release", "r": "4.6.0", "check": "OK", "artifact": "7108596689" } ], "_buildurl": "https://github.com/r-universe/watanabe-j/actions/runs/26158759774", "_status": "success", "_host": "GitHub-Actions", "_upstream": "https://github.com/watanabe-j/qfratio", "_commit": { "id": "4c906aadb6717c9e8fd1c885ae36c5c47e98513b", "author": "Junya Watanabe ", "committer": "Junya Watanabe ", "message": "Update contact\n", "time": 1779264637 }, "_maintainer": { "name": "Junya Watanabe", "email": "junya.watanabe@vetmeduni.ac.at", "login": "watanabe-j", "description": "", "uuid": 26689590, "orcid": "0000-0002-9810-5286" }, "_registered": true, "_dependencies": [ { "package": "Rcpp", "role": "LinkingTo" }, { "package": "RcppEigen", "role": "LinkingTo" }, { "package": "Rcpp", "role": "Imports" }, { "package": "MASS", "role": "Imports" }, { "package": "stats", "role": "Imports" }, { "package": "mvtnorm", "role": "Suggests" }, { "package": "CompQuadForm", "role": "Suggests" }, { "package": "graphics", "role": "Suggests" }, { "package": "testthat", "version": ">= 3.0.0", "role": "Suggests" }, { "package": "knitr", "role": "Suggests" }, { "package": "rmarkdown", "role": "Suggests" } ], "_owner": "watanabe-j", "_selfowned": true, "_usedby": 0, "_updates": [ { "week": "2025-49", "n": 2 }, { "week": "2025-50", "n": 3 }, { "week": "2026-03", "n": 1 }, { "week": "2026-21", "n": 1 } ], "_tags": [], "_topics": [ "quadratic-forms", "rcpp", "rcppeigen", "zonal-polynomials", "cpp", "openmp" ], "_stars": 2, "_contributors": [ { "user": "watanabe-j", "count": 310, "uuid": 26689590 } ], "_userbio": { "uuid": 26689590, "type": "user", "name": "Junya Watanabe" }, "_downloads": { "count": 219, "source": "https://cranlogs.r-pkg.org/downloads/total/last-month/qfratio" }, "_devurl": "https://github.com/watanabe-j/qfratio", "_searchresults": 6, "_rbuild": "4.6.0", "_assets": [ "extra/citation.cff", "extra/citation.html", "extra/citation.json", "extra/citation.txt", "extra/contents.json", "extra/NEWS.html", "extra/NEWS.txt", "extra/qfratio.html", "extra/readme.html", "extra/readme.md", "manual.pdf" ], "_homeurl": "https://github.com/watanabe-j/qfratio", "_realowner": "watanabe-j", "_cranurl": true, "_releases": [ { "version": "1.0.0", "date": "2023-03-16" }, { "version": "1.0.1", "date": "2023-04-02" }, { "version": "1.1.0", "date": "2023-10-02" }, { "version": "1.1.1", "date": "2024-02-09" } ], "_exports": [ "dqfr", "pqfr", "qfm_Ap_int", "qfmrm", "qfmrm_ApBDqr_int", "qfmrm_ApBDqr_npi", "qfmrm_ApBIqr_int", "qfmrm_ApBIqr_npi", "qfmrm_IpBDqr_gen", "qfpm_ABDpqr_int", "qfpm_ABpq_int", "qfrm", "qfrm_ApBq_int", "qfrm_ApBq_npi", "qfrm_ApIq_int", "qfrm_ApIq_npi", "qqfr", "rqfmr", "rqfp", "rqfr" ], "_help": [ { "page": "a1_pk", "title": "Recursion for a_{p,k}", "topics": [ "a1_pk" ] }, { "page": "d1_i", "title": "Coefficients in polynomial expansion of generating function-single matrix", "topics": [ "d1_i", "dtil1_i", "dtil1_i_m", "dtil1_i_v" ] }, { "page": "d2_ij", "title": "Coefficients in polynomial expansion of generating function-for ratios with two matrices", "topics": [ "d2_1j", "d2_1j_m", "d2_1j_v", "d2_ij", "d2_ij_m", "d2_ij_v", "d2_pj", "d2_pj_m", "d2_pj_v", "h2_ij", "h2_ij_m", "h2_ij_v", "hhat2_1j", "hhat2_1j_m", "hhat2_1j_v", "hhat2_pj", "hhat2_pj_m", "hhat2_pj_v", "htil2_1j", "htil2_1j_m", "htil2_1j_v", "htil2_pj", "htil2_pj_m", "htil2_pj_v" ] }, { "page": "d3_ijk", "title": "Coefficients in polynomial expansion of generating function-for ratios with three matrices", "topics": [ "d3_ijk", "d3_ijk_m", "d3_ijk_v", "d3_pjk", "d3_pjk_m", "d3_pjk_v", "h3_ijk", "h3_ijk_m", "h3_ijk_v", "hhat3_pjk", "hhat3_pjk_m", "hhat3_pjk_v", "htil3_pjk", "htil3_pjk_m", "htil3_pjk_v" ] }, { "page": "pqfr", "title": "Probability distribution of ratio of quadratic forms", "topics": [ "dqfr", "dqfr_A1I1", "dqfr_broda", "dqfr_butler", "pqfr", "pqfr_A1B1", "pqfr_butler", "pqfr_davies", "pqfr_imhof", "qqfr" ] }, { "page": "dtil2_pq", "title": "Coefficients in polynomial expansion of generating function-for products", "topics": [ "dtil2_1q_m", "dtil2_1q_v", "dtil2_pq", "dtil2_pq_m", "dtil2_pq_v", "dtil3_pqr", "dtil3_pqr_m", "dtil3_pqr_v" ] }, { "page": "hgs", "title": "Calculate hypergeometric series", "topics": [ "hgs", "hgs_1d", "hgs_2d", "hgs_3d" ] }, { "page": "gsl_wrap", "title": "Internal C++ wrappers for GSL", "topics": [ "gsl_wrap", "hyperg_1F1_vec_b", "hyperg_2F1_mat_a_vec_c" ] }, { "page": "is_diagonal", "title": "Is this matrix diagonal?", "topics": [ "is_diagonal" ] }, { "page": "iseq", "title": "Are these vectors equal?", "topics": [ "iseq" ] }, { "page": "KiK", "title": "Matrix square root and generalized inverse", "topics": [ "KiK" ] }, { "page": "new_qfrm", "title": "Construct qfrm object", "topics": [ "new_qfpm", "new_qfrm" ] }, { "page": "qfrm_cpp", "title": "Internal C++ functions", "topics": [ "ABDpqr_int_E", "ABpq_int_E", "ApBDqr_int_Ec", "ApBDqr_int_Ed", "ApBDqr_int_El", "ApBDqr_npi_Ec", "ApBDqr_npi_Ed", "ApBDqr_npi_El", "ApBIqr_int_cEd", "ApBIqr_int_nEc", "ApBIqr_int_nEd", "ApBIqr_int_nEl", "ApBIqr_npi_Ec", "ApBIqr_npi_Ed", "ApBIqr_npi_El", "ApBq_int_E", "ApBq_npi_Ec", "ApBq_npi_Ed", "ApBq_npi_El", "ApIq_int_cE", "ApIq_int_nE", "ApIq_npi_cE", "ApIq_npi_nEc", "ApIq_npi_nEd", "ApIq_npi_nEl", "Ap_int_E", "d_A1I1_Ed", "d_broda_Ed", "d_butler_Ed", "IpBDqr_gen_Ec", "IpBDqr_gen_Ed", "IpBDqr_gen_El", "p_A1B1_Ec", "p_A1B1_Ed", "p_A1B1_El", "p_butler_Ed", "p_imhof_Ed", "qfrm_cpp", "rqfpE" ] }, { "page": "methods.qfrm", "title": "Methods for qfrm and qfpm objects", "topics": [ "methods.qfrm", "plot.qfrm", "print.qfpm", "print.qfrm" ] }, { "page": "qfmrm", "title": "Moment of multiple ratio of quadratic forms in normal variables", "topics": [ "qfmrm", "qfmrm_ApBDqr_int", "qfmrm_ApBDqr_npi", "qfmrm_ApBIqr_int", "qfmrm_ApBIqr_npi", "qfmrm_IpBDqr_gen" ] }, { "page": "qfpm", "title": "Moment of (product of) quadratic forms in normal variables", "topics": [ "qfm_Ap_int", "qfpm", "qfpm_ABDpqr_int", "qfpm_ABpq_int" ] }, { "page": "qfrm", "title": "Moment of ratio of quadratic forms in normal variables", "topics": [ "qfrm", "qfrm_ApBq_int", "qfrm_ApBq_npi", "qfrm_ApIq_int", "qfrm_ApIq_npi" ] }, { "page": "range_qfr", "title": "Get range of ratio of quadratic forms", "topics": [ "gen_eig", "range_qfr" ] }, { "page": "rqfr", "title": "Monte Carlo sampling of ratio/product of quadratic forms", "topics": [ "rqfmr", "rqfp", "rqfr" ] }, { "page": "S_fromUL", "title": "Make covariance matrix from eigenstructure", "topics": [ "S_fromUL" ] }, { "page": "sum_counterdiag", "title": "Summing up counter-diagonal elements", "topics": [ "sum_counterdiag", "sum_counterdiag3D" ] }, { "page": "tr", "title": "Matrix trace function", "topics": [ "tr" ] } ], "_readme": "https://github.com/watanabe-j/qfratio/raw/HEAD/README.md", "_rundeps": [ "MASS", "Rcpp", "RcppEigen" ], "_sysdeps": [ { "shlib": "libstdc++", "package": "libstdc++6", "source": "gcc", "version": "14.2.0-4ubuntu2~24.04.1", "name": "c++", "homepage": "http://gcc.gnu.org/", "description": "GNU Standard C++ Library v3" }, { "shlib": "libgomp", "package": "libgomp1", "source": "gcc", "version": "14.2.0-4ubuntu2~24.04.1", "name": "openmp", "homepage": "http://gcc.gnu.org/", "description": "GCC OpenMP (GOMP) support library" } ], "_vignettes": [ { "source": "qfratio.Rmd", "filename": "qfratio.html", "title": "qfratio: Moments of Ratios of Quadratic Forms", "engine": "knitr::rmarkdown", "headings": [ "Symbols used", "Target", "First examples", "Mathematical details", "Moment existence conditions", "Expressions for moments", "In these expressions, $\\beta_{\\cdot}$ are arbitrary scaling constants thatsatisfy $0 < \\beta < 2 / \\qfrlmax$, with $\\qfrlmax$ beingthe largest eigenvalue of the argument matrix.In addition, $h_{k_1, \\dots k_s}$ and $\\tilde{h}_{k_1; k_2 \\dots k_s}$ arethe coefficients of $t_1^{k_1} \\dots t_s^{k_s}$ in the following power seriesexpansions:\\begin{multline}\\det{ \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s }^{-\\frac{1}{2}}\\\\cdot\\exp \\left( \\frac{(1 - t_1 - \\dots - t_s) \\boldsymbol{\\mu}^T\\left( \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s \\right)^{-1}\\boldsymbol{\\mu}- \\boldsymbol{\\mu}^T \\boldsymbol{\\mu}}{2} \\right)\\", "\\sum_{k_1 = 0}^{\\infty} \\dots \\sum_{k_s = 0}^{\\infty} \\qfrhijk[k_1, \\dots, k_s]{ \\mathbf{A}_1 }{\\dots}{ \\mathbf{A}_s } t_1^{k_1} \\dots t_s^{k_s}, \\label{gfun_hij} \\\\end{multline}\\begin{multline}\\det{ \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s }^{-\\frac{1}{2}}\\ \\cdot\\exp \\left( \\frac{(1 - t_2 - \\dots - t_s) \\boldsymbol{\\mu}^T\\left( \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s \\right)^{-1}\\boldsymbol{\\mu}- \\boldsymbol{\\mu}^T \\boldsymbol{\\mu}}{2} \\right)\\", "A common special case is when $\\boldsymbol", "Special cases", "A notable special case for moments of simple ratios is when $p$ is a positiveinteger and $\\mathbf{B} = \\mathbf{I}_n$.In this case, (2) simplifies into [@HillierEtAl2014, theorem 4]\\begin{equation}\\qfrE \\left( \\frac{(\\mathbf{x}^T \\mathbf{A} \\mathbf{x})^p}{(\\mathbf{x}^T \\mathbf{x})^q} \\right)", "2^{p - q} p!\\sum_{k=0}^{p}\\frac{ \\qfrGmf{ \\frac{n}{2} + p - q + k } }{ 2^k k! \\qfrGmf{ \\frac{n}{2} + p + k } }{}1 F_1 \\left( q ; \\frac{n}{2} + p + k ; - \\frac{\\boldsymbol{\\mu}^T \\boldsymbol{\\mu}}{2} \\right) a{p, k} \\left( \\mathbf{A}, \\boldsymbol{\\mu} \\right),\\tag{5}\\end{equation}where ${}1 F_1 \\left( \\cdot ; \\cdot ; \\cdot \\right)$ is the confluenthypergeometric function, and $a{p, k}$ are the coefficients of $t^p$ in\\begin{align}&\\det{ \\mathbf{I}_n - t \\mathbf{A} }^{-\\frac{1}{2}}\\left(\\boldsymbol{\\mu}^T \\left( \\mathbf{I}_n - t \\mathbf{A} \\right)^{-1} \\boldsymbol{\\mu}- \\boldsymbol{\\mu}^T \\boldsymbol{\\mu}\\right) ^ k", "Numerical evaluation", "Truncation error", "A great advantage in the above expressions is that an error bound is availablefor a partial (truncated) sum for the simple ratio, provided that $p$ is apositive integer and $\\mathbf{B}$ is positive definite.By denoting the expression (2) as $M \\left( \\mathbf{A}, \\mathbf{B}, p, q \\right)$and the partial sum of the same up to $j = m$ as$\\hat{M}m \\left( \\mathbf{A}, \\mathbf{B}, p, q \\right)$, the error bound is[@HillierEtAl2014, theorem 7]\\begin{multline}\\lvert M \\left( \\mathbf{A}, \\mathbf{B}, p, q \\right) - \\hat{M}m \\left( \\mathbf{A}, \\mathbf{B}, p, q \\right) \\rvert \\\\leq\\frac{ 2^{p - q} \\beta{\\mathbf{B}}^{q} p! \\qfrGmf{ \\frac{n}{2} + p - q } \\qfrrf[m+1]{q} }{ \\qfrGmf{ \\frac{n}{2} + p + m + 1 } }\\left[\\frac{\\exp \\left( \\frac{ \\bar{\\boldsymbol{\\mu}}^T \\bar{\\boldsymbol{\\mu}} - \\boldsymbol{\\mu}^T \\boldsymbol{\\mu} }{2} \\right)\\qfrdtk[p]{ \\bar{A} }{ \\bar{\\boldsymbol{\\mu}} }}{\\det{\\beta{\\mathbf{B}} \\mathbf{B}}^{\\frac{1}{2}}}- \\sum_{j=0}^{m}\\qfrhhij[p;j]{ \\mathbf{A}^+ }{ \\mathbf{I}n - \\beta{\\mathbf{B}} \\mathbf{B} }\\right],\\end{multline}where $\\mathbf{A}^+$ is a symmetric matrix constructed from the eigenvectors and\"positivized\" eigenvalues of $\\mathbf{A}$ (above),$\\bar{\\boldsymbol{\\mu}} = \\sqrt{2}\\left( \\beta_\\mathbf{B} \\mathbf{B} \\right)^{-\\frac{1}{2}} \\boldsymbol{\\mu}$,$\\bar{\\mathbf{A}} = \\beta_{\\mathbf{B}}^{-1} \\mathbf{B}^{-\\frac{1}{2}} \\mathbf{A}^+ \\mathbf{B}^{-\\frac{1}{2}}$,and $\\tilde{d}$ and $\\hat{h}$ are coefficients in the following generating functions:\\begin{equation}\\det{ \\mathbf{I}_n - t \\mathbf{A} }^{-\\frac{1}{2}}\\exp \\left( \\frac{\\boldsymbol{\\mu}^T \\left( \\mathbf{I}_n - t \\mathbf{A} \\right)^{-1} \\boldsymbol{\\mu}- \\boldsymbol{\\mu}^T \\boldsymbol{\\mu}}{2} \\right)", "\\sum_{k = 0}^{\\infty} \\qfrdtk[k]{ \\mathbf{A} }{ \\boldsymbol{\\mu} } t^{k},\\end{equation}\\begin{multline}\\det{ \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s }^{-\\frac{1}{2}}\\\\quad \\cdot\\exp \\left( \\frac{(1 + t_2 + \\dots + t_s) \\boldsymbol{\\mu}^T\\left( \\mathbf{I}_n - t_1 \\mathbf{A}_1 - \\dots - t_s \\mathbf{A}_s \\right)^{-1}\\boldsymbol{\\mu}- \\boldsymbol{\\mu}^T \\boldsymbol{\\mu}}{2} \\right) \\", "Recursions", "Functions", "qfrm(): quadratic form ratio moment", "Usage", "Inside the function", "qfmrm(): quadratic form multiple ratio moment", "qfm_Ap_int(), qfpm_ABpq_int(), qfpm_ABDpqr_int(): quadratic form (product) moment", "rqfr(), rqfmr(), rqfp(): random number generation", "d1_i(), d2_*j_*(), d3_*jk_*(), etc.: recursion algorithms", "Using the functionality", "Recommended workflow", "Checking for numerical convergence", "Computational cost", "References" ], "created": "2023-02-16 19:47:59", "modified": "2025-12-04 16:24:58", "commits": 17 }, { "source": "qfratio_distr.Rmd", "filename": "qfratio_distr.html", "title": "Probability Distribution Functions in Package qfratio", "engine": "knitr::rmarkdown", "headings": [ "Symbols used", "Theory", "Preliminaries", "Series expression", "Distribution function", "Density function", "Numerical inversion", "Saddlepoint approximation", "Let $M_{X_q}(s)$ be the moment generating function of $X_q$,\\begin{equation}M_{X_q}(s)", "A first-order saddlepoint approximation formula for the distribution function$F_Q$ is [@ButlerPaolella2007; @ButlerPaolella2008]:\\begin{equation}\\widehat{\\Pr{}}_1 (Q < q)", "A more accurate second-order approximation is [@ButlerPaolella2007]\\begin{equation}\\widehat{\\Pr{}}_2 (Q < q)", "A first-order saddlepoint approximation for the density function $f_Q$ is[@ButlerPaolella2007; @ButlerPaolella2008]\\begin{equation}\\hat{f_1}(q)", "A second-order approximation is [@ButlerPaolella2007]\\begin{equation}\\hat{f_2}(q)", "\\hat{f_1}(q) (1 + O) ,\\end{equation}where\\begin{equation}O", "Implementation details", "Exported functions", "Choosing a method", "Use with ks.test()", "Series expressions", "Specifying integration error", "autoscale_args", "trim_values", "Options", "Error bound", "pqfr() and dqfr()", "qqfr()", "Distribution of powers", "When $\\mathbf{A}$ is nonnegative definite or $p$ is an odd integer", "When $\\mathbf{A}$ is indefinite and $p$ is an even integer", "When $\\mathbf{A}$ is indefinite and $p$ is non-integer", "Graphical examples", "References" ], "created": "2023-07-12 21:29:04", "modified": "2023-10-20 15:38:37", "commits": 15 } ], "_score": 4.903089986991944, "_indexed": true, "_nocasepkg": "qfratio", "_universes": [ "watanabe-j" ], "_binaries": [ { "r": "4.6.0", "os": "mac", "version": "1.1.1.9000", "date": "2026-05-12T08:43:29.000Z", "arch": "x86_64", "commit": "0ecb1faa1a9cda4ef424c337d54e4dec1780fc3a", "fileid": "45678723310f25385c403434e321797efe7a2cc235988208127b0222f6b62a06", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/watanabe-j/actions/runs/25723102391" }, { "r": "4.7.0", "os": "linux", "version": "1.1.1.9000", "date": "2026-05-20T11:20:14.000Z", "distro": "noble", "arch": "aarch64", "commit": "4c906aadb6717c9e8fd1c885ae36c5c47e98513b", "fileid": 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