R Under development (unstable) (2024-08-15 r87022 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ## Copyright (C) 2012 Marius Hofert, Ivan Kojadinovic, Martin Maechler, and Jun Yan > ## > ## This program is free software; you can redistribute it and/or modify it under > ## the terms of the GNU General Public License as published by the Free Software > ## Foundation; either version 3 of the License, or (at your option) any later > ## version. > ## > ## This program is distributed in the hope that it will be useful, but WITHOUT > ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS > ## FOR A PARTICULAR PURPOSE. See the GNU General Public License for more > ## details. > ## > ## You should have received a copy of the GNU General Public License along with > ## this program; if not, see . > > ## MM --- addition: to be put into /tests/*.R > ## --- diagnose the .libPaths setup and why the wrong lme4 is found ... > (.lP <- .libPaths()) [1] "D:/temp/RtmpwvZ414/RLIBS_2994846db6cdd" [2] "D:/RCompile/recent/R/library" > (.ip <- installed.packages(lib.loc = .lP[1]))[,c("Version", "Priority", "Built")] Version Priority Built ADGofTest "0.3" NA "4.5.0" DistributionUtils "0.6-1" NA "4.5.0" FNN "1.1.4" NA "4.5.0" GeneralizedHyperbolic "0.8-6" NA "4.5.0" KernSmooth "2.23-24" "recommended" "4.5.0" MASS "7.3-61" "recommended" "4.5.0" Matrix "1.7-0" "recommended" "4.5.0" R6 "2.5.1" NA "4.5.0" Rcpp "1.0.13" NA "4.5.0" RcppArmadillo "14.0.0-1" NA "4.5.0" Rdpack "2.6.1" NA "4.5.0" Rmpfr "0.9-5" NA "4.5.0" Rsolnp "1.16" NA "4.5.0" Runuran "0.38" NA "4.5.0" SkewHyperbolic "0.4-2" NA "4.5.0" TTR "0.24.4" NA "4.5.0" VGAM "1.1-11" NA "4.5.0" VineCopula "2.5.0" NA "4.5.0" abind "1.4-5" NA "4.5.0" alabama "2023.1.0" NA "4.5.0" base64enc "0.1-3" NA "4.5.0" bbmle "1.0.25.1" NA "4.5.0" bdsmatrix "1.3-7" NA "4.5.0" bslib "0.8.0" NA "4.5.0" cachem "1.1.0" NA "4.5.0" chron "2.3-61" NA "4.5.0" cli "3.6.3" NA "4.5.0" colorspace "2.1-1" NA "4.5.0" copula "1.1-4" NA "4.5.0" crop "0.0-3" NA "4.5.0" curl "5.2.1" NA "4.5.0" digest "0.6.36" NA "4.5.0" evaluate "0.24.0" NA "4.5.0" fastmap "1.2.0" NA "4.5.0" fontawesome "0.5.2" NA "4.5.0" fs "1.6.4" NA "4.5.0" glue "1.7.0" NA "4.5.0" gmp "0.7-4" NA "4.5.0" gridExtra "2.3" NA "4.5.0" gsl "2.1-8" NA "4.5.0" gtable "0.3.5" NA "4.5.0" highr "0.11" NA "4.5.0" htmltools "0.5.8.1" NA "4.5.0" jquerylib "0.1.4" NA "4.5.0" jsonlite "1.8.8" NA "4.5.0" kernlab "0.9-33" NA "4.5.0" knitr "1.48" NA "4.5.0" ks "1.14.2" NA "4.5.0" lattice "0.22-6" "recommended" "4.5.0" lcopula "1.0.7" NA "4.5.0" lifecycle "1.0.4" NA "4.5.0" mathjaxr "1.6-0" NA "4.5.0" mclust "6.1.1" NA "4.5.0" memoise "2.0.1" NA "4.5.0" mev "1.17" NA "4.5.0" mgcv "1.9-1" "recommended" "4.5.0" mime "0.12" NA "4.5.0" multicool "1.0.1" NA "4.5.0" mvnormtest "0.1-9-3" NA "4.5.0" mvtnorm "1.2-5" NA "4.5.0" nleqslv "3.3.5" NA "4.5.0" nlme "3.1-165" "recommended" "4.5.0" nloptr "2.1.1" NA "4.5.0" numDeriv "2016.8-1.1" NA "4.5.0" partitions "1.10-7" NA "4.5.0" pcaPP "2.0-4-1" NA "4.5.0" polynom "1.4-1" NA "4.5.0" pracma "2.4.4" NA "4.5.0" pspline "1.0-20" NA "4.5.0" qrng "0.0-10" NA "4.5.0" quadprog "1.5-8" NA "4.5.0" quantmod "0.4.26" NA "4.5.0" randtoolbox "2.0.4" NA "4.5.0" rappdirs "0.3.3" NA "4.5.0" rbibutils "2.2.16" NA "4.5.0" rlang "1.1.4" NA "4.5.0" rmarkdown "2.28" NA "4.5.0" rngWELL "0.10-9" NA "4.5.0" rugarch "1.5-1" NA "4.5.0" sass "0.4.9" NA "4.5.0" scatterplot3d "0.3-44" NA "4.5.0" sets "1.0-25" NA "4.5.0" sfsmisc "1.1-18" NA "4.5.0" spd "2.0-1" NA "4.5.0" stabledist "0.7-1" NA "4.5.0" tinytex "0.52" NA "4.5.0" truncnorm "1.0-9" NA "4.5.0" tseries "0.10-57" NA "4.5.0" xfun "0.47" NA "4.5.0" xts "0.14.0" NA "4.5.0" yaml "2.3.10" NA "4.5.0" zoo "1.8-12" NA "4.5.0" > ## (l.lme4 <- with(ll, results[results[,"Package"] == "lme4", , drop=FALSE])) > ## sapply(l.lme4[,"LibPath"], function(lib) packageDescription("lme4", lib.loc=lib)) > sessionInfo() R Under development (unstable) (2024-08-15 r87022 ucrt) Platform: x86_64-w64-mingw32/x64 Running under: Windows Server 2022 x64 (build 20348) Matrix products: default locale: [1] LC_COLLATE=C LC_CTYPE=German_Germany.utf8 [3] LC_MONETARY=C LC_NUMERIC=C [5] LC_TIME=C time zone: Europe/Berlin tzcode source: internal attached base packages: [1] stats graphics grDevices utils datasets methods base loaded via a namespace (and not attached): [1] compiler_4.5.0 tools_4.5.0 > ## ------ end{diagnose_libPaths} > > require(copula) Loading required package: copula > (isLinux <- identical("Linux", Sys.info()[["sysname"]])) [1] FALSE > (doExtras <- copula:::doExtras()) [1] FALSE > sessionInfo() R Under development (unstable) (2024-08-15 r87022 ucrt) Platform: x86_64-w64-mingw32/x64 Running under: Windows Server 2022 x64 (build 20348) Matrix products: default locale: [1] LC_COLLATE=C LC_CTYPE=German_Germany.utf8 [3] LC_MONETARY=C LC_NUMERIC=C [5] LC_TIME=C time zone: Europe/Berlin tzcode source: internal attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] copula_1.1-4 loaded via a namespace (and not attached): [1] compiler_4.5.0 Matrix_1.7-0 ADGofTest_0.3 [4] tools_4.5.0 pspline_1.0-20 gsl_2.1-8 [7] mvtnorm_1.2-5 grid_4.5.0 pcaPP_2.0-4-1 [10] numDeriv_2016.8-1.1 stats4_4.5.0 lattice_0.22-6 [13] stabledist_0.7-1 > > ## From source(system.file("test-tools-1.R", package = "Matrix")) : > showSys.time <- function(expr) { + ## prepend 'Time' for R CMD Rdiff + st <- system.time(expr) + writeLines(paste("Time", capture.output(print(st)))) + invisible(st) + } > > ### Stirling numbers of the 1st kind ########################################### > > S1.10 <- c(0, -362880, 1026576, -1172700, 723680, + -269325, 63273, -9450, 870, -45, 1) > stopifnot(sapply(0:10, Stirling1, n=10) == S1.10, + Stirling1.all(10) == S1.10[-1]) > > options(str = strOptions(vec.len = 10, digits.d = 20)) # for ls.str() below > > ls.str(copula:::.nacopEnv) Bern.tab : list() Eul.full.n : num 0 Eul.tab : list() S1.full.n : num 10 S1.tab : List of 10 $ : num 1 $ : num [1:2] -1 1 $ : num [1:3] 2 -3 1 $ : num [1:4] -6 11 -6 1 $ : num [1:5] 24 -50 35 -10 1 $ : num [1:6] -120 274 -225 85 -15 1 $ : num [1:7] 720 -1764 1624 -735 175 -21 1 $ : num [1:8] -5040 13068 -13132 6769 -1960 322 -28 1 $ : num [1:9] 40320 -109584 118124 -67284 22449 -4536 546 -36 1 $ : num [1:10] -362880 1026576 -1172700 723680 -269325 63273 -9450 870 -45 1 S2.full.n : num 0 S2.tab : list() > showSys.time(S <- Stirling1(30, 7))# updating table -> typically not zero Time user system elapsed Time 0 0 0 > showSys.time(S. <- Stirling1(30, 7))# lookup --> should be zero Time user system elapsed Time 0 0 0 > stopifnot(identical(S, S.)) > > ls.str(copula:::.nacopEnv) Bern.tab : list() Eul.full.n : num 0 Eul.tab : list() S1.full.n : num 10 S1.tab : List of 30 $ : num 1 $ : num [1:2] -1 1 $ : num [1:3] 2 -3 1 $ : num [1:4] -6 11 -6 1 $ : num [1:5] 24 -50 35 -10 1 $ : num [1:6] -120 274 -225 85 -15 1 $ : num [1:7] 720 -1764 1624 -735 175 -21 1 $ : num [1:8] -5040 13068 -13132 6769 -1960 322 -28 1 $ : num [1:9] 40320 -109584 118124 -67284 22449 -4536 546 -36 1 $ : num [1:10] -362880 1026576 -1172700 723680 -269325 63273 -9450 870 -45 1 $ : num [1:11] 3628800 -10628640 12753576 -8409500 3416930 -902055 157773 NA NA NA NA $ : num [1:12] -39916800 120543840 -150917976 105258076 -45995730 13339535 -2637558 NA NA NA NA NA $ : num [1:13] 479001600 -1486442880 1931559552 -1414014888 657206836 -206070150 44990231 NA NA NA NA NA NA $ : num [1:14] -6227020800 19802759040 -26596717056 20313753096 -9957703756 3336118786 -790943153 NA NA NA NA NA ... $ : num [1:15] 87178291200 -283465647360 392156797824 -310989260400 159721605680 -56663366760 14409322928 NA NA NA NA NA ... $ : num [1:16] -1307674368000 4339163001600 -6165817614720 5056995703824 -2706813345600 1009672107080 -272803210680 NA NA NA NA NA ... $ : num [1:17] 20922789888000 -70734282393600 102992244837120 -87077748875904 48366009233424 -18861567058880 5374523477960 NA NA NA NA NA ... $ : num [1:18] -355687428096000 1223405590579200 -1821602444624640 1583313975727488 -909299905844112 369012649234384 -1102284661| __truncated__ ... $ : num [1:19] 6402373705728000 -22376988058521600 34012249593822720 -30321254007719424 17950712280921504 -7551527592063024 2353| __truncated__ ... $ : num [1:20] -121645100408832000 431565146817638400 -668609730341153280 610116075740491776 -371384787345228032 161429736530118| __truncated__ ... $ : num [1:21] 2432902008176640000 -8752948036761600000 13803759753640704000 -12870931245150988288 8037811822645052416 -35999795| __truncated__ ... $ : num [1:22] -51090942171709440000 186244810780170256384 -298631902863216410624 284093315901811458048 -181664979520697106432 8| __truncated__ ... $ : num [1:23] 1124000727777607680000 -4148476779335455342422 6756146673770930635882 -6548684852703068684468 4280722865357148127| __truncated__ ... $ : num [1:24] -25852016738884978212844 96538966652493089472062 -159539850276066841072420 157375898285941509328800 -105005310755| __truncated__ ... $ : num [1:25] NA -2342787216398719066880266 3925495373278097342488426 -3936561409138662762882662 2677503356427960596806604 -132| __truncated__ ... $ : num [1:26] NA NA -1.0048017154835114860e+26 1.0233953060174467286e+26 -7.0874145319837676608e+25 3.5770355645907608595e+25 -| __truncated__ ... $ : num [1:27] NA NA NA -2.7613079671937127630e+27 1.9450673089175241960e+27 -1.0009033921134356117e+27 3.9317852931307364446e+2| __truncated__ ... $ : num [1:28] NA NA NA NA -5.5278125307966864133e+28 2.8969458895980284752e+28 -1.1616723683566424906e+28 NA NA NA NA NA ... $ : num [1:29] NA NA NA NA NA -8.6642297439541484600e+29 3.5423772203584016891e+29 NA NA NA NA NA ... $ : num [1:30] NA NA NA NA NA NA -1.1139316913434780448e+31 NA NA NA NA NA ... S2.full.n : num 0 S2.tab : list() > > showSys.time(s1c <- Stirling1(100,10)) Time user system elapsed Time 0 0 0 > s1c [1] 1.125272e+156 > (s1 <- system.time(for(i in 1:20) S. <- Stirling1(100, 10))[[1]]) [1] 0.01 > stopifnot(identical(S., s1c), !isLinux || s1 <= 0.020) > showSys.time(s2c <- Stirling1(200,190)); s2c Time user system elapsed Time 0 0 0 [1] 1.976591e+36 > (s2 <- system.time(for(i in 1:20) S. <- Stirling1(200,190))[[1]]) [1] 0 > stopifnot(identical(S., s2c), !isLinux || s2 <= 0.020) > ## 0.010 occasionally barely fails (prints "0.010") on Martin's X201 > > > ### Stirling numbers of the 2nd kind ########################################### > > S2.10 <- c(0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1) > stopifnot(sapply(0:10, Stirling2, n=10, method="direct") == S2.10, + sapply(0:10, Stirling2, n=10, method="lookup") == S2.10, + Stirling2.all(10) == S2.10[-1]) > > ls.str(copula:::.nacopEnv) Bern.tab : list() Eul.full.n : num 0 Eul.tab : list() S1.full.n : num 10 S1.tab : List of 200 $ : num 1 $ : num [1:2] -1 1 $ : num [1:3] 2 -3 1 $ : num [1:4] -6 11 -6 1 $ : num [1:5] 24 -50 35 -10 1 $ : num [1:6] -120 274 -225 85 -15 1 $ : num [1:7] 720 -1764 1624 -735 175 -21 1 $ : num [1:8] -5040 13068 -13132 6769 -1960 322 -28 1 $ : num [1:9] 40320 -109584 118124 -67284 22449 -4536 546 -36 1 $ : num [1:10] -362880 1026576 -1172700 723680 -269325 63273 -9450 870 -45 1 $ : num [1:11] 3628800 -10628640 12753576 -8409500 3416930 -902055 157773 -18150 1320 -55 1 $ : num [1:12] -39916800 120543840 -150917976 105258076 -45995730 13339535 -2637558 357423 -32670 1925 -66 1 $ : num [1:13] 479001600 -1486442880 1931559552 -1414014888 657206836 -206070150 44990231 -6926634 749463 -55770 2717 -78 1 $ : num [1:14] -6227020800 19802759040 -26596717056 20313753096 -9957703756 3336118786 -790943153 135036473 -16669653 1474473 -91091 3731 ... $ : num [1:15] 87178291200 -283465647360 392156797824 -310989260400 159721605680 -56663366760 14409322928 -2681453775 368411615 | __truncated__ ... $ : num [1:16] -1307674368000 4339163001600 -6165817614720 5056995703824 -2706813345600 1009672107080 -272803210680 54631129553 | __truncated__ ... $ : num [1:17] 20922789888000 -70734282393600 102992244837120 -87077748875904 48366009233424 -18861567058880 5374523477960 -1146| __truncated__ ... $ : num [1:18] -355687428096000 1223405590579200 -1821602444624640 1583313975727488 -909299905844112 369012649234384 -1102284661| __truncated__ ... $ : num [1:19] 6402373705728000 -22376988058521600 34012249593822720 -30321254007719424 17950712280921504 -7551527592063024 2353| __truncated__ ... $ : num [1:20] -121645100408832000 431565146817638400 -668609730341153280 610116075740491776 -371384787345228032 161429736530118| __truncated__ ... $ : num [1:21] 2432902008176640000 -8752948036761600000 13803759753640704000 -12870931245150988288 8037811822645052416 -35999795| __truncated__ ... $ : num [1:22] -51090942171709440000 186244810780170256384 -298631902863216410624 284093315901811458048 -181664979520697106432 8| __truncated__ ... $ : num [1:23] 1124000727777607680000 -4148476779335455342422 6756146673770930635882 -6548684852703068684468 4280722865357148127| __truncated__ ... $ : num [1:24] -25852016738884978212844 96538966652493089472062 -159539850276066841072420 157375898285941509328800 -105005310755| __truncated__ ... $ : num [1:25] 620448401733239410004482 -2342787216398719066880266 3925495373278097342488426 -3936561409138662762882662 26775033| __truncated__ ... $ : num [1:26] -1.5511210043330986055e+25 5.9190128811701209102e+25 -1.0048017154835114860e+26 1.0233953060174467286e+26 -7.0874| __truncated__ ... $ : num [1:27] 4.0329146112660565035e+26 -1.5544545591475622315e+27 2.6716745890688309436e+27 -2.7613079671937127630e+27 1.94506| __truncated__ ... $ : num [1:28] -1.0888869450418351940e+28 4.2373564558110791470e+28 -7.3689668464005995789e+28 7.7226989703299075002e+28 -5.5278| __truncated__ ... $ : num [1:29] 3.0488834461171383673e+29 -1.1973486770775205350e+30 2.1056842815502785854e+30 -2.2360453801563801659e+30 1.62501| __truncated__ ... $ : num [1:30] -8.8417619937397007720e+30 3.5027999979859809425e+31 -6.2262192842035595300e+31 6.6951000306085306220e+31 -4.9361| __truncated__ ... $ : num [1:31] 2.6525285981219103217e+32 -1.0596817613895339068e+33 1.9028937852409277222e+33 -2.0707922020245950068e+33 1.54779| __truncated__ ... $ : num [1:32] -8.2228386541779224300e+33 3.3115387462887740419e+34 -6.0049389103858293445e+34 6.6097452048003371788e+34 -5.0052| __truncated__ ... $ : num [1:33] 2.6313083693369351778e+35 -1.0679152374665855743e+36 1.9546958387863532367e+36 -2.1751678546399660615e+36 1.66777| __truncated__ ... $ : num [1:34] -8.6833176188118859386e+36 3.5504333673331013781e+37 -6.5572877917416238255e+37 7.3735235041905231499e+37 -5.7211| __truncated__ ... $ : num [1:35] 2.9523279903960411956e+38 -1.2158306625120664949e+39 2.2649821828654830341e+39 -2.5725708693421940525e+39 2.01893| __truncated__ ... $ : num [1:36] -1.0333147966386144222e+40 4.2849305986961928384e+40 -8.0490207062803971931e+40 9.2304962609842273660e+40 -7.3235| __truncated__ ... $ : num [1:37] 3.7199332678990117750e+41 -1.5529081634970156107e+42 2.9404967602479048550e+42 -3.4034688610171260751e+42 2.72877| __truncated__ ... $ : num [1:38] -1.3763753091226343103e+43 5.7829595376179477378e+43 -1.1035128829266950670e+44 1.2886884461788156777e+44 -1.0436| __truncated__ ... $ : num [1:39] 5.2302261746660103788e+44 -2.2112883773860464835e+45 4.2511785504976208109e+45 -5.0073673837721691814e+45 4.09485| __truncated__ ... $ : num [1:40] -2.0397882081197441589e+46 8.6763269335522420394e+46 -1.6800725184679326193e+47 1.9953850651761219480e+47 -1.6470| __truncated__ ... $ : num [1:41] 8.1591528324789768384e+47 -3.4909286555020941686e+48 6.8070533432072529174e+48 -8.1495475125512810534e+48 6.78781| __truncated__ ... $ : num [1:42] -3.3452526613163802765e+49 1.4394399015883375567e+50 -2.8258011572699944885e+50 3.4093850135780975664e+50 -2.8644| __truncated__ ... $ : num [1:43] 1.4050061177528797887e+51 -6.0791001132841810165e+51 1.2012308850692809361e+52 -1.4601997172755010058e+52 1.23718| __truncated__ ... $ : num [1:44] -6.0415263063373834070e+52 2.6280631098897264241e+53 -5.2260838069307500881e+53 6.3989818727915826584e+53 -5.4659| __truncated__ ... $ : num [1:45] 2.6582715747884485291e+54 -1.1623892946578170823e+55 2.3257575061484273881e+55 -2.8678128620976040829e+55 2.46898| __truncated__ ... $ : num [1:46] -1.1962222086548018857e+56 5.2573345417080618387e+56 -1.0582147707133705935e+57 1.3137733630054062175e+57 -1.1397| __truncated__ ... $ : num [1:47] 5.5026221598120884566e+57 -2.4303361112722566149e+58 4.9203612906985852524e+58 -6.1491789468962053632e+58 5.37410| __truncated__ ... $ : num [1:48] -2.5862324151116817769e+59 1.1477605944577728557e+60 -2.3368731677410574843e+60 2.9393177179482025238e+60 -2.5873| __truncated__ ... $ : num [1:49] 1.2413915592536072529e+61 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num [1:96] NA NA NA NA NA 1.7380300131616246036e+149 -1.1478465763741815726e+149 6.2428783283887463338e+148 -2.8607775787970| __truncated__ ... $ : num [1:97] NA NA NA NA NA NA 1.1193130134508306829e+151 -6.1079478528906147963e+150 2.8087752589290090883e+150 -1.1077977617| __truncated__ ... $ : num [1:98] NA NA NA NA NA NA NA 6.0366407186489795377e+152 -2.7855914796900449384e+152 1.1026515814854526896e+152 NA NA ... $ : num [1:99] NA NA NA NA NA NA NA NA 2.7902460572827344116e+154 -1.1084544646526441131e+154 NA NA ... [list output truncated] S2.full.n : num 10 S2.tab : List of 10 $ : num 1 $ : num [1:2] 1 1 $ : num [1:3] 1 3 1 $ : num [1:4] 1 7 6 1 $ : num [1:5] 1 15 25 10 1 $ : num [1:6] 1 31 90 65 15 1 $ : num [1:7] 1 63 301 350 140 21 1 $ : num [1:8] 1 127 966 1701 1050 266 28 1 $ : num [1:9] 1 255 3025 7770 6951 2646 462 36 1 $ : num [1:10] 1 511 9330 34105 42525 22827 5880 750 45 1 > showSys.time(S <- Stirling2(30, 7))# updating table -> typically not zero Time user system elapsed Time 0 0 0 > showSys.time(S. <- Stirling2(30, 7))# lookup --> should be zero Time user system elapsed Time 0 0 0 > stopifnot(identical(S, S.), + all.equal(S, Stirling2(30,7, method="direct"), tolerance=1e-15)) > > ls.str(copula:::.nacopEnv) Bern.tab : list() Eul.full.n : num 0 Eul.tab : list() S1.full.n : num 10 S1.tab : List of 200 $ : num 1 $ : num [1:2] -1 1 $ : num [1:3] 2 -3 1 $ : num [1:4] -6 11 -6 1 $ : num [1:5] 24 -50 35 -10 1 $ : num [1:6] -120 274 -225 85 -15 1 $ : num [1:7] 720 -1764 1624 -735 175 -21 1 $ : num [1:8] -5040 13068 -13132 6769 -1960 322 -28 1 $ : num [1:9] 40320 -109584 118124 -67284 22449 -4536 546 -36 1 $ : num [1:10] -362880 1026576 -1172700 723680 -269325 63273 -9450 870 -45 1 $ : num [1:11] 3628800 -10628640 12753576 -8409500 3416930 -902055 157773 -18150 1320 -55 1 $ : num [1:12] -39916800 120543840 -150917976 105258076 -45995730 13339535 -2637558 357423 -32670 1925 -66 1 $ : num [1:13] 479001600 -1486442880 1931559552 -1414014888 657206836 -206070150 44990231 -6926634 749463 -55770 2717 -78 1 $ : num [1:14] -6227020800 19802759040 -26596717056 20313753096 -9957703756 3336118786 -790943153 135036473 -16669653 1474473 -91091 3731 ... $ : num [1:15] 87178291200 -283465647360 392156797824 -310989260400 159721605680 -56663366760 14409322928 -2681453775 368411615 | __truncated__ ... $ : num [1:16] -1307674368000 4339163001600 -6165817614720 5056995703824 -2706813345600 1009672107080 -272803210680 54631129553 | __truncated__ ... $ : num [1:17] 20922789888000 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__truncated__ ... $ : num [1:24] -25852016738884978212844 96538966652493089472062 -159539850276066841072420 157375898285941509328800 -105005310755| __truncated__ ... $ : num [1:25] 620448401733239410004482 -2342787216398719066880266 3925495373278097342488426 -3936561409138662762882662 26775033| __truncated__ ... $ : num [1:26] -1.5511210043330986055e+25 5.9190128811701209102e+25 -1.0048017154835114860e+26 1.0233953060174467286e+26 -7.0874| __truncated__ ... $ : num [1:27] 4.0329146112660565035e+26 -1.5544545591475622315e+27 2.6716745890688309436e+27 -2.7613079671937127630e+27 1.94506| __truncated__ ... $ : num [1:28] -1.0888869450418351940e+28 4.2373564558110791470e+28 -7.3689668464005995789e+28 7.7226989703299075002e+28 -5.5278| __truncated__ ... $ : num [1:29] 3.0488834461171383673e+29 -1.1973486770775205350e+30 2.1056842815502785854e+30 -2.2360453801563801659e+30 1.62501| __truncated__ ... $ : num [1:30] -8.8417619937397007720e+30 3.5027999979859809425e+31 -6.2262192842035595300e+31 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-1.5529081634970156107e+42 2.9404967602479048550e+42 -3.4034688610171260751e+42 2.72877| __truncated__ ... $ : num [1:38] -1.3763753091226343103e+43 5.7829595376179477378e+43 -1.1035128829266950670e+44 1.2886884461788156777e+44 -1.0436| __truncated__ ... $ : num [1:39] 5.2302261746660103788e+44 -2.2112883773860464835e+45 4.2511785504976208109e+45 -5.0073673837721691814e+45 4.09485| __truncated__ ... $ : num [1:40] -2.0397882081197441589e+46 8.6763269335522420394e+46 -1.6800725184679326193e+47 1.9953850651761219480e+47 -1.6470| __truncated__ ... $ : num [1:41] 8.1591528324789768384e+47 -3.4909286555020941686e+48 6.8070533432072529174e+48 -8.1495475125512810534e+48 6.78781| __truncated__ ... $ : num [1:42] -3.3452526613163802765e+49 1.4394399015883375567e+50 -2.8258011572699944885e+50 3.4093850135780975664e+50 -2.8644| __truncated__ ... $ : num [1:43] 1.4050061177528797887e+51 -6.0791001132841810165e+51 1.2012308850692809361e+52 -1.4601997172755010058e+52 1.23718| __truncated__ ... $ : 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7.1410997304795127091e+63 -6.3728| __truncated__ ... $ : num [1:51] 3.0414093201713375575e+64 -1.3683925049359751420e+65 2.8312047394413541550e+65 -3.6266290361540651078e+65 3.25782| __truncated__ ... $ : num [1:52] -1.5511187532873821895e+66 7.0092158683751869855e+66 -1.4575983421644503002e+67 1.8778928558329868306e+67 -1.6977| __truncated__ ... $ : num [1:53] 8.0658175170943876850e+67 -3.6603034390879711215e+68 7.6496035379388942692e+68 -9.9108026845479753521e+68 9.01612| __truncated__ ... $ : num [1:54] -4.2748832840600254849e+69 1.9480266402337188631e+70 -4.0908929094984936119e+70 5.3292214581898156305e+70 -4.8776| __truncated__ ... $ : num [1:55] 2.3084369733924137926e+71 -1.0562092690102681180e+72 2.2285624375315236164e+72 -2.9186885165174851988e+72 2.68722| __truncated__ ... $ : num [1:56] -1.2696403353658276447e+73 5.8322353492903995721e+73 -1.2362714333324404367e+74 1.6275643084599320405e+74 -1.5071| __truncated__ ... $ : num [1:57] 7.1099858780486348106e+74 -3.2787481989562819739e+75 6.9814423801545704919e+75 -9.2379872707088637723e+75 8.60286| __truncated__ ... $ : num [1:58] -4.0526919504877220528e+76 1.8759964592831294131e+77 -4.0122096386776682731e+77 5.3354671681055976127e+77 -4.9960| __truncated__ ... $ : num [1:59] 2.3505613312828789064e+78 -1.0921306383347028158e+79 2.3458415550258790135e+79 -3.1346930538880236430e+79 2.95104| __truncated__ ... $ : num [1:60] -1.3868311854568986494e+80 6.4670763794875757023e+80 -1.3949678238486155096e+81 1.8729273173441927954e+81 -1.7724| __truncated__ ... $ : num [1:61] 8.3209871127413915807e+81 -3.8941141395471144579e+82 8.4344777068865678027e+82 -1.1377060686450018470e+83 1.08220| __truncated__ ... $ : num [1:62] -5.0758021387722483584e+83 2.3837306122364814367e+84 -5.1839725425962773224e+84 7.0243517958033766216e+84 -6.7152| __truncated__ ... $ : num [1:63] 3.1469973260387939392e+85 -1.4829887817253904824e+86 3.2379002825320564868e+86 -4.4069378388240559937e+86 4.23368| __truncated__ ... $ : 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-6.1079478528906147963e+150 2.8087752589290090883e+150 -1.1077977617| __truncated__ ... $ : num [1:98] NA NA NA NA NA NA NA 6.0366407186489795377e+152 -2.7855914796900449384e+152 1.1026515814854526896e+152 NA NA ... $ : num [1:99] NA NA NA NA NA NA NA NA 2.7902460572827344116e+154 -1.1084544646526441131e+154 NA NA ... [list output truncated] S2.full.n : num 10 S2.tab : List of 30 $ : num 1 $ : num [1:2] 1 1 $ : num [1:3] 1 3 1 $ : num [1:4] 1 7 6 1 $ : num [1:5] 1 15 25 10 1 $ : num [1:6] 1 31 90 65 15 1 $ : num [1:7] 1 63 301 350 140 21 1 $ : num [1:8] 1 127 966 1701 1050 266 28 1 $ : num [1:9] 1 255 3025 7770 6951 2646 462 36 1 $ : num [1:10] 1 511 9330 34105 42525 22827 5880 750 45 1 $ : num [1:11] 1 1023 28501 145750 246730 179487 63987 NA NA NA NA $ : num [1:12] 1 2047 86526 611501 1379400 1323652 627396 NA NA NA NA NA $ : num [1:13] 1 4095 261625 2532530 7508501 9321312 5715424 NA NA NA NA NA NA $ : num [1:14] 1 8191 788970 10391745 40075035 63436373 49329280 NA NA NA NA NA NA NA $ : num [1:15] 1 16383 2375101 42355950 210766920 420693273 408741333 NA NA NA NA NA NA NA NA $ : num [1:16] 1 32767 7141686 171798901 1096190550 2734926558 3281882604 NA NA NA NA NA NA NA NA NA $ : num [1:17] 1 65535 21457825 694337290 5652751651 17505749898 25708104786 NA NA NA NA NA ... $ : num [1:18] 1 131071 64439010 2798806985 28958095545 110687251039 197462483400 NA NA NA NA NA ... $ : num [1:19] 1 262143 193448101 11259666950 147589284710 693081601779 1492924634839 NA NA NA NA NA ... $ : num [1:20] 1 524287 580606446 45232115901 749206090500 4306078895384 11143554045652 NA NA NA NA NA ... $ : num [1:21] 1 1048575 1742343625 181509070050 3791262568401 26585679462804 82310957214948 NA NA NA NA NA ... $ : num [1:22] 1 2097151 5228079450 727778623825 19137821912055 163305339345225 602762379967440 NA NA NA NA NA ... $ : num [1:23] 1 4194303 15686335501 2916342574750 96416888184100 998969857983405 4382641999117305 NA NA NA NA NA ... $ : num [1:24] 1 8388607 47063200806 11681056634501 485000783495250 6090236036084530 31677463851804540 NA NA NA NA NA ... $ : num [1:25] NA 16777215 141197991025 46771289738810 2436684974110751 37026417000002432 227832482998716320 NA NA NA NA NA ... $ : num [1:26] NA NA 423610750290 187226356946265 12230196160292566 224595186974125344 1631853797991016448 NA NA NA NA NA ... $ : num [1:27] NA NA NA 749329038535350 61338207158409096 1359801318005044736 11647571772911241216 NA NA NA NA NA ... $ : num [1:28] NA NA NA NA 307440364830580864 8220146115188677632 82892803728383737856 NA NA NA NA NA ... $ : num [1:29] NA NA NA NA NA 49628317055962644480 588469772213874851840 NA NA NA NA NA ... $ : num [1:30] NA NA NA NA NA NA 4168916722553086541064 NA NA NA NA NA ... > > rbind(C.direct = system.time(Sd <- Stirling2(100,10, method="direct")), + C.lookup = system.time(Sl <- Stirling2(100,10, method="lookup"))) user.self sys.self elapsed user.child sys.child C.direct 0 0 0 NA NA C.lookup 0 0 0 NA NA > ## should be equal; and lookup time should be "zero" when called again: > (s3 <- system.time(for(i in 1:20) S. <- Stirling2(100, 10))[[1]]) [1] 0 > stopifnot(all.equal(Sd, Sl, tolerance = 1e-15), !isLinux || s3 <= 0.020) > ## 0.010 fails on good ole' Solaris when that is busy.. > ## Here, the direct method already overflows, but the "lookup" still works > rbind(C.direct = system.time(Sd <- Stirling2(200,190, method="direct")), + C.lookup = system.time(Sl <- Stirling2(200,190, method="lookup"))) user.self sys.self elapsed user.child sys.child C.direct 0 0.00 0.00 NA NA C.lookup 0 0.02 0.01 NA NA > Sd ; Sl [1] NaN [1] 1.452971e+36 > (s4 <- system.time(for(i in 1:20) S. <- Stirling2(200,190))[[1]]) [1] 0 > stopifnot(!isLinux || s4 <= 0.025) > # 0.010 occasionally barely fails (prints "0.010") on Martin's X201 > > > ### Eulerian Numbers ########################################################### > > ##' cheap "direct" version of Eulerian.all(): > Euleri.A <- function(n) + sapply(0:max(0,n-1), Eulerian, n=n, method="direct") > stopifnot(identical(Euler.l5 <- lapply(0:5, Euleri.A), + list(1, + 1, + c(1, 1), + c(1, 4, 1), + c(1, 11, 11, 1), + c(1, 26, 66, 26, 1)))) > > p.Eul <- function(n) { + plot(E1 <- Eulerian.all(n), log="y", yaxt="n", + xlab = "k", ylab = bquote(A(.(n), k)), + main = bquote("Eulerian numbers "* A(.(n), k))) + if(require("sfsmisc")) + eaxis(2, quantile(axTicks(2), (0:16)/16, type=3), at.small=numeric()) + else axis(2) + lines(E2 <- Euleri.A(n), col="green3", type="o") + invisible(cbind(E1=E1, E2=E2)) + } > > if(!dev.interactive(orNone=TRUE)) pdf("Eulerian-ex.pdf") > > e60 <- p.Eul(60); all.equal(e60[,2],e60[,1], tolerance=0) ## 3.82e-09 Loading required package: sfsmisc [1] "Mean relative difference: 3.821322e-09" > e70 <- p.Eul(70); all.equal(e70[,2],e70[,1]) ## 2.97e-6 [1] "Mean relative difference: 2.974384e-06" > e90 <- p.Eul(90); all.equal(e90[,2],e90[,1]) ## 0.032 [1] "Mean relative difference: 0.03194358" > e100 <- p.Eul(100); all.equal(e100[,2],e100[,1]) ## 0.80028 --- visible in center [1] "Mean relative difference: 0.8002766" > e110 <- p.Eul(110); all.equal(e110[,2],e110[,1]) ## 0.992 --- visible in center [1] "Mean relative difference: 0.9924735" > e120 <- p.Eul(120); all.equal(e120[,2],e120[,1]) ## 1 -- problem in center [1] "Mean relative difference: 1.000044" > e150 <- p.Eul(150) ## clear problem in center -- close to overflow though > e170 <- p.Eul(170) ## clear problem in center -- close to overflow though > max(e170[,"E1"]) # 7.5964e+305 -- almost maximum [1] 7.596386e+305 > dev.off() null device 1 > > ### Bernoulli numbers ========================================================= > > ##--- see example(Bernoulli) ---> ../man/Bernoulli.Rd ------ > ##--- ~~~~~~~~~~~~~~~~~~~ ------ > > ## BUT -- the algorithm is *really* not accurate enough ... > ## ---> try to work with higher precision > ## ---> Use package "Rmpfr" and its own Bernoulli() / Bernoulli.all() > > ## NB: The following does not print *unless* you evaluate it *outside* > ## the if(..) clause > if(doExtras && require("Rmpfr")) { ## note that it has its own Bernoulli() ! + if(!dev.interactive(orNone=TRUE)) pdf("Bernoulli-ex.pdf") + ## Bernoulli.all(.. prec = ) --> automatically uses 'Rmpfr' arithmetic + showSys.time(B100 <- Bernoulli.all(100)) # still less than a milli second + showSys.time(B100.250 <- as.numeric(Bernoulli.all(100, prec = 250))) + ## 0.75 sec [Core i5 (2010)] + re <- log(abs(1 - B100/B100.250)) + m <- cbind(Bn = B100, Bn.250 = B100.250, "-log10(rel.Err)" = + -round(re/log(10), 2)) + rownames(m) <- paste("n=",0:100, sep="") + m[1:5,] + print(m[2*(1:15) -1,]) ## for n=10: still 8 correct digits + + showSys.time(B100.1k <- as.numeric(Bernoulli.all(100, prec = 1024))) + ## The first 34 are "the same", but after [41], + ## even 250 precBits were *not* sufficient: + print(round(log10(abs(1 - B100.250/B100.1k))[seq(1,99,by=2)], 2)) + + ## some accuracy investigation: + nn <- 8:100; nn <- nn[nn %% 2 == 0]; nn + B.asy <- sapply(nn, copula::Bernoulli, method="asymp") + B.sumB <- sapply(nn, copula::Bernoulli, method="sumBin") + B.prec <- Rmpfr::Bernoulli(nn, precBits = 2048) + relErr <- as.numeric(1 - B.asy / B.prec) + relE2 <- as.numeric(1 - B.sumB / B.prec) + + matplot(nn, abs(cbind(relErr, relE2)), pch=1:2, + main = "| rel.Error { Bernoulli(n) } |", + xlab = expression(n), axes=FALSE, + ylim = c(1e-15, 1e-4), log="y", type="b") + sfsmisc::eaxis(1); sfsmisc::eaxis(2) + legend("topright", c("asymp","sumBin"), bty="n", col=1:2, lty=1:2, pch=1:2) + ##--> an optimal "hybrid" method will use "asymp" from about n ~= 20 + + dev.off() + } ## end if(require("Rmpfr")) > > > > ### Polylogarithm Function ##################################################### > > EQ <- function(x,y, tol = 1e-15) all.equal(x,y, tolerance=tol) > > x <- (0:127)/128 # < 1 > stopifnot(EQ(polylog(s = 1, x, n.sum=10000), -log(1-x)), + EQ(polylog(s = -1, .1, n.sum= 100), 10/81), + EQ(polylog(s = -1, .1, "negI-s-Stirling"), 10/81), + EQ(polylog(x, -1, "negI-s-Stirling"), x /(1-x)^2), + EQ(polylog(x, -2, "negI-s-Stirling"), x*(1+x)/(1-x)^3), + EQ(polylog(x, -4, "negI-s-Stirling"), x*(1+x)*(1+x*(10+x)) / (1-x)^5), + identical( polylog (x, -4, "negI-s-Stirling"), + Vectorize(polylog,"z")(x, -4, "negI-s-Stirling")), + identical( polylog (x, -4, "sum", n.sum=10000), + Vectorize(polylog,"z")(x, -4, "sum", n.sum=10000)), + EQ(polylog(x, -1, "negI-s-Eulerian"), x /(1-x)^2), + EQ(polylog(x, -2, "negI-s-Eulerian"), x*(1+x)/(1-x)^3), + EQ(polylog(x, -4, "negI-s-Eulerian"), x*(1+x)*(1+x*(10+x)) / (1-x)^5), + TRUE) > > ##--> now do plots etc in ../man/polylog.Rd : > ## ~~~~~~~~~~~~~~~~~ > > > ### Debye Functions ---- Better treat with (NA, NaN, Inf) than gsl's debye: > ## --------------- -> ../R/special-func.R > x <- c(NA, NaN, 0, 1e-100, 1e-10, .01, .1, 1:10, 20, 1e10, 1e100, Inf) > D1 <- copula:::debye1(x) > D2 <- copula:::debye2(x) > (isI <- which(x == Inf)) [1] 21 > cbind(x, D1, D2) x D1 D2 [1,] NA NA NA [2,] NaN NaN NaN [3,] 0e+00 1.000000e+00 1.000000e+00 [4,] 1e-100 1.000000e+00 1.000000e+00 [5,] 1e-10 1.000000e+00 1.000000e+00 [6,] 1e-02 9.975028e-01 9.966708e-01 [7,] 1e-01 9.752778e-01 9.670833e-01 [8,] 1e+00 7.775046e-01 7.078785e-01 [9,] 2e+00 6.069473e-01 4.930826e-01 [10,] 3e+00 4.804352e-01 3.426140e-01 [11,] 4e+00 3.881480e-01 2.405537e-01 [12,] 5e+00 3.208762e-01 1.723292e-01 [13,] 6e+00 2.712605e-01 1.266692e-01 [14,] 7e+00 2.339480e-01 9.570686e-02 [15,] 8e+00 2.052393e-01 7.426881e-02 [16,] 9e+00 1.826333e-01 5.905305e-02 [17,] 1e+01 1.644435e-01 4.797150e-02 [18,] 2e+01 8.224670e-02 1.202056e-02 [19,] 1e+10 1.644934e-10 4.808228e-20 [20,] 1e+100 1.644934e-100 4.808228e-200 [21,] Inf 0.000000e+00 0.000000e+00 > > stopifnot(is.na(c(D1[1],D2[1])), is.nan(c(D1[2],D2[2])), + !is.na(D1[-(1:2)]), !is.nan(D1[-2]), + !is.na(D2[-(1:2)]), !is.nan(D2[-2]), + D1[isI] == 0, + D2[isI] == 0) > > ### lsum() and lssum() -------------- > lsum <- copula:::lsum > lssum <- copula:::lssum > lsum0 <- function(lx) log(sum(exp(lx))) > > lx1 <- 10*(-80:70) # is easy > lx2 <- 600:750 # lsum0() not ok [could work with rescaling] > lx3 <- -(750:900) # lsum0() = -Inf - not good enough > m3 <- cbind(lx1,lx2,lx3) > lx6 <- lx5 <- lx4 <- lx3 > lx4[149:151] <- -Inf ## = log(0) > lx5[150] <- Inf > lx6[1] <- NA_real_ > m6 <- cbind(m3,lx4,lx5,lx6) > stopifnot(all.equal(lsum(lx1), lsum0(lx1)), + all.equal((ls1 <- lsum(lx1)), 700.000045400960403, tol=8e-16), + all.equal((ls2 <- lsum(lx2)), 750.458675145387133, tol=8e-16), + all.equal((ls3 <- lsum(lx3)), -749.541324854612867, tol=8e-16), + ## identical: matrix-version <==> vector versions + identical(lsum(lx4), ls3), + identical(lsum(lx4), lsum(head(lx4, -3))), # the last three were -Inf + identical(lsum(lx5), Inf), + identical(lsum(lx6), lx6[1]), + identical((lm3 <- lsum(m3)), c(lx1=ls1, lx2=ls2, lx3=ls3)), + identical(lsum(m6), c(lm3, lx4=ls3, lx5=Inf, lx6=lx6[1])), + TRUE) > > ## TODO: lssum() testing !! > > proc.time() user system elapsed 2.84 0.29 3.12