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 -5.5351131775484266502e+61 1.1331767264602853192e+62 -1.4342412362925477399e+62 1.27130| __truncated__ ...
$ : num [1:50] -6.0828186403426752248e+62 2.7246193725912650997e+63 -5.6079170914308826279e+63 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__ ...
$ : num [1:64] -1.9826083154044400851e+87 9.3742992981303482139e+87 -2.0547070658124494391e+88 2.8087498412844758467e+88 -2.7112| __truncated__ ...
$ : num [1:65] 1.2688693218588416544e+89 -6.0193776339574670939e+89 1.3243868214180979203e+90 -1.8181469690801889866e+90 1.76331| __truncated__ ...
$ : num [1:66] -8.2476505920824715167e+90 3.9252841552909421832e+91 -8.6687081155572118882e+91 1.1950393981163038974e+92 -1.1643| __truncated__ ...
$ : num [1:67] 5.4434493907744306946e+92 -2.5989351930841040122e+93 5.7606001978206695939e+93 -7.9739471087231774803e+93 7.80411| __truncated__ ...
$ : num [1:68] -3.6471110918188683221e+94 1.7467300287571241478e+95 -3.8855914844706894178e+95 5.4001505648227364044e+95 -5.3084| __truncated__ ...
$ : num [1:69] 2.4800355424368305480e+96 -1.1914235306466632910e+97 2.6596695097276399535e+97 -3.7109582989241675186e+97 3.66377| __truncated__ ...
$ : num [1:70] -1.7112245242814129737e+98 8.2456227168863450421e+98 -1.8470861970185381536e+99 2.5871579213549518927e+99 -2.5651| __truncated__ ...
$ : num [1:71] 1.1978571669969890270e+100 -5.7890481470632557228e+100 1.3012059606298630538e+101 -1.8294814069186518424e+101 1.8| __truncated__ ...
$ : num [1:72] -8.5047858856786217622e+101 4.1222027560848813702e+102 -9.2964528019426593605e+102 1.3119438585185413500e+103 -1.| __truncated__ ...
$ : num [1:73] 6.1234458376886076684e+103 -2.9764907702667928401e+104 6.7346680449595642394e+104 -9.5389603093529251486e+104 9.5| __truncated__ ...
$ : num [1:74] -4.4701154615126833672e+105 2.1789617081324474724e+106 -4.9460725805231493713e+106 7.0307877062772313318e+106 -7.| __truncated__ ...
$ : num [1:75] 3.3078854415193855896e+107 -1.6169017794795238364e+108 3.6818833266684551845e+108 -5.2522436284503823860e+108 5.3| __truncated__ ...
$ : num [1:76] -2.4809140811395391402e+109 1.2159842200511623568e+110 -2.7775815127961368041e+110 3.9760015546044713572e+110 -4.| __truncated__ ...
$ : num [1:77] 1.8854947016660498467e+111 -9.2662892132002297125e+111 2.1231217919255758633e+112 -3.0495369966273592590e+112 3.1| __truncated__ ...
$ : num [1:78] -1.4518309202828583793e+113 7.1538976411808377692e+113 -1.6440700689958935868e+114 2.3693747053223224138e+114 -2.| __truncated__ ...
$ : num [1:79] 1.1324281178206294607e+115 -5.5945584693238817257e+115 1.2895285514579778519e+116 -1.8645529708413703255e+116 1.9| __truncated__ ...
$ : num [1:80] -8.9461821307829729136e+116 4.4310254719440726042e+117 -1.0243221141211265501e+118 1.4858921324792623760e+118 -1.| __truncated__ ...
$ : num [1:81] 7.1569457046263778833e+118 -3.5537665596860405048e+119 8.2388871676884535807e+119 -1.1989569271246211327e+120 1.2| __truncated__ ...
$ : num [1:82] -5.7971260207473655482e+120 2.8857078590503191689e+121 -6.7090362714245079987e+121 9.7939399813863161548e+121 -1.| __truncated__ ...
$ : num [1:83] 4.7536433370128398181e+122 -2.3720775704420091149e+123 5.5302668211585995946e+123 -8.0981211474510242168e+123 8.4| __truncated__ ...
$ : num [1:84] -3.9455239697206569096e+124 1.9735780268038804985e+125 -4.6138422372660575078e+125 6.7767432205959360725e+125 -7.| __truncated__ ...
$ : num [1:85] 3.3142401345653519917e+126 -1.6617510664849802615e+127 3.8953632595715271720e+127 -5.7386027276732462302e+127 6.0| __truncated__ ...
$ : num [1:86] -2.8171041143805493616e+128 1.4158026466467986873e+129 -3.3276762813006478699e+129 4.9167659511179746439e+129 -5.| __truncated__ ...
$ : num [1:87] 2.4227095383672724281e+130 -1.2204073802306273493e+131 2.8759596283850249550e+131 -4.2616954807744647036e+131 4.4| __truncated__ ...
$ : num [1:88] -2.1077572983795269089e+132 1.0641771303390130589e+133 -2.5142889504972779273e+133 3.7364346645576347861e+133 -3.| __truncated__ ...
$ : num [1:89] 1.8548264225739835537e+134 -9.3858363199671108468e+134 2.2232160477409944922e+135 -3.3132053943156916684e+135 3.5| __truncated__ ...
$ : num [1:90] -1.6507955160908452499e+136 8.3719425889964682154e+136 -1.9880481188094522282e+137 2.9709849614183752036e+137 -3.| __truncated__ ...
$ : num [1:91] 1.4857159644817606887e+138 -7.5512562852577294662e+138 1.7976152495175036245e+139 -2.6937669464646323008e+139 2.8| __truncated__ ...
$ : num [1:92] NA 6.8865003792293521135e+140 -1.6433811333461860699e+141 2.4693040737779904589e+141 -2.6434198406811229404e+141 | __truncated__ ...
$ : num [1:93] NA NA 1.5187971430577206482e+143 -2.2881935592092131505e+143 2.4566392941644126205e+143 -2.0135884670620576933e+1| __truncated__ ...
$ : num [1:94] NA NA NA 2.1432079814951455513e+145 -2.3075564791649958167e+145 1.8972036673093578071e+145 -1.2449705167011399568| __truncated__ ...
$ : num [1:95] NA NA NA NA 2.1905351702300476589e+147 -1.8064470120624465352e+147 1.1892443223721652732e+147 -6.4462672591068725| __truncated__ ...
$ : 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 -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 -5.5351131775484266502e+61 1.1331767264602853192e+62 -1.4342412362925477399e+62 1.27130| __truncated__ ...
$ : num [1:50] -6.0828186403426752248e+62 2.7246193725912650997e+63 -5.6079170914308826279e+63 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__ ...
$ : num [1:64] -1.9826083154044400851e+87 9.3742992981303482139e+87 -2.0547070658124494391e+88 2.8087498412844758467e+88 -2.7112| __truncated__ ...
$ : num [1:65] 1.2688693218588416544e+89 -6.0193776339574670939e+89 1.3243868214180979203e+90 -1.8181469690801889866e+90 1.76331| __truncated__ ...
$ : num [1:66] -8.2476505920824715167e+90 3.9252841552909421832e+91 -8.6687081155572118882e+91 1.1950393981163038974e+92 -1.1643| __truncated__ ...
$ : num [1:67] 5.4434493907744306946e+92 -2.5989351930841040122e+93 5.7606001978206695939e+93 -7.9739471087231774803e+93 7.80411| __truncated__ ...
$ : num [1:68] -3.6471110918188683221e+94 1.7467300287571241478e+95 -3.8855914844706894178e+95 5.4001505648227364044e+95 -5.3084| __truncated__ ...
$ : num [1:69] 2.4800355424368305480e+96 -1.1914235306466632910e+97 2.6596695097276399535e+97 -3.7109582989241675186e+97 3.66377| __truncated__ ...
$ : num [1:70] -1.7112245242814129737e+98 8.2456227168863450421e+98 -1.8470861970185381536e+99 2.5871579213549518927e+99 -2.5651| __truncated__ ...
$ : num [1:71] 1.1978571669969890270e+100 -5.7890481470632557228e+100 1.3012059606298630538e+101 -1.8294814069186518424e+101 1.8| __truncated__ ...
$ : num [1:72] -8.5047858856786217622e+101 4.1222027560848813702e+102 -9.2964528019426593605e+102 1.3119438585185413500e+103 -1.| __truncated__ ...
$ : num [1:73] 6.1234458376886076684e+103 -2.9764907702667928401e+104 6.7346680449595642394e+104 -9.5389603093529251486e+104 9.5| __truncated__ ...
$ : num [1:74] -4.4701154615126833672e+105 2.1789617081324474724e+106 -4.9460725805231493713e+106 7.0307877062772313318e+106 -7.| __truncated__ ...
$ : num [1:75] 3.3078854415193855896e+107 -1.6169017794795238364e+108 3.6818833266684551845e+108 -5.2522436284503823860e+108 5.3| __truncated__ ...
$ : num [1:76] -2.4809140811395391402e+109 1.2159842200511623568e+110 -2.7775815127961368041e+110 3.9760015546044713572e+110 -4.| __truncated__ ...
$ : num [1:77] 1.8854947016660498467e+111 -9.2662892132002297125e+111 2.1231217919255758633e+112 -3.0495369966273592590e+112 3.1| __truncated__ ...
$ : num [1:78] -1.4518309202828583793e+113 7.1538976411808377692e+113 -1.6440700689958935868e+114 2.3693747053223224138e+114 -2.| __truncated__ ...
$ : num [1:79] 1.1324281178206294607e+115 -5.5945584693238817257e+115 1.2895285514579778519e+116 -1.8645529708413703255e+116 1.9| __truncated__ ...
$ : num [1:80] -8.9461821307829729136e+116 4.4310254719440726042e+117 -1.0243221141211265501e+118 1.4858921324792623760e+118 -1.| __truncated__ ...
$ : num [1:81] 7.1569457046263778833e+118 -3.5537665596860405048e+119 8.2388871676884535807e+119 -1.1989569271246211327e+120 1.2| __truncated__ ...
$ : num [1:82] -5.7971260207473655482e+120 2.8857078590503191689e+121 -6.7090362714245079987e+121 9.7939399813863161548e+121 -1.| __truncated__ ...
$ : num [1:83] 4.7536433370128398181e+122 -2.3720775704420091149e+123 5.5302668211585995946e+123 -8.0981211474510242168e+123 8.4| __truncated__ ...
$ : num [1:84] -3.9455239697206569096e+124 1.9735780268038804985e+125 -4.6138422372660575078e+125 6.7767432205959360725e+125 -7.| __truncated__ ...
$ : num [1:85] 3.3142401345653519917e+126 -1.6617510664849802615e+127 3.8953632595715271720e+127 -5.7386027276732462302e+127 6.0| __truncated__ ...
$ : num [1:86] -2.8171041143805493616e+128 1.4158026466467986873e+129 -3.3276762813006478699e+129 4.9167659511179746439e+129 -5.| __truncated__ ...
$ : num [1:87] 2.4227095383672724281e+130 -1.2204073802306273493e+131 2.8759596283850249550e+131 -4.2616954807744647036e+131 4.4| __truncated__ ...
$ : num [1:88] -2.1077572983795269089e+132 1.0641771303390130589e+133 -2.5142889504972779273e+133 3.7364346645576347861e+133 -3.| __truncated__ ...
$ : num [1:89] 1.8548264225739835537e+134 -9.3858363199671108468e+134 2.2232160477409944922e+135 -3.3132053943156916684e+135 3.5| __truncated__ ...
$ : num [1:90] -1.6507955160908452499e+136 8.3719425889964682154e+136 -1.9880481188094522282e+137 2.9709849614183752036e+137 -3.| __truncated__ ...
$ : num [1:91] 1.4857159644817606887e+138 -7.5512562852577294662e+138 1.7976152495175036245e+139 -2.6937669464646323008e+139 2.8| __truncated__ ...
$ : num [1:92] NA 6.8865003792293521135e+140 -1.6433811333461860699e+141 2.4693040737779904589e+141 -2.6434198406811229404e+141 | __truncated__ ...
$ : num [1:93] NA NA 1.5187971430577206482e+143 -2.2881935592092131505e+143 2.4566392941644126205e+143 -2.0135884670620576933e+1| __truncated__ ...
$ : num [1:94] NA NA NA 2.1432079814951455513e+145 -2.3075564791649958167e+145 1.8972036673093578071e+145 -1.2449705167011399568| __truncated__ ...
$ : num [1:95] NA NA NA NA 2.1905351702300476589e+147 -1.8064470120624465352e+147 1.1892443223721652732e+147 -6.4462672591068725| __truncated__ ...
$ : 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 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