Last updated on 2024-11-08 00:50:00 CET.
| Package | ERROR | WARN | NOTE | OK |
|---|---|---|---|---|
| Bessel | 13 | |||
| bitops | 13 | |||
| CLA | 13 | |||
| classGraph | 13 | |||
| cluster | 3 | 10 | ||
| cobs | 2 | 11 | ||
| copula | 2 | 6 | 5 | |
| diptest | 13 | |||
| DPQ | 1 | 12 | ||
| DPQmpfr | 13 | |||
| expm | 13 | |||
| fracdiff | 13 | |||
| lokern | 13 | |||
| longmemo | 2 | 1 | 10 | |
| lpridge | 13 | |||
| nor1mix | 13 | |||
| plugdensity | 13 | |||
| Rmpfr | 3 | 10 | ||
| robustbase | 13 | |||
| robustX | 13 | |||
| round | 13 | |||
| sca | 13 | |||
| sfsmisc | 13 | |||
| stabledist | 13 | |||
| supclust | 13 | |||
| VLMC | 2 | 11 |
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: NOTE: 3, OK: 10
Version: 2.1.6
Check: tests
Result: NOTE
Running ‘agnes-ex.R’ [3s/10s]
Comparing ‘agnes-ex.Rout’ to ‘agnes-ex.Rout.save’ ... OK
Running ‘clara-NAs.R’
Comparing ‘clara-NAs.Rout’ to ‘clara-NAs.Rout.save’ ... OK
Running ‘clara-ex.R’ [3s/11s]
Comparing ‘clara-ex.Rout’ to ‘clara-ex.Rout.save’ ... OK
Running ‘clara-gower.R’
Running ‘clara.R’ [5s/18s]
Comparing ‘clara.Rout’ to ‘clara.Rout.save’ ... OK
Running ‘clusplot-out.R’
Comparing ‘clusplot-out.Rout’ to ‘clusplot-out.Rout.save’ ... OK
Running ‘daisy-ex.R’
Comparing ‘daisy-ex.Rout’ to ‘daisy-ex.Rout.save’ ... OK
Running ‘diana-boots.R’
Running ‘diana-ex.R’
Comparing ‘diana-ex.Rout’ to ‘diana-ex.Rout.save’ ... OK
Running ‘ellipsoid-ex.R’
Comparing ‘ellipsoid-ex.Rout’ to ‘ellipsoid-ex.Rout.save’ ... OK
Running ‘fanny-ex.R’
Comparing ‘fanny-ex.Rout’ to ‘fanny-ex.Rout.save’ ...194c194
< iterations 42
---
> iterations 45
Running ‘mona.R’
Comparing ‘mona.Rout’ to ‘mona.Rout.save’ ... OK
Running ‘pam.R’ [79s/139s]
Comparing ‘pam.Rout’ to ‘pam.Rout.save’ ... OK
Running ‘silhouette-default.R’ [5s/18s]
Comparing ‘silhouette-default.Rout’ to ‘silhouette-default.Rout.save’ ... OK
Running ‘sweep-ex.R’
Flavor: r-devel-linux-x86_64-fedora-clang
Version: 2.1.6
Check: tests
Result: NOTE
Running ‘agnes-ex.R’
Comparing ‘agnes-ex.Rout’ to ‘agnes-ex.Rout.save’ ... OK
Running ‘clara-NAs.R’
Comparing ‘clara-NAs.Rout’ to ‘clara-NAs.Rout.save’ ... OK
Running ‘clara-ex.R’
Comparing ‘clara-ex.Rout’ to ‘clara-ex.Rout.save’ ... OK
Running ‘clara-gower.R’
Running ‘clara.R’ [5s/16s]
Comparing ‘clara.Rout’ to ‘clara.Rout.save’ ... OK
Running ‘clusplot-out.R’
Comparing ‘clusplot-out.Rout’ to ‘clusplot-out.Rout.save’ ... OK
Running ‘daisy-ex.R’
Comparing ‘daisy-ex.Rout’ to ‘daisy-ex.Rout.save’ ... OK
Running ‘diana-boots.R’
Running ‘diana-ex.R’
Comparing ‘diana-ex.Rout’ to ‘diana-ex.Rout.save’ ... OK
Running ‘ellipsoid-ex.R’
Comparing ‘ellipsoid-ex.Rout’ to ‘ellipsoid-ex.Rout.save’ ... OK
Running ‘fanny-ex.R’
Comparing ‘fanny-ex.Rout’ to ‘fanny-ex.Rout.save’ ...194c194
< iterations 42
---
> iterations 45
Running ‘mona.R’
Comparing ‘mona.Rout’ to ‘mona.Rout.save’ ... OK
Running ‘pam.R’ [76s/213s]
Comparing ‘pam.Rout’ to ‘pam.Rout.save’ ... OK
Running ‘silhouette-default.R’ [5s/13s]
Comparing ‘silhouette-default.Rout’ to ‘silhouette-default.Rout.save’ ... OK
Running ‘sweep-ex.R’
Flavor: r-devel-linux-x86_64-fedora-gcc
Version: 2.1.6
Check: tests
Result: NOTE
Running 'agnes-ex.R' [2s]
Comparing 'agnes-ex.Rout' to 'agnes-ex.Rout.save' ... OK
Running 'clara-NAs.R' [0s]
Comparing 'clara-NAs.Rout' to 'clara-NAs.Rout.save' ... OK
Running 'clara-ex.R' [2s]
Comparing 'clara-ex.Rout' to 'clara-ex.Rout.save' ... OK
Running 'clara-gower.R' [0s]
Running 'clara.R' [3s]
Comparing 'clara.Rout' to 'clara.Rout.save' ... OK
Running 'clusplot-out.R' [1s]
Comparing 'clusplot-out.Rout' to 'clusplot-out.Rout.save' ... OK
Running 'daisy-ex.R' [1s]
Comparing 'daisy-ex.Rout' to 'daisy-ex.Rout.save' ... OK
Running 'diana-boots.R' [2s]
Running 'diana-ex.R' [0s]
Comparing 'diana-ex.Rout' to 'diana-ex.Rout.save' ... OK
Running 'ellipsoid-ex.R' [0s]
Comparing 'ellipsoid-ex.Rout' to 'ellipsoid-ex.Rout.save' ... OK
Running 'fanny-ex.R' [1s]
Comparing 'fanny-ex.Rout' to 'fanny-ex.Rout.save' ...194c194
< iterations 43
---
> iterations 45
1056c1056
< Converged after 46 iterations, obj = 2665.982
---
> Converged after 44 iterations, obj = 2665.982
Running 'mona.R' [1s]
Comparing 'mona.Rout' to 'mona.Rout.save' ... OK
Running 'pam.R' [31s]
Comparing 'pam.Rout' to 'pam.Rout.save' ... OK
Running 'silhouette-default.R' [2s]
Comparing 'silhouette-default.Rout' to 'silhouette-default.Rout.save' ... OK
Running 'sweep-ex.R' [0s]
Flavor: r-devel-windows-x86_64
Current CRAN status: ERROR: 2, OK: 11
Version: 1.3-8
Check: examples
Result: ERROR
Running examples in ‘cobs-Ex.R’ failed
The error most likely occurred in:
> base::assign(".ptime", proc.time(), pos = "CheckExEnv")
> ### Name: cobs-methods
> ### Title: Methods for COBS Objects
> ### Aliases: coef.cobs fitted.cobs knots.cobs print.cobs residuals.cobs
> ### summary.cobs
> ### Keywords: print
>
> ### ** Examples
>
> example(cobs)
cobs> x <- seq(-1,3,,150)
cobs> y <- (f.true <- pnorm(2*x)) + rnorm(150)/10
cobs> ## specify pointwise constraints (boundary conditions)
cobs> con <- rbind(c( 1,min(x),0), # f(min(x)) >= 0
cobs+ c(-1,max(x),1), # f(max(x)) <= 1
cobs+ c(0, 0, 0.5))# f(0) = 0.5
cobs> ## obtain the median REGRESSION B-spline using automatically selected knots
cobs> Rbs <- cobs(x,y, constraint= "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning in cobs(x, y, constraint = "increase", pointwise = con) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
cobs> Rbs
COBS regression spline (degree = 2) from call:
cobs(x = x, y = y, constraint = "increase", pointwise = con)
**** ERROR in algorithm: ifl = 21
{tau=0.5}-quantile; dimensionality of fit: 5 from {5}
x$knots[1:4]: -1.0000040, -0.2214765, 1.3892617, 3.0000040
cobs> plot(Rbs, lwd = 2.5)
cobs> lines(spline(x, f.true), col = "gray40")
cobs> lines(predict(cobs(x,y)), col = "blue")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning in cobs(x, y) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
cobs> mtext("cobs(x,y) # completely unconstrained", 3, col= "blue")
cobs> ## compute the median SMOOTHING B-spline using automatically chosen lambda
cobs> Sbs <- cobs(x,y, constraint="increase", pointwise= con, lambda= -1)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Warning in min(sol1["k", i.keep]) :
no non-missing arguments to min; returning Inf
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: example ... source -> withVisible -> eval -> eval -> cobs -> drqssbc2
Execution halted
Flavor: r-devel-linux-x86_64-debian-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [3s/4s]
Running ‘ex1.R’ [3s/5s]
Running ‘ex2-long.R’ [5s/6s]
Running ‘ex3.R’ [2s/3s]
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [5s/7s]
Running ‘roof.R’ [4s/5s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ... OK
Running ‘small-ex.R’ [3s/4s]
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’ [2s/3s]
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [3s/4s]
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ... OK
Running ‘wind.R’ [4s/5s]
Running the tests in ‘tests/ex1.R’ failed.
Complete output:
> #### OOps! Running this in 'CMD check' or in *R* __for the first time__
> #### ===== gives a wrong result (at the end) than when run a 2nd time
> ####-- problem disappears with introduction of if (psw) call ... in Fortran
>
> suppressMessages(library(cobs))
> options(digits = 6)
> if(!dev.interactive(orNone=TRUE)) pdf("ex1.pdf")
>
> source(system.file("util.R", package = "cobs"))
>
> ## Simple example from example(cobs)
> set.seed(908)
> x <- seq(-1,1, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> ## specify constraints (boundary conditions)
> con <- rbind(c( 1,min(x),0),
+ c(-1,max(x),1),
+ c( 0, 0, 0.5))
> ## obtain the median *regression* B-spline using automatically selected knots
> coR <- cobs(x,y,constraint = "increase", pointwise = con)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning message:
In cobs(x, y, constraint = "increase", pointwise = con) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
> summaryCobs(coR)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", pointwise = con)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : chr "AIC"
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:50] -1 -0.959 -0.918 -0.878 -0.837 ...
$ y : num [1:50] 0.2254 0.0916 0.0803 -0.0272 -0.0454 ...
$ resid : num [1:50] 0.148 0.019 0.0105 -0.0962 -0.1156 ...
$ fitted : num [1:50] 0.0774 0.0726 0.0698 0.069 0.0702 ...
$ coef : num [1:4] 0.0774 0.0226 0.8067 1.074
$ knots : num [1:3] -1 -0.224 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : num 0
$ icyc : int 1
$ ifl : int 21
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -0.02569206 0.0153529 0.0773974 0.139442 0.180487
2 -0.02467377 0.0149258 0.0747853 0.134645 0.174244
3 -0.02343992 0.0148223 0.0726602 0.130498 0.168760
4 -0.02198644 0.0150449 0.0710223 0.127000 0.164031
5 -0.02030765 0.0155971 0.0698714 0.124146 0.160050
6 -0.01839614 0.0164832 0.0692075 0.121932 0.156811
7 -0.01624274 0.0177089 0.0690308 0.120353 0.154304
8 -0.01383648 0.0192806 0.0693410 0.119401 0.152519
9 -0.01116467 0.0212061 0.0701384 0.119071 0.151441
10 -0.00821304 0.0234939 0.0714227 0.119352 0.151059
11 -0.00496594 0.0261535 0.0731942 0.120235 0.151354
12 -0.00140661 0.0291949 0.0754527 0.121711 0.152312
13 0.00248257 0.0326287 0.0781983 0.123768 0.153914
14 0.00671972 0.0364659 0.0814309 0.126396 0.156142
15 0.01132316 0.0407175 0.0851506 0.129584 0.158978
16 0.01631107 0.0453944 0.0893573 0.133320 0.162404
17 0.02170124 0.0505073 0.0940511 0.137595 0.166401
18 0.02751079 0.0560665 0.0992320 0.142397 0.170953
19 0.03375595 0.0620819 0.1048999 0.147718 0.176044
20 0.04045190 0.0685624 0.1110549 0.153547 0.181658
21 0.04761262 0.0755166 0.1176969 0.159877 0.187781
22 0.05525079 0.0829521 0.1248260 0.166700 0.194401
23 0.06337769 0.0908757 0.1324422 0.174009 0.201507
24 0.07200318 0.0992932 0.1405454 0.181798 0.209088
25 0.08113560 0.1082098 0.1491357 0.190062 0.217136
26 0.09078179 0.1176295 0.1582130 0.198797 0.225644
27 0.10094701 0.1275555 0.1677774 0.207999 0.234608
28 0.11163490 0.1379900 0.1778288 0.217668 0.244023
29 0.12284746 0.1489342 0.1883674 0.227801 0.253887
30 0.13458491 0.1603882 0.1993929 0.238398 0.264201
31 0.14684569 0.1723511 0.2109056 0.249460 0.274965
32 0.15962625 0.1848207 0.2229052 0.260990 0.286184
33 0.17292100 0.1977938 0.2353920 0.272990 0.297863
34 0.18672210 0.2112655 0.2483658 0.285466 0.310009
35 0.20101931 0.2252297 0.2618267 0.298424 0.322634
36 0.21579978 0.2396787 0.2757746 0.311870 0.335749
37 0.23104789 0.2546031 0.2902096 0.325816 0.349371
38 0.24674505 0.2699916 0.3051316 0.340272 0.363518
39 0.26286963 0.2858313 0.3205407 0.355250 0.378212
40 0.27927345 0.3019880 0.3363239 0.370660 0.393374
41 0.29546082 0.3179864 0.3520365 0.386087 0.408612
42 0.31139379 0.3337855 0.3676333 0.401481 0.423873
43 0.32708550 0.3493933 0.3831143 0.416835 0.439143
44 0.34254943 0.3648179 0.3984794 0.432141 0.454409
45 0.35779910 0.3800674 0.4137287 0.447390 0.469658
46 0.37284780 0.3951499 0.4288622 0.462574 0.484877
47 0.38770842 0.4100730 0.4438798 0.477687 0.500051
48 0.40239320 0.4248442 0.4587815 0.492719 0.515170
49 0.41691367 0.4394703 0.4735674 0.507665 0.530221
50 0.43128050 0.4539579 0.4882375 0.522517 0.545195
51 0.44550348 0.4683128 0.5027918 0.537271 0.560080
52 0.45959144 0.4825403 0.5172301 0.551920 0.574869
53 0.47355229 0.4966451 0.5315527 0.566460 0.589553
54 0.48739298 0.5106315 0.5457594 0.580887 0.604126
55 0.50111956 0.5245032 0.5598503 0.595197 0.618581
56 0.51473718 0.5382631 0.5738253 0.609388 0.632913
57 0.52825014 0.5519139 0.5876845 0.623455 0.647119
58 0.54166189 0.5654577 0.6014278 0.637398 0.661194
59 0.55497510 0.5788960 0.6150553 0.651215 0.675136
60 0.56819166 0.5922301 0.6285670 0.664904 0.688942
61 0.58131273 0.6054605 0.6419628 0.678465 0.702613
62 0.59433873 0.6185876 0.6552428 0.691898 0.716147
63 0.60726940 0.6316113 0.6684069 0.705203 0.729544
64 0.62010376 0.6445308 0.6814552 0.718380 0.742807
65 0.63284018 0.6573453 0.6943876 0.731430 0.755935
66 0.64547632 0.6700533 0.7072042 0.744355 0.768932
67 0.65800921 0.6826530 0.7199050 0.757157 0.781801
68 0.67043520 0.6951423 0.7324899 0.769838 0.794545
69 0.68274995 0.7075185 0.7449590 0.782400 0.807168
70 0.69494850 0.7197786 0.7573122 0.794846 0.819676
71 0.70702523 0.7319193 0.7695496 0.807180 0.832074
72 0.71897385 0.7439368 0.7816712 0.819406 0.844369
73 0.73078747 0.7558269 0.7936769 0.831527 0.856566
74 0.74245861 0.7675851 0.8055668 0.843548 0.868675
75 0.75397921 0.7792066 0.8173408 0.855475 0.880702
76 0.76534070 0.7906862 0.8289990 0.867312 0.892657
77 0.77653408 0.8020185 0.8405413 0.879064 0.904549
78 0.78754996 0.8131979 0.8519678 0.890738 0.916386
79 0.79837866 0.8242185 0.8632785 0.902338 0.928178
80 0.80901036 0.8350744 0.8744733 0.913872 0.939936
81 0.81943516 0.8457597 0.8855523 0.925345 0.951669
82 0.82964324 0.8562684 0.8965154 0.936762 0.963388
83 0.83962502 0.8665947 0.9073627 0.948131 0.975100
84 0.84937122 0.8767332 0.9180941 0.959455 0.986817
85 0.85887309 0.8866785 0.9287098 0.970741 0.998546
86 0.86812243 0.8964257 0.9392095 0.981993 1.010297
87 0.87711179 0.9059703 0.9495934 0.993217 1.022075
88 0.88583447 0.9153083 0.9598615 1.004415 1.033889
89 0.89428462 0.9244361 0.9700138 1.015591 1.045743
90 0.90245726 0.9333508 0.9800502 1.026749 1.057643
91 0.91034831 0.9420499 0.9899707 1.037891 1.069593
92 0.91795453 0.9505315 0.9997754 1.049019 1.081596
93 0.92527350 0.9587940 1.0094643 1.060135 1.093655
94 0.93230358 0.9668366 1.0190373 1.071238 1.105771
95 0.93904380 0.9746586 1.0284945 1.082330 1.117945
96 0.94549385 0.9822598 1.0378359 1.093412 1.130178
97 0.95165390 0.9896403 1.0470614 1.104482 1.142469
98 0.95752462 0.9968006 1.0561710 1.115541 1.154817
99 0.96310704 1.0037413 1.0651648 1.126588 1.167223
100 0.96840246 1.0104631 1.0740428 1.137623 1.179683
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0773974 0.0225871 0.8067413 1.0740429
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Warning message:
In cobs(x, y, constraint = "increase", pointwise = con, degree = 1) :
drqssbc2(): Not all flags are normal (== 1), ifl : 20
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
**** ERROR in algorithm: ifl = 20
{tau=0.5}-quantile; dimensionality of fit: 3 from {3}
x$knots[1:3]: -1.000002, -0.632653, 1.000002
with 3 pointwise constraints
coef[1:3]: 0.0781509, 0.0820419, 1.1196697
R^2 = 94.72% ; empirical tau (over all): 25/50 = 0.5 (target tau= 0.5)
>
> ## compute the median *smoothing* B-spline using automatically chosen lambda
> coS <- cobs(x,y,constraint = "increase", pointwise = con,
+ lambda = -1, trace = 3)
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
loo.design2(): -> Xeq 51 x 22 (nz = 151 =^= 0.13%)
Xieq 62 x 22 (nz = 224 =^= 0.16%)
........................
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: cobs -> drqssbc2
In addition: Warning message:
In min(sol1["k", i.keep]) : no non-missing arguments to min; returning Inf
Execution halted
Running the tests in ‘tests/ex2-long.R’ failed.
Complete output:
> ####
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time()
Time (user system elapsed): 0.001 0 0.002
>
> options(digits = 5)
> if(!dev.interactive(orNone=TRUE)) pdf("ex2.pdf")
>
> set.seed(821)
> x <- round(sort(rnorm(200)), 3) # rounding -> multiple values
> sum(duplicated(x)) # 9
[1] 3
> y <- (fx <- exp(-x)) + rt(200,4)/4
> summaryCobs(cxy <- cobs(x,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0.72 -0.149 0 -0.195 0.545 ...
$ fitted : num [1:200] 11.98 8.39 6.67 6.07 5.87 ...
$ coef : num [1:5] 11.9769 3.5917 1.0544 0.0295 0.0295
$ knots : num [1:4] -2.557 -0.813 0.418 2.573
$ k0 : num 5
$ k : num 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0
$ icyc : int 11
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 11.4448128 11.6875576 11.976923 12.26629 12.50903
2 10.9843366 11.2126114 11.484728 11.75684 11.98512
3 10.5344633 10.7489871 11.004712 11.26044 11.47496
4 10.0951784 10.2966768 10.536874 10.77707 10.97857
5 9.6664684 9.8556730 10.081215 10.30676 10.49596
6 9.2483213 9.4259693 9.637736 9.84950 10.02715
7 8.8407282 9.0075609 9.206435 9.40531 9.57214
8 8.4436848 8.6004453 8.787313 8.97418 9.13094
9 8.0571928 8.2046236 8.380369 8.55612 8.70355
10 7.6812627 7.8201015 7.985605 8.15111 8.28995
11 7.3159159 7.4468904 7.603020 7.75915 7.89012
12 6.9611870 7.0850095 7.232613 7.38022 7.50404
13 6.6171269 6.7344861 6.874385 7.01428 7.13164
14 6.2838041 6.3953578 6.528336 6.66131 6.77287
15 5.9613061 6.0676719 6.194466 6.32126 6.42763
16 5.6497392 5.7514863 5.872775 5.99406 6.09581
17 5.3492272 5.4468683 5.563262 5.67966 5.77730
18 5.0599086 5.1538933 5.265928 5.37796 5.47195
19 4.7819325 4.8726424 4.980774 5.08891 5.17961
20 4.5154542 4.6031999 4.707798 4.81240 4.90014
21 4.2606295 4.3456507 4.447001 4.54835 4.63337
22 4.0176099 4.1000771 4.198383 4.29669 4.37916
23 3.7865383 3.8665567 3.961943 4.05733 4.13735
24 3.5675443 3.6451602 3.737683 3.83021 3.90782
25 3.3607413 3.4359491 3.525601 3.61525 3.69046
26 3.1662231 3.2389744 3.325698 3.41242 3.48517
27 2.9840608 3.0542750 3.137974 3.22167 3.29189
28 2.8142997 2.8818753 2.962429 3.04298 3.11056
29 2.6569546 2.7217833 2.799063 2.87634 2.94117
30 2.5120031 2.5739870 2.647875 2.72176 2.78375
31 2.3793776 2.4384496 2.508867 2.57928 2.63836
32 2.2589520 2.3151025 2.382037 2.44897 2.50512
33 2.1505256 2.2038366 2.267386 2.33094 2.38425
34 2.0538038 2.1044916 2.164914 2.22534 2.27602
35 1.9677723 2.0162522 2.074043 2.13183 2.18031
36 1.8846710 1.9316617 1.987677 2.04369 2.09068
37 1.8024456 1.8486425 1.903712 1.95878 2.00498
38 1.7213655 1.7673410 1.822146 1.87695 1.92293
39 1.6417290 1.6879196 1.742982 1.79804 1.84423
40 1.5638322 1.6105393 1.666217 1.72189 1.76860
41 1.4879462 1.5353474 1.591852 1.64836 1.69576
42 1.4143040 1.4624707 1.519888 1.57731 1.62547
43 1.3430975 1.3920136 1.450324 1.50864 1.55755
44 1.2744792 1.3240589 1.383161 1.44226 1.49184
45 1.2085658 1.2586702 1.318397 1.37812 1.42823
46 1.1454438 1.1958944 1.256034 1.31617 1.36662
47 1.0851730 1.1357641 1.196072 1.25638 1.30697
48 1.0277900 1.0782992 1.138509 1.19872 1.24923
49 0.9733099 1.0235079 1.083347 1.14319 1.19338
50 0.9217268 0.9713870 1.030585 1.08978 1.13944
51 0.8730129 0.9219214 0.980223 1.03852 1.08743
52 0.8271160 0.8750827 0.932262 0.98944 1.03741
53 0.7839554 0.8308269 0.886700 0.94257 0.98945
54 0.7434158 0.7890916 0.843540 0.89799 0.94366
55 0.7053406 0.7497913 0.802779 0.85577 0.90022
56 0.6695233 0.7128138 0.764419 0.81602 0.85931
57 0.6357022 0.6780170 0.728459 0.77890 0.82121
58 0.6035616 0.6452289 0.694899 0.74457 0.78624
59 0.5724566 0.6139693 0.663455 0.71294 0.75445
60 0.5410437 0.5829503 0.632905 0.68286 0.72477
61 0.5094333 0.5521679 0.603110 0.65405 0.69679
62 0.4778879 0.5217649 0.574069 0.62637 0.67025
63 0.4466418 0.4918689 0.545782 0.59970 0.64492
64 0.4158910 0.4625864 0.518250 0.57391 0.62061
65 0.3857918 0.4340022 0.491472 0.54894 0.59715
66 0.3564634 0.4061813 0.465448 0.52471 0.57443
67 0.3279928 0.3791711 0.440179 0.50119 0.55236
68 0.3004403 0.3530042 0.415663 0.47832 0.53089
69 0.2738429 0.3277009 0.391903 0.45610 0.50996
70 0.2482184 0.3032707 0.368896 0.43452 0.48957
71 0.2235676 0.2797141 0.346644 0.41357 0.46972
72 0.1998762 0.2570233 0.325146 0.39327 0.45042
73 0.1771158 0.2351830 0.304402 0.37362 0.43169
74 0.1552452 0.2141706 0.284413 0.35466 0.41358
75 0.1342101 0.1939567 0.265178 0.33640 0.39615
76 0.1139444 0.1745054 0.246697 0.31889 0.37945
77 0.0943704 0.1557743 0.228971 0.30217 0.36357
78 0.0753996 0.1377153 0.211999 0.28628 0.34860
79 0.0569347 0.1202755 0.195781 0.27129 0.33463
80 0.0388708 0.1033980 0.180318 0.25724 0.32177
81 0.0210989 0.0870233 0.165609 0.24419 0.31012
82 0.0035089 0.0710917 0.151654 0.23222 0.29980
83 -0.0140062 0.0555449 0.138454 0.22136 0.29091
84 -0.0315470 0.0403283 0.126008 0.21169 0.28356
85 -0.0492034 0.0253928 0.114316 0.20324 0.27783
86 -0.0670524 0.0106968 0.103378 0.19606 0.27381
87 -0.0851561 -0.0037936 0.093195 0.19018 0.27155
88 -0.1035613 -0.0181039 0.083766 0.18564 0.27109
89 -0.1223000 -0.0322515 0.075091 0.18243 0.27248
90 -0.1413914 -0.0462467 0.067171 0.18059 0.27573
91 -0.1608432 -0.0600938 0.060005 0.18010 0.28085
92 -0.1806546 -0.0737923 0.053594 0.18098 0.28784
93 -0.2008180 -0.0873382 0.047936 0.18321 0.29669
94 -0.2213213 -0.1007247 0.043033 0.18679 0.30739
95 -0.2421494 -0.1139438 0.038884 0.19171 0.31992
96 -0.2632855 -0.1269863 0.035490 0.19797 0.33427
97 -0.2847123 -0.1398427 0.032850 0.20554 0.35041
98 -0.3064126 -0.1525038 0.030964 0.21443 0.36834
99 -0.3283696 -0.1649603 0.029833 0.22463 0.38804
100 -0.3505674 -0.1772037 0.029456 0.23611 0.40948
knots :
[1] -2.557 -0.813 0.418 2.573
coef :
[1] 11.976924 3.591747 1.054378 0.029456 0.029456
> 1 - sum(cxy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 97.6%
[1] 0.95969
> showProc.time()
Time (user system elapsed): 0.441 0.003 0.604
>
> if(doExtra) {
+ ## Interpolation
+ cxyI <- cobs(x,y, "decrease", knots = unique(x))
+ ## takes quite long : 63 sec. (Pent. III, 700 MHz) --- this is because
+ ## each knot is added sequentially... {{improve!}}
+
+ summaryCobs(cxyI)# only 7 knots remaining!
+ showProc.time()
+ }
>
> summaryCobs(cxy1 <- cobs(x,y, "decrease", lambda = 0.1))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.1)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.315 0 -0.161 0.586 ...
$ fitted : num [1:200] 12.7 8.56 6.67 6.04 5.83 ...
$ coef : num [1:22] 12.7 5.78 3.16 2.43 2.11 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 15
$ k : int 15
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.1
$ icyc : int 23
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0912847 12.4849933 12.6970034 12.90901 13.30272
2 11.5452819 11.9166521 12.1166331 12.31661 12.68798
3 11.0146966 11.3650966 11.5537853 11.74247 12.09287
4 10.4995535 10.8303355 11.0084599 11.18658 11.51737
5 9.9998870 10.3123808 10.4806571 10.64893 10.96143
6 9.5157430 9.8112485 9.9703768 10.12951 10.42501
7 9.0471805 9.3269594 9.4776191 9.62828 9.90806
8 8.5942728 8.8595392 9.0023838 9.14523 9.41049
9 8.1571088 8.4090188 8.5446710 8.68032 8.93223
10 7.7357927 7.9754347 8.1044808 8.23353 8.47317
11 7.3304438 7.5588289 7.6818131 7.80480 8.03318
12 6.9411951 7.1592477 7.2766679 7.39409 7.61214
13 6.5681906 6.7767415 6.8890452 7.00135 7.20990
14 6.2115819 6.4113636 6.5189450 6.62653 6.82631
15 5.8715240 6.0631680 6.1663674 6.26957 6.46121
16 5.5481704 5.7322086 5.8313123 5.93042 6.11445
17 5.2416676 5.4185366 5.5137796 5.60902 5.78589
18 4.9521494 5.1221988 5.2137695 5.30534 5.47539
19 4.6797308 4.8432355 4.9312819 5.01933 5.18283
20 4.4245017 4.5816781 4.6663169 4.75096 4.90813
21 4.1865199 4.3375470 4.4188743 4.50020 4.65123
22 3.9658032 4.1108482 4.1889542 4.26706 4.41211
23 3.7623206 3.9015710 3.9765567 4.05154 4.19079
24 3.5759813 3.7096836 3.7816817 3.85368 3.98738
25 3.4043771 3.5329043 3.6021155 3.67133 3.79985
26 3.2347309 3.3585931 3.4252922 3.49199 3.61585
27 3.0652721 3.1848437 3.2492325 3.31362 3.43319
28 2.8962030 3.0117271 3.0739363 3.13615 3.25167
29 2.7276530 2.8392885 2.8994037 2.95952 3.07115
30 2.5596612 2.6675415 2.7256346 2.78373 2.89161
31 2.3944947 2.4988186 2.5549966 2.61117 2.71550
32 2.2444821 2.3455939 2.4000421 2.45449 2.55560
33 2.1114672 2.2097080 2.2626102 2.31551 2.41375
34 1.9954176 2.0911496 2.1427009 2.19425 2.28998
35 1.8963846 1.9899366 2.0403140 2.09069 2.18424
36 1.8125024 1.9041996 1.9535781 2.00296 2.09465
37 1.7347658 1.8248332 1.8733340 1.92183 2.01190
38 1.6620975 1.7506630 1.7983550 1.84605 1.93461
39 1.5945123 1.6816941 1.7286411 1.77559 1.86277
40 1.5278221 1.6138190 1.6601279 1.70644 1.79243
41 1.4573347 1.5423451 1.5881227 1.63390 1.71891
42 1.3839943 1.4682138 1.5135655 1.55892 1.64314
43 1.3227219 1.4063482 1.4513806 1.49641 1.58004
44 1.2787473 1.3619265 1.4067181 1.45151 1.53469
45 1.2488624 1.3317463 1.3763789 1.42101 1.50390
46 1.2168724 1.2994789 1.3439621 1.38845 1.47105
47 1.1806389 1.2628708 1.3071522 1.35143 1.43367
48 1.1401892 1.2219316 1.2659495 1.30997 1.39171
49 1.0941843 1.1754044 1.2191410 1.26288 1.34410
50 1.0326549 1.1134412 1.1569442 1.20045 1.28123
51 0.9535058 1.0339215 1.0772249 1.12053 1.20094
52 0.8632281 0.9433870 0.9865521 1.02972 1.10988
53 0.7875624 0.8676441 0.9107678 0.95389 1.03397
54 0.7267897 0.8069673 0.8501425 0.89332 0.97350
55 0.6673925 0.7477244 0.7909827 0.83424 0.91457
56 0.6072642 0.6877460 0.7310850 0.77442 0.85491
57 0.5471548 0.6278279 0.6712700 0.71471 0.79539
58 0.4995140 0.5804770 0.6240752 0.66767 0.74864
59 0.4686435 0.5499607 0.5937495 0.63754 0.71886
60 0.4531016 0.5348803 0.5789177 0.62296 0.70473
61 0.4381911 0.5206110 0.5649937 0.60938 0.69180
62 0.4199957 0.5032331 0.5480561 0.59288 0.67612
63 0.4036491 0.4879280 0.5333117 0.57870 0.66297
64 0.3952493 0.4807890 0.5268517 0.57291 0.65845
65 0.3926229 0.4796600 0.5265291 0.57340 0.66044
66 0.3900185 0.4787485 0.5265291 0.57431 0.66304
67 0.3870480 0.4776752 0.5264774 0.57528 0.66591
68 0.3738545 0.4665585 0.5164792 0.56640 0.65910
69 0.3432056 0.4380737 0.4891596 0.54025 0.63511
70 0.2950830 0.3922142 0.4445189 0.49682 0.59395
71 0.2295290 0.3291123 0.3827373 0.43636 0.53595
72 0.1670195 0.2693294 0.3244228 0.37952 0.48183
73 0.1216565 0.2269375 0.2836308 0.34032 0.44561
74 0.0934100 0.2019260 0.2603613 0.31880 0.42731
75 0.0787462 0.1907702 0.2510947 0.31142 0.42344
76 0.0658428 0.1813823 0.2435998 0.30582 0.42136
77 0.0538230 0.1727768 0.2368329 0.30089 0.41984
78 0.0427388 0.1649719 0.2307938 0.29662 0.41885
79 0.0325663 0.1579592 0.2254827 0.29301 0.41840
80 0.0232151 0.1517072 0.2208995 0.29009 0.41858
81 0.0145359 0.1461634 0.2170442 0.28792 0.41955
82 0.0063272 0.1412575 0.2139168 0.28658 0.42151
83 -0.0016568 0.1369034 0.2115173 0.28613 0.42469
84 -0.0096967 0.1330028 0.2098457 0.28669 0.42939
85 -0.0180957 0.1294496 0.2089021 0.28835 0.43590
86 -0.0272134 0.1260791 0.2086264 0.29117 0.44447
87 -0.0387972 0.1210358 0.2071052 0.29317 0.45301
88 -0.0534279 0.1135207 0.2034217 0.29332 0.46027
89 -0.0709531 0.1035871 0.1975762 0.29157 0.46611
90 -0.0912981 0.0912612 0.1895684 0.28788 0.47043
91 -0.1144525 0.0765465 0.1793985 0.28225 0.47325
92 -0.1404576 0.0594287 0.1670665 0.27470 0.47459
93 -0.1693951 0.0398791 0.1525723 0.26527 0.47454
94 -0.2013769 0.0178586 0.1359159 0.25397 0.47321
95 -0.2365365 -0.0066795 0.1170974 0.24087 0.47073
96 -0.2750210 -0.0337868 0.0961167 0.22602 0.46725
97 -0.3169840 -0.0635170 0.0729738 0.20946 0.46293
98 -0.3625797 -0.0959240 0.0476688 0.19126 0.45792
99 -0.4119579 -0.1310604 0.0202016 0.17146 0.45236
100 -0.4652595 -0.1689754 -0.0094278 0.15012 0.44640
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.6970048 5.7788265 3.1620633 2.4291174 2.1069607 1.8462166
[7] 1.6371062 1.4304905 1.3348346 1.1758220 0.9413974 0.7863913
[13] 0.5998958 0.5697029 0.5265291 0.5265291 0.5265291 0.2707227
[19] 0.2086712 0.2086712 -0.0094278 6.5257497
> 1 - sum(cxy1 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2%
[1] 0.96169
>
> summaryCobs(cxy2 <- cobs(x,y, "decrease", lambda = 1e-2))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.01)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.146 0.1468 -0.0463 0.6868 ...
$ fitted : num [1:200] 12.7 8.39 6.52 5.92 5.73 ...
$ coef : num [1:22] 12.7 5.34 3.59 2.19 2.13 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 21
$ k : int 21
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.01
$ icyc : int 35
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0477594 12.4997491 12.6970071 12.89427 13.34625
2 11.4687308 11.8950752 12.0811411 12.26721 12.69355
3 10.9090823 11.3113523 11.4869116 11.66247 12.06474
4 10.3688404 10.7485883 10.9143185 11.08005 11.45980
5 9.8480420 10.2067945 10.3633618 10.51993 10.87868
6 9.3467363 9.6859859 9.8340417 9.98210 10.32135
7 8.8649866 9.1861815 9.3263579 9.46653 9.78773
8 8.4028715 8.7074055 8.8403106 8.97322 9.27775
9 7.9604861 8.2496865 8.3758998 8.50211 8.79131
10 7.5379421 7.8130586 7.9331254 8.05319 8.32831
11 7.1353676 7.3975607 7.5119874 7.62641 7.88861
12 6.7529050 7.0032361 7.1124859 7.22174 7.47207
13 6.3907086 6.6301316 6.7346209 6.83911 7.07853
14 6.0489410 6.2782966 6.3783923 6.47849 6.70784
15 5.7277684 5.9477816 6.0438001 6.13982 6.35983
16 5.4273551 5.6386366 5.7308444 5.82305 6.03433
17 5.1478583 5.3509094 5.4395252 5.52814 5.73119
18 4.8894214 5.0846433 5.1698424 5.25504 5.45026
19 4.6521676 4.8398760 4.9217960 5.00372 5.19142
20 4.4361933 4.6166367 4.6953861 4.77414 4.95458
21 4.2415605 4.4149443 4.4906127 4.56628 4.73966
22 4.0682883 4.2348044 4.3074756 4.38015 4.54666
23 3.9163432 4.0762071 4.1459751 4.21574 4.37561
24 3.7856282 3.9391227 4.0061110 4.07310 4.22659
25 3.6683774 3.8159306 3.8803259 3.94472 4.09227
26 3.5214653 3.6636629 3.7257209 3.78778 3.92998
27 3.3383583 3.4756303 3.5355387 3.59545 3.73272
28 3.1192735 3.2518988 3.3097793 3.36766 3.50028
29 2.8643493 2.9925103 3.0484425 3.10437 3.23254
30 2.5736278 2.6974778 2.7515286 2.80558 2.92943
31 2.2696062 2.3893733 2.4416422 2.49391 2.61368
32 2.0718959 2.1879754 2.2386350 2.28929 2.40537
33 1.9979346 2.1107181 2.1599392 2.20916 2.32194
34 1.9710324 2.0809358 2.1288999 2.17686 2.28677
35 1.9261503 2.0335510 2.0804229 2.12729 2.23470
36 1.8645775 1.9698487 2.0157914 2.06173 2.16701
37 1.7927585 1.8961587 1.9412848 1.98641 2.08981
38 1.7116948 1.8133707 1.8577443 1.90212 2.00379
39 1.6214021 1.7214896 1.7651699 1.80885 1.90894
40 1.5242004 1.6229275 1.6660141 1.70910 1.80783
41 1.4229217 1.5205162 1.5631086 1.60570 1.70330
42 1.3194940 1.4161806 1.4583766 1.50057 1.59726
43 1.2442053 1.3402109 1.3821098 1.42401 1.52001
44 1.2075941 1.3030864 1.3447613 1.38644 1.48193
45 1.2023778 1.2975311 1.3390581 1.38059 1.47574
46 1.1914924 1.2863272 1.3277152 1.36910 1.46394
47 1.1698641 1.2642688 1.3054691 1.34667 1.44107
48 1.1375221 1.2313649 1.2723199 1.31327 1.40712
49 1.0934278 1.1866710 1.2273643 1.26806 1.36130
50 1.0300956 1.1228408 1.1633168 1.20379 1.29654
51 0.9459780 1.0382977 1.0785880 1.11888 1.21120
52 0.8492712 0.9412961 0.9814577 1.02162 1.11364
53 0.7724392 0.8643755 0.9044985 0.94462 1.03656
54 0.7154255 0.8074718 0.8476428 0.88781 0.97986
55 0.6587891 0.7510125 0.7912608 0.83151 0.92373
56 0.5994755 0.6918710 0.7321944 0.77252 0.86491
57 0.5383570 0.6309722 0.6713915 0.71181 0.80443
58 0.4898228 0.5827709 0.6233354 0.66390 0.75685
59 0.4588380 0.5521926 0.5929345 0.63368 0.72703
60 0.4438719 0.5377564 0.5787296 0.61970 0.71359
61 0.4293281 0.5239487 0.5652432 0.60654 0.70116
62 0.4110511 0.5066103 0.5483143 0.59002 0.68558
63 0.3944126 0.4911673 0.5333932 0.57562 0.67237
64 0.3857958 0.4839980 0.5268556 0.56971 0.66792
65 0.3830000 0.4829213 0.5265291 0.57014 0.67006
66 0.3802084 0.4820731 0.5265291 0.57099 0.67285
67 0.3770181 0.4810608 0.5264673 0.57187 0.67592
68 0.3616408 0.4680678 0.5145149 0.56096 0.66739
69 0.3254129 0.4343244 0.4818557 0.52939 0.63830
70 0.2683149 0.3798245 0.4284897 0.47715 0.58866
71 0.1904294 0.3047541 0.3546478 0.40454 0.51887
72 0.1179556 0.2354105 0.2866704 0.33793 0.45539
73 0.0689088 0.1897746 0.2425231 0.29527 0.41614
74 0.0432569 0.1678366 0.2222059 0.27658 0.40115
75 0.0359906 0.1645977 0.2207246 0.27685 0.40546
76 0.0301934 0.1628364 0.2207246 0.27861 0.41126
77 0.0245630 0.1611257 0.2207246 0.28032 0.41689
78 0.0191553 0.1594827 0.2207246 0.28197 0.42229
79 0.0139446 0.1578996 0.2207246 0.28355 0.42750
80 0.0088340 0.1563468 0.2207246 0.28510 0.43262
81 0.0036634 0.1547759 0.2207246 0.28667 0.43779
82 -0.0017830 0.1531211 0.2207246 0.28833 0.44323
83 -0.0077688 0.1513025 0.2207246 0.29015 0.44922
84 -0.0145948 0.1492286 0.2207246 0.29222 0.45604
85 -0.0225859 0.1468007 0.2207246 0.29465 0.46404
86 -0.0321107 0.1438739 0.2206774 0.29748 0.47347
87 -0.0445016 0.1389916 0.2190720 0.29915 0.48265
88 -0.0601227 0.1315395 0.2151851 0.29883 0.49049
89 -0.0788103 0.1215673 0.2090164 0.29647 0.49684
90 -0.1004844 0.1090993 0.2005661 0.29203 0.50162
91 -0.1251339 0.0941388 0.1898342 0.28553 0.50480
92 -0.1528032 0.0766725 0.1768206 0.27697 0.50644
93 -0.1835797 0.0566736 0.1615253 0.26638 0.50663
94 -0.2175834 0.0341058 0.1439484 0.25379 0.50548
95 -0.2549574 0.0089256 0.1240898 0.23925 0.50314
96 -0.2958592 -0.0189149 0.1019496 0.22281 0.49976
97 -0.3404537 -0.0494657 0.0775277 0.20452 0.49551
98 -0.3889062 -0.0827771 0.0508241 0.18443 0.49055
99 -0.4413769 -0.1188979 0.0218389 0.16258 0.48505
100 -0.4980173 -0.1578738 -0.0094279 0.13902 0.47916
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.697009 5.337850 3.591398 2.187733 2.133993 1.936435 1.631856
[8] 1.340650 1.340650 1.185401 0.931750 0.789326 0.598245 0.570221
[15] 0.526529 0.526529 0.526529 0.220725 0.220725 0.220725 -0.009428
[22] 46.342964
> 1 - sum(cxy2 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2% (tiny bit better)
[1] 0.96257
>
> summaryCobs(cxy3 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 60))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", nknots = 60, lambda = 1e-06)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 0 0 -0.382 0.309 ...
$ fitted : num [1:200] 12.7 8.24 6.67 6.26 6.11 ...
$ coef : num [1:62] 12.7 7.69 6.09 4.35 3.73 3.73 2.74 2.57 2.57 2.25 ...
$ knots : num [1:60] -2.56 -1.81 -1.73 -1.38 -1.23 ...
$ k0 : int 61
$ k : int 61
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 1e-06
$ icyc : int 46
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0247124 12.56890432 12.6970139 12.825123 13.36932
2 11.3797843 11.89599414 12.0175164 12.139039 12.65525
3 10.7668218 11.25721357 11.3726579 11.488102 11.97849
4 10.1860204 10.65259986 10.7624385 10.872277 11.33886
5 9.6375946 10.08219388 10.1868581 10.291522 10.73612
6 9.1217734 9.54603927 9.6459167 9.745794 10.17006
7 8.6387946 9.04418136 9.1396144 9.235048 9.64043
8 8.1888978 8.57666578 8.6679512 8.759237 9.14700
9 7.7723156 8.14353686 8.2309270 8.318317 8.68954
10 7.3892646 7.74483589 7.8285418 7.912248 8.26782
11 7.0399352 7.38059913 7.4607957 7.540992 7.88166
12 6.7244802 7.05085572 7.1276886 7.204521 7.53090
13 6.4430029 6.75562533 6.8292205 6.902816 7.21544
14 6.1955428 6.49491547 6.5653915 6.635868 6.93524
15 5.9820595 6.26871848 6.3362016 6.403685 6.69034
16 5.7696526 6.04428975 6.1089428 6.173596 6.44823
17 5.4339991 5.69759119 5.7596440 5.821697 6.08529
18 5.0454361 5.29908138 5.3587927 5.418504 5.67215
19 4.6993977 4.94405130 5.0016458 5.059240 5.30389
20 4.3963458 4.63268699 4.6883247 4.743962 4.98030
21 4.1365583 4.36504142 4.4188292 4.472617 4.70110
22 3.9202312 4.14115193 4.1931594 4.245167 4.46609
23 3.7474595 3.96103662 4.0113153 4.061594 4.27517
24 3.6182953 3.82478434 3.8733944 3.922005 4.12849
25 3.5335861 3.73343196 3.7804782 3.827524 4.02737
26 3.4937186 3.68729597 3.7328665 3.778437 3.97201
27 3.4752667 3.66292175 3.7070981 3.751274 3.93893
28 3.3043525 3.48641351 3.5292729 3.572132 3.75419
29 2.9458452 3.12249549 3.1640812 3.205667 3.38232
30 2.4899112 2.66132542 2.7016785 2.742031 2.91345
31 2.3652956 2.53186083 2.5710724 2.610284 2.77685
32 2.2382402 2.40029503 2.4384448 2.476594 2.63865
33 2.0486975 2.20653724 2.2436947 2.280852 2.43869
34 2.0511798 2.20522276 2.2414864 2.277750 2.43179
35 2.0553528 2.20601792 2.2414864 2.276955 2.42762
36 2.0385642 2.18623332 2.2209965 2.255760 2.40343
37 1.8391470 1.98414706 2.0182819 2.052417 2.19742
38 1.6312788 1.77395114 1.8075380 1.841125 1.98380
39 1.5314449 1.67192652 1.7049976 1.738069 1.87855
40 1.5208780 1.65927041 1.6918497 1.724429 1.86282
41 1.4986364 1.63513027 1.6672626 1.699395 1.83589
42 1.4498027 1.58470514 1.6164629 1.648221 1.78312
43 1.2247043 1.35830771 1.3897596 1.421211 1.55481
44 1.1772885 1.30980813 1.3410049 1.372202 1.50472
45 1.1781750 1.30997706 1.3410049 1.372033 1.50383
46 1.1786125 1.31005757 1.3410014 1.371945 1.50339
47 1.1644262 1.29555858 1.3264288 1.357299 1.48843
48 1.1223208 1.25286982 1.2836027 1.314336 1.44488
49 1.0583227 1.18805529 1.2185960 1.249137 1.37887
50 1.0360396 1.16504088 1.1954094 1.225778 1.35478
51 1.0366880 1.16516444 1.1954094 1.225654 1.35413
52 0.9728290 1.10089058 1.1310379 1.161185 1.28925
53 0.6458992 0.77387319 0.8039998 0.834127 0.96210
54 0.6278378 0.75589463 0.7860408 0.816187 0.94424
55 0.6233664 0.75144260 0.7815933 0.811744 0.93982
56 0.6203139 0.74853170 0.7787158 0.808900 0.93712
57 0.4831205 0.61171664 0.6419898 0.672263 0.80086
58 0.4152141 0.54435194 0.5747526 0.605153 0.73429
59 0.4143942 0.54419570 0.5747526 0.605309 0.73511
60 0.4133407 0.54399495 0.5747526 0.605510 0.73616
61 0.3912541 0.52305164 0.5540784 0.585105 0.71690
62 0.3615872 0.49479624 0.5261553 0.557514 0.69072
63 0.3595156 0.49440150 0.5261553 0.557909 0.69279
64 0.3572502 0.49396981 0.5261553 0.558341 0.69506
65 0.3545874 0.49346241 0.5261553 0.558848 0.69772
66 0.3515435 0.49288238 0.5261553 0.559428 0.70077
67 0.3482098 0.49224713 0.5261553 0.560063 0.70410
68 0.3447026 0.49157882 0.5261553 0.560732 0.70761
69 0.3265062 0.47651151 0.5118246 0.547138 0.69714
70 0.2579257 0.41132297 0.4474346 0.483546 0.63694
71 0.2081857 0.36515737 0.4021105 0.439064 0.59604
72 0.1349572 0.29569526 0.3335350 0.371375 0.53211
73 0.0020438 0.16674762 0.2055209 0.244294 0.40900
74 -0.0243664 0.14460810 0.1843868 0.224166 0.39314
75 -0.0362635 0.13720915 0.1780468 0.218884 0.39236
76 -0.0421115 0.13609478 0.1780468 0.219999 0.39820
77 -0.0482083 0.13493301 0.1780468 0.221161 0.40430
78 -0.0546034 0.13371440 0.1780468 0.222379 0.41070
79 -0.0610386 0.13248816 0.1780468 0.223605 0.41713
80 -0.0674722 0.13126221 0.1780468 0.224831 0.42357
81 -0.0740291 0.13001276 0.1780468 0.226081 0.43012
82 -0.0809567 0.12869267 0.1780468 0.227401 0.43705
83 -0.0885308 0.12724941 0.1780468 0.228844 0.44462
84 -0.0966886 0.12569491 0.1780468 0.230399 0.45278
85 -0.1053882 0.12403716 0.1780468 0.232056 0.46148
86 -0.1147206 0.12225885 0.1780468 0.233835 0.47081
87 -0.1248842 0.12032213 0.1780468 0.235771 0.48098
88 -0.1360096 0.11820215 0.1780468 0.237891 0.49210
89 -0.1480747 0.11590310 0.1780468 0.240190 0.50417
90 -0.1611528 0.11337745 0.1780053 0.242633 0.51716
91 -0.1772967 0.10838384 0.1756366 0.242889 0.52857
92 -0.1976403 0.09964452 0.1696291 0.239614 0.53690
93 -0.2221958 0.08715720 0.1599828 0.232808 0.54216
94 -0.2510614 0.07090314 0.1466976 0.222492 0.54446
95 -0.2844042 0.05085051 0.1297736 0.208697 0.54395
96 -0.3224450 0.02695723 0.1092109 0.191465 0.54087
97 -0.3654434 -0.00082617 0.0850093 0.170845 0.53546
98 -0.4136843 -0.03255395 0.0571689 0.146892 0.52802
99 -0.4674640 -0.06828261 0.0256897 0.119662 0.51884
100 -0.5270786 -0.10806856 -0.0094284 0.089212 0.50822
knots :
[1] -2.557 -1.812 -1.726 -1.384 -1.233 -1.082 -1.046 -1.009 -0.932 -0.902
[11] -0.877 -0.838 -0.813 -0.765 -0.707 -0.665 -0.568 -0.498 -0.460 -0.413
[21] -0.347 -0.333 -0.299 -0.274 -0.226 -0.089 -0.024 -0.011 0.063 0.094
[31] 0.118 0.136 0.231 0.285 0.328 0.392 0.460 0.473 0.517 0.551
[41] 0.602 0.623 0.692 0.715 0.742 0.787 0.812 0.892 0.934 0.988
[51] 1.070 1.162 1.178 1.276 1.402 1.655 1.877 1.988 2.047 2.573
coef :
[1] 12.6970155 7.6878537 6.0937652 4.3540061 3.7259911 3.7259911
[7] 2.7408131 2.5727608 2.5727608 2.2478639 2.2414864 2.2414864
[13] 2.2414864 2.2414864 2.2414864 1.9875889 1.6964374 1.6964374
[19] 1.6623718 1.6623718 1.3410049 1.3410049 1.3410049 1.3410049
[25] 1.3410049 1.3410049 1.1954094 1.1954094 1.1954094 1.1954094
[31] 0.9829296 0.8091342 0.7815933 0.7815933 0.7815933 0.5747526
[37] 0.5747526 0.5747526 0.5747526 0.5747526 0.5261553 0.5261553
[43] 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553
[49] 0.5261553 0.5261553 0.4273578 0.3741431 0.2060752 0.1780468
[55] 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468
[61] -0.0094285 432.6957871
> 1 - sum(cxy3 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.36%
[1] 0.96502
> showProc.time()
Time (user system elapsed): 0.153 0.004 0.176
>
> cpuTime(cxy4 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 100))# ~ 3 sec.
Time elapsed: 0.027
> 1 - sum(cxy4 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.443%
[1] 0.96603
>
> cpuTime(cxy5 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 150))# ~ 8.7 sec.
Time elapsed: 0.03
> 1 - sum(cxy5 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.4396%
[1] 0.96835
> showProc.time()
Time (user system elapsed): 0.421 0 0.461
>
>
> ## regularly spaced x :
> X <- seq(-1,1, len = 201)
> xx <- c(seq(-1.1, -1, len = 11), X,
+ seq( 1, 1.1, len = 11))
> y <- (fx <- exp(-X)) + rt(201,4)/4
> summaryCobs(cXy <- cobs(X,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = X, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:201] -1 -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92 -0.91 ...
$ y : num [1:201] 2.67 2.77 3.46 3.14 1.79 ...
$ resid : num [1:201] 0 0.125 0.84 0.555 -0.77 ...
$ fitted : num [1:201] 2.67 2.64 2.62 2.59 2.56 ...
$ coef : num [1:4] 2.672 1.556 0.7 0.356
$ knots : num [1:3] -1 -0.2 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 100
$ lambda : num 0
$ icyc : int 9
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 2.46750 2.55064 2.67153 2.79242 2.87556
2 2.42251 2.50122 2.61568 2.73013 2.80884
3 2.37783 2.45240 2.56081 2.66923 2.74379
4 2.33345 2.40414 2.50694 2.60973 2.68043
5 2.28933 2.35645 2.45404 2.55164 2.61876
6 2.24548 2.30932 2.40214 2.49496 2.55879
7 2.20189 2.26274 2.35122 2.43970 2.50055
8 2.15855 2.21672 2.30129 2.38586 2.44402
9 2.11547 2.17124 2.25234 2.33344 2.38922
10 2.07265 2.12633 2.20438 2.28244 2.33611
11 2.03013 2.08199 2.15741 2.23283 2.28470
12 1.98791 2.03824 2.11142 2.18461 2.23494
13 1.94605 1.99510 2.06642 2.13775 2.18680
14 1.90459 1.95260 2.02241 2.09222 2.14023
15 1.86359 1.91078 1.97938 2.04799 2.09517
16 1.82311 1.86966 1.93734 2.00502 2.05157
17 1.78322 1.82929 1.89629 1.96328 2.00936
18 1.74397 1.78971 1.85622 1.92273 1.96847
19 1.70544 1.75096 1.81714 1.88332 1.92883
20 1.66769 1.71307 1.77904 1.84502 1.89039
21 1.63079 1.67608 1.74193 1.80779 1.85308
22 1.59478 1.64002 1.70581 1.77160 1.81684
23 1.55972 1.60493 1.67067 1.73642 1.78163
24 1.52564 1.57083 1.63653 1.70222 1.74741
25 1.49260 1.53773 1.60336 1.66899 1.71412
26 1.46062 1.50567 1.57118 1.63670 1.68175
27 1.42972 1.47466 1.53999 1.60533 1.65026
28 1.39994 1.44470 1.50979 1.57488 1.61964
29 1.37128 1.41581 1.48057 1.54533 1.58987
30 1.34375 1.38800 1.45234 1.51668 1.56093
31 1.31736 1.36126 1.42510 1.48893 1.53283
32 1.29211 1.33560 1.39884 1.46207 1.50556
33 1.26800 1.31101 1.37357 1.43612 1.47914
34 1.24500 1.28749 1.34928 1.41107 1.45356
35 1.22310 1.26502 1.32598 1.38694 1.42886
36 1.20228 1.24360 1.30367 1.36374 1.40505
37 1.18250 1.22319 1.28234 1.34150 1.38218
38 1.16372 1.20377 1.26200 1.32023 1.36028
39 1.14589 1.18532 1.24265 1.29998 1.33941
40 1.12894 1.16779 1.22428 1.28077 1.31962
41 1.11271 1.15106 1.20683 1.26259 1.30094
42 1.09639 1.13439 1.18963 1.24488 1.28287
43 1.07982 1.11760 1.17253 1.22747 1.26525
44 1.06303 1.10072 1.15553 1.21034 1.24803
45 1.04607 1.08378 1.13862 1.19346 1.23117
46 1.02898 1.06681 1.12181 1.17681 1.21463
47 1.01180 1.04982 1.10509 1.16037 1.19838
48 0.99458 1.03284 1.08847 1.14411 1.18237
49 0.97734 1.01589 1.07195 1.12801 1.16656
50 0.96011 0.99899 1.05552 1.11205 1.15092
51 0.94294 0.98216 1.03919 1.09621 1.13543
52 0.92585 0.96541 1.02295 1.08049 1.12005
53 0.90885 0.94877 1.00681 1.06485 1.10477
54 0.89197 0.93223 0.99076 1.04930 1.08956
55 0.87523 0.91581 0.97482 1.03382 1.07440
56 0.85865 0.89952 0.95896 1.01840 1.05928
57 0.84223 0.88337 0.94321 1.00304 1.04419
58 0.82598 0.86736 0.92755 0.98773 1.02911
59 0.80991 0.85150 0.91198 0.97246 1.01405
60 0.79403 0.83579 0.89651 0.95723 0.99899
61 0.77834 0.82023 0.88114 0.94205 0.98394
62 0.76284 0.80482 0.86586 0.92690 0.96888
63 0.74753 0.78956 0.85068 0.91180 0.95383
64 0.73241 0.77446 0.83559 0.89673 0.93878
65 0.71747 0.75950 0.82060 0.88171 0.92374
66 0.70271 0.74468 0.80571 0.86674 0.90871
67 0.68812 0.73001 0.79091 0.85182 0.89371
68 0.67368 0.71546 0.77621 0.83696 0.87874
69 0.65939 0.70104 0.76161 0.82217 0.86382
70 0.64523 0.68674 0.74710 0.80745 0.84896
71 0.63118 0.67254 0.73268 0.79282 0.83419
72 0.61722 0.65844 0.71836 0.77829 0.81951
73 0.60333 0.64441 0.70414 0.76388 0.80495
74 0.58948 0.63045 0.69002 0.74958 0.79055
75 0.57565 0.61654 0.67599 0.73544 0.77632
76 0.56181 0.60266 0.66205 0.72145 0.76230
77 0.54792 0.58879 0.64821 0.70764 0.74851
78 0.53395 0.57491 0.63447 0.69403 0.73500
79 0.51986 0.56100 0.62083 0.68065 0.72179
80 0.50563 0.54705 0.60728 0.66750 0.70892
81 0.49121 0.53302 0.59382 0.65462 0.69643
82 0.47657 0.51891 0.58046 0.64202 0.68435
83 0.46169 0.50468 0.56720 0.62972 0.67271
84 0.44652 0.49033 0.55403 0.61774 0.66155
85 0.43105 0.47584 0.54096 0.60609 0.65087
86 0.41526 0.46119 0.52799 0.59478 0.64072
87 0.39912 0.44638 0.51511 0.58383 0.63109
88 0.38264 0.43141 0.50233 0.57324 0.62202
89 0.36579 0.41626 0.48964 0.56302 0.61349
90 0.34858 0.40093 0.47705 0.55317 0.60552
91 0.33101 0.38542 0.46455 0.54368 0.59810
92 0.31307 0.36975 0.45215 0.53456 0.59123
93 0.29478 0.35390 0.43985 0.52580 0.58492
94 0.27615 0.33788 0.42764 0.51741 0.57914
95 0.25717 0.32170 0.41553 0.50936 0.57389
96 0.23787 0.30536 0.40352 0.50167 0.56917
97 0.21824 0.28888 0.39160 0.49431 0.56495
98 0.19830 0.27225 0.37977 0.48730 0.56125
99 0.17806 0.25547 0.36804 0.48062 0.55803
100 0.15752 0.23857 0.35641 0.47426 0.55531
knots :
[1] -1.0 -0.2 1.0
coef :
[1] 2.67153 1.55592 0.70045 0.35641
> 1 - sum(cXy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 77.2%
[1] 0.77644
> showProc.time()
Time (user system elapsed): 0.099 0 0.101
>
> (cXy.9 <- cobs(X,y, "decrease", tau = 0.9))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.9)
{tau=0.9}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> (cXy.1 <- cobs(X,y, "decrease", tau = 0.1))
qbsks2():
Performing general knot selection ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.1)
{tau=0.1}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, 0.6, 1.0
> (cXy.99<- cobs(X,y, "decrease", tau = 0.99))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.99)
{tau=0.99}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, -0.2, 1.0
> (cXy.01<- cobs(X,y, "decrease", tau = 0.01))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.01)
{tau=0.01}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> plot(X,y, xlim = range(xx),
+ main = "cobs(*, \"decrease\"), N=201, tau = 50% (Med.), 1,10, 90,99%")
> lines(predict(cXy, xx), col = 2)
> lines(predict(cXy.1, xx), col = 3)
> lines(predict(cXy.9, xx), col = 3)
> lines(predict(cXy.01, xx), col = 4)
> lines(predict(cXy.99, xx), col = 4)
>
> showProc.time()
Time (user system elapsed): 0.505 0.001 0.568
>
> ## Interpolation
> cpuTime(cXyI <- cobs(X,y, "decrease", knots = unique(X)))
qbsks2():
Performing general knot selection ...
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cpuTime ... cobs -> qbsks2 -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
In addition: Warning message:
In cobs(X, y, "decrease", knots = unique(X)) :
The number of knots can't be equal to the number of unique x for degree = 2.
'cobs' has automatically deleted the middle knot.
Timing stopped at: 0.703 0.007 0.928
Execution halted
Running the tests in ‘tests/multi-constr.R’ failed.
Complete output:
> #### Examples which use the new feature of more than one 'constraint'.
>
> suppressMessages(library(cobs))
>
> ## do *not* show platform info here (as have *.Rout.save), but in 0_pt-ex.R
> options(digits = 6)
>
> if(!dev.interactive(orNone=TRUE)) pdf("multi-constr.pdf")
>
> source(system.file("util.R", package = "cobs"))
> source(system.file(package="Matrix", "test-tools-1.R", mustWork=TRUE))
Loading required package: tools
> ##--> tryCatch.W.E(), showProc.time(), assertError(), relErrV(), ...
> Lnx <- Sys.info()[["sysname"]] == "Linux"
> isMac <- Sys.info()[["sysname"]] == "Darwin"
> x86 <- (arch <- Sys.info()[["machine"]]) == "x86_64"
> noLdbl <- (.Machine$sizeof.longdouble <= 8) ## TRUE when --disable-long-double
> ## IGNORE_RDIFF_BEGIN
> Sys.info()
sysname
"Linux"
release
"6.10.11-amd64"
version
"#1 SMP PREEMPT_DYNAMIC Debian 6.10.11-1 (2024-09-22)"
nodename
"gimli2"
machine
"x86_64"
login
"hornik"
user
"hornik"
effective_user
"hornik"
> noLdbl
[1] FALSE
> ## IGNORE_RDIFF_END
>
>
> Rsq <- function(obj) {
+ stopifnot(inherits(obj, "cobs"), is.numeric(res <- obj$resid))
+ 1 - sum(res^2)/obj$SSy
+ }
> list_ <- function (...) `names<-`(list(...), vapply(sys.call()[-1L], as.character, ""))
> is.cobs <- function(x) inherits(x, "cobs")
>
> set.seed(908)
> x <- seq(-1,2, len = 50)
> f.true <- pnorm(2*x)
> y <- f.true + rnorm(50)/10
> plot(x,y); lines(x, f.true, col="gray", lwd=2, lty=3)
>
> ## constraint on derivative at right end:
> (con <- rbind(c(2 , max(x), 0))) # f'(x_n) == 0
[,1] [,2] [,3]
[1,] 2 2 0
>
> ## Using 'trace = 3' --> 'trace = 2' inside drqssbc2()
>
> ## Regression splines (lambda = 0)
> c2 <- cobs(x,y, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
> c2i <- cobs(x,y, constraint = c("increase"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 2 x 3 (nz = 6 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 5 x 6 (nz = 15 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 6 x 7 (nz = 18 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 4 x 5 (nz = 12 =^= 0.6%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 2 x 3 (nz = 6 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 3 x 4 (nz = 9 =^= 0.75%)
Warning message:
In cobs(x, y, constraint = c("increase"), trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
> c2c <- cobs(x,y, constraint = c("concave"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 1 x 3 (nz = 3 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 3 x 5 (nz = 9 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 4 x 6 (nz = 12 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 5 x 7 (nz = 15 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 3 x 5 (nz = 9 =^= 0.6%)
>
> c2IC <- cobs(x,y, constraint = c("inc", "concave"), trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 5 x 4 (nz = 15 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 7 x 5 (nz = 21 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 11 x 7 (nz = 33 =^= 0.43%)
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 9 x 6 (nz = 27 =^= 0.5%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 7 x 5 (nz = 21 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 7 x 5 (nz = 21 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 7 x 5 (nz = 21 =^= 0.6%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 5 x 4 (nz = 15 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 5 x 4 (nz = 15 =^= 0.75%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 5 x 4 (nz = 15 =^= 0.75%)
Warning message:
In cobs(x, y, constraint = c("inc", "concave"), trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 20
> ## here, it's the same as just "i":
> all.equal(fitted(c2i), fitted(c2IC))
[1] TRUE
>
> c1 <- cobs(x,y, degree = 1, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
> c1i <- cobs(x,y, degree = 1, constraint = c("increase"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 1 x 2 (nz = 2 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 2 x 3 (nz = 4 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 4 x 5 (nz = 8 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 5 x 6 (nz = 10 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 3 x 4 (nz = 6 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 4 x 5 (nz = 8 =^= 0.4%)
> c1c <- cobs(x,y, degree = 1, constraint = c("concave"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 3 x 5 (nz = 9 =^= 0.6%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 4 x 6 (nz = 12 =^= 0.5%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 1 x 3 (nz = 3 =^= 1%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
Warning message:
In cobs(x, y, degree = 1, constraint = c("concave"), trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
>
> plot(c1)
> lines(predict(c1i), col="forest green")
> all.equal(fitted(c1), fitted(c1i), tol = 1e-9)# but not 1e-10
[1] TRUE
>
> ## now gives warning (not error):
> c1IC <- cobs(x,y, degree = 1, constraint = c("inc", "concave"), trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 1 x 2 (nz = 2 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 12 =^= 0.6%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 7 x 5 (nz = 17 =^= 0.49%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 9 x 6 (nz = 22 =^= 0.41%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 12 =^= 0.6%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 12 =^= 0.6%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 12 =^= 0.6%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 7 x 5 (nz = 17 =^= 0.49%)
Warning message:
In l1.design2(x, w, constraint, ptConstr, knots, pw, nrq = n, nl1, :
too few knots ==> nk <= 4; could not add constraint 'concave'
>
> cp2 <- cobs(x,y, pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 2 x 3 (nz = 6 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 2 x 5 (nz = 6 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 2 x 6 (nz = 6 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 2 x 7 (nz = 6 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 2 x 4 (nz = 6 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 2 x 5 (nz = 6 =^= 0.6%)
Warning message:
In cobs(x, y, pointwise = con, trace = 3) :
drqssbc2(): Not all flags are normal (== 1), ifl : 21
>
> ## Here, warning ".. 'ifl'.. " on *some* platforms (e.g. Windows 32bit) :
> r2i <- tryCatch.W.E( cobs(x,y, constraint = "increase", pointwise = con) )
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> cp2i <- r2i$value
> ## IGNORE_RDIFF_BEGIN
> r2i$warning
<simpleWarning in cobs(x, y, constraint = "increase", pointwise = con): drqssbc2(): Not all flags are normal (== 1), ifl : 21>
> ## IGNORE_RDIFF_END
> ## when plotting it, we see that it gave a trivial constant!!
> cp2c <- cobs(x,y, constraint = "concave", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 3 x 3 (nz = 9 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 4 x 4 (nz = 12 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 6 x 6 (nz = 18 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 7 x 7 (nz = 21 =^= 0.43%)
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 4 x 4 (nz = 12 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 4 x 4 (nz = 12 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 5 x 5 (nz = 15 =^= 0.6%)
>
> ## now gives warning (not error): but no warning on M1 mac -> IGNORE
> ## IGNORE_RDIFF_BEGIN
> cp2IC <- cobs(x,y, constraint = c("inc", "concave"), pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 5 x 3 (nz = 15 =^= 1%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 7 x 4 (nz = 21 =^= 0.75%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 9 x 5 (nz = 27 =^= 0.6%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 7 (nz = 150 =^= 0.43%)
Xieq 13 x 7 (nz = 39 =^= 0.43%)
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 6 (nz = 150 =^= 0.5%)
Xieq 11 x 6 (nz = 33 =^= 0.5%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 9 x 5 (nz = 27 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 9 x 5 (nz = 27 =^= 0.6%)
loo.design2(): -> Xeq 50 x 5 (nz = 150 =^= 0.6%)
Xieq 9 x 5 (nz = 27 =^= 0.6%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 7 x 4 (nz = 21 =^= 0.75%)
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 7 x 4 (nz = 21 =^= 0.75%)
loo.design2(): -> Xeq 50 x 3 (nz = 150 =^= 1%)
Xieq 5 x 3 (nz = 15 =^= 1%)
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
loo.design2(): -> Xeq 50 x 4 (nz = 150 =^= 0.75%)
Xieq 7 x 4 (nz = 21 =^= 0.75%)
Warning message:
In cobs(x, y, constraint = c("inc", "concave"), pointwise = con, :
drqssbc2(): Not all flags are normal (== 1), ifl : 20
> ## IGNORE_RDIFF_END
> cp1 <- cobs(x,y, degree = 1, pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 2 x 2 (nz = 4 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 2 x 3 (nz = 4 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 2 x 5 (nz = 4 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 2 x 6 (nz = 4 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 2 x 4 (nz = 4 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 2 x 5 (nz = 4 =^= 0.4%)
> cp1i <- cobs(x,y, degree = 1, constraint = "increase", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 4 x 3 (nz = 8 =^= 0.67%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 6 x 5 (nz = 12 =^= 0.4%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 7 x 6 (nz = 14 =^= 0.33%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 5 x 4 (nz = 10 =^= 0.5%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 6 x 5 (nz = 12 =^= 0.4%)
> cp1c <- cobs(x,y, degree = 1, constraint = "concave", pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 2 x 2 (nz = 4 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 3 x 3 (nz = 7 =^= 0.78%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 4 x 4 (nz = 10 =^= 0.62%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 5 x 5 (nz = 13 =^= 0.52%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 6 x 6 (nz = 16 =^= 0.44%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 4 x 4 (nz = 10 =^= 0.62%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 4 x 4 (nz = 10 =^= 0.62%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 4 x 4 (nz = 10 =^= 0.62%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 5 x 5 (nz = 13 =^= 0.52%)
>
> cp1IC <- cobs(x,y, degree = 1, constraint = c("inc", "concave"), pointwise = con, trace = 3)
qbsks2():
Performing general knot selection ...
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 4 (nz = 100 =^= 0.5%)
Xieq 7 x 4 (nz = 16 =^= 0.57%)
l1.design2(): -> Xeq 50 x 5 (nz = 100 =^= 0.4%)
Xieq 9 x 5 (nz = 21 =^= 0.47%)
l1.design2(): -> Xeq 50 x 6 (nz = 100 =^= 0.33%)
Xieq 11 x 6 (nz = 26 =^= 0.39%)
Deleting unnecessary knots ...
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
l1.design2(): -> Xeq 50 x 2 (nz = 100 =^= 1%)
Xieq 3 x 2 (nz = 6 =^= 1%)
l1.design2(): -> Xeq 50 x 3 (nz = 100 =^= 0.67%)
Xieq 5 x 3 (nz = 11 =^= 0.73%)
Warning messages:
1: In l1.design2(x, w, constraint, ptConstr, knots, pw, nrq = n, nl1, :
too few knots ==> nk <= 4; could not add constraint 'concave'
2: In l1.design2(x, w, constraint, ptConstr, knots, pw, nrq = n, nl1, :
too few knots ==> nk <= 4; could not add constraint 'concave'
>
> ## Named list of all cobs() results above -- sort() collation order matters for ls() !
> (curLC <- Sys.getlocale("LC_COLLATE"))
[1] "C"
> Sys.setlocale("LC_COLLATE", "C")
[1] "C"
> cobsL <- mget(Filter(\(nm) is.cobs(.GlobalEnv[[nm]]), ls(patt="c[12p]")),
+ envir = .GlobalEnv)
> Sys.setlocale("LC_COLLATE", curLC) # reverting
[1] "C"
>
> knL <- lapply(cobsL, `[[`, "knots")
> str(knL[order(lengths(knL))])
List of 16
$ c2 : num [1:3] -1 -0.449 2
$ c2IC : num [1:3] -1 -0.449 2
$ c2i : num [1:3] -1 -0.449 2
$ cp1IC: num [1:3] -1 0.776 2
$ cp2IC: num [1:3] -1 -0.449 2
$ cp2i : num [1:3] -1 -0.449 2
$ c1c : num [1:4] -1 -0.449 0.776 2
$ c2c : num [1:4] -1 -0.449 0.776 2
$ cp2 : num [1:4] -1 -0.449 0.776 2
$ cp2c : num [1:4] -1 -0.449 0.776 2
$ c1 : num [1:5] -1 -0.449 0.163 0.776 2
$ c1IC : num [1:5] -1 -0.449 0.163 0.776 2
$ c1i : num [1:5] -1 -0.449 0.163 0.776 2
$ cp1 : num [1:5] -1 -0.449 0.163 0.776 2
$ cp1c : num [1:5] -1 -0.449 0.163 0.776 2
$ cp1i : num [1:5] -1 -0.449 0.163 0.776 2
>
> gotRsqrs <- sapply(cobsL, Rsq)
> Rsqrs <- c(c1 = 0.95079126, c1IC = 0.92974549, c1c = 0.92974549, c1i = 0.95079126,
+ c2 = 0.94637437, c2IC = 0.91375404, c2c = 0.92505977, c2i = 0.95022829,
+ cp1 = 0.9426453, cp1IC = 0.92223149, cp1c = 0.92223149, cp1i = 0.9426453,
+ cp2 = 0.94988863, cp2IC= 0.90051964, cp2c = 0.91375409, cp2i = 0.93611487)
> ## M1 mac " = " , cp2IC= 0.91704726, " = " , cp2i = 0.94620178
> ## noLD " = " , cp2IC=-0.08244284, " = " , cp2i = 0.94636815
> ## ATLAS " = " , cp2IC= 0.91471729, " = " , cp2i = 0.94506339
> ## openBLAS " = " , cp2IC= 0.91738019, " = " , cp2i = 0.93589404
> ## MKL " = " , cp2IC= 0.91765403, " = " , cp2i = 0.94501205
> ## Intel " = " , cp2IC= 0.91765403, " = " , cp2i = 0.94501205
> ## ^^^^^^^^^^ ^^^^^^^^^^
> ## remove these two from testing, notably for the M1 Mac & noLD .. :
> ##iR2 <- if(!x86 || noLdbl) setdiff(names(cobsL), c("cp2IC", "cp2i")) else TRUE
> ## actually everywhere, because of ATLAS, openBLAS, MKL, Intel... :
> iR2 <- setdiff(names(cobsL), nR2 <- c("cp2IC", "cp2i"))
> ## IGNORE_RDIFF_BEGIN
> dput(signif(gotRsqrs, digits=8))
c(c1 = 0.95079126, c1IC = 0.92985539, c1c = 0.94255545, c1i = 0.95079126,
c2 = 0.94637437, c2IC = 0.94864721, c2c = 0.91964571, c2i = 0.94864721,
cp1 = 0.9426453, cp1IC = 0.92223149, cp1c = 0.92223149, cp1i = 0.9426453,
cp2 = 0.95501214, cp2IC = 0.94864721, cp2c = 0.91867996, cp2i = 0.94864721
)
> all.equal(Rsqrs[iR2], gotRsqrs[iR2], tolerance=0)# 2.6277e-9 (Lnx F 38); 2.6898e-9 (M1 mac)
[1] "Mean relative difference: 0.00495479"
> all.equal(Rsqrs[nR2], gotRsqrs[nR2], tolerance=0)# differ; drastically only for 'noLD'
[1] "Mean relative difference: 0.0330278"
> ## IGNORE_RDIFF_END
> stopifnot(exprs = {
+ all.equal(Rsqrs[iR2], gotRsqrs[iR2])
+ identical(c(5L, 3L, 3L, 5L,
+ 3L, 2L, 3L, 4L,
+ 5L, 3L, 3L, 5L,
+ 4L, 2L, 2L, 4L), unname(lengths(knL)))
+ })
Error: Rsqrs[iR2] and gotRsqrs[iR2] are not equal:
Mean relative difference: 0.00495479
Execution halted
Running the tests in ‘tests/wind.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time() # timing here (to be faster by default)
Time (user system elapsed): 0.001 0 0.001
>
> data(DublinWind)
> attach(DublinWind)##-> speed & day (instead of "wind.x" & "DUB.")
> iday <- sort.list(day)
>
> if(!dev.interactive(orNone=TRUE)) pdf("wind.pdf", width=10)
>
> stopifnot(identical(day,c(rep(c(rep(1:365,3),1:366),4),
+ rep(1:365,2))))
> co50.1 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 1)
Warning message:
In cobs(day, speed, constraint = "periodic", tau = 0.5, lambda = 2.2, :
drqssbc2(): Not all flags are normal (== 1), ifl : 37
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
Warning message:
In cobs(day, speed, constraint = "periodic", tau = 0.5, lambda = 2.2, :
drqssbc2(): Not all flags are normal (== 1), ifl : 38
>
> showProc.time()
Time (user system elapsed): 0.403 0.032 0.644
>
> plot(day,speed, pch = ".", col = "gray20")
> lines(day[iday], fitted(co50.1)[iday], col="orange", lwd = 2)
> lines(day[iday], fitted(co50.2)[iday], col="sky blue", lwd = 2)
> rug(knots(co50.1), col=3, lwd=2)
>
> nknots <- 13
>
>
> if(doExtra) {
+ ## Compute the quadratic median smoothing B-spline using SIC
+ ## lambda selection
+ co.o50 <-
+ cobs(day, speed, knots.add = TRUE, constraint="periodic", nknots = nknots,
+ tau = .5, lambda = -1, method = "uniform")
+ summary(co.o50) # [does print]
+
+ showProc.time()
+
+ op <- par(mfrow = c(3,1), mgp = c(1.5, 0.6,0), mar=.1 + c(3,3:1))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o",
+ col=2, log = "x", main = "co.o50: periodic"))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o", ylim = robrng(pp.sic),
+ col=2, log = "x", main = "co.o50: periodic"))
+ of <- 0.64430538125795
+ with(co.o50, plot(pp.sic - of ~ pp.lambda, type ="o", ylim = c(6e-15, 8e-15),
+ ylab = paste("sic -",formatC(of, dig=14, small.m = "'")),
+ col=2, log = "x", main = "co.o50: periodic"))
+ par(op)
+ }
>
> showProc.time()
Time (user system elapsed): 0.033 0.001 0.07
>
> ## cobs99: Since SIC chooses a lambda that corresponds to the smoothest
> ## possible fit, rerun cobs with a larger lstart value
> ## (lstart <- log(.Machine$double.xmax)^3) # 3.57 e9
> ##
> co.o50. <-
+ cobs(day,speed, knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: cobs -> drqssbc2
In addition: Warning message:
In min(sol1["k", i.keep]) : no non-missing arguments to min; returning Inf
Execution halted
Flavor: r-devel-linux-x86_64-debian-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’ [4s/12s]
Running ‘ex1.R’ [12s/60s]
Running ‘ex2-long.R’ [8s/29s]
Running ‘ex3.R’
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [7s/22s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [5s/20s]
Running ‘small-ex.R’ [5s/18s]
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’ [4s/21s]
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’ [5s/25s]
Comparing ‘temp.Rout’ to ‘temp.Rout.save’ ...29,31d28
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
35,42c32,35
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
52,54d44
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "increase", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
58,65c48,51
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> {tau=0.5}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
69,71d54
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
75,82c58,61
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.1}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.1)
---
> {tau=0.1}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.5700016, -0.1700000, -0.1700000, 0.1300024
> empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
85,87d63
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
91,98c67,70
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.9}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.39324885, -0.28115087, 0.05916295, -0.07465159, 0.31227907
< empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.9)
---
> {tau=0.9}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.2576939, 0.1300000, 0.1300000, 0.4961568
> empirical tau (over all): 104/113 = 0.920354 (target tau= 0.9)
101,103c73
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 74 102 111
105,108c75
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 28 38 39 85 86 92 95 97 113
113,225c80,192
< [1,] 1880 -0.393247953 -0.568567598 -0.217928308 -0.497693198 -0.2888027083
< [2,] 1881 -0.389244486 -0.556686706 -0.221802266 -0.488996819 -0.2894921527
< [3,] 1882 -0.385241019 -0.544932639 -0.225549398 -0.480375996 -0.2901060418
< [4,] 1883 -0.381237552 -0.533324789 -0.229150314 -0.471842280 -0.2906328235
< [5,] 1884 -0.377234084 -0.521886218 -0.232581951 -0.463409410 -0.2910587589
< [6,] 1885 -0.373230617 -0.510644405 -0.235816829 -0.455093758 -0.2913674769
< [7,] 1886 -0.369227150 -0.499632120 -0.238822180 -0.446914845 -0.2915394558
< [8,] 1887 -0.365223683 -0.488888394 -0.241558972 -0.438895923 -0.2915514428
< [9,] 1888 -0.361220216 -0.478459556 -0.243980875 -0.431064594 -0.2913758376
< [10,] 1889 -0.357216749 -0.468400213 -0.246033284 -0.423453388 -0.2909801092
< [11,] 1890 -0.353213282 -0.458773976 -0.247652588 -0.416100202 -0.2903263615
< [12,] 1891 -0.349209814 -0.449653605 -0.248766024 -0.409048381 -0.2893712477
< [13,] 1892 -0.345206347 -0.441120098 -0.249292596 -0.402346180 -0.2880665146
< [14,] 1893 -0.341202880 -0.433260133 -0.249145628 -0.396045236 -0.2863605248
< [15,] 1894 -0.337199413 -0.426161346 -0.248237480 -0.390197757 -0.2842010691
< [16,] 1895 -0.333195946 -0.419905293 -0.246486599 -0.384852330 -0.2815395617
< [17,] 1896 -0.329192479 -0.414558712 -0.243826246 -0.380048714 -0.2783362437
< [18,] 1897 -0.325189012 -0.410164739 -0.240213284 -0.375812606 -0.2745654171
< [19,] 1898 -0.321185545 -0.406736420 -0.235634669 -0.372151779 -0.2702193101
< [20,] 1899 -0.317182077 -0.404254622 -0.230109533 -0.369054834 -0.2653093212
< [21,] 1900 -0.313178610 -0.402671075 -0.223686145 -0.366493014 -0.2598642062
< [22,] 1901 -0.309175143 -0.401915491 -0.216434795 -0.364424447 -0.2539258394
< [23,] 1902 -0.305171676 -0.401904507 -0.208438845 -0.362799469 -0.2475438831
< [24,] 1903 -0.301168209 -0.402550192 -0.199786225 -0.361565696 -0.2407707212
< [25,] 1904 -0.297164742 -0.403766666 -0.190562818 -0.360671966 -0.2336575172
< [26,] 1905 -0.293161275 -0.405474370 -0.180848179 -0.360070883 -0.2262516664
< [27,] 1906 -0.289157807 -0.407602268 -0.170713347 -0.359720126 -0.2185954887
< [28,] 1907 -0.285154340 -0.410088509 -0.160220171 -0.359582850 -0.2107258307
< [29,] 1908 -0.281150873 -0.412880143 -0.149421603 -0.359627508 -0.2026742377
< [30,] 1909 -0.268996808 -0.394836115 -0.143157501 -0.343964546 -0.1940290700
< [31,] 1910 -0.256842743 -0.376961386 -0.136724100 -0.328402442 -0.1852830438
< [32,] 1911 -0.244688678 -0.359281315 -0.130096042 -0.312956304 -0.1764210522
< [33,] 1912 -0.232534613 -0.341825431 -0.123243796 -0.297643724 -0.1674255025
< [34,] 1913 -0.220380548 -0.324627946 -0.116133151 -0.282485083 -0.1582760137
< [35,] 1914 -0.208226483 -0.307728160 -0.108724807 -0.267503793 -0.1489491732
< [36,] 1915 -0.196072418 -0.291170651 -0.100974185 -0.252726413 -0.1394184235
< [37,] 1916 -0.183918353 -0.275005075 -0.092831631 -0.238182523 -0.1296541835
< [38,] 1917 -0.171764288 -0.259285340 -0.084243236 -0.223904239 -0.1196243373
< [39,] 1918 -0.159610223 -0.244067933 -0.075152513 -0.209925213 -0.1092952334
< [40,] 1919 -0.147456158 -0.229409203 -0.065503113 -0.196279015 -0.0986333019
< [41,] 1920 -0.135302093 -0.215361603 -0.055242584 -0.182996891 -0.0876072953
< [42,] 1921 -0.123148028 -0.201969188 -0.044326869 -0.170105089 -0.0761909673
< [43,] 1922 -0.110993963 -0.189263062 -0.032724864 -0.157622139 -0.0643657877
< [44,] 1923 -0.098839898 -0.177257723 -0.020422074 -0.145556676 -0.0521231208
< [45,] 1924 -0.086685833 -0.165949224 -0.007422442 -0.133906350 -0.0394653164
< [46,] 1925 -0.074531768 -0.155315688 0.006252152 -0.122658128 -0.0264054087
< [47,] 1926 -0.062377703 -0.145320002 0.020564595 -0.111789900 -0.0129655072
< [48,] 1927 -0.050223638 -0.135913981 0.035466704 -0.101272959 0.0008256822
< [49,] 1928 -0.038069573 -0.127043003 0.050903856 -0.091074767 0.0149356198
< [50,] 1929 -0.025915508 -0.118650261 0.066819244 -0.081161479 0.0293304619
< [51,] 1930 -0.013761444 -0.110680090 0.083157203 -0.071499934 0.0439770474
< [52,] 1931 -0.001607379 -0.103080234 0.099865477 -0.062059002 0.0588442451
< [53,] 1932 0.010546686 -0.095803129 0.116896502 -0.052810346 0.0739037194
< [54,] 1933 0.022700751 -0.088806436 0.134207939 -0.043728744 0.0891302464
< [55,] 1934 0.034854816 -0.082053049 0.151762682 -0.034792088 0.1045017213
< [56,] 1935 0.047008881 -0.075510798 0.169528561 -0.025981216 0.1199989785
< [57,] 1936 0.059162946 -0.069151984 0.187477877 -0.017279624 0.1356055167
< [58,] 1937 0.054383856 -0.068135824 0.176903535 -0.018606241 0.1273739530
< [59,] 1938 0.049604765 -0.067303100 0.166512631 -0.020042139 0.1192516703
< [60,] 1939 0.044825675 -0.066681512 0.156332862 -0.021603820 0.1112551700
< [61,] 1940 0.040046585 -0.066303231 0.146396400 -0.023310448 0.1034036175
< [62,] 1941 0.035267494 -0.066205361 0.136740349 -0.025184129 0.0957191177
< [63,] 1942 0.030488404 -0.066430243 0.127407050 -0.027250087 0.0882268946
< [64,] 1943 0.025709313 -0.067025439 0.118444066 -0.029536657 0.0809552836
< [65,] 1944 0.020930223 -0.068043207 0.109903653 -0.032074970 0.0739354160
< [66,] 1945 0.016151132 -0.069539210 0.101841475 -0.034898188 0.0672004530
< [67,] 1946 0.011372042 -0.071570257 0.094314341 -0.038040154 0.0607842381
< [68,] 1947 0.006592951 -0.074190969 0.087376871 -0.041533408 0.0547193111
< [69,] 1948 0.001813861 -0.077449530 0.081077252 -0.045406656 0.0490343779
< [70,] 1949 -0.002965230 -0.081383054 0.075452595 -0.049682007 0.0437515481
< [71,] 1950 -0.007744320 -0.086013419 0.070524779 -0.054372496 0.0388838557
< [72,] 1951 -0.012523410 -0.091344570 0.066297749 -0.059480471 0.0344336506
< [73,] 1952 -0.017302501 -0.097362010 0.062757009 -0.064997299 0.0303922971
< [74,] 1953 -0.022081591 -0.104034636 0.059871454 -0.070904448 0.0267412650
< [75,] 1954 -0.026860682 -0.111318392 0.057597028 -0.077175672 0.0234543081
< [76,] 1955 -0.031639772 -0.119160824 0.055881280 -0.083779723 0.0205001786
< [77,] 1956 -0.036418863 -0.127505585 0.054667859 -0.090683032 0.0178453070
< [78,] 1957 -0.041197953 -0.136296186 0.053900280 -0.097851948 0.0154560415
< [79,] 1958 -0.045977044 -0.145478720 0.053524633 -0.105254354 0.0133002664
< [80,] 1959 -0.050756134 -0.155003532 0.053491263 -0.112860669 0.0113484004
< [81,] 1960 -0.055535225 -0.164826042 0.053755593 -0.120644335 0.0095738862
< [82,] 1961 -0.060314315 -0.174906951 0.054278321 -0.128581941 0.0079533109
< [83,] 1962 -0.065093405 -0.185212049 0.055025238 -0.136653105 0.0064662939
< [84,] 1963 -0.069872496 -0.195711803 0.055966811 -0.144840234 0.0050952422
< [85,] 1964 -0.074651586 -0.206380857 0.057077684 -0.153128222 0.0038250490
< [86,] 1965 -0.060832745 -0.185766914 0.064101424 -0.135261254 0.0135957648
< [87,] 1966 -0.047013903 -0.165458364 0.071430557 -0.117576222 0.0235484155
< [88,] 1967 -0.033195062 -0.145508157 0.079118034 -0.100104670 0.0337145466
< [89,] 1968 -0.019376220 -0.125978144 0.087225704 -0.082883444 0.0441310044
< [90,] 1969 -0.005557378 -0.106939362 0.095824605 -0.065954866 0.0548401092
< [91,] 1970 0.008261463 -0.088471368 0.104994294 -0.049366330 0.0658892560
< [92,] 1971 0.022080305 -0.070660043 0.114820653 -0.033168999 0.0773296085
< [93,] 1972 0.035899146 -0.053593318 0.125391611 -0.017415258 0.0892135504
< [94,] 1973 0.049717988 -0.037354556 0.136790532 -0.002154768 0.1015907442
< [95,] 1974 0.063536830 -0.022014046 0.149087705 0.012570595 0.1145030640
< [96,] 1975 0.077355671 -0.007620056 0.162331398 0.026732077 0.1279792657
< [97,] 1976 0.091174513 0.005808280 0.176540746 0.040318278 0.1420307479
< [98,] 1977 0.104993354 0.018284008 0.191702701 0.053336970 0.1566497385
< [99,] 1978 0.118812196 0.029850263 0.207774129 0.065813852 0.1718105399
< [100,] 1979 0.132631038 0.040573785 0.224688290 0.077788682 0.1874733929
< [101,] 1980 0.146449879 0.050536128 0.242363630 0.089310046 0.2035897119
< [102,] 1981 0.160268721 0.059824930 0.260712511 0.100430154 0.2201072876
< [103,] 1982 0.174087562 0.068526868 0.279648256 0.111200642 0.2369744825
< [104,] 1983 0.187906404 0.076722940 0.299089868 0.121669764 0.2541430435
< [105,] 1984 0.201725246 0.084485905 0.318964586 0.131880867 0.2715696238
< [106,] 1985 0.215544087 0.091879376 0.339208798 0.141871847 0.2892163274
< [107,] 1986 0.229362929 0.098957959 0.359767899 0.151675234 0.3070506231
< [108,] 1987 0.243181770 0.105767982 0.380595558 0.161318630 0.3250449108
< [109,] 1988 0.257000612 0.112348478 0.401652745 0.170825286 0.3431759375
< [110,] 1989 0.270819454 0.118732216 0.422906691 0.180214725 0.3614241817
< [111,] 1990 0.284638295 0.124946675 0.444329916 0.189503318 0.3797732721
< [112,] 1991 0.298457137 0.131014917 0.465899357 0.198704804 0.3982094699
< [113,] 1992 0.312275978 0.136956333 0.487595623 0.207830734 0.4167212231
---
> [1,] 1880 -0.470540541 -0.580395233 -0.360685849 -0.541226637 -0.399854444
> [2,] 1881 -0.462432432 -0.569650451 -0.355214414 -0.531421959 -0.393442906
> [3,] 1882 -0.454324324 -0.558928137 -0.349720511 -0.521631738 -0.387016910
> [4,] 1883 -0.446216216 -0.548230020 -0.344202412 -0.511857087 -0.380575346
> [5,] 1884 -0.438108108 -0.537557989 -0.338658227 -0.502099220 -0.374116996
> [6,] 1885 -0.430000000 -0.526914115 -0.333085885 -0.492359472 -0.367640528
> [7,] 1886 -0.421891892 -0.516300667 -0.327483116 -0.482639300 -0.361144484
> [8,] 1887 -0.413783784 -0.505720132 -0.321847435 -0.472940307 -0.354627261
> [9,] 1888 -0.405675676 -0.495175238 -0.316176113 -0.463264247 -0.348087105
> [10,] 1889 -0.397567568 -0.484668976 -0.310466159 -0.453613044 -0.341522091
> [11,] 1890 -0.389459459 -0.474204626 -0.304714293 -0.443988810 -0.334930108
> [12,] 1891 -0.381351351 -0.463785782 -0.298916920 -0.434393857 -0.328308845
> [13,] 1892 -0.373243243 -0.453416379 -0.293070107 -0.424830717 -0.321655770
> [14,] 1893 -0.365135135 -0.443100719 -0.287169552 -0.415302157 -0.314968113
> [15,] 1894 -0.357027027 -0.432843496 -0.281210558 -0.405811200 -0.308242854
> [16,] 1895 -0.348918919 -0.422649821 -0.275188017 -0.396361132 -0.301476706
> [17,] 1896 -0.340810811 -0.412525238 -0.269096384 -0.386955521 -0.294666101
> [18,] 1897 -0.332702703 -0.402475737 -0.262929668 -0.377598222 -0.287807183
> [19,] 1898 -0.324594595 -0.392507759 -0.256681430 -0.368293379 -0.280895810
> [20,] 1899 -0.316486486 -0.382628180 -0.250344793 -0.359045416 -0.273927557
> [21,] 1900 -0.308378378 -0.372844288 -0.243912468 -0.349859024 -0.266897733
> [22,] 1901 -0.300270270 -0.363163733 -0.237376807 -0.340739124 -0.259801417
> [23,] 1902 -0.292162162 -0.353594450 -0.230729874 -0.331690821 -0.252633503
> [24,] 1903 -0.284054054 -0.344144557 -0.223963551 -0.322719340 -0.245388768
> [25,] 1904 -0.275945946 -0.334822217 -0.217069675 -0.313829934 -0.238061958
> [26,] 1905 -0.267837838 -0.325635470 -0.210040206 -0.305027774 -0.230647901
> [27,] 1906 -0.259729730 -0.316592032 -0.202867427 -0.296317828 -0.223141632
> [28,] 1907 -0.251621622 -0.307699075 -0.195544168 -0.287704708 -0.215538535
> [29,] 1908 -0.243513514 -0.298962989 -0.188064038 -0.279192527 -0.207834500
> [30,] 1909 -0.235405405 -0.290389150 -0.180421661 -0.270784743 -0.200026067
> [31,] 1910 -0.227297297 -0.281981702 -0.172612893 -0.262484025 -0.192110570
> [32,] 1911 -0.219189189 -0.273743385 -0.164634993 -0.254292134 -0.184086245
> [33,] 1912 -0.211081081 -0.265675409 -0.156486753 -0.246209849 -0.175952313
> [34,] 1913 -0.202972973 -0.257777400 -0.148168546 -0.238236929 -0.167709017
> [35,] 1914 -0.194864865 -0.250047417 -0.139682313 -0.230372126 -0.159357604
> [36,] 1915 -0.186756757 -0.242482039 -0.131031475 -0.222613238 -0.150900276
> [37,] 1916 -0.178648649 -0.235076516 -0.122220781 -0.214957209 -0.142340088
> [38,] 1917 -0.170540541 -0.227824968 -0.113256113 -0.207400255 -0.133680826
> [39,] 1918 -0.162432432 -0.220720606 -0.104144259 -0.199938008 -0.124926856
> [40,] 1919 -0.154324324 -0.213755974 -0.094892674 -0.192565671 -0.116082978
> [41,] 1920 -0.146216216 -0.206923176 -0.085509256 -0.185278162 -0.107154270
> [42,] 1921 -0.138108108 -0.200214092 -0.076002124 -0.178070257 -0.098145959
> [43,] 1922 -0.130000000 -0.193620560 -0.066379440 -0.170936704 -0.089063296
> [44,] 1923 -0.121891892 -0.187134533 -0.056649251 -0.163872326 -0.079911458
> [45,] 1924 -0.113783784 -0.180748200 -0.046819367 -0.156872096 -0.070695472
> [46,] 1925 -0.105675676 -0.174454074 -0.036897277 -0.149931196 -0.061420156
> [47,] 1926 -0.097567568 -0.168245056 -0.026890080 -0.143045058 -0.052090077
> [48,] 1927 -0.089459459 -0.162114471 -0.016804448 -0.136209390 -0.042709529
> [49,] 1928 -0.081351351 -0.156056093 -0.006646610 -0.129420182 -0.033282521
> [50,] 1929 -0.073243243 -0.150064140 0.003577654 -0.122673716 -0.023812771
> [51,] 1930 -0.065135135 -0.144133276 0.013863006 -0.115966557 -0.014303713
> [52,] 1931 -0.057027027 -0.138258588 0.024204534 -0.109295545 -0.004758509
> [53,] 1932 -0.048918919 -0.132435569 0.034597732 -0.102657780 0.004819942
> [54,] 1933 -0.040810811 -0.126660095 0.045038473 -0.096050607 0.014428985
> [55,] 1934 -0.032702703 -0.120928393 0.055522988 -0.089471600 0.024066194
> [56,] 1935 -0.024594595 -0.115237021 0.066047832 -0.082918542 0.033729353
> [57,] 1936 -0.016486486 -0.109582838 0.076609865 -0.076389415 0.043416442
> [58,] 1937 -0.016486486 -0.105401253 0.072428280 -0.073698770 0.040725797
> [59,] 1938 -0.016486486 -0.101403226 0.068430253 -0.071126236 0.038153263
> [60,] 1939 -0.016486486 -0.097615899 0.064642926 -0.068689277 0.035716305
> [61,] 1940 -0.016486486 -0.094070136 0.061097163 -0.066407753 0.033434780
> [62,] 1941 -0.016486486 -0.090800520 0.057827547 -0.064303916 0.031330943
> [63,] 1942 -0.016486486 -0.087845022 0.054872049 -0.062402198 0.029429225
> [64,] 1943 -0.016486486 -0.085244160 0.052271187 -0.060728671 0.027755698
> [65,] 1944 -0.016486486 -0.083039523 0.050066550 -0.059310095 0.026337122
> [66,] 1945 -0.016486486 -0.081271575 0.048298602 -0.058172508 0.025199535
> [67,] 1946 -0.016486486 -0.079976806 0.047003833 -0.057339388 0.024366415
> [68,] 1947 -0.016486486 -0.079184539 0.046211566 -0.056829602 0.023856629
> [69,] 1948 -0.016486486 -0.078913907 0.045940934 -0.056655464 0.023682491
> [70,] 1949 -0.016486486 -0.079171667 0.046198694 -0.056821320 0.023848347
> [71,] 1950 -0.016486486 -0.079951382 0.046978409 -0.057323028 0.024350055
> [72,] 1951 -0.016486486 -0.081234197 0.048261224 -0.058148457 0.025175484
> [73,] 1952 -0.016486486 -0.082991006 0.050018033 -0.059278877 0.026305904
> [74,] 1953 -0.016486486 -0.085185454 0.052212481 -0.060690897 0.027717924
> [75,] 1954 -0.016486486 -0.087777140 0.054804167 -0.062358519 0.029385546
> [76,] 1955 -0.016486486 -0.090724471 0.057751498 -0.064254982 0.031282009
> [77,] 1956 -0.016486486 -0.093986883 0.061013910 -0.066354184 0.033381211
> [78,] 1957 -0.016486486 -0.097526332 0.064553359 -0.068631645 0.035658672
> [79,] 1958 -0.016486486 -0.101308145 0.068335172 -0.071065056 0.038092083
> [80,] 1959 -0.016486486 -0.105301366 0.072328393 -0.073634498 0.040661525
> [81,] 1960 -0.016486486 -0.109478765 0.076505793 -0.076322449 0.043349476
> [82,] 1961 -0.016486486 -0.113816631 0.080843658 -0.079113653 0.046140680
> [83,] 1962 -0.016486486 -0.118294454 0.085321481 -0.081994911 0.049021938
> [84,] 1963 -0.016486486 -0.122894566 0.089921593 -0.084954858 0.051981885
> [85,] 1964 -0.016486486 -0.127601781 0.094628808 -0.087983719 0.055010746
> [86,] 1965 -0.006054054 -0.111440065 0.099331957 -0.073864774 0.061756666
> [87,] 1966 0.004378378 -0.095541433 0.104298190 -0.059915111 0.068671868
> [88,] 1967 0.014810811 -0.079951422 0.109573043 -0.046164030 0.075785651
> [89,] 1968 0.025243243 -0.064723125 0.115209611 -0.032645694 0.083132181
> [90,] 1969 0.035675676 -0.049917365 0.121268716 -0.019399240 0.090750592
> [91,] 1970 0.046108108 -0.035602017 0.127818233 -0.006468342 0.098684559
> [92,] 1971 0.056540541 -0.021849988 0.134931069 0.006100087 0.106980994
> [93,] 1972 0.066972973 -0.008735416 0.142681362 0.018258345 0.115687601
> [94,] 1973 0.077405405 0.003672103 0.151138707 0.029961648 0.124849163
> [95,] 1974 0.087837838 0.015314778 0.160360898 0.041172812 0.134502863
> [96,] 1975 0.098270270 0.026154092 0.170386449 0.051867053 0.144673488
> [97,] 1976 0.108702703 0.036176523 0.181228883 0.062035669 0.155369736
> [98,] 1977 0.119135135 0.045395695 0.192874575 0.071687429 0.166582842
> [99,] 1978 0.129567568 0.053850212 0.205284923 0.080847170 0.178287965
> [100,] 1979 0.140000000 0.061597925 0.218402075 0.089552117 0.190447883
> [101,] 1980 0.150432432 0.068708461 0.232156404 0.097847072 0.203017792
> [102,] 1981 0.160864865 0.075255962 0.246473767 0.105779742 0.215949987
> [103,] 1982 0.171297297 0.081313324 0.261281271 0.113397031 0.229197563
> [104,] 1983 0.181729730 0.086948395 0.276511065 0.120742598 0.242716862
> [105,] 1984 0.192162162 0.092221970 0.292102355 0.127855559 0.256468766
> [106,] 1985 0.202594595 0.097187112 0.308002077 0.134770059 0.270419130
> [107,] 1986 0.213027027 0.101889333 0.324164721 0.141515381 0.284538673
> [108,] 1987 0.223459459 0.106367224 0.340551695 0.148116359 0.298802560
> [109,] 1988 0.233891892 0.110653299 0.357130484 0.154593913 0.313189871
> [110,] 1989 0.244324324 0.114774857 0.373873791 0.160965608 0.327683041
> [111,] 1990 0.254756757 0.118754798 0.390758715 0.167246179 0.342267335
> [112,] 1991 0.265189189 0.122612348 0.407766030 0.173447997 0.356930381
> [113,] 1992 0.275621622 0.126363680 0.424879564 0.179581470 0.371661774
228,340c195,307
< [1,] 1880 -0.393247953 -0.638616081 -0.147879825 -0.539424009 -0.247071897
< [2,] 1881 -0.389244486 -0.623587786 -0.154901186 -0.528852590 -0.249636382
< [3,] 1882 -0.385241019 -0.608736988 -0.161745049 -0.518386915 -0.252095123
< [4,] 1883 -0.381237552 -0.594090828 -0.168384275 -0.508043150 -0.254431953
< [5,] 1884 -0.377234084 -0.579681581 -0.174786588 -0.497840525 -0.256627644
< [6,] 1885 -0.373230617 -0.565547708 -0.180913527 -0.487801951 -0.258659284
< [7,] 1886 -0.369227150 -0.551735068 -0.186719232 -0.477954750 -0.260499551
< [8,] 1887 -0.365223683 -0.538298290 -0.192149076 -0.468331465 -0.262115901
< [9,] 1888 -0.361220216 -0.525302213 -0.197138218 -0.458970724 -0.263469708
< [10,] 1889 -0.357216749 -0.512823261 -0.201610236 -0.449918056 -0.264515441
< [11,] 1890 -0.353213282 -0.500950461 -0.205476102 -0.441226498 -0.265200065
< [12,] 1891 -0.349209814 -0.489785646 -0.208633983 -0.432956717 -0.265462912
< [13,] 1892 -0.345206347 -0.479442174 -0.210970520 -0.425176244 -0.265236451
< [14,] 1893 -0.341202880 -0.470041356 -0.212364405 -0.417957348 -0.264448412
< [15,] 1894 -0.337199413 -0.461705842 -0.212692984 -0.411373100 -0.263025726
< [16,] 1895 -0.333195946 -0.454549774 -0.211842118 -0.405491497 -0.260900395
< [17,] 1896 -0.329192479 -0.448666556 -0.209718402 -0.400368183 -0.258016774
< [18,] 1897 -0.325189012 -0.444116558 -0.206261466 -0.396039125 -0.254338899
< [19,] 1898 -0.321185545 -0.440918038 -0.201453051 -0.392515198 -0.249855891
< [20,] 1899 -0.317182077 -0.439044218 -0.195319937 -0.389780451 -0.244583704
< [21,] 1900 -0.313178610 -0.438427544 -0.187929677 -0.387794638 -0.238562582
< [22,] 1901 -0.309175143 -0.438969642 -0.179380644 -0.386499155 -0.231851132
< [23,] 1902 -0.305171676 -0.440553844 -0.169789508 -0.385824495 -0.224518857
< [24,] 1903 -0.301168209 -0.443057086 -0.159279332 -0.385697347 -0.216639071
< [25,] 1904 -0.297164742 -0.446359172 -0.147970311 -0.386046103 -0.208283380
< [26,] 1905 -0.293161275 -0.450348759 -0.135973790 -0.386804433 -0.199518116
< [27,] 1906 -0.289157807 -0.454926427 -0.123389188 -0.387913107 -0.190402508
< [28,] 1907 -0.285154340 -0.460005614 -0.110303066 -0.389320557 -0.180988124
< [29,] 1908 -0.281150873 -0.465512212 -0.096789534 -0.390982633 -0.171319113
< [30,] 1909 -0.268996808 -0.445114865 -0.092878751 -0.373917700 -0.164075916
< [31,] 1910 -0.256842743 -0.424954461 -0.088731025 -0.356993924 -0.156691562
< [32,] 1911 -0.244688678 -0.405066488 -0.084310868 -0.340232447 -0.149144910
< [33,] 1912 -0.232534613 -0.385492277 -0.079576949 -0.323657890 -0.141411336
< [34,] 1913 -0.220380548 -0.366279707 -0.074481389 -0.307298779 -0.133462317
< [35,] 1914 -0.208226483 -0.347483782 -0.068969185 -0.291187880 -0.125265087
< [36,] 1915 -0.196072418 -0.329166890 -0.062977947 -0.275362361 -0.116782475
< [37,] 1916 -0.183918353 -0.311398525 -0.056438181 -0.259863623 -0.107973083
< [38,] 1917 -0.171764288 -0.294254136 -0.049274440 -0.244736614 -0.098791963
< [39,] 1918 -0.159610223 -0.277812779 -0.041407667 -0.230028429 -0.089192017
< [40,] 1919 -0.147456158 -0.262153318 -0.032758999 -0.215786053 -0.079126264
< [41,] 1920 -0.135302093 -0.247349160 -0.023255026 -0.202053217 -0.068550970
< [42,] 1921 -0.123148028 -0.233461966 -0.012834091 -0.188866654 -0.057429402
< [43,] 1922 -0.110993963 -0.220535266 -0.001452661 -0.176252299 -0.045735628
< [44,] 1923 -0.098839898 -0.208589350 0.010909553 -0.164222236 -0.033457560
< [45,] 1924 -0.086685833 -0.197618695 0.024247028 -0.152773178 -0.020598488
< [46,] 1925 -0.074531768 -0.187592682 0.038529145 -0.141886883 -0.007176654
< [47,] 1926 -0.062377703 -0.178459370 0.053703964 -0.131532407 0.006777000
< [48,] 1927 -0.050223638 -0.170151322 0.069704045 -0.121669575 0.021222298
< [49,] 1928 -0.038069573 -0.162592093 0.086452946 -0.112252846 0.036113699
< [50,] 1929 -0.025915508 -0.155702177 0.103871160 -0.103234855 0.051403838
< [51,] 1930 -0.013761444 -0.149403669 0.121880782 -0.094569190 0.067046303
< [52,] 1931 -0.001607379 -0.143623435 0.140408678 -0.086212283 0.082997525
< [53,] 1932 0.010546686 -0.138294906 0.159388279 -0.078124475 0.099217848
< [54,] 1933 0.022700751 -0.133358827 0.178760330 -0.070270466 0.115671969
< [55,] 1934 0.034854816 -0.128763266 0.198472899 -0.062619318 0.132328951
< [56,] 1935 0.047008881 -0.124463200 0.218480963 -0.055144209 0.149161972
< [57,] 1936 0.059162946 -0.120419862 0.238745755 -0.047822043 0.166147936
< [58,] 1937 0.054383856 -0.117088225 0.225855937 -0.047769234 0.156536946
< [59,] 1938 0.049604765 -0.114013317 0.213222848 -0.047869369 0.147078900
< [60,] 1939 0.044825675 -0.111233903 0.200885253 -0.048145542 0.137796893
< [61,] 1940 0.040046585 -0.108795008 0.188888177 -0.048624577 0.128717746
< [62,] 1941 0.035267494 -0.106748562 0.177283550 -0.049337410 0.119872398
< [63,] 1942 0.030488404 -0.105153822 0.166130629 -0.050319343 0.111296150
< [64,] 1943 0.025709313 -0.104077355 0.155495982 -0.051610033 0.103028659
< [65,] 1944 0.020930223 -0.103592297 0.145452743 -0.053253050 0.095113496
< [66,] 1945 0.016151132 -0.103776551 0.136078816 -0.055294804 0.087597069
< [67,] 1946 0.011372042 -0.104709625 0.127453709 -0.057782662 0.080526746
< [68,] 1947 0.006592951 -0.106467962 0.119653865 -0.060762163 0.073948066
< [69,] 1948 0.001813861 -0.109119001 0.112746722 -0.064273484 0.067901206
< [70,] 1949 -0.002965230 -0.112714681 0.106784222 -0.068347568 0.062417108
< [71,] 1950 -0.007744320 -0.117285623 0.101796983 -0.073002655 0.057514015
< [72,] 1951 -0.012523410 -0.122837348 0.097790527 -0.078242036 0.053195215
< [73,] 1952 -0.017302501 -0.129349568 0.094744566 -0.084053625 0.049448623
< [74,] 1953 -0.022081591 -0.136778751 0.092615568 -0.090411486 0.046248303
< [75,] 1954 -0.026860682 -0.145063238 0.091341874 -0.097278888 0.043557524
< [76,] 1955 -0.031639772 -0.154129620 0.090850076 -0.104612098 0.041332553
< [77,] 1956 -0.036418863 -0.163899035 0.091061309 -0.112364133 0.039526407
< [78,] 1957 -0.041197953 -0.174292425 0.091896518 -0.120487896 0.038091990
< [79,] 1958 -0.045977044 -0.185234342 0.093280255 -0.128938440 0.036984353
< [80,] 1959 -0.050756134 -0.196655293 0.095143025 -0.137674365 0.036162097
< [81,] 1960 -0.055535225 -0.208492888 0.097422439 -0.146658502 0.035588053
< [82,] 1961 -0.060314315 -0.220692125 0.100063495 -0.155858084 0.035229454
< [83,] 1962 -0.065093405 -0.233205123 0.103018312 -0.165244586 0.035057775
< [84,] 1963 -0.069872496 -0.245990553 0.106245561 -0.174793388 0.035048396
< [85,] 1964 -0.074651586 -0.259012925 0.109709752 -0.184483346 0.035180173
< [86,] 1965 -0.060832745 -0.235684019 0.114018529 -0.164998961 0.043333472
< [87,] 1966 -0.047013903 -0.212782523 0.118754717 -0.145769203 0.051741396
< [88,] 1967 -0.033195062 -0.190382546 0.123992423 -0.126838220 0.060448097
< [89,] 1968 -0.019376220 -0.168570650 0.129818210 -0.108257582 0.069505142
< [90,] 1969 -0.005557378 -0.147446255 0.136331499 -0.090086516 0.078971760
< [91,] 1970 0.008261463 -0.127120705 0.143643631 -0.072391356 0.088914283
< [92,] 1971 0.022080305 -0.107714195 0.151874804 -0.055243707 0.099404316
< [93,] 1972 0.035899146 -0.089349787 0.161148080 -0.038716881 0.110515174
< [94,] 1973 0.049717988 -0.072144153 0.171580129 -0.022880386 0.122316362
< [95,] 1974 0.063536830 -0.056195664 0.183269323 -0.007792824 0.134866483
< [96,] 1975 0.077355671 -0.041571875 0.196283217 0.006505558 0.148205784
< [97,] 1976 0.091174513 -0.028299564 0.210648590 0.019998808 0.162350217
< [98,] 1977 0.104993354 -0.016360474 0.226347183 0.032697804 0.177288905
< [99,] 1978 0.118812196 -0.005694233 0.243318625 0.044638509 0.192985883
< [100,] 1979 0.132631038 0.003792562 0.261469513 0.055876570 0.209385506
< [101,] 1980 0.146449879 0.012214052 0.280685706 0.066479983 0.226419775
< [102,] 1981 0.160268721 0.019692889 0.300844552 0.076521819 0.244015623
< [103,] 1982 0.174087562 0.026350383 0.321824742 0.086074346 0.262100779
< [104,] 1983 0.187906404 0.032299891 0.343512917 0.095205097 0.280607711
< [105,] 1984 0.201725246 0.037643248 0.365807243 0.103974737 0.299475754
< [106,] 1985 0.215544087 0.042469480 0.388618694 0.112436305 0.318651869
< [107,] 1986 0.229362929 0.046855011 0.411870847 0.120635329 0.338090528
< [108,] 1987 0.243181770 0.050864680 0.435498861 0.128610437 0.357753104
< [109,] 1988 0.257000612 0.054553115 0.459448109 0.136394171 0.377607052
< [110,] 1989 0.270819454 0.057966177 0.483672730 0.144013855 0.397625052
< [111,] 1990 0.284638295 0.061142326 0.508134265 0.151492399 0.417784191
< [112,] 1991 0.298457137 0.064113837 0.532800436 0.158849032 0.438065241
< [113,] 1992 0.312275978 0.066907850 0.557644107 0.166099922 0.458452034
---
> [1,] 1880 -0.570000000 -0.7989007 -0.3410992837 -0.71728636 -0.422713636
> [2,] 1881 -0.562857143 -0.7862639 -0.3394503795 -0.70660842 -0.419105867
> [3,] 1882 -0.555714286 -0.7736739 -0.3377546582 -0.69596060 -0.415467975
> [4,] 1883 -0.548571429 -0.7611343 -0.3360085204 -0.68534522 -0.411797641
> [5,] 1884 -0.541428571 -0.7486491 -0.3342080272 -0.67476481 -0.408092333
> [6,] 1885 -0.534285714 -0.7362226 -0.3323488643 -0.66422216 -0.404349273
> [7,] 1886 -0.527142857 -0.7238594 -0.3304263043 -0.65372029 -0.400565421
> [8,] 1887 -0.520000000 -0.7115648 -0.3284351643 -0.64326256 -0.396737440
> [9,] 1888 -0.512857143 -0.6993445 -0.3263697605 -0.63285261 -0.392861675
> [10,] 1889 -0.505714286 -0.6872047 -0.3242238599 -0.62249446 -0.388934114
> [11,] 1890 -0.498571429 -0.6751522 -0.3219906288 -0.61219250 -0.384950360
> [12,] 1891 -0.491428571 -0.6631946 -0.3196625782 -0.60195155 -0.380905594
> [13,] 1892 -0.484285714 -0.6513399 -0.3172315093 -0.59177689 -0.376794541
> [14,] 1893 -0.477142857 -0.6395973 -0.3146884583 -0.58167428 -0.372611433
> [15,] 1894 -0.470000000 -0.6279764 -0.3120236430 -0.57165002 -0.368349976
> [16,] 1895 -0.462857143 -0.6164879 -0.3092264155 -0.56171097 -0.364003318
> [17,] 1896 -0.455714286 -0.6051433 -0.3062852230 -0.55186455 -0.359564026
> [18,] 1897 -0.448571429 -0.5939553 -0.3031875831 -0.54211879 -0.355024067
> [19,] 1898 -0.441428571 -0.5829371 -0.2999200783 -0.53248233 -0.350374809
> [20,] 1899 -0.434285714 -0.5721031 -0.2964683783 -0.52296440 -0.345607030
> [21,] 1900 -0.427142857 -0.5614684 -0.2928172976 -0.51357475 -0.340710959
> [22,] 1901 -0.420000000 -0.5510491 -0.2889508980 -0.50432366 -0.335676342
> [23,] 1902 -0.412857143 -0.5408616 -0.2848526441 -0.49522175 -0.330492537
> [24,] 1903 -0.405714286 -0.5309229 -0.2805056214 -0.48627991 -0.325148662
> [25,] 1904 -0.398571429 -0.5212500 -0.2758928205 -0.47750909 -0.319633772
> [26,] 1905 -0.391428571 -0.5118597 -0.2709974894 -0.46892006 -0.313937087
> [27,] 1906 -0.384285714 -0.5027679 -0.2658035488 -0.46052317 -0.308048262
> [28,] 1907 -0.377142857 -0.4939897 -0.2602960562 -0.45232803 -0.301957682
> [29,] 1908 -0.370000000 -0.4855383 -0.2544616963 -0.44434322 -0.295656778
> [30,] 1909 -0.362857143 -0.4774250 -0.2482892691 -0.43657594 -0.289138345
> [31,] 1910 -0.355714286 -0.4696584 -0.2417701364 -0.42903175 -0.282396824
> [32,] 1911 -0.348571429 -0.4622443 -0.2348985912 -0.42171431 -0.275428543
> [33,] 1912 -0.341428571 -0.4551850 -0.2276721117 -0.41462526 -0.268231879
> [34,] 1913 -0.334285714 -0.4484800 -0.2200914777 -0.40776409 -0.260807334
> [35,] 1914 -0.327142857 -0.4421250 -0.2121607344 -0.40112820 -0.253157511
> [36,] 1915 -0.320000000 -0.4361130 -0.2038870084 -0.39471301 -0.245286995
> [37,] 1916 -0.312857143 -0.4304341 -0.1952801960 -0.38851213 -0.237202155
> [38,] 1917 -0.305714286 -0.4250760 -0.1863525523 -0.38251770 -0.228910875
> [39,] 1918 -0.298571429 -0.4200246 -0.1771182205 -0.37672060 -0.220422257
> [40,] 1919 -0.291428571 -0.4152644 -0.1675927388 -0.37111085 -0.211746298
> [41,] 1920 -0.284285714 -0.4107789 -0.1577925583 -0.36567785 -0.202893584
> [42,] 1921 -0.277142857 -0.4065511 -0.1477346004 -0.36041071 -0.193875002
> [43,] 1922 -0.270000000 -0.4025641 -0.1374358695 -0.35529850 -0.184701495
> [44,] 1923 -0.262857143 -0.3988012 -0.1269131329 -0.35033043 -0.175383852
> [45,] 1924 -0.255714286 -0.3952459 -0.1161826679 -0.34549603 -0.165932545
> [46,] 1925 -0.248571429 -0.3918828 -0.1052600744 -0.34078524 -0.156357614
> [47,] 1926 -0.241428571 -0.3886970 -0.0941601449 -0.33618857 -0.146668575
> [48,] 1927 -0.234285714 -0.3856746 -0.0828967845 -0.33169705 -0.136874376
> [49,] 1928 -0.227142857 -0.3828027 -0.0714829715 -0.32730235 -0.126983369
> [50,] 1929 -0.220000000 -0.3800693 -0.0599307484 -0.32299670 -0.117003301
> [51,] 1930 -0.212857143 -0.3774630 -0.0482512378 -0.31877296 -0.106941331
> [52,] 1931 -0.205714286 -0.3749739 -0.0364546744 -0.31462453 -0.096804042
> [53,] 1932 -0.198571429 -0.3725924 -0.0245504487 -0.31054538 -0.086597478
> [54,] 1933 -0.191428571 -0.3703100 -0.0125471577 -0.30652997 -0.076327171
> [55,] 1934 -0.184285714 -0.3681188 -0.0004526588 -0.30257325 -0.065998175
> [56,] 1935 -0.177142857 -0.3660116 0.0117258745 -0.29867061 -0.055615108
> [57,] 1936 -0.170000000 -0.3639819 0.0239818977 -0.29481782 -0.045182180
> [58,] 1937 -0.170000000 -0.3552689 0.0152688616 -0.28921141 -0.050788591
> [59,] 1938 -0.170000000 -0.3469383 0.0069383006 -0.28385110 -0.056148897
> [60,] 1939 -0.170000000 -0.3390468 -0.0009532311 -0.27877329 -0.061226710
> [61,] 1940 -0.170000000 -0.3316586 -0.0083414258 -0.27401935 -0.065980650
> [62,] 1941 -0.170000000 -0.3248458 -0.0151542191 -0.26963565 -0.070364348
> [63,] 1942 -0.170000000 -0.3186875 -0.0213124962 -0.26567310 -0.074326897
> [64,] 1943 -0.170000000 -0.3132682 -0.0267318303 -0.26218603 -0.077813972
> [65,] 1944 -0.170000000 -0.3086744 -0.0313255619 -0.25923019 -0.080769813
> [66,] 1945 -0.170000000 -0.3049906 -0.0350093787 -0.25685983 -0.083140168
> [67,] 1946 -0.170000000 -0.3022928 -0.0377072467 -0.25512389 -0.084876113
> [68,] 1947 -0.170000000 -0.3006419 -0.0393580695 -0.25406166 -0.085938337
> [69,] 1948 -0.170000000 -0.3000780 -0.0399219767 -0.25369882 -0.086301183
> [70,] 1949 -0.170000000 -0.3006151 -0.0393848898 -0.25404441 -0.085955594
> [71,] 1950 -0.170000000 -0.3022398 -0.0377602233 -0.25508980 -0.084910201
> [72,] 1951 -0.170000000 -0.3049127 -0.0350872623 -0.25680972 -0.083190282
> [73,] 1952 -0.170000000 -0.3085733 -0.0314266558 -0.25916514 -0.080834862
> [74,] 1953 -0.170000000 -0.3131458 -0.0268541535 -0.26210732 -0.077892681
> [75,] 1954 -0.170000000 -0.3185461 -0.0214539408 -0.26558209 -0.074417909
> [76,] 1955 -0.170000000 -0.3246873 -0.0153126807 -0.26953369 -0.070466310
> [77,] 1956 -0.170000000 -0.3314851 -0.0085148970 -0.27390773 -0.066092271
> [78,] 1957 -0.170000000 -0.3388601 -0.0011398598 -0.27865320 -0.061346797
> [79,] 1958 -0.170000000 -0.3467402 0.0067401824 -0.28372362 -0.056276377
> [80,] 1959 -0.170000000 -0.3550607 0.0150607304 -0.28907749 -0.050922513
> [81,] 1960 -0.170000000 -0.3637650 0.0237650445 -0.29467829 -0.045321714
> [82,] 1961 -0.170000000 -0.3728037 0.0328037172 -0.30049423 -0.039505772
> [83,] 1962 -0.170000000 -0.3821340 0.0421340134 -0.30649781 -0.033502185
> [84,] 1963 -0.170000000 -0.3917191 0.0517191202 -0.31266536 -0.027334640
> [85,] 1964 -0.170000000 -0.4015274 0.0615273928 -0.31897650 -0.021023499
> [86,] 1965 -0.159285714 -0.3788752 0.0603037544 -0.30058075 -0.017990680
> [87,] 1966 -0.148571429 -0.3567712 0.0596282943 -0.28253772 -0.014605137
> [88,] 1967 -0.137857143 -0.3353102 0.0595958975 -0.26490847 -0.010805813
> [89,] 1968 -0.127142857 -0.3146029 0.0603171930 -0.24776419 -0.006521525
> [90,] 1969 -0.116428571 -0.2947761 0.0619189162 -0.23118642 -0.001670726
> [91,] 1970 -0.105714286 -0.2759711 0.0645424939 -0.21526616 0.003837587
> [92,] 1971 -0.095000000 -0.2583398 0.0683398431 -0.20010116 0.010101164
> [93,] 1972 -0.084285714 -0.2420369 0.0734654391 -0.18579083 0.017219402
> [94,] 1973 -0.073571429 -0.2272072 0.0800643002 -0.17242847 0.025285614
> [95,] 1974 -0.062857143 -0.2139711 0.0882568427 -0.16009157 0.034377282
> [96,] 1975 -0.052142857 -0.2024090 0.0981233226 -0.14883176 0.044546046
> [97,] 1976 -0.041428571 -0.1925491 0.1096919157 -0.13866718 0.055810037
> [98,] 1977 -0.030714286 -0.1843628 0.1229342326 -0.12957956 0.068150987
> [99,] 1978 -0.020000000 -0.1777698 0.1377698370 -0.12151714 0.081517138
> [100,] 1979 -0.009285714 -0.1726496 0.1540781875 -0.11440236 0.095830930
> [101,] 1980 0.001428571 -0.1688571 0.1717142023 -0.10814187 0.110999008
> [102,] 1981 0.012142857 -0.1662377 0.1905233955 -0.10263625 0.126921969
> [103,] 1982 0.022857143 -0.1646396 0.2103538775 -0.09778779 0.143502079
> [104,] 1983 0.033571429 -0.1639214 0.2310642722 -0.09350551 0.160648370
> [105,] 1984 0.044285714 -0.1639565 0.2525279044 -0.08970790 0.178279332
> [106,] 1985 0.055000000 -0.1646342 0.2746342071 -0.08632382 0.196323821
> [107,] 1986 0.065714286 -0.1658598 0.2972883534 -0.08329225 0.214720820
> [108,] 1987 0.076428571 -0.1675528 0.3204099260 -0.08056144 0.233418585
> [109,] 1988 0.087142857 -0.1696455 0.3439311798 -0.07808781 0.252373526
> [110,] 1989 0.097857143 -0.1720809 0.3677952332 -0.07583476 0.271549041
> [111,] 1990 0.108571429 -0.1748115 0.3919543697 -0.07377157 0.290914428
> [112,] 1991 0.119285714 -0.1777971 0.4163685288 -0.07187248 0.310443909
> [113,] 1992 0.130000000 -0.1810040 0.4410040109 -0.07011580 0.330115800
343,455c310,422
< [1,] 1880 -0.393247953 -0.693805062 -0.092690844 -0.572302393 -0.214193513
< [2,] 1881 -0.389244486 -0.676297026 -0.102191945 -0.560253689 -0.218235282
< [3,] 1882 -0.385241019 -0.659006413 -0.111475624 -0.548334514 -0.222147524
< [4,] 1883 -0.381237552 -0.641966465 -0.120508639 -0.536564669 -0.225910434
< [5,] 1884 -0.377234084 -0.625216717 -0.129251452 -0.524967709 -0.229500459
< [6,] 1885 -0.373230617 -0.608804280 -0.137656955 -0.513571700 -0.232889535
< [7,] 1886 -0.369227150 -0.592785330 -0.145668970 -0.502410107 -0.236044193
< [8,] 1887 -0.365223683 -0.577226782 -0.153220584 -0.491522795 -0.238924571
< [9,] 1888 -0.361220216 -0.562208058 -0.160232373 -0.480957079 -0.241483352
< [10,] 1889 -0.357216749 -0.547822773 -0.166610724 -0.470768729 -0.243664768
< [11,] 1890 -0.353213282 -0.534179978 -0.172246585 -0.461022711 -0.245403852
< [12,] 1891 -0.349209814 -0.521404410 -0.177015219 -0.451793336 -0.246626293
< [13,] 1892 -0.345206347 -0.509634924 -0.180777771 -0.443163327 -0.247249368
< [14,] 1893 -0.341202880 -0.499020116 -0.183385645 -0.435221208 -0.247184553
< [15,] 1894 -0.337199413 -0.489710224 -0.184688602 -0.428056482 -0.246342344
< [16,] 1895 -0.333195946 -0.481845064 -0.184546828 -0.421752442 -0.244639450
< [17,] 1896 -0.329192479 -0.475539046 -0.182845912 -0.416377249 -0.242007708
< [18,] 1897 -0.325189012 -0.470866120 -0.179511904 -0.411974957 -0.238403066
< [19,] 1898 -0.321185545 -0.467848651 -0.174522438 -0.408558891 -0.233812198
< [20,] 1899 -0.317182077 -0.466453839 -0.167910316 -0.406109508 -0.228254646
< [21,] 1900 -0.313178610 -0.466598933 -0.159758288 -0.404577513 -0.221779708
< [22,] 1901 -0.309175143 -0.468163434 -0.150186852 -0.403891117 -0.214459169
< [23,] 1902 -0.305171676 -0.471004432 -0.139338920 -0.403965184 -0.206378168
< [24,] 1903 -0.301168209 -0.474971184 -0.127365234 -0.404709910 -0.197626508
< [25,] 1904 -0.297164742 -0.479916458 -0.114413025 -0.406037582 -0.188291901
< [26,] 1905 -0.293161275 -0.485703869 -0.100618680 -0.407866950 -0.178455599
< [27,] 1906 -0.289157807 -0.492211633 -0.086103982 -0.410125463 -0.168190151
< [28,] 1907 -0.285154340 -0.499333719 -0.070974961 -0.412749954 -0.157558727
< [29,] 1908 -0.281150873 -0.506979351 -0.055322395 -0.415686342 -0.146615404
< [30,] 1909 -0.268996808 -0.484727899 -0.053265717 -0.397516841 -0.140476775
< [31,] 1910 -0.256842743 -0.462766683 -0.050918803 -0.379520246 -0.134165240
< [32,] 1911 -0.244688678 -0.441139176 -0.048238181 -0.361722455 -0.127654901
< [33,] 1912 -0.232534613 -0.419896002 -0.045173225 -0.344153628 -0.120915598
< [34,] 1913 -0.220380548 -0.399095811 -0.041665286 -0.326848704 -0.113912392
< [35,] 1914 -0.208226483 -0.378805976 -0.037646990 -0.309847821 -0.106605145
< [36,] 1915 -0.196072418 -0.359102922 -0.033041915 -0.293196507 -0.098948329
< [37,] 1916 -0.183918353 -0.340071771 -0.027764935 -0.276945475 -0.090891232
< [38,] 1917 -0.171764288 -0.321804943 -0.021723634 -0.261149781 -0.082378795
< [39,] 1918 -0.159610223 -0.304399275 -0.014821172 -0.245867116 -0.073353330
< [40,] 1919 -0.147456158 -0.287951368 -0.006960949 -0.231155030 -0.063757286
< [41,] 1920 -0.135302093 -0.272551143 0.001946957 -0.217067092 -0.053537094
< [42,] 1921 -0.123148028 -0.258274127 0.011978071 -0.203648297 -0.042647760
< [43,] 1922 -0.110993963 -0.245173645 0.023185718 -0.190930411 -0.031057516
< [44,] 1923 -0.098839898 -0.233274545 0.035594749 -0.178928240 -0.018751557
< [45,] 1924 -0.086685833 -0.222570067 0.049198400 -0.167637754 -0.005733912
< [46,] 1925 -0.074531768 -0.213022703 0.063959166 -0.157036610 0.007973073
< [47,] 1926 -0.062377703 -0.204568828 0.079813422 -0.147086903 0.022331496
< [48,] 1927 -0.050223638 -0.197125838 0.096678562 -0.137739423 0.037292146
< [49,] 1928 -0.038069573 -0.190600095 0.114460948 -0.128938384 0.052799237
< [50,] 1929 -0.025915508 -0.184894207 0.133063191 -0.120625768 0.068794751
< [51,] 1930 -0.013761444 -0.179912750 0.152389863 -0.112744726 0.085221839
< [52,] 1931 -0.001607379 -0.175566138 0.172351381 -0.105241887 0.102027130
< [53,] 1932 0.010546686 -0.171772831 0.192866204 -0.098068675 0.119162048
< [54,] 1933 0.022700751 -0.168460244 0.213861747 -0.091181848 0.136583351
< [55,] 1934 0.034854816 -0.165564766 0.235274399 -0.084543511 0.154253144
< [56,] 1935 0.047008881 -0.163031246 0.257049009 -0.078120807 0.172138570
< [57,] 1936 0.059162946 -0.160812199 0.279138092 -0.071885448 0.190211340
< [58,] 1937 0.054383856 -0.155656272 0.264423984 -0.070745832 0.179513544
< [59,] 1938 0.049604765 -0.150814817 0.250024348 -0.069793562 0.169003093
< [60,] 1939 0.044825675 -0.146335320 0.235986670 -0.069056925 0.158708275
< [61,] 1940 0.040046585 -0.142272933 0.222366102 -0.068568777 0.148661946
< [62,] 1941 0.035267494 -0.138691265 0.209226254 -0.068367014 0.138902002
< [63,] 1942 0.030488404 -0.135662903 0.196639710 -0.068494879 0.129471686
< [64,] 1943 0.025709313 -0.133269386 0.184688012 -0.069000947 0.120419573
< [65,] 1944 0.020930223 -0.131600299 0.173460744 -0.069938588 0.111799033
< [66,] 1945 0.016151132 -0.130751068 0.163053332 -0.071364652 0.103666917
< [67,] 1946 0.011372042 -0.130819083 0.153563167 -0.073337158 0.096081242
< [68,] 1947 0.006592951 -0.131897983 0.145083886 -0.075911890 0.089097793
< [69,] 1948 0.001813861 -0.134070373 0.137698095 -0.079138060 0.082765782
< [70,] 1949 -0.002965230 -0.137399877 0.131469418 -0.083053571 0.077123112
< [71,] 1950 -0.007744320 -0.141924001 0.126435361 -0.087680768 0.072192128
< [72,] 1951 -0.012523410 -0.147649510 0.122602689 -0.093023679 0.067976858
< [73,] 1952 -0.017302501 -0.154551551 0.119946549 -0.099067500 0.064462498
< [74,] 1953 -0.022081591 -0.162576801 0.118413618 -0.105780463 0.061617281
< [75,] 1954 -0.026860682 -0.171649733 0.117928369 -0.113117575 0.059396211
< [76,] 1955 -0.031639772 -0.181680427 0.118400882 -0.121025265 0.057745721
< [77,] 1956 -0.036418863 -0.192572281 0.119734555 -0.129445984 0.056608259
< [78,] 1957 -0.041197953 -0.204228457 0.121832550 -0.138322042 0.055926136
< [79,] 1958 -0.045977044 -0.216556537 0.124602449 -0.147598382 0.055644294
< [80,] 1959 -0.050756134 -0.229471397 0.127959128 -0.157224290 0.055712022
< [81,] 1960 -0.055535225 -0.242896613 0.131826164 -0.167154239 0.056083790
< [82,] 1961 -0.060314315 -0.256764812 0.136136182 -0.177348092 0.056719462
< [83,] 1962 -0.065093405 -0.271017346 0.140830535 -0.187770909 0.057584098
< [84,] 1963 -0.069872496 -0.285603587 0.145858595 -0.198392529 0.058647537
< [85,] 1964 -0.074651586 -0.300480064 0.151176891 -0.209187055 0.059883882
< [86,] 1965 -0.060832745 -0.275012124 0.153346634 -0.188428358 0.066762869
< [87,] 1966 -0.047013903 -0.250067729 0.156039922 -0.167981559 0.073953753
< [88,] 1967 -0.033195062 -0.225737656 0.159347533 -0.147900737 0.081510614
< [89,] 1968 -0.019376220 -0.202127937 0.163375497 -0.128249061 0.089496621
< [90,] 1969 -0.005557378 -0.179360353 0.168245596 -0.109099079 0.097984322
< [91,] 1970 0.008261463 -0.157571293 0.174094219 -0.090532045 0.107054971
< [92,] 1971 0.022080305 -0.136907986 0.181068596 -0.072635669 0.116796279
< [93,] 1972 0.035899146 -0.117521176 0.189319469 -0.055499756 0.127298049
< [94,] 1973 0.049717988 -0.099553773 0.198989749 -0.039209443 0.138645419
< [95,] 1974 0.063536830 -0.083126277 0.210199936 -0.023836517 0.150910176
< [96,] 1975 0.077355671 -0.068321437 0.223032779 -0.009430275 0.164141617
< [97,] 1976 0.091174513 -0.055172054 0.237521080 0.003989742 0.178359283
< [98,] 1977 0.104993354 -0.043655763 0.253642472 0.016436858 0.193549851
< [99,] 1978 0.118812196 -0.033698615 0.271323007 0.027955127 0.209669265
< [100,] 1979 0.132631038 -0.025186198 0.290448273 0.038612710 0.226649365
< [101,] 1980 0.146449879 -0.017978697 0.310878456 0.048492899 0.244406859
< [102,] 1981 0.160268721 -0.011925874 0.332463316 0.057685199 0.262852243
< [103,] 1982 0.174087562 -0.006879134 0.355054259 0.066278133 0.281896992
< [104,] 1983 0.187906404 -0.002699621 0.378512429 0.074354424 0.301458384
< [105,] 1984 0.201725246 0.000737403 0.402713088 0.081988382 0.321462109
< [106,] 1985 0.215544087 0.003540988 0.427547186 0.089244975 0.341843199
< [107,] 1986 0.229362929 0.005804749 0.452921108 0.096179971 0.362545886
< [108,] 1987 0.243181770 0.007608108 0.478755433 0.102840688 0.383522853
< [109,] 1988 0.257000612 0.009017980 0.504983244 0.109266987 0.404734237
< [110,] 1989 0.270819454 0.010090540 0.531548367 0.115492336 0.426146571
< [111,] 1990 0.284638295 0.010872901 0.558403689 0.121544800 0.447731790
< [112,] 1991 0.298457137 0.011404596 0.585509677 0.127447933 0.469466340
< [113,] 1992 0.312275978 0.011718869 0.612833087 0.133221539 0.491330418
---
> [1,] 1880 -0.257692308 -3.867500e-01 -0.128634653 -0.340734568 -0.174650048
> [2,] 1881 -0.250769231 -3.767293e-01 -0.124809149 -0.331818355 -0.169720107
> [3,] 1882 -0.243846154 -3.667351e-01 -0.120957249 -0.322919126 -0.164773181
> [4,] 1883 -0.236923077 -3.567692e-01 -0.117076923 -0.314038189 -0.159807965
> [5,] 1884 -0.230000000 -3.468340e-01 -0.113165951 -0.305176970 -0.154823030
> [6,] 1885 -0.223076923 -3.369319e-01 -0.109221900 -0.296337036 -0.149816810
> [7,] 1886 -0.216153846 -3.270656e-01 -0.105242105 -0.287520102 -0.144787590
> [8,] 1887 -0.209230769 -3.172379e-01 -0.101223643 -0.278728048 -0.139733491
> [9,] 1888 -0.202307692 -3.074521e-01 -0.097163311 -0.269962936 -0.134652449
> [10,] 1889 -0.195384615 -2.977116e-01 -0.093057593 -0.261227027 -0.129542204
> [11,] 1890 -0.188461539 -2.880204e-01 -0.088902637 -0.252522800 -0.124400277
> [12,] 1891 -0.181538462 -2.783827e-01 -0.084694220 -0.243852973 -0.119223950
> [13,] 1892 -0.174615385 -2.688030e-01 -0.080427720 -0.235220519 -0.114010250
> [14,] 1893 -0.167692308 -2.592865e-01 -0.076098083 -0.226628691 -0.108755924
> [15,] 1894 -0.160769231 -2.498387e-01 -0.071699793 -0.218081038 -0.103457424
> [16,] 1895 -0.153846154 -2.404655e-01 -0.067226847 -0.209581422 -0.098110886
> [17,] 1896 -0.146923077 -2.311734e-01 -0.062672732 -0.201134035 -0.092712119
> [18,] 1897 -0.140000000 -2.219696e-01 -0.058030409 -0.192743405 -0.087256595
> [19,] 1898 -0.133076923 -2.128615e-01 -0.053292314 -0.184414399 -0.081739447
> [20,] 1899 -0.126153846 -2.038573e-01 -0.048450366 -0.176152218 -0.076155475
> [21,] 1900 -0.119230769 -1.949655e-01 -0.043496005 -0.167962369 -0.070499170
> [22,] 1901 -0.112307692 -1.861951e-01 -0.038420244 -0.159850635 -0.064764750
> [23,] 1902 -0.105384615 -1.775555e-01 -0.033213760 -0.151823015 -0.058946216
> [24,] 1903 -0.098461539 -1.690561e-01 -0.027867017 -0.143885645 -0.053037432
> [25,] 1904 -0.091538462 -1.607065e-01 -0.022370423 -0.136044696 -0.047032227
> [26,] 1905 -0.084615385 -1.525162e-01 -0.016714535 -0.128306245 -0.040924524
> [27,] 1906 -0.077692308 -1.444943e-01 -0.010890287 -0.120676126 -0.034708490
> [28,] 1907 -0.070769231 -1.366492e-01 -0.004889253 -0.113159760 -0.028378702
> [29,] 1908 -0.063846154 -1.289884e-01 0.001296074 -0.105761977 -0.021930331
> [30,] 1909 -0.056923077 -1.215182e-01 0.007672008 -0.098486840 -0.015359314
> [31,] 1910 -0.050000000 -1.142434e-01 0.014243419 -0.091337484 -0.008662516
> [32,] 1911 -0.043076923 -1.071674e-01 0.021013527 -0.084315978 -0.001837868
> [33,] 1912 -0.036153846 -1.002914e-01 0.027983751 -0.077423239 0.005115546
> [34,] 1913 -0.029230769 -9.361519e-02 0.035153653 -0.070658982 0.012197443
> [35,] 1914 -0.022307692 -8.713634e-02 0.042520952 -0.064021740 0.019406355
> [36,] 1915 -0.015384615 -8.085086e-02 0.050081630 -0.057508928 0.026739697
> [37,] 1916 -0.008461538 -7.475318e-02 0.057830107 -0.051116955 0.034193878
> [38,] 1917 -0.001538462 -6.883640e-02 0.065759473 -0.044841376 0.041764453
> [39,] 1918 0.005384615 -6.309252e-02 0.073861755 -0.038677059 0.049446290
> [40,] 1919 0.012307692 -5.751281e-02 0.082128191 -0.032618368 0.057233753
> [41,] 1920 0.019230769 -5.208797e-02 0.090549507 -0.026659334 0.065120873
> [42,] 1921 0.026153846 -4.680847e-02 0.099116161 -0.020793819 0.073101511
> [43,] 1922 0.033076923 -4.166472e-02 0.107818567 -0.015015652 0.081169499
> [44,] 1923 0.040000000 -3.664727e-02 0.116647271 -0.009318753 0.089318753
> [45,] 1924 0.046923077 -3.174694e-02 0.125593095 -0.003697214 0.097543368
> [46,] 1925 0.053846154 -2.695494e-02 0.134647244 0.001854623 0.105837685
> [47,] 1926 0.060769231 -2.226292e-02 0.143801377 0.007342124 0.114196337
> [48,] 1927 0.067692308 -1.766304e-02 0.153047656 0.012770335 0.122614280
> [49,] 1928 0.074615385 -1.314799e-02 0.162378762 0.018143964 0.131086806
> [50,] 1929 0.081538462 -8.710982e-03 0.171787905 0.023467379 0.139609544
> [51,] 1930 0.088461538 -4.345738e-03 0.181268815 0.028744616 0.148178461
> [52,] 1931 0.095384615 -4.649065e-05 0.190815721 0.033979388 0.156789843
> [53,] 1932 0.102307692 4.192055e-03 0.200423329 0.039175101 0.165440284
> [54,] 1933 0.109230769 8.374747e-03 0.210086792 0.044334874 0.174126664
> [55,] 1934 0.116153846 1.250601e-02 0.219801679 0.049461559 0.182846134
> [56,] 1935 0.123076923 1.658990e-02 0.229563945 0.054557757 0.191596090
> [57,] 1936 0.130000000 2.063010e-02 0.239369902 0.059625842 0.200374158
> [58,] 1937 0.130000000 2.554264e-02 0.234457361 0.062786820 0.197213180
> [59,] 1938 0.130000000 3.023953e-02 0.229760466 0.065809042 0.194190958
> [60,] 1939 0.130000000 3.468890e-02 0.225311102 0.068671989 0.191328011
> [61,] 1940 0.130000000 3.885447e-02 0.221145527 0.071352331 0.188647669
> [62,] 1941 0.130000000 4.269563e-02 0.217304372 0.073823926 0.186176074
> [63,] 1942 0.130000000 4.616776e-02 0.213832244 0.076058070 0.183941930
> [64,] 1943 0.130000000 4.922326e-02 0.210776742 0.078024136 0.181975864
> [65,] 1944 0.130000000 5.181327e-02 0.208186727 0.079690683 0.180309317
> [66,] 1945 0.130000000 5.389026e-02 0.206109736 0.081027125 0.178972875
> [67,] 1946 0.130000000 5.541136e-02 0.204588637 0.082005877 0.177994123
> [68,] 1947 0.130000000 5.634212e-02 0.203657879 0.082604774 0.177395226
> [69,] 1948 0.130000000 5.666006e-02 0.203339939 0.082809352 0.177190648
> [70,] 1949 0.130000000 5.635724e-02 0.203642757 0.082614504 0.177385496
> [71,] 1950 0.130000000 5.544123e-02 0.204558768 0.082025096 0.177974904
> [72,] 1951 0.130000000 5.393418e-02 0.206065824 0.081055380 0.178944620
> [73,] 1952 0.130000000 5.187027e-02 0.208129729 0.079727358 0.180272642
> [74,] 1953 0.130000000 4.929223e-02 0.210707774 0.078068513 0.181931487
> [75,] 1954 0.130000000 4.624751e-02 0.213752495 0.076109385 0.183890615
> [76,] 1955 0.130000000 4.278497e-02 0.217215029 0.073881414 0.186118586
> [77,] 1956 0.130000000 3.895228e-02 0.221047722 0.071415265 0.188584735
> [78,] 1957 0.130000000 3.479412e-02 0.225205878 0.068739695 0.191260305
> [79,] 1958 0.130000000 3.035124e-02 0.229648764 0.065880916 0.194119084
> [80,] 1959 0.130000000 2.565999e-02 0.234340014 0.062862328 0.197137672
> [81,] 1960 0.130000000 2.075236e-02 0.239247637 0.059704514 0.200295486
> [82,] 1961 0.130000000 1.565622e-02 0.244343776 0.056425398 0.203574602
> [83,] 1962 0.130000000 1.039566e-02 0.249604337 0.053040486 0.206959514
> [84,] 1963 0.130000000 4.991436e-03 0.255008564 0.049563131 0.210436869
> [85,] 1964 0.130000000 -5.386147e-04 0.260538615 0.046004815 0.213995185
> [86,] 1965 0.143076923 1.926909e-02 0.266884757 0.063412665 0.222741181
> [87,] 1966 0.156153846 3.876772e-02 0.273539971 0.080621643 0.231686050
> [88,] 1967 0.169230769 5.790379e-02 0.280557753 0.097597325 0.240864213
> [89,] 1968 0.182307692 7.661491e-02 0.288000479 0.114299577 0.250315807
> [90,] 1969 0.195384615 9.482963e-02 0.295939602 0.130682422 0.260086809
> [91,] 1970 0.208461538 1.124682e-01 0.304454863 0.146694551 0.270228526
> [92,] 1971 0.221538461 1.294450e-01 0.313631914 0.162280850 0.280796073
> [93,] 1972 0.234615385 1.456729e-01 0.323557850 0.177385278 0.291845491
> [94,] 1973 0.247692308 1.610702e-01 0.334314435 0.191955225 0.303429390
> [95,] 1974 0.260769231 1.755689e-01 0.345969561 0.205947004 0.315591457
> [96,] 1975 0.273846154 1.891238e-01 0.358568478 0.219331501 0.328360807
> [97,] 1976 0.286923077 2.017191e-01 0.372127073 0.232098492 0.341747662
> [98,] 1977 0.300000000 2.133707e-01 0.386629338 0.244258277 0.355741722
> [99,] 1978 0.313076923 2.241239e-01 0.402029922 0.255840039 0.370313807
> [100,] 1979 0.326153846 2.340468e-01 0.418260863 0.266887506 0.385420186
> [101,] 1980 0.339230769 2.432212e-01 0.435240360 0.277453314 0.401008224
> [102,] 1981 0.352307692 2.517341e-01 0.452881314 0.287593508 0.417021876
> [103,] 1982 0.365384615 2.596711e-01 0.471098085 0.297363192 0.433406039
> [104,] 1983 0.378461538 2.671121e-01 0.489810964 0.306813654 0.450109423
> [105,] 1984 0.391538461 2.741284e-01 0.508948530 0.315990851 0.467086072
> [106,] 1985 0.404615384 2.807823e-01 0.528448443 0.324934896 0.484295873
> [107,] 1986 0.417692308 2.871274e-01 0.548257238 0.333680190 0.501704425
> [108,] 1987 0.430769231 2.932089e-01 0.568329576 0.342255907 0.519282554
> [109,] 1988 0.443846154 2.990650e-01 0.588627259 0.350686626 0.537005682
> [110,] 1989 0.456923077 3.047279e-01 0.609118218 0.358992981 0.554853173
> [111,] 1990 0.470000000 3.102244e-01 0.629775550 0.367192284 0.572807716
> [112,] 1991 0.483076923 3.155772e-01 0.650576667 0.375299067 0.590854778
> [113,] 1992 0.496153846 3.208051e-01 0.671502569 0.383325558 0.608982134
478,480d444
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
490,492d453
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
496,499d456
<
< **** ERROR in algorithm: ifl = 22
<
<
502,503c459,460
< coef[1:5]: -0.39324840, -0.28115087, 0.05916295, -0.07465159, 0.31227753
< R^2 = 73.22% ; empirical tau (over all): 63/113 = 0.5575221 (target tau= 0.5)
---
> coef[1:5]: -0.40655906, -0.31473700, 0.05651823, -0.05681818, 0.28681956
> R^2 = 72.56% ; empirical tau (over all): 54/113 = 0.4778761 (target tau= 0.5)
509,512d465
<
< **** ERROR in algorithm: ifl = 22
<
<
515,517d467
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
522,525d471
<
< **** ERROR in algorithm: ifl = 22
<
<
528,530d473
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
532,534c475
< [1] 1 2 9 10 17 18 20 21 22 23 26 27 35 36 42 47 48 49 52
< [20] 53 58 59 61 62 63 64 65 68 73 74 78 79 80 81 82 83 84 88
< [39] 90 91 94 98 100 101 102 104 108 109 111 112
---
> [1] 10 18 21 22 47 61 68 74 78 79 102 111
536,539c477
< [1] 3 4 5 6 7 8 11 12 13 14 15 16 19 24 25 28 29 30 31
< [20] 32 33 34 37 38 39 40 41 43 44 45 46 50 51 54 55 56 57 60
< [39] 66 67 69 70 71 72 75 76 77 85 86 87 89 92 93 95 96 97 99
< [58] 103 105 106 107 110 113
---
> [1] 5 8 25 38 39 50 54 77 85 97 113
Running ‘wind.R’ [10s/29s]
Running the tests in ‘tests/ex2-long.R’ failed.
Complete output:
> ####
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time()
Time (user system elapsed): 0.003 0 0.066
>
> options(digits = 5)
> if(!dev.interactive(orNone=TRUE)) pdf("ex2.pdf")
>
> set.seed(821)
> x <- round(sort(rnorm(200)), 3) # rounding -> multiple values
> sum(duplicated(x)) # 9
[1] 3
> y <- (fx <- exp(-x)) + rt(200,4)/4
> summaryCobs(cxy <- cobs(x,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0.72 -0.149 0 -0.195 0.545 ...
$ fitted : num [1:200] 11.98 8.39 6.67 6.07 5.87 ...
$ coef : num [1:5] 11.9769 3.5917 1.0544 0.0295 0.0295
$ knots : num [1:4] -2.557 -0.813 0.418 2.573
$ k0 : num 5
$ k : num 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0
$ icyc : int 11
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 11.4448128 11.6875576 11.976923 12.26629 12.50903
2 10.9843366 11.2126114 11.484728 11.75684 11.98512
3 10.5344633 10.7489871 11.004712 11.26044 11.47496
4 10.0951784 10.2966768 10.536874 10.77707 10.97857
5 9.6664684 9.8556730 10.081215 10.30676 10.49596
6 9.2483213 9.4259693 9.637736 9.84950 10.02715
7 8.8407282 9.0075609 9.206435 9.40531 9.57214
8 8.4436848 8.6004453 8.787313 8.97418 9.13094
9 8.0571928 8.2046236 8.380369 8.55612 8.70355
10 7.6812627 7.8201015 7.985605 8.15111 8.28995
11 7.3159159 7.4468904 7.603020 7.75915 7.89012
12 6.9611870 7.0850095 7.232613 7.38022 7.50404
13 6.6171269 6.7344861 6.874385 7.01428 7.13164
14 6.2838041 6.3953578 6.528336 6.66131 6.77287
15 5.9613061 6.0676719 6.194466 6.32126 6.42763
16 5.6497392 5.7514863 5.872775 5.99406 6.09581
17 5.3492272 5.4468683 5.563262 5.67966 5.77730
18 5.0599086 5.1538933 5.265928 5.37796 5.47195
19 4.7819325 4.8726424 4.980774 5.08891 5.17961
20 4.5154542 4.6031999 4.707798 4.81240 4.90014
21 4.2606295 4.3456507 4.447001 4.54835 4.63337
22 4.0176099 4.1000771 4.198383 4.29669 4.37916
23 3.7865383 3.8665567 3.961943 4.05733 4.13735
24 3.5675443 3.6451602 3.737683 3.83021 3.90782
25 3.3607413 3.4359491 3.525601 3.61525 3.69046
26 3.1662231 3.2389744 3.325698 3.41242 3.48517
27 2.9840608 3.0542750 3.137974 3.22167 3.29189
28 2.8142997 2.8818753 2.962429 3.04298 3.11056
29 2.6569546 2.7217833 2.799063 2.87634 2.94117
30 2.5120031 2.5739870 2.647875 2.72176 2.78375
31 2.3793776 2.4384496 2.508867 2.57928 2.63836
32 2.2589520 2.3151025 2.382037 2.44897 2.50512
33 2.1505256 2.2038366 2.267386 2.33094 2.38425
34 2.0538038 2.1044916 2.164914 2.22534 2.27602
35 1.9677723 2.0162522 2.074043 2.13183 2.18031
36 1.8846710 1.9316617 1.987677 2.04369 2.09068
37 1.8024456 1.8486425 1.903712 1.95878 2.00498
38 1.7213655 1.7673410 1.822146 1.87695 1.92293
39 1.6417290 1.6879196 1.742982 1.79804 1.84423
40 1.5638322 1.6105393 1.666217 1.72189 1.76860
41 1.4879462 1.5353474 1.591852 1.64836 1.69576
42 1.4143040 1.4624707 1.519888 1.57731 1.62547
43 1.3430975 1.3920136 1.450324 1.50864 1.55755
44 1.2744792 1.3240589 1.383161 1.44226 1.49184
45 1.2085658 1.2586702 1.318397 1.37812 1.42823
46 1.1454438 1.1958944 1.256034 1.31617 1.36662
47 1.0851730 1.1357641 1.196072 1.25638 1.30697
48 1.0277900 1.0782992 1.138509 1.19872 1.24923
49 0.9733099 1.0235079 1.083347 1.14319 1.19338
50 0.9217268 0.9713870 1.030585 1.08978 1.13944
51 0.8730129 0.9219214 0.980223 1.03852 1.08743
52 0.8271160 0.8750827 0.932262 0.98944 1.03741
53 0.7839554 0.8308269 0.886700 0.94257 0.98945
54 0.7434158 0.7890916 0.843540 0.89799 0.94366
55 0.7053406 0.7497913 0.802779 0.85577 0.90022
56 0.6695233 0.7128138 0.764419 0.81602 0.85931
57 0.6357022 0.6780170 0.728459 0.77890 0.82121
58 0.6035616 0.6452289 0.694899 0.74457 0.78624
59 0.5724566 0.6139693 0.663455 0.71294 0.75445
60 0.5410437 0.5829503 0.632905 0.68286 0.72477
61 0.5094333 0.5521679 0.603110 0.65405 0.69679
62 0.4778879 0.5217649 0.574069 0.62637 0.67025
63 0.4466418 0.4918689 0.545782 0.59970 0.64492
64 0.4158910 0.4625864 0.518250 0.57391 0.62061
65 0.3857918 0.4340022 0.491472 0.54894 0.59715
66 0.3564634 0.4061813 0.465448 0.52471 0.57443
67 0.3279928 0.3791711 0.440179 0.50119 0.55236
68 0.3004403 0.3530042 0.415663 0.47832 0.53089
69 0.2738429 0.3277009 0.391903 0.45610 0.50996
70 0.2482184 0.3032707 0.368896 0.43452 0.48957
71 0.2235676 0.2797141 0.346644 0.41357 0.46972
72 0.1998762 0.2570233 0.325146 0.39327 0.45042
73 0.1771158 0.2351830 0.304402 0.37362 0.43169
74 0.1552452 0.2141706 0.284413 0.35466 0.41358
75 0.1342101 0.1939567 0.265178 0.33640 0.39615
76 0.1139444 0.1745054 0.246697 0.31889 0.37945
77 0.0943704 0.1557743 0.228971 0.30217 0.36357
78 0.0753996 0.1377153 0.211999 0.28628 0.34860
79 0.0569347 0.1202755 0.195781 0.27129 0.33463
80 0.0388708 0.1033980 0.180318 0.25724 0.32177
81 0.0210989 0.0870233 0.165609 0.24419 0.31012
82 0.0035089 0.0710917 0.151654 0.23222 0.29980
83 -0.0140062 0.0555449 0.138454 0.22136 0.29091
84 -0.0315470 0.0403283 0.126008 0.21169 0.28356
85 -0.0492034 0.0253928 0.114316 0.20324 0.27783
86 -0.0670524 0.0106968 0.103378 0.19606 0.27381
87 -0.0851561 -0.0037936 0.093195 0.19018 0.27155
88 -0.1035613 -0.0181039 0.083766 0.18564 0.27109
89 -0.1223000 -0.0322515 0.075091 0.18243 0.27248
90 -0.1413914 -0.0462467 0.067171 0.18059 0.27573
91 -0.1608432 -0.0600938 0.060005 0.18010 0.28085
92 -0.1806546 -0.0737923 0.053594 0.18098 0.28784
93 -0.2008180 -0.0873382 0.047936 0.18321 0.29669
94 -0.2213213 -0.1007247 0.043033 0.18679 0.30739
95 -0.2421494 -0.1139438 0.038884 0.19171 0.31992
96 -0.2632855 -0.1269863 0.035490 0.19797 0.33427
97 -0.2847123 -0.1398427 0.032850 0.20554 0.35041
98 -0.3064126 -0.1525038 0.030964 0.21443 0.36834
99 -0.3283696 -0.1649603 0.029833 0.22463 0.38804
100 -0.3505674 -0.1772037 0.029456 0.23611 0.40948
knots :
[1] -2.557 -0.813 0.418 2.573
coef :
[1] 11.976924 3.591747 1.054378 0.029456 0.029456
> 1 - sum(cxy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 97.6%
[1] 0.95969
> showProc.time()
Time (user system elapsed): 0.751 0.039 3.036
>
> if(doExtra) {
+ ## Interpolation
+ cxyI <- cobs(x,y, "decrease", knots = unique(x))
+ ## takes quite long : 63 sec. (Pent. III, 700 MHz) --- this is because
+ ## each knot is added sequentially... {{improve!}}
+
+ summaryCobs(cxyI)# only 7 knots remaining!
+ showProc.time()
+ }
>
> summaryCobs(cxy1 <- cobs(x,y, "decrease", lambda = 0.1))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.1)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.315 0 -0.161 0.586 ...
$ fitted : num [1:200] 12.7 8.56 6.67 6.04 5.83 ...
$ coef : num [1:22] 12.7 5.78 3.16 2.43 2.11 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 15
$ k : int 15
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.1
$ icyc : int 23
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0912847 12.4849933 12.6970034 12.90901 13.30272
2 11.5452819 11.9166521 12.1166331 12.31661 12.68798
3 11.0146966 11.3650966 11.5537853 11.74247 12.09287
4 10.4995535 10.8303355 11.0084599 11.18658 11.51737
5 9.9998870 10.3123808 10.4806571 10.64893 10.96143
6 9.5157430 9.8112485 9.9703768 10.12951 10.42501
7 9.0471805 9.3269594 9.4776191 9.62828 9.90806
8 8.5942728 8.8595392 9.0023838 9.14523 9.41049
9 8.1571088 8.4090188 8.5446710 8.68032 8.93223
10 7.7357927 7.9754347 8.1044808 8.23353 8.47317
11 7.3304438 7.5588289 7.6818131 7.80480 8.03318
12 6.9411951 7.1592477 7.2766679 7.39409 7.61214
13 6.5681906 6.7767415 6.8890452 7.00135 7.20990
14 6.2115819 6.4113636 6.5189450 6.62653 6.82631
15 5.8715240 6.0631680 6.1663674 6.26957 6.46121
16 5.5481704 5.7322086 5.8313123 5.93042 6.11445
17 5.2416676 5.4185366 5.5137796 5.60902 5.78589
18 4.9521494 5.1221988 5.2137695 5.30534 5.47539
19 4.6797308 4.8432355 4.9312819 5.01933 5.18283
20 4.4245017 4.5816781 4.6663169 4.75096 4.90813
21 4.1865199 4.3375470 4.4188743 4.50020 4.65123
22 3.9658032 4.1108482 4.1889542 4.26706 4.41211
23 3.7623206 3.9015710 3.9765567 4.05154 4.19079
24 3.5759813 3.7096836 3.7816817 3.85368 3.98738
25 3.4043771 3.5329043 3.6021155 3.67133 3.79985
26 3.2347309 3.3585931 3.4252922 3.49199 3.61585
27 3.0652721 3.1848437 3.2492325 3.31362 3.43319
28 2.8962030 3.0117271 3.0739363 3.13615 3.25167
29 2.7276530 2.8392885 2.8994037 2.95952 3.07115
30 2.5596612 2.6675415 2.7256346 2.78373 2.89161
31 2.3944947 2.4988186 2.5549966 2.61117 2.71550
32 2.2444821 2.3455939 2.4000421 2.45449 2.55560
33 2.1114672 2.2097080 2.2626102 2.31551 2.41375
34 1.9954176 2.0911496 2.1427009 2.19425 2.28998
35 1.8963846 1.9899366 2.0403140 2.09069 2.18424
36 1.8125024 1.9041996 1.9535781 2.00296 2.09465
37 1.7347658 1.8248332 1.8733340 1.92183 2.01190
38 1.6620975 1.7506630 1.7983550 1.84605 1.93461
39 1.5945123 1.6816941 1.7286411 1.77559 1.86277
40 1.5278221 1.6138190 1.6601279 1.70644 1.79243
41 1.4573347 1.5423451 1.5881227 1.63390 1.71891
42 1.3839943 1.4682138 1.5135655 1.55892 1.64314
43 1.3227219 1.4063482 1.4513806 1.49641 1.58004
44 1.2787473 1.3619265 1.4067181 1.45151 1.53469
45 1.2488624 1.3317463 1.3763789 1.42101 1.50390
46 1.2168724 1.2994789 1.3439621 1.38845 1.47105
47 1.1806389 1.2628708 1.3071522 1.35143 1.43367
48 1.1401892 1.2219316 1.2659495 1.30997 1.39171
49 1.0941843 1.1754044 1.2191410 1.26288 1.34410
50 1.0326549 1.1134412 1.1569442 1.20045 1.28123
51 0.9535058 1.0339215 1.0772249 1.12053 1.20094
52 0.8632281 0.9433870 0.9865521 1.02972 1.10988
53 0.7875624 0.8676441 0.9107678 0.95389 1.03397
54 0.7267897 0.8069673 0.8501425 0.89332 0.97350
55 0.6673925 0.7477244 0.7909827 0.83424 0.91457
56 0.6072642 0.6877460 0.7310850 0.77442 0.85491
57 0.5471548 0.6278279 0.6712700 0.71471 0.79539
58 0.4995140 0.5804770 0.6240752 0.66767 0.74864
59 0.4686435 0.5499607 0.5937495 0.63754 0.71886
60 0.4531016 0.5348803 0.5789177 0.62296 0.70473
61 0.4381911 0.5206110 0.5649937 0.60938 0.69180
62 0.4199957 0.5032331 0.5480561 0.59288 0.67612
63 0.4036491 0.4879280 0.5333117 0.57870 0.66297
64 0.3952493 0.4807890 0.5268517 0.57291 0.65845
65 0.3926229 0.4796600 0.5265291 0.57340 0.66044
66 0.3900185 0.4787485 0.5265291 0.57431 0.66304
67 0.3870480 0.4776752 0.5264774 0.57528 0.66591
68 0.3738545 0.4665585 0.5164792 0.56640 0.65910
69 0.3432056 0.4380737 0.4891596 0.54025 0.63511
70 0.2950830 0.3922142 0.4445189 0.49682 0.59395
71 0.2295290 0.3291123 0.3827373 0.43636 0.53595
72 0.1670195 0.2693294 0.3244228 0.37952 0.48183
73 0.1216565 0.2269375 0.2836308 0.34032 0.44561
74 0.0934100 0.2019260 0.2603613 0.31880 0.42731
75 0.0787462 0.1907702 0.2510947 0.31142 0.42344
76 0.0658428 0.1813823 0.2435998 0.30582 0.42136
77 0.0538230 0.1727768 0.2368329 0.30089 0.41984
78 0.0427388 0.1649719 0.2307938 0.29662 0.41885
79 0.0325663 0.1579592 0.2254827 0.29301 0.41840
80 0.0232151 0.1517072 0.2208995 0.29009 0.41858
81 0.0145359 0.1461634 0.2170442 0.28792 0.41955
82 0.0063272 0.1412575 0.2139168 0.28658 0.42151
83 -0.0016568 0.1369034 0.2115173 0.28613 0.42469
84 -0.0096967 0.1330028 0.2098457 0.28669 0.42939
85 -0.0180957 0.1294496 0.2089021 0.28835 0.43590
86 -0.0272134 0.1260791 0.2086264 0.29117 0.44447
87 -0.0387972 0.1210358 0.2071052 0.29317 0.45301
88 -0.0534279 0.1135207 0.2034217 0.29332 0.46027
89 -0.0709531 0.1035871 0.1975762 0.29157 0.46611
90 -0.0912981 0.0912612 0.1895684 0.28788 0.47043
91 -0.1144525 0.0765465 0.1793985 0.28225 0.47325
92 -0.1404576 0.0594287 0.1670665 0.27470 0.47459
93 -0.1693951 0.0398791 0.1525723 0.26527 0.47454
94 -0.2013769 0.0178586 0.1359159 0.25397 0.47321
95 -0.2365365 -0.0066795 0.1170974 0.24087 0.47073
96 -0.2750210 -0.0337868 0.0961167 0.22602 0.46725
97 -0.3169840 -0.0635170 0.0729738 0.20946 0.46293
98 -0.3625797 -0.0959240 0.0476688 0.19126 0.45792
99 -0.4119579 -0.1310604 0.0202016 0.17146 0.45236
100 -0.4652595 -0.1689754 -0.0094278 0.15012 0.44640
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.6970048 5.7788265 3.1620633 2.4291174 2.1069607 1.8462166
[7] 1.6371062 1.4304905 1.3348346 1.1758220 0.9413974 0.7863913
[13] 0.5998958 0.5697029 0.5265291 0.5265291 0.5265291 0.2707227
[19] 0.2086712 0.2086712 -0.0094278 6.5257497
> 1 - sum(cxy1 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2%
[1] 0.96169
>
> summaryCobs(cxy2 <- cobs(x,y, "decrease", lambda = 1e-2))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", lambda = 0.01)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 -0.146 0.1468 -0.0463 0.6868 ...
$ fitted : num [1:200] 12.7 8.39 6.52 5.92 5.73 ...
$ coef : num [1:22] 12.7 5.34 3.59 2.19 2.13 ...
$ knots : num [1:20] -2.557 -1.34 -1.03 -0.901 -0.772 ...
$ k0 : int 21
$ k : int 21
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 0.01
$ icyc : int 35
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0477594 12.4997491 12.6970071 12.89427 13.34625
2 11.4687308 11.8950752 12.0811411 12.26721 12.69355
3 10.9090823 11.3113523 11.4869116 11.66247 12.06474
4 10.3688404 10.7485883 10.9143185 11.08005 11.45980
5 9.8480420 10.2067945 10.3633618 10.51993 10.87868
6 9.3467363 9.6859859 9.8340417 9.98210 10.32135
7 8.8649866 9.1861815 9.3263579 9.46653 9.78773
8 8.4028715 8.7074055 8.8403106 8.97322 9.27775
9 7.9604861 8.2496865 8.3758998 8.50211 8.79131
10 7.5379421 7.8130586 7.9331254 8.05319 8.32831
11 7.1353676 7.3975607 7.5119874 7.62641 7.88861
12 6.7529050 7.0032361 7.1124859 7.22174 7.47207
13 6.3907086 6.6301316 6.7346209 6.83911 7.07853
14 6.0489410 6.2782966 6.3783923 6.47849 6.70784
15 5.7277684 5.9477816 6.0438001 6.13982 6.35983
16 5.4273551 5.6386366 5.7308444 5.82305 6.03433
17 5.1478583 5.3509094 5.4395252 5.52814 5.73119
18 4.8894214 5.0846433 5.1698424 5.25504 5.45026
19 4.6521676 4.8398760 4.9217960 5.00372 5.19142
20 4.4361933 4.6166367 4.6953861 4.77414 4.95458
21 4.2415605 4.4149443 4.4906127 4.56628 4.73966
22 4.0682883 4.2348044 4.3074756 4.38015 4.54666
23 3.9163432 4.0762071 4.1459751 4.21574 4.37561
24 3.7856282 3.9391227 4.0061110 4.07310 4.22659
25 3.6683774 3.8159306 3.8803259 3.94472 4.09227
26 3.5214653 3.6636629 3.7257209 3.78778 3.92998
27 3.3383583 3.4756303 3.5355387 3.59545 3.73272
28 3.1192735 3.2518988 3.3097793 3.36766 3.50028
29 2.8643493 2.9925103 3.0484425 3.10437 3.23254
30 2.5736278 2.6974778 2.7515286 2.80558 2.92943
31 2.2696062 2.3893733 2.4416422 2.49391 2.61368
32 2.0718959 2.1879754 2.2386350 2.28929 2.40537
33 1.9979346 2.1107181 2.1599392 2.20916 2.32194
34 1.9710324 2.0809358 2.1288999 2.17686 2.28677
35 1.9261503 2.0335510 2.0804229 2.12729 2.23470
36 1.8645775 1.9698487 2.0157914 2.06173 2.16701
37 1.7927585 1.8961587 1.9412848 1.98641 2.08981
38 1.7116948 1.8133707 1.8577443 1.90212 2.00379
39 1.6214021 1.7214896 1.7651699 1.80885 1.90894
40 1.5242004 1.6229275 1.6660141 1.70910 1.80783
41 1.4229217 1.5205162 1.5631086 1.60570 1.70330
42 1.3194940 1.4161806 1.4583766 1.50057 1.59726
43 1.2442053 1.3402109 1.3821098 1.42401 1.52001
44 1.2075941 1.3030864 1.3447613 1.38644 1.48193
45 1.2023778 1.2975311 1.3390581 1.38059 1.47574
46 1.1914924 1.2863272 1.3277152 1.36910 1.46394
47 1.1698641 1.2642688 1.3054691 1.34667 1.44107
48 1.1375221 1.2313649 1.2723199 1.31327 1.40712
49 1.0934278 1.1866710 1.2273643 1.26806 1.36130
50 1.0300956 1.1228408 1.1633168 1.20379 1.29654
51 0.9459780 1.0382977 1.0785880 1.11888 1.21120
52 0.8492712 0.9412961 0.9814577 1.02162 1.11364
53 0.7724392 0.8643755 0.9044985 0.94462 1.03656
54 0.7154255 0.8074718 0.8476428 0.88781 0.97986
55 0.6587891 0.7510125 0.7912608 0.83151 0.92373
56 0.5994755 0.6918710 0.7321944 0.77252 0.86491
57 0.5383570 0.6309722 0.6713915 0.71181 0.80443
58 0.4898228 0.5827709 0.6233354 0.66390 0.75685
59 0.4588380 0.5521926 0.5929345 0.63368 0.72703
60 0.4438719 0.5377564 0.5787296 0.61970 0.71359
61 0.4293281 0.5239487 0.5652432 0.60654 0.70116
62 0.4110511 0.5066103 0.5483143 0.59002 0.68558
63 0.3944126 0.4911673 0.5333932 0.57562 0.67237
64 0.3857958 0.4839980 0.5268556 0.56971 0.66792
65 0.3830000 0.4829213 0.5265291 0.57014 0.67006
66 0.3802084 0.4820731 0.5265291 0.57099 0.67285
67 0.3770181 0.4810608 0.5264673 0.57187 0.67592
68 0.3616408 0.4680678 0.5145149 0.56096 0.66739
69 0.3254129 0.4343244 0.4818557 0.52939 0.63830
70 0.2683149 0.3798245 0.4284897 0.47715 0.58866
71 0.1904294 0.3047541 0.3546478 0.40454 0.51887
72 0.1179556 0.2354105 0.2866704 0.33793 0.45539
73 0.0689088 0.1897746 0.2425231 0.29527 0.41614
74 0.0432569 0.1678366 0.2222059 0.27658 0.40115
75 0.0359906 0.1645977 0.2207246 0.27685 0.40546
76 0.0301934 0.1628364 0.2207246 0.27861 0.41126
77 0.0245630 0.1611257 0.2207246 0.28032 0.41689
78 0.0191553 0.1594827 0.2207246 0.28197 0.42229
79 0.0139446 0.1578996 0.2207246 0.28355 0.42750
80 0.0088340 0.1563468 0.2207246 0.28510 0.43262
81 0.0036634 0.1547759 0.2207246 0.28667 0.43779
82 -0.0017830 0.1531211 0.2207246 0.28833 0.44323
83 -0.0077688 0.1513025 0.2207246 0.29015 0.44922
84 -0.0145948 0.1492286 0.2207246 0.29222 0.45604
85 -0.0225859 0.1468007 0.2207246 0.29465 0.46404
86 -0.0321107 0.1438739 0.2206774 0.29748 0.47347
87 -0.0445016 0.1389916 0.2190720 0.29915 0.48265
88 -0.0601227 0.1315395 0.2151851 0.29883 0.49049
89 -0.0788103 0.1215673 0.2090164 0.29647 0.49684
90 -0.1004844 0.1090993 0.2005661 0.29203 0.50162
91 -0.1251339 0.0941388 0.1898342 0.28553 0.50480
92 -0.1528032 0.0766725 0.1768206 0.27697 0.50644
93 -0.1835797 0.0566736 0.1615253 0.26638 0.50663
94 -0.2175834 0.0341058 0.1439484 0.25379 0.50548
95 -0.2549574 0.0089256 0.1240898 0.23925 0.50314
96 -0.2958592 -0.0189149 0.1019496 0.22281 0.49976
97 -0.3404537 -0.0494657 0.0775277 0.20452 0.49551
98 -0.3889062 -0.0827771 0.0508241 0.18443 0.49055
99 -0.4413769 -0.1188979 0.0218389 0.16258 0.48505
100 -0.4980173 -0.1578738 -0.0094279 0.13902 0.47916
knots :
[1] -2.557 -1.340 -1.030 -0.901 -0.772 -0.586 -0.448 -0.305 -0.092 0.054
[11] 0.163 0.329 0.481 0.606 0.722 0.859 1.065 1.244 1.837 2.573
coef :
[1] 12.697009 5.337850 3.591398 2.187733 2.133993 1.936435 1.631856
[8] 1.340650 1.340650 1.185401 0.931750 0.789326 0.598245 0.570221
[15] 0.526529 0.526529 0.526529 0.220725 0.220725 0.220725 -0.009428
[22] 46.342964
> 1 - sum(cxy2 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.2% (tiny bit better)
[1] 0.96257
>
> summaryCobs(cxy3 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 60))
List of 24
$ call : language cobs(x = x, y = y, constraint = "decrease", nknots = 60, lambda = 1e-06)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : NULL
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:200] -2.56 -2.14 -1.91 -1.81 -1.78 ...
$ y : num [1:200] 12.7 8.24 6.67 5.88 6.42 ...
$ resid : num [1:200] 0 0 0 -0.382 0.309 ...
$ fitted : num [1:200] 12.7 8.24 6.67 6.26 6.11 ...
$ coef : num [1:62] 12.7 7.69 6.09 4.35 3.73 3.73 2.74 2.57 2.57 2.25 ...
$ knots : num [1:60] -2.56 -1.81 -1.73 -1.38 -1.23 ...
$ k0 : int 61
$ k : int 61
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 488
$ lambda : num 1e-06
$ icyc : int 46
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 12.0247124 12.56890432 12.6970139 12.825123 13.36932
2 11.3797843 11.89599414 12.0175164 12.139039 12.65525
3 10.7668218 11.25721357 11.3726579 11.488102 11.97849
4 10.1860204 10.65259986 10.7624385 10.872277 11.33886
5 9.6375946 10.08219388 10.1868581 10.291522 10.73612
6 9.1217734 9.54603927 9.6459167 9.745794 10.17006
7 8.6387946 9.04418136 9.1396144 9.235048 9.64043
8 8.1888978 8.57666578 8.6679512 8.759237 9.14700
9 7.7723156 8.14353686 8.2309270 8.318317 8.68954
10 7.3892646 7.74483589 7.8285418 7.912248 8.26782
11 7.0399352 7.38059913 7.4607957 7.540992 7.88166
12 6.7244802 7.05085572 7.1276886 7.204521 7.53090
13 6.4430029 6.75562533 6.8292205 6.902816 7.21544
14 6.1955428 6.49491547 6.5653915 6.635868 6.93524
15 5.9820595 6.26871848 6.3362016 6.403685 6.69034
16 5.7696526 6.04428975 6.1089428 6.173596 6.44823
17 5.4339991 5.69759119 5.7596440 5.821697 6.08529
18 5.0454361 5.29908138 5.3587927 5.418504 5.67215
19 4.6993977 4.94405130 5.0016458 5.059240 5.30389
20 4.3963458 4.63268699 4.6883247 4.743962 4.98030
21 4.1365583 4.36504142 4.4188292 4.472617 4.70110
22 3.9202312 4.14115193 4.1931594 4.245167 4.46609
23 3.7474595 3.96103662 4.0113153 4.061594 4.27517
24 3.6182953 3.82478434 3.8733944 3.922005 4.12849
25 3.5335861 3.73343196 3.7804782 3.827524 4.02737
26 3.4937186 3.68729597 3.7328665 3.778437 3.97201
27 3.4752667 3.66292175 3.7070981 3.751274 3.93893
28 3.3043525 3.48641351 3.5292729 3.572132 3.75419
29 2.9458452 3.12249549 3.1640812 3.205667 3.38232
30 2.4899112 2.66132542 2.7016785 2.742031 2.91345
31 2.3652956 2.53186083 2.5710724 2.610284 2.77685
32 2.2382402 2.40029503 2.4384448 2.476594 2.63865
33 2.0486975 2.20653724 2.2436947 2.280852 2.43869
34 2.0511798 2.20522276 2.2414864 2.277750 2.43179
35 2.0553528 2.20601792 2.2414864 2.276955 2.42762
36 2.0385642 2.18623332 2.2209965 2.255760 2.40343
37 1.8391470 1.98414706 2.0182819 2.052417 2.19742
38 1.6312788 1.77395114 1.8075380 1.841125 1.98380
39 1.5314449 1.67192652 1.7049976 1.738069 1.87855
40 1.5208780 1.65927041 1.6918497 1.724429 1.86282
41 1.4986364 1.63513027 1.6672626 1.699395 1.83589
42 1.4498027 1.58470514 1.6164629 1.648221 1.78312
43 1.2247043 1.35830771 1.3897596 1.421211 1.55481
44 1.1772885 1.30980813 1.3410049 1.372202 1.50472
45 1.1781750 1.30997706 1.3410049 1.372033 1.50383
46 1.1786125 1.31005757 1.3410014 1.371945 1.50339
47 1.1644262 1.29555858 1.3264288 1.357299 1.48843
48 1.1223208 1.25286982 1.2836027 1.314336 1.44488
49 1.0583227 1.18805529 1.2185960 1.249137 1.37887
50 1.0360396 1.16504088 1.1954094 1.225778 1.35478
51 1.0366880 1.16516444 1.1954094 1.225654 1.35413
52 0.9728290 1.10089058 1.1310379 1.161185 1.28925
53 0.6458992 0.77387319 0.8039998 0.834127 0.96210
54 0.6278378 0.75589463 0.7860408 0.816187 0.94424
55 0.6233664 0.75144260 0.7815933 0.811744 0.93982
56 0.6203139 0.74853170 0.7787158 0.808900 0.93712
57 0.4831205 0.61171664 0.6419898 0.672263 0.80086
58 0.4152141 0.54435194 0.5747526 0.605153 0.73429
59 0.4143942 0.54419570 0.5747526 0.605309 0.73511
60 0.4133407 0.54399495 0.5747526 0.605510 0.73616
61 0.3912541 0.52305164 0.5540784 0.585105 0.71690
62 0.3615872 0.49479624 0.5261553 0.557514 0.69072
63 0.3595156 0.49440150 0.5261553 0.557909 0.69279
64 0.3572502 0.49396981 0.5261553 0.558341 0.69506
65 0.3545874 0.49346241 0.5261553 0.558848 0.69772
66 0.3515435 0.49288238 0.5261553 0.559428 0.70077
67 0.3482098 0.49224713 0.5261553 0.560063 0.70410
68 0.3447026 0.49157882 0.5261553 0.560732 0.70761
69 0.3265062 0.47651151 0.5118246 0.547138 0.69714
70 0.2579257 0.41132297 0.4474346 0.483546 0.63694
71 0.2081857 0.36515737 0.4021105 0.439064 0.59604
72 0.1349572 0.29569526 0.3335350 0.371375 0.53211
73 0.0020438 0.16674762 0.2055209 0.244294 0.40900
74 -0.0243664 0.14460810 0.1843868 0.224166 0.39314
75 -0.0362635 0.13720915 0.1780468 0.218884 0.39236
76 -0.0421115 0.13609478 0.1780468 0.219999 0.39820
77 -0.0482083 0.13493301 0.1780468 0.221161 0.40430
78 -0.0546034 0.13371440 0.1780468 0.222379 0.41070
79 -0.0610386 0.13248816 0.1780468 0.223605 0.41713
80 -0.0674722 0.13126221 0.1780468 0.224831 0.42357
81 -0.0740291 0.13001276 0.1780468 0.226081 0.43012
82 -0.0809567 0.12869267 0.1780468 0.227401 0.43705
83 -0.0885308 0.12724941 0.1780468 0.228844 0.44462
84 -0.0966886 0.12569491 0.1780468 0.230399 0.45278
85 -0.1053882 0.12403716 0.1780468 0.232056 0.46148
86 -0.1147206 0.12225885 0.1780468 0.233835 0.47081
87 -0.1248842 0.12032213 0.1780468 0.235771 0.48098
88 -0.1360096 0.11820215 0.1780468 0.237891 0.49210
89 -0.1480747 0.11590310 0.1780468 0.240190 0.50417
90 -0.1611528 0.11337745 0.1780053 0.242633 0.51716
91 -0.1772967 0.10838384 0.1756366 0.242889 0.52857
92 -0.1976403 0.09964452 0.1696291 0.239614 0.53690
93 -0.2221958 0.08715720 0.1599828 0.232808 0.54216
94 -0.2510614 0.07090314 0.1466976 0.222492 0.54446
95 -0.2844042 0.05085051 0.1297736 0.208697 0.54395
96 -0.3224450 0.02695723 0.1092109 0.191465 0.54087
97 -0.3654434 -0.00082617 0.0850093 0.170845 0.53546
98 -0.4136843 -0.03255395 0.0571689 0.146892 0.52802
99 -0.4674640 -0.06828261 0.0256897 0.119662 0.51884
100 -0.5270786 -0.10806856 -0.0094284 0.089212 0.50822
knots :
[1] -2.557 -1.812 -1.726 -1.384 -1.233 -1.082 -1.046 -1.009 -0.932 -0.902
[11] -0.877 -0.838 -0.813 -0.765 -0.707 -0.665 -0.568 -0.498 -0.460 -0.413
[21] -0.347 -0.333 -0.299 -0.274 -0.226 -0.089 -0.024 -0.011 0.063 0.094
[31] 0.118 0.136 0.231 0.285 0.328 0.392 0.460 0.473 0.517 0.551
[41] 0.602 0.623 0.692 0.715 0.742 0.787 0.812 0.892 0.934 0.988
[51] 1.070 1.162 1.178 1.276 1.402 1.655 1.877 1.988 2.047 2.573
coef :
[1] 12.6970155 7.6878537 6.0937652 4.3540061 3.7259911 3.7259911
[7] 2.7408131 2.5727608 2.5727608 2.2478639 2.2414864 2.2414864
[13] 2.2414864 2.2414864 2.2414864 1.9875889 1.6964374 1.6964374
[19] 1.6623718 1.6623718 1.3410049 1.3410049 1.3410049 1.3410049
[25] 1.3410049 1.3410049 1.1954094 1.1954094 1.1954094 1.1954094
[31] 0.9829296 0.8091342 0.7815933 0.7815933 0.7815933 0.5747526
[37] 0.5747526 0.5747526 0.5747526 0.5747526 0.5261553 0.5261553
[43] 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553 0.5261553
[49] 0.5261553 0.5261553 0.4273578 0.3741431 0.2060752 0.1780468
[55] 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468 0.1780468
[61] -0.0094285 432.6957871
> 1 - sum(cxy3 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.36%
[1] 0.96502
> showProc.time()
Time (user system elapsed): 0.26 0.015 0.277
>
> cpuTime(cxy4 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 100))# ~ 3 sec.
Time elapsed: 0.281
> 1 - sum(cxy4 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.443%
[1] 0.96603
>
> cpuTime(cxy5 <- cobs(x,y, "decrease", lambda = 1e-6, nknots = 150))# ~ 8.7 sec.
Time elapsed: 0.273
> 1 - sum(cxy5 $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 98.4396%
[1] 0.96835
> showProc.time()
Time (user system elapsed): 0.575 0.008 2.819
>
>
> ## regularly spaced x :
> X <- seq(-1,1, len = 201)
> xx <- c(seq(-1.1, -1, len = 11), X,
+ seq( 1, 1.1, len = 11))
> y <- (fx <- exp(-X)) + rt(201,4)/4
> summaryCobs(cXy <- cobs(X,y, "decrease"))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
List of 24
$ call : language cobs(x = X, y = y, constraint = "decrease")
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "decrease"
$ ic : chr "AIC"
$ pointwise : NULL
$ select.knots : logi TRUE
$ select.lambda: logi FALSE
$ x : num [1:201] -1 -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92 -0.91 ...
$ y : num [1:201] 2.67 2.77 3.46 3.14 1.79 ...
$ resid : num [1:201] 0 0.125 0.84 0.555 -0.77 ...
$ fitted : num [1:201] 2.67 2.64 2.62 2.59 2.56 ...
$ coef : num [1:4] 2.672 1.556 0.7 0.356
$ knots : num [1:3] -1 -0.2 1
$ k0 : num 4
$ k : num 4
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 100
$ lambda : num 0
$ icyc : int 9
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 2.46750 2.55064 2.67153 2.79242 2.87556
2 2.42251 2.50122 2.61568 2.73013 2.80884
3 2.37783 2.45240 2.56081 2.66923 2.74379
4 2.33345 2.40414 2.50694 2.60973 2.68043
5 2.28933 2.35645 2.45404 2.55164 2.61876
6 2.24548 2.30932 2.40214 2.49496 2.55879
7 2.20189 2.26274 2.35122 2.43970 2.50055
8 2.15855 2.21672 2.30129 2.38586 2.44402
9 2.11547 2.17124 2.25234 2.33344 2.38922
10 2.07265 2.12633 2.20438 2.28244 2.33611
11 2.03013 2.08199 2.15741 2.23283 2.28470
12 1.98791 2.03824 2.11142 2.18461 2.23494
13 1.94605 1.99510 2.06642 2.13775 2.18680
14 1.90459 1.95260 2.02241 2.09222 2.14023
15 1.86359 1.91078 1.97938 2.04799 2.09517
16 1.82311 1.86966 1.93734 2.00502 2.05157
17 1.78322 1.82929 1.89629 1.96328 2.00936
18 1.74397 1.78971 1.85622 1.92273 1.96847
19 1.70544 1.75096 1.81714 1.88332 1.92883
20 1.66769 1.71307 1.77904 1.84502 1.89039
21 1.63079 1.67608 1.74193 1.80779 1.85308
22 1.59478 1.64002 1.70581 1.77160 1.81684
23 1.55972 1.60493 1.67067 1.73642 1.78163
24 1.52564 1.57083 1.63653 1.70222 1.74741
25 1.49260 1.53773 1.60336 1.66899 1.71412
26 1.46062 1.50567 1.57118 1.63670 1.68175
27 1.42972 1.47466 1.53999 1.60533 1.65026
28 1.39994 1.44470 1.50979 1.57488 1.61964
29 1.37128 1.41581 1.48057 1.54533 1.58987
30 1.34375 1.38800 1.45234 1.51668 1.56093
31 1.31736 1.36126 1.42510 1.48893 1.53283
32 1.29211 1.33560 1.39884 1.46207 1.50556
33 1.26800 1.31101 1.37357 1.43612 1.47914
34 1.24500 1.28749 1.34928 1.41107 1.45356
35 1.22310 1.26502 1.32598 1.38694 1.42886
36 1.20228 1.24360 1.30367 1.36374 1.40505
37 1.18250 1.22319 1.28234 1.34150 1.38218
38 1.16372 1.20377 1.26200 1.32023 1.36028
39 1.14589 1.18532 1.24265 1.29998 1.33941
40 1.12894 1.16779 1.22428 1.28077 1.31962
41 1.11271 1.15106 1.20683 1.26259 1.30094
42 1.09639 1.13439 1.18963 1.24488 1.28287
43 1.07982 1.11760 1.17253 1.22747 1.26525
44 1.06303 1.10072 1.15553 1.21034 1.24803
45 1.04607 1.08378 1.13862 1.19346 1.23117
46 1.02898 1.06681 1.12181 1.17681 1.21463
47 1.01180 1.04982 1.10509 1.16037 1.19838
48 0.99458 1.03284 1.08847 1.14411 1.18237
49 0.97734 1.01589 1.07195 1.12801 1.16656
50 0.96011 0.99899 1.05552 1.11205 1.15092
51 0.94294 0.98216 1.03919 1.09621 1.13543
52 0.92585 0.96541 1.02295 1.08049 1.12005
53 0.90885 0.94877 1.00681 1.06485 1.10477
54 0.89197 0.93223 0.99076 1.04930 1.08956
55 0.87523 0.91581 0.97482 1.03382 1.07440
56 0.85865 0.89952 0.95896 1.01840 1.05928
57 0.84223 0.88337 0.94321 1.00304 1.04419
58 0.82598 0.86736 0.92755 0.98773 1.02911
59 0.80991 0.85150 0.91198 0.97246 1.01405
60 0.79403 0.83579 0.89651 0.95723 0.99899
61 0.77834 0.82023 0.88114 0.94205 0.98394
62 0.76284 0.80482 0.86586 0.92690 0.96888
63 0.74753 0.78956 0.85068 0.91180 0.95383
64 0.73241 0.77446 0.83559 0.89673 0.93878
65 0.71747 0.75950 0.82060 0.88171 0.92374
66 0.70271 0.74468 0.80571 0.86674 0.90871
67 0.68812 0.73001 0.79091 0.85182 0.89371
68 0.67368 0.71546 0.77621 0.83696 0.87874
69 0.65939 0.70104 0.76161 0.82217 0.86382
70 0.64523 0.68674 0.74710 0.80745 0.84896
71 0.63118 0.67254 0.73268 0.79282 0.83419
72 0.61722 0.65844 0.71836 0.77829 0.81951
73 0.60333 0.64441 0.70414 0.76388 0.80495
74 0.58948 0.63045 0.69002 0.74958 0.79055
75 0.57565 0.61654 0.67599 0.73544 0.77632
76 0.56181 0.60266 0.66205 0.72145 0.76230
77 0.54792 0.58879 0.64821 0.70764 0.74851
78 0.53395 0.57491 0.63447 0.69403 0.73500
79 0.51986 0.56100 0.62083 0.68065 0.72179
80 0.50563 0.54705 0.60728 0.66750 0.70892
81 0.49121 0.53302 0.59382 0.65462 0.69643
82 0.47657 0.51891 0.58046 0.64202 0.68435
83 0.46169 0.50468 0.56720 0.62972 0.67271
84 0.44652 0.49033 0.55403 0.61774 0.66155
85 0.43105 0.47584 0.54096 0.60609 0.65087
86 0.41526 0.46119 0.52799 0.59478 0.64072
87 0.39912 0.44638 0.51511 0.58383 0.63109
88 0.38264 0.43141 0.50233 0.57324 0.62202
89 0.36579 0.41626 0.48964 0.56302 0.61349
90 0.34858 0.40093 0.47705 0.55317 0.60552
91 0.33101 0.38542 0.46455 0.54368 0.59810
92 0.31307 0.36975 0.45215 0.53456 0.59123
93 0.29478 0.35390 0.43985 0.52580 0.58492
94 0.27615 0.33788 0.42764 0.51741 0.57914
95 0.25717 0.32170 0.41553 0.50936 0.57389
96 0.23787 0.30536 0.40352 0.50167 0.56917
97 0.21824 0.28888 0.39160 0.49431 0.56495
98 0.19830 0.27225 0.37977 0.48730 0.56125
99 0.17806 0.25547 0.36804 0.48062 0.55803
100 0.15752 0.23857 0.35641 0.47426 0.55531
knots :
[1] -1.0 -0.2 1.0
coef :
[1] 2.67153 1.55592 0.70045 0.35641
> 1 - sum(cXy $ resid ^ 2) / sum((y - mean(y))^2) # R^2 = 77.2%
[1] 0.77644
> showProc.time()
Time (user system elapsed): 0.169 0.003 0.174
>
> (cXy.9 <- cobs(X,y, "decrease", tau = 0.9))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.9)
{tau=0.9}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> (cXy.1 <- cobs(X,y, "decrease", tau = 0.1))
qbsks2():
Performing general knot selection ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.1)
{tau=0.1}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, 0.6, 1.0
> (cXy.99<- cobs(X,y, "decrease", tau = 0.99))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.99)
{tau=0.99}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:3]: -1.0, -0.2, 1.0
> (cXy.01<- cobs(X,y, "decrease", tau = 0.01))
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
COBS regression spline (degree = 2) from call:
cobs(x = X, y = y, constraint = "decrease", tau = 0.01)
{tau=0.01}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:5]: -1.0, -0.6, -0.2, 0.2, 1.0
> plot(X,y, xlim = range(xx),
+ main = "cobs(*, \"decrease\"), N=201, tau = 50% (Med.), 1,10, 90,99%")
> lines(predict(cXy, xx), col = 2)
> lines(predict(cXy.1, xx), col = 3)
> lines(predict(cXy.9, xx), col = 3)
> lines(predict(cXy.01, xx), col = 4)
> lines(predict(cXy.99, xx), col = 4)
>
> showProc.time()
Time (user system elapsed): 0.81 0.001 0.979
>
> ## Interpolation
> cpuTime(cXyI <- cobs(X,y, "decrease", knots = unique(X)))
qbsks2():
Performing general knot selection ...
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cpuTime ... cobs -> qbsks2 -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
In addition: Warning message:
In cobs(X, y, "decrease", knots = unique(X)) :
The number of knots can't be equal to the number of unique x for degree = 2.
'cobs' has automatically deleted the middle knot.
Timing stopped at: 1.843 0.024 7.219
Execution halted
Running the tests in ‘tests/roof.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> data(USArmyRoofs)
> attach(USArmyRoofs)#-> "age" and "fci"
>
> if(!dev.interactive(orNone=TRUE)) pdf("roof.pdf", width=10)
>
> ## Compute the quadratic median smoothing B-spline with SIC
> ## chosen lambda
> a50 <- cobs(age,fci,constraint = "decrease",lambda = -1,nknots = 10,
+ degree = 2,pointwise = rbind(c(0,0,100)),
+ trace = 2)# trace > 1 : more tracing
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
fieq=TRUE -> Tnobs = 184, n0 = 29, |ptConstr| = 2
Error in drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda, :
The problem is degenerate for the range of lambda specified.
Calls: cobs -> drqssbc2
In addition: Warning message:
In min(sol1["k", i.keep]) : no non-missing arguments to min; returning Inf
Execution halted
Running the tests in ‘tests/wind.R’ failed.
Complete output:
> suppressMessages(library(cobs))
>
> source(system.file("util.R", package = "cobs"))
> (doExtra <- doExtras())
[1] FALSE
> source(system.file("test-tools-1.R", package="Matrix", mustWork=TRUE))
Loading required package: tools
> showProc.time() # timing here (to be faster by default)
Time (user system elapsed): 0.001 0.002 0.032
>
> data(DublinWind)
> attach(DublinWind)##-> speed & day (instead of "wind.x" & "DUB.")
> iday <- sort.list(day)
>
> if(!dev.interactive(orNone=TRUE)) pdf("wind.pdf", width=10)
>
> stopifnot(identical(day,c(rep(c(rep(1:365,3),1:366),4),
+ rep(1:365,2))))
> co50.1 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 1)
> co50.2 <- cobs(day, speed, constraint= "periodic", tau= .5, lambda= 2.2,
+ degree = 2)
>
> showProc.time()
Time (user system elapsed): 0.722 0.048 2.589
>
> plot(day,speed, pch = ".", col = "gray20")
> lines(day[iday], fitted(co50.1)[iday], col="orange", lwd = 2)
> lines(day[iday], fitted(co50.2)[iday], col="sky blue", lwd = 2)
> rug(knots(co50.1), col=3, lwd=2)
>
> nknots <- 13
>
>
> if(doExtra) {
+ ## Compute the quadratic median smoothing B-spline using SIC
+ ## lambda selection
+ co.o50 <-
+ cobs(day, speed, knots.add = TRUE, constraint="periodic", nknots = nknots,
+ tau = .5, lambda = -1, method = "uniform")
+ summary(co.o50) # [does print]
+
+ showProc.time()
+
+ op <- par(mfrow = c(3,1), mgp = c(1.5, 0.6,0), mar=.1 + c(3,3:1))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o",
+ col=2, log = "x", main = "co.o50: periodic"))
+ with(co.o50, plot(pp.sic ~ pp.lambda, type ="o", ylim = robrng(pp.sic),
+ col=2, log = "x", main = "co.o50: periodic"))
+ of <- 0.64430538125795
+ with(co.o50, plot(pp.sic - of ~ pp.lambda, type ="o", ylim = c(6e-15, 8e-15),
+ ylab = paste("sic -",formatC(of, dig=14, small.m = "'")),
+ col=2, log = "x", main = "co.o50: periodic"))
+ par(op)
+ }
>
> showProc.time()
Time (user system elapsed): 0.049 0.003 0.144
>
> ## cobs99: Since SIC chooses a lambda that corresponds to the smoothest
> ## possible fit, rerun cobs with a larger lstart value
> ## (lstart <- log(.Machine$double.xmax)^3) # 3.57 e9
> ##
> co.o50. <-
+ cobs(day,speed, knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
The algorithm has converged. You might
plot() the returned object (which plots 'sic' against 'lambda')
to see if you have found the global minimum of the information criterion
so that you can determine if you need to adjust any or all of
'lambda.lo', 'lambda.hi' and 'lambda.length' and refit the model.
> summary(co.o50.)
COBS smoothing spline (degree = 2) from call:
cobs(x = day, y = speed, constraint = "periodic", nknots = 10, method = "quantile", tau = 0.5, lambda = -1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 7 from {14,13,11,8,7,30}
x$knots[1:10]: 0.999635, 41.000000, 82.000000, ... , 366.000365
lambda = 101002.6, selected via SIC, out of 25 ones.
coef[1:12]: 1.121550e+01, 1.139573e+01, 1.089025e+01, 9.954427e+00, 8.148158e+00, ... , 5.373106e-04
R^2 = 8.22% ; empirical tau (over all): 3287/6574 = 0.5 (target tau= 0.5)
> summary(pc.5 <- predict(co.o50., interval = "both"))
z fit cb.lo cb.up
Min. : 0.9996 Min. : 7.212 Min. : 6.351 Min. : 7.951
1st Qu.: 92.2498 1st Qu.: 7.790 1st Qu.: 7.000 1st Qu.: 8.600
Median :183.5000 Median : 9.436 Median : 8.555 Median :10.326
Mean :183.5000 Mean : 9.314 Mean : 8.388 Mean :10.241
3rd Qu.:274.7502 3rd Qu.:10.798 3rd Qu.: 9.716 3rd Qu.:11.787
Max. :366.0004 Max. :11.290 Max. :10.347 Max. :13.416
ci.lo ci.up
Min. : 6.782 Min. : 7.598
1st Qu.: 7.370 1st Qu.: 8.213
Median : 8.974 Median : 9.901
Mean : 8.830 Mean : 9.798
3rd Qu.:10.197 3rd Qu.:11.311
Max. :10.797 Max. :12.366
>
> showProc.time()
Time (user system elapsed): 2.897 0.029 5.435
>
> if(doExtra) { ## + repeat.delete.add
+ co.o50.. <- cobs(day,speed, knots.add = TRUE, repeat.delete.add=TRUE,
+ constraint = "periodic", nknots = 10,
+ tau = .5, lambda = -1, method = "quantile")
+ summary(co.o50..)
+ showProc.time()
+ }
>
> co.o9 <- ## Compute the .9 quantile smoothing B-spline
+ cobs(day,speed,knots.add = TRUE, constraint = "periodic", nknots = 10,
+ tau = .9,lambda = -1, method = "uniform")
Searching for optimal lambda. This may take a while.
While you are waiting, here is something you can consider
to speed up the process:
(a) Use a smaller number of knots;
(b) Set lambda==0 to exclude the penalty term;
(c) Use a coarser grid by reducing the argument
'lambda.length' from the default value of 25.
Error in x %*% coefficients : NA/NaN/Inf in foreign function call (arg 2)
Calls: cobs -> drqssbc2 -> rq.fit.sfnc -> %*% -> %*%
Execution halted
Flavor: r-devel-linux-x86_64-fedora-clang
Current CRAN status: ERROR: 2, NOTE: 6, OK: 5
Version: 1.1-4
Check: re-building of vignette outputs
Result: WARN
Error(s) in re-building vignettes:
--- re-building ‘AC_Liouville.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-rACsimp-1.png
288x288 pixels, 8 bits/pixel, 196 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7776 bytes
Input file size = 8454 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6976
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6976
Output IDAT size = 6976 bytes (800 bytes decrease)
Output file size = 7054 bytes (1400 bytes = 16.56% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-Liouville-1.png
288x288 pixels, 8 bits/pixel, 198 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7699 bytes
Input file size = 8383 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6969
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6969
Output IDAT size = 6969 bytes (730 bytes decrease)
Output file size = 7047 bytes (1336 bytes = 15.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-ACLiou-1.png
288x288 pixels, 8 bits/pixel, 199 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7802 bytes
Input file size = 8489 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7033
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7033
Output IDAT size = 7033 bytes (769 bytes decrease)
Output file size = 7111 bytes (1378 bytes = 16.23% decrease)
--- finished re-building ‘AC_Liouville.Rmd’
--- re-building ‘AR_Clayton.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/AR_Clayton_files/figure-html/unnamed-chunk-7-1.png
576x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 58750 bytes
Input file size = 58912 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 50100
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 50100
Output IDAT size = 50100 bytes (8650 bytes decrease)
Output file size = 50178 bytes (8734 bytes = 14.83% decrease)
--- finished re-building ‘AR_Clayton.Rmd’
--- re-building ‘GIG.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-4-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 30633 bytes
Input file size = 30747 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26518
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26518
Output IDAT size = 26518 bytes (4115 bytes decrease)
Output file size = 26596 bytes (4151 bytes = 13.50% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-6-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 371877 bytes
Input file size = 372495 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 277143
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 277143
Output IDAT size = 277143 bytes (94734 bytes decrease)
Output file size = 277221 bytes (95274 bytes = 25.58% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-10-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 95974 bytes
Input file size = 96184 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 77702
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 77702
Output IDAT size = 77702 bytes (18272 bytes decrease)
Output file size = 77780 bytes (18404 bytes = 19.13% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-11-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 52469 bytes
Input file size = 52619 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 46680
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 46680
Output IDAT size = 46680 bytes (5789 bytes decrease)
Output file size = 46758 bytes (5861 bytes = 11.14% decrease)
--- finished re-building ‘GIG.Rmd’
--- re-building ‘HAXC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-5-1.png
288x288 pixels, 8 bits/pixel, 204 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10349 bytes
Input file size = 11063 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9726
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9726
Output IDAT size = 9726 bytes (623 bytes decrease)
Output file size = 9804 bytes (1259 bytes = 11.38% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-6-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9063 bytes
Input file size = 9774 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 8364
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 8364
Output IDAT size = 8364 bytes (699 bytes decrease)
Output file size = 8442 bytes (1332 bytes = 13.63% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-7-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10512 bytes
Input file size = 11223 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9784
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9783
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9783
Output IDAT size = 9783 bytes (729 bytes decrease)
Output file size = 9861 bytes (1362 bytes = 12.14% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-8-1.png
288x288 pixels, 8 bits/pixel, 207 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9924 bytes
Input file size = 10647 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9203
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9203
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9203
Output IDAT size = 9203 bytes (721 bytes decrease)
Output file size = 9281 bytes (1366 bytes = 12.83% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-9-1.png
288x288 pixels, 8 bits/pixel, 205 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9679 bytes
Input file size = 10396 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9018
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
Output IDAT size = 9007 bytes (672 bytes decrease)
Output file size = 9085 bytes (1311 bytes = 12.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-10-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10157 bytes
Input file size = 10877 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9400
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
Output IDAT size = 9391 bytes (766 bytes decrease)
Output file size = 9469 bytes (1408 bytes = 12.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-11-1.png
288x288 pixels, 8 bits/pixel, 202 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10828 bytes
Input file size = 11536 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 10091
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10074
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10074
Output IDAT size = 10074 bytes (754 bytes decrease)
Output file size = 10152 bytes (1384 bytes = 12.00% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-12-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10954 bytes
Input file size = 11674 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 10178
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10174
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10174
Output IDAT size = 10174 bytes (780 bytes decrease)
Output file size = 10252 bytes (1422 bytes = 12.18% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-13-1.png
288x288 pixels, 8 bits/pixel, 207 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10163 bytes
Input file size = 10886 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9466
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9466
Output IDAT size = 9466 bytes (697 bytes decrease)
Output file size = 9544 bytes (1342 bytes = 12.33% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-14-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10181 bytes
Input file size = 10892 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9492
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9476
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9476
Output IDAT size = 9476 bytes (705 bytes decrease)
Output file size = 9554 bytes (1338 bytes = 12.28% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-15-1.png
288x288 pixels, 8 bits/pixel, 205 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9679 bytes
Input file size = 10396 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9018
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
Output IDAT size = 9007 bytes (672 bytes decrease)
Output file size = 9085 bytes (1311 bytes = 12.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-16-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10157 bytes
Input file size = 10877 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9400
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
Output IDAT size = 9391 bytes (766 bytes decrease)
Output file size = 9469 bytes (1408 bytes = 12.94% decrease)
--- finished re-building ‘HAXC.Rmd’
--- re-building ‘NALC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-12-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 48687 bytes
Input file size = 48825 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 47679
zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 47159
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 47159
Output IDAT size = 47159 bytes (1528 bytes decrease)
Output file size = 47237 bytes (1588 bytes = 3.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-12-2.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31122 bytes
Input file size = 31236 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28096
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28096
Output IDAT size = 28096 bytes (3026 bytes decrease)
Output file size = 28174 bytes (3062 bytes = 9.80% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-13-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 34828 bytes
Input file size = 34954 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 32747
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 32747
Output IDAT size = 32747 bytes (2081 bytes decrease)
Output file size = 32825 bytes (2129 bytes = 6.09% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-13-2.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 35630 bytes
Input file size = 35756 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 32399
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 32399
Output IDAT size = 32399 bytes (3231 bytes decrease)
Output file size = 32477 bytes (3279 bytes = 9.17% decrease)
--- finished re-building ‘NALC.Rmd’
--- re-building ‘copula_GARCH.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-3-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 62204 bytes
Input file size = 62366 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 59134
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 59134
Output IDAT size = 59134 bytes (3070 bytes decrease)
Output file size = 59212 bytes (3154 bytes = 5.06% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-5-1.png
576x576 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 20748 bytes
Input file size = 21630 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 19100
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 18890
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 18890
Output IDAT size = 18890 bytes (1858 bytes decrease)
Output file size = 18968 bytes (2662 bytes = 12.31% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-7-1.png
576x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 61628 bytes
Input file size = 61790 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 60748
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 58413
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 58413
Output IDAT size = 58413 bytes (3215 bytes decrease)
Output file size = 58491 bytes (3299 bytes = 5.34% decrease)
--- finished re-building ‘copula_GARCH.Rmd’
--- re-building ‘dNAC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/dNAC_files/figure-html/wire+level-1.png
288x288 pixels, 8 bits/pixel, 255 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17088 bytes
Input file size = 17967 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 15997
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 15724
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 15724
Output IDAT size = 15724 bytes (1364 bytes decrease)
Output file size = 15802 bytes (2165 bytes = 12.05% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/dNAC_files/figure-html/wire+level-2.png
288x288 pixels, 8 bits/pixel, 255 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 12058 bytes
Input file size = 12925 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 11518
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 11518
Output IDAT size = 11518 bytes (540 bytes decrease)
Output file size = 11596 bytes (1329 bytes = 10.28% decrease)
--- finished re-building ‘dNAC.Rmd’
--- re-building ‘empiricial_copulas.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3976 bytes
Input file size = 4684 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3502
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3502
Output IDAT size = 3502 bytes (474 bytes decrease)
Output file size = 3580 bytes (1104 bytes = 23.57% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-2.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3877 bytes
Input file size = 4585 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3418
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3418
Output IDAT size = 3418 bytes (459 bytes decrease)
Output file size = 3496 bytes (1089 bytes = 23.75% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-3.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3940 bytes
Input file size = 4648 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3449
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3449
Output IDAT size = 3449 bytes (491 bytes decrease)
Output file size = 3527 bytes (1121 bytes = 24.12% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-4.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3883 bytes
Input file size = 4591 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3406
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3406
Output IDAT size = 3406 bytes (477 bytes decrease)
Output file size = 3484 bytes (1107 bytes = 24.11% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-mass-1.png
288x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 10251 bytes
Input file size = 10341 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7064
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7064
Output IDAT size = 7064 bytes (3187 bytes decrease)
Output file size = 7142 bytes (3199 bytes = 30.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-mass-2.png
288x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 7637 bytes
Input file size = 7715 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6019
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6019
Output IDAT size = 6019 bytes (1618 bytes decrease)
Output file size = 6097 bytes (1618 bytes = 20.97% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/wireframes-1.png
288x288 pixels, 8 bits/pixel, 219 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17773 bytes
Input file size = 18544 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16959
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16959
Output IDAT size = 16959 bytes (814 bytes decrease)
Output file size = 17037 bytes (1507 bytes = 8.13% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/wireframes-2.png
288x288 pixels, 8 bits/pixel, 220 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17712 bytes
Input file size = 18486 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16901
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16901
Output IDAT size = 16901 bytes (811 bytes decrease)
Output file size = 16979 bytes (1507 bytes = 8.15% decrease)
--- finished re-building ‘empiricial_copulas.Rmd’
--- re-building ‘logL_visualization.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-6-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31975 bytes
Input file size = 32089 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26245
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26245
Output IDAT size = 26245 bytes (5730 bytes decrease)
Output file size = 26323 bytes (5766 bytes = 17.97% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-8-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 28591 bytes
Input file size = 28705 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24027
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24027
Output IDAT size = 24027 bytes (4564 bytes decrease)
Output file size = 24105 bytes (4600 bytes = 16.03% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-11-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31104 bytes
Input file size = 31218 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24067
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24067
Output IDAT size = 24067 bytes (7037 bytes decrease)
Output file size = 24145 bytes (7073 bytes = 22.66% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-15-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31402 bytes
Input file size = 31516 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 25526
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 25526
Output IDAT size = 25526 bytes (5876 bytes decrease)
Output file size = 25604 bytes (5912 bytes = 18.76% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-19-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 28772 bytes
Input file size = 28886 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22690
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22690
Output IDAT size = 22690 bytes (6082 bytes decrease)
Output file size = 22768 bytes (6118 bytes = 21.18% decrease)
--- finished re-building ‘logL_visualization.Rmd’
--- re-building ‘qrng.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/indep-copula-1.png
576x288 pixels, 8 bits/pixel, 232 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 37006 bytes
Input file size = 37840 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 34692
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 34170
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 34170
Output IDAT size = 34170 bytes (2836 bytes decrease)
Output file size = 34248 bytes (3592 bytes = 9.49% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-clayton-1.png
576x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5788 bytes
Input file size = 6454 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4981
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4981
Output IDAT size = 4981 bytes (807 bytes decrease)
Output file size = 5059 bytes (1395 bytes = 21.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/t-Cop-fig-1.png
576x288 pixels, 8 bits/pixel, 199 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5920 bytes
Input file size = 6607 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5040
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5040
Output IDAT size = 5040 bytes (880 bytes decrease)
Output file size = 5118 bytes (1489 bytes = 22.54% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-MO-1.png
576x288 pixels, 8 bits/pixel, 194 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5831 bytes
Input file size = 6503 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5066
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5066
Output IDAT size = 5066 bytes (765 bytes decrease)
Output file size = 5144 bytes (1359 bytes = 20.90% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-t3d-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 29019 bytes
Input file size = 29913 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 27790
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 27581
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 27581
Output IDAT size = 27581 bytes (1438 bytes decrease)
Output file size = 27659 bytes (2254 bytes = 7.54% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl-q-t3d-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 29925 bytes
Input file size = 30819 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28713
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 28521
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 28521
Output IDAT size = 28521 bytes (1404 bytes decrease)
Output file size = 28599 bytes (2220 bytes = 7.20% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/clouds.t3d-1.png
576x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 23769 bytes
Input file size = 24651 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22605
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 22351
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 22351
Output IDAT size = 22351 bytes (1418 bytes decrease)
Output file size = 22429 bytes (2222 bytes = 9.01% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl.col-CMD-1.png
576x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 63931 bytes
Input file size = 64093 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41402
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41402
Output IDAT size = 41402 bytes (22529 bytes decrease)
Output file size = 41480 bytes (22613 bytes = 35.28% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl.col-MO-1.png
576x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 51058 bytes
Input file size = 51208 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41141
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41141
Output IDAT size = 41141 bytes (9917 bytes decrease)
Output file size = 41219 bytes (9989 bytes = 19.51% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-sim-1.png
336x336 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 25556 bytes
Input file size = 25670 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 17946
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 17946
Output IDAT size = 17946 bytes (7610 bytes decrease)
Output file size = 18024 bytes (7646 bytes = 29.79% decrease)
--- finished re-building ‘qrng.Rmd’
--- re-building ‘wild_animals.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-1.png
288x288 pixels, 8 bits/pixel, 233 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 2808 bytes
Input file size = 3597 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2480
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2480
Output IDAT size = 2480 bytes (328 bytes decrease)
Output file size = 2558 bytes (1039 bytes = 28.89% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-2.png
288x288 pixels, 8 bits/pixel, 243 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 2807 bytes
Input file size = 3626 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2468
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2468
Output IDAT size = 2468 bytes (339 bytes decrease)
Output file size = 2546 bytes (1080 bytes = 29.78% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-3.png
288x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5186 bytes
Input file size = 5852 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4606
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4606
Output IDAT size = 4606 bytes (580 bytes decrease)
Output file size = 4684 bytes (1168 bytes = 19.96% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-2-1.png
288x288 pixels, 8 bits/pixel, 248 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 14931 bytes
Input file size = 15777 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 14036
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 13451
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 13451
Output IDAT size = 13451 bytes (1480 bytes decrease)
Output file size = 13529 bytes (2248 bytes = 14.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/plot.margins-1.png
288x288 pixels, 8 bits/pixel, 249 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3365 bytes
Input file size = 4202 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3147
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3147
Output IDAT size = 3147 bytes (218 bytes decrease)
Output file size = 3225 bytes (977 bytes = 23.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/plot.U-1.png
288x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 4475 bytes
Input file size = 5141 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3998
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3998
Output IDAT size = 3998 bytes (477 bytes decrease)
Output file size = 4076 bytes (1065 bytes = 20.72% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/splom.U-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 30756 bytes
Input file size = 31650 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 30404
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 29440
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 29440
Output IDAT size = 29440 bytes (1316 bytes decrease)
Output file size = 29518 bytes (2132 bytes = 6.74% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-clang/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/cloud.U-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 20411 bytes
Input file size = 21293 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 19454
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 19168
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 19168
Output IDAT size = 19168 bytes (1243 bytes decrease)
Output file size = 19246 bytes (2047 bytes = 9.61% decrease)
--- finished re-building ‘wild_animals.Rmd’
--- re-building ‘Frank-Rmpfr.Rnw’ using Sweave
Loading required package: copula
Loading required package: Rmpfr
Loading required package: gmp
Attaching package: 'gmp'
The following objects are masked from 'package:copula':
Eulerian, Eulerian.all, Stirling1, Stirling1.all, Stirling2,
Stirling2.all
The following objects are masked from 'package:base':
%*%, apply, crossprod, matrix, tcrossprod
C code of R package 'Rmpfr': GMP using 64 bits per limb
Attaching package: 'Rmpfr'
The following object is masked from 'package:gmp':
outer
The following objects are masked from 'package:copula':
Bernoulli, log1mexp, log1pexp
The following objects are masked from 'package:stats':
dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm
The following objects are masked from 'package:base':
cbind, pmax, pmin, rbind
--- finished re-building ‘Frank-Rmpfr.Rnw’
--- re-building ‘nacopula-pkg.Rnw’ using Sweave
Loading required package: copula
Loading required package: lattice
Warning in pnacopula(C3joe.5, c(0.5, 0.5, 0.5)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C3joe.5, c(0.99, 0.99, 0.99)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C_9_clayton, rep(0.5, 9)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C_9_clayton, rep(0.99, 9)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
--- finished re-building ‘nacopula-pkg.Rnw’
Warning: elapsed-time limit of 1 hours reached for sub-process
--- re-building ‘rhoAMH-dilog.Rnw’ using Sweave
Loading required package: copula
Loading required package: sfsmisc
Warning in xy.coords(x, y, xlabel, ylabel, log) :
190 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
1509 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
36 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
6323 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
7933 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
24289 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
148 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
6323 y values <= 0 omitted from logarithmic plot
Error: processing vignette 'rhoAMH-dilog.Rnw' failed with diagnostics:
Running 'texi2dvi' on 'rhoAMH-dilog.tex' failed.
LaTeX errors:
! Interruption.
\GenericError ...@ \else 6\fi \endcsname \protect
\GenericError
l.279 \end{align}
! Emergency stop.
\GenericError ...@ \else 6\fi \endcsname \protect
\GenericError
l.279 \end{align}
! ==> Fatal error occurred, no output PDF file produced!
--- failed re-building ‘rhoAMH-dilog.Rnw’
SUMMARY: processing the following file failed:
‘rhoAMH-dilog.Rnw’
Error: Vignette re-building failed.
Execution halted
Flavor: r-devel-linux-x86_64-fedora-clang
Version: 1.1-4
Check: PDF version of manual
Result: WARN
LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! TeX capacity exceeded, sorry [input stack size=10000].
\@latex@warning #1->\GenericWarning
{\space \space \space \@spaces \@spaces ...
l.10796 \eqn{s \in \{0,-1,\dots\}}{}
! ==> Fatal error occurred, no output PDF file produced!
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.1-4
Check: PDF version of manual without index
Result: ERROR
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.1-4
Check: for non-standard things in the check directory
Result: NOTE
Found the following files/directories:
‘copula-manual.tex’
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.1-4
Check: re-building of vignette outputs
Result: WARN
Error(s) in re-building vignettes:
--- re-building ‘AC_Liouville.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-rACsimp-1.png
288x288 pixels, 8 bits/pixel, 196 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7776 bytes
Input file size = 8454 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6976
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6976
Output IDAT size = 6976 bytes (800 bytes decrease)
Output file size = 7054 bytes (1400 bytes = 16.56% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-Liouville-1.png
288x288 pixels, 8 bits/pixel, 198 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7699 bytes
Input file size = 8383 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6969
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6969
Output IDAT size = 6969 bytes (730 bytes decrease)
Output file size = 7047 bytes (1336 bytes = 15.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/AC_Liouville_files/figure-html/pairs-ACLiou-1.png
288x288 pixels, 8 bits/pixel, 199 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 7802 bytes
Input file size = 8489 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7033
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7033
Output IDAT size = 7033 bytes (769 bytes decrease)
Output file size = 7111 bytes (1378 bytes = 16.23% decrease)
--- finished re-building ‘AC_Liouville.Rmd’
--- re-building ‘AR_Clayton.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/AR_Clayton_files/figure-html/unnamed-chunk-7-1.png
576x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 58750 bytes
Input file size = 58912 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 50100
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 50100
Output IDAT size = 50100 bytes (8650 bytes decrease)
Output file size = 50178 bytes (8734 bytes = 14.83% decrease)
--- finished re-building ‘AR_Clayton.Rmd’
--- re-building ‘GIG.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-4-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 30633 bytes
Input file size = 30747 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26518
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26518
Output IDAT size = 26518 bytes (4115 bytes decrease)
Output file size = 26596 bytes (4151 bytes = 13.50% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-6-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 371877 bytes
Input file size = 372495 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 277143
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 277143
Output IDAT size = 277143 bytes (94734 bytes decrease)
Output file size = 277221 bytes (95274 bytes = 25.58% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-10-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 95974 bytes
Input file size = 96184 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 77702
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 77702
Output IDAT size = 77702 bytes (18272 bytes decrease)
Output file size = 77780 bytes (18404 bytes = 19.13% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/GIG_files/figure-html/unnamed-chunk-11-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 52469 bytes
Input file size = 52619 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 46680
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 46680
Output IDAT size = 46680 bytes (5789 bytes decrease)
Output file size = 46758 bytes (5861 bytes = 11.14% decrease)
--- finished re-building ‘GIG.Rmd’
--- re-building ‘HAXC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-5-1.png
288x288 pixels, 8 bits/pixel, 204 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10349 bytes
Input file size = 11063 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9726
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9726
Output IDAT size = 9726 bytes (623 bytes decrease)
Output file size = 9804 bytes (1259 bytes = 11.38% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-6-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9063 bytes
Input file size = 9774 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 8364
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 8364
Output IDAT size = 8364 bytes (699 bytes decrease)
Output file size = 8442 bytes (1332 bytes = 13.63% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-7-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10512 bytes
Input file size = 11223 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9784
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9783
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9783
Output IDAT size = 9783 bytes (729 bytes decrease)
Output file size = 9861 bytes (1362 bytes = 12.14% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-8-1.png
288x288 pixels, 8 bits/pixel, 207 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9924 bytes
Input file size = 10647 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9203
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9203
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9203
Output IDAT size = 9203 bytes (721 bytes decrease)
Output file size = 9281 bytes (1366 bytes = 12.83% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-9-1.png
288x288 pixels, 8 bits/pixel, 205 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9679 bytes
Input file size = 10396 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9018
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
Output IDAT size = 9007 bytes (672 bytes decrease)
Output file size = 9085 bytes (1311 bytes = 12.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-10-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10157 bytes
Input file size = 10877 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9400
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
Output IDAT size = 9391 bytes (766 bytes decrease)
Output file size = 9469 bytes (1408 bytes = 12.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-11-1.png
288x288 pixels, 8 bits/pixel, 202 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10828 bytes
Input file size = 11536 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 10091
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10074
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10074
Output IDAT size = 10074 bytes (754 bytes decrease)
Output file size = 10152 bytes (1384 bytes = 12.00% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-12-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10954 bytes
Input file size = 11674 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 10178
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10174
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 10174
Output IDAT size = 10174 bytes (780 bytes decrease)
Output file size = 10252 bytes (1422 bytes = 12.18% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-13-1.png
288x288 pixels, 8 bits/pixel, 207 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10163 bytes
Input file size = 10886 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9466
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9466
Output IDAT size = 9466 bytes (697 bytes decrease)
Output file size = 9544 bytes (1342 bytes = 12.33% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-14-1.png
288x288 pixels, 8 bits/pixel, 203 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10181 bytes
Input file size = 10892 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9492
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9476
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9476
Output IDAT size = 9476 bytes (705 bytes decrease)
Output file size = 9554 bytes (1338 bytes = 12.28% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-15-1.png
288x288 pixels, 8 bits/pixel, 205 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 9679 bytes
Input file size = 10396 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9018
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9007
Output IDAT size = 9007 bytes (672 bytes decrease)
Output file size = 9085 bytes (1311 bytes = 12.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/HAXC_files/figure-html/unnamed-chunk-16-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 10157 bytes
Input file size = 10877 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 9400
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 9391
Output IDAT size = 9391 bytes (766 bytes decrease)
Output file size = 9469 bytes (1408 bytes = 12.94% decrease)
--- finished re-building ‘HAXC.Rmd’
--- re-building ‘NALC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-12-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 48687 bytes
Input file size = 48825 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 47679
zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 47159
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 47159
Output IDAT size = 47159 bytes (1528 bytes decrease)
Output file size = 47237 bytes (1588 bytes = 3.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-12-2.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31122 bytes
Input file size = 31236 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28096
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28096
Output IDAT size = 28096 bytes (3026 bytes decrease)
Output file size = 28174 bytes (3062 bytes = 9.80% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-13-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 34828 bytes
Input file size = 34954 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 32747
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 32747
Output IDAT size = 32747 bytes (2081 bytes decrease)
Output file size = 32825 bytes (2129 bytes = 6.09% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/NALC_files/figure-html/unnamed-chunk-13-2.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 35630 bytes
Input file size = 35756 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 32399
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 32399
Output IDAT size = 32399 bytes (3231 bytes decrease)
Output file size = 32477 bytes (3279 bytes = 9.17% decrease)
--- finished re-building ‘NALC.Rmd’
--- re-building ‘copula_GARCH.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-3-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 62204 bytes
Input file size = 62366 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 59134
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 59134
Output IDAT size = 59134 bytes (3070 bytes decrease)
Output file size = 59212 bytes (3154 bytes = 5.06% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-5-1.png
576x576 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 20748 bytes
Input file size = 21630 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 19100
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 18890
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 18890
Output IDAT size = 18890 bytes (1858 bytes decrease)
Output file size = 18968 bytes (2662 bytes = 12.31% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/copula_GARCH_files/figure-html/unnamed-chunk-7-1.png
576x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 61628 bytes
Input file size = 61790 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 60748
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 58413
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 5 IDAT size = 58413
Output IDAT size = 58413 bytes (3215 bytes decrease)
Output file size = 58491 bytes (3299 bytes = 5.34% decrease)
--- finished re-building ‘copula_GARCH.Rmd’
--- re-building ‘dNAC.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/dNAC_files/figure-html/wire+level-1.png
288x288 pixels, 8 bits/pixel, 255 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17088 bytes
Input file size = 17967 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 15997
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 15724
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 15724
Output IDAT size = 15724 bytes (1364 bytes decrease)
Output file size = 15802 bytes (2165 bytes = 12.05% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/dNAC_files/figure-html/wire+level-2.png
288x288 pixels, 8 bits/pixel, 255 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 12058 bytes
Input file size = 12925 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 11518
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 11518
Output IDAT size = 11518 bytes (540 bytes decrease)
Output file size = 11596 bytes (1329 bytes = 10.28% decrease)
--- finished re-building ‘dNAC.Rmd’
--- re-building ‘empiricial_copulas.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-1.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3976 bytes
Input file size = 4684 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3502
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3502
Output IDAT size = 3502 bytes (474 bytes decrease)
Output file size = 3580 bytes (1104 bytes = 23.57% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-2.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3877 bytes
Input file size = 4585 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3418
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3418
Output IDAT size = 3418 bytes (459 bytes decrease)
Output file size = 3496 bytes (1089 bytes = 23.75% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-3.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3940 bytes
Input file size = 4648 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3449
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3449
Output IDAT size = 3449 bytes (491 bytes decrease)
Output file size = 3527 bytes (1121 bytes = 24.12% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-margins-4.png
288x288 pixels, 8 bits/pixel, 206 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3883 bytes
Input file size = 4591 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3406
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3406
Output IDAT size = 3406 bytes (477 bytes decrease)
Output file size = 3484 bytes (1107 bytes = 24.11% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-mass-1.png
288x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 10251 bytes
Input file size = 10341 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7064
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 7064
Output IDAT size = 7064 bytes (3187 bytes decrease)
Output file size = 7142 bytes (3199 bytes = 30.94% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/plot-mass-2.png
288x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 7637 bytes
Input file size = 7715 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6019
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 6019
Output IDAT size = 6019 bytes (1618 bytes decrease)
Output file size = 6097 bytes (1618 bytes = 20.97% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/wireframes-1.png
288x288 pixels, 8 bits/pixel, 219 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17773 bytes
Input file size = 18544 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16959
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16959
Output IDAT size = 16959 bytes (814 bytes decrease)
Output file size = 17037 bytes (1507 bytes = 8.13% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/empiricial_copulas_files/figure-html/wireframes-2.png
288x288 pixels, 8 bits/pixel, 220 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 17712 bytes
Input file size = 18486 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16901
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 16901
Output IDAT size = 16901 bytes (811 bytes decrease)
Output file size = 16979 bytes (1507 bytes = 8.15% decrease)
--- finished re-building ‘empiricial_copulas.Rmd’
--- re-building ‘logL_visualization.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-6-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31975 bytes
Input file size = 32089 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26245
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 26245
Output IDAT size = 26245 bytes (5730 bytes decrease)
Output file size = 26323 bytes (5766 bytes = 17.97% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-8-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 28591 bytes
Input file size = 28705 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24027
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24027
Output IDAT size = 24027 bytes (4564 bytes decrease)
Output file size = 24105 bytes (4600 bytes = 16.03% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-11-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31104 bytes
Input file size = 31218 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24067
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 24067
Output IDAT size = 24067 bytes (7037 bytes decrease)
Output file size = 24145 bytes (7073 bytes = 22.66% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-15-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 31402 bytes
Input file size = 31516 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 25526
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 25526
Output IDAT size = 25526 bytes (5876 bytes decrease)
Output file size = 25604 bytes (5912 bytes = 18.76% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/logL_visualization_files/figure-html/unnamed-chunk-19-1.png
720x576 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 28772 bytes
Input file size = 28886 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22690
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22690
Output IDAT size = 22690 bytes (6082 bytes decrease)
Output file size = 22768 bytes (6118 bytes = 21.18% decrease)
--- finished re-building ‘logL_visualization.Rmd’
--- re-building ‘qrng.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/indep-copula-1.png
576x288 pixels, 8 bits/pixel, 232 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 37006 bytes
Input file size = 37840 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 34692
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 34170
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 34170
Output IDAT size = 34170 bytes (2836 bytes decrease)
Output file size = 34248 bytes (3592 bytes = 9.49% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-clayton-1.png
576x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5788 bytes
Input file size = 6454 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4981
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4981
Output IDAT size = 4981 bytes (807 bytes decrease)
Output file size = 5059 bytes (1395 bytes = 21.61% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/t-Cop-fig-1.png
576x288 pixels, 8 bits/pixel, 199 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5920 bytes
Input file size = 6607 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5040
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5040
Output IDAT size = 5040 bytes (880 bytes decrease)
Output file size = 5118 bytes (1489 bytes = 22.54% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-MO-1.png
576x288 pixels, 8 bits/pixel, 194 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5831 bytes
Input file size = 6503 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5066
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 5066
Output IDAT size = 5066 bytes (765 bytes decrease)
Output file size = 5144 bytes (1359 bytes = 20.90% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-t3d-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 29019 bytes
Input file size = 29913 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 27790
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 27581
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 27581
Output IDAT size = 27581 bytes (1438 bytes decrease)
Output file size = 27659 bytes (2254 bytes = 7.54% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl-q-t3d-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 29925 bytes
Input file size = 30819 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 28713
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 28521
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 28521
Output IDAT size = 28521 bytes (1404 bytes decrease)
Output file size = 28599 bytes (2220 bytes = 7.20% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/clouds.t3d-1.png
576x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 23769 bytes
Input file size = 24651 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 22605
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 22351
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 22351
Output IDAT size = 22351 bytes (1418 bytes decrease)
Output file size = 22429 bytes (2222 bytes = 9.01% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl.col-CMD-1.png
576x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 63931 bytes
Input file size = 64093 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41402
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41402
Output IDAT size = 41402 bytes (22529 bytes decrease)
Output file size = 41480 bytes (22613 bytes = 35.28% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/pl.col-MO-1.png
576x288 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 51058 bytes
Input file size = 51208 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41141
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 41141
Output IDAT size = 41141 bytes (9917 bytes decrease)
Output file size = 41219 bytes (9989 bytes = 19.51% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/qrng_files/figure-html/plot-sim-1.png
336x336 pixels, 3x8 bits/pixel, RGB
Input IDAT size = 25556 bytes
Input file size = 25670 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 17946
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 17946
Output IDAT size = 17946 bytes (7610 bytes decrease)
Output file size = 18024 bytes (7646 bytes = 29.79% decrease)
--- finished re-building ‘qrng.Rmd’
--- re-building ‘wild_animals.Rmd’ using rmarkdown
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-1.png
288x288 pixels, 8 bits/pixel, 233 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 2808 bytes
Input file size = 3597 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2480
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2480
Output IDAT size = 2480 bytes (328 bytes decrease)
Output file size = 2558 bytes (1039 bytes = 28.89% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-2.png
288x288 pixels, 8 bits/pixel, 243 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 2807 bytes
Input file size = 3626 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2468
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 2468
Output IDAT size = 2468 bytes (339 bytes decrease)
Output file size = 2546 bytes (1080 bytes = 29.78% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-1-3.png
288x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 5186 bytes
Input file size = 5852 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4606
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 4606
Output IDAT size = 4606 bytes (580 bytes decrease)
Output file size = 4684 bytes (1168 bytes = 19.96% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/unnamed-chunk-2-1.png
288x288 pixels, 8 bits/pixel, 248 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 14931 bytes
Input file size = 15777 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 14036
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 13451
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 13451
Output IDAT size = 13451 bytes (1480 bytes decrease)
Output file size = 13529 bytes (2248 bytes = 14.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/plot.margins-1.png
288x288 pixels, 8 bits/pixel, 249 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 3365 bytes
Input file size = 4202 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3147
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3147
Output IDAT size = 3147 bytes (218 bytes decrease)
Output file size = 3225 bytes (977 bytes = 23.25% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/plot.U-1.png
288x288 pixels, 8 bits/pixel, 192 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 4475 bytes
Input file size = 5141 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3998
zc = 9 zm = 8 zs = 1 f = 0
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 3998
Output IDAT size = 3998 bytes (477 bytes decrease)
Output file size = 4076 bytes (1065 bytes = 20.72% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/splom.U-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 30756 bytes
Input file size = 31650 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 30404
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 29440
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 29440
Output IDAT size = 29440 bytes (1316 bytes decrease)
Output file size = 29518 bytes (2132 bytes = 6.74% decrease)
** Processing: /data/gannet/ripley/R/packages/tests-devel/copula.Rcheck/vign_test/copula/vignettes/wild_animals_files/figure-html/cloud.U-1.png
288x288 pixels, 8 bits/pixel, 256 colors in palette
Reducing image to 8 bits/pixel, grayscale
Input IDAT size = 20411 bytes
Input file size = 21293 bytes
Trying:
zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 19454
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 19168
zc = 1 zm = 8 zs = 2 f = 0
zc = 9 zm = 8 zs = 3 f = 0
zc = 9 zm = 8 zs = 0 f = 5
zc = 9 zm = 8 zs = 1 f = 5
zc = 1 zm = 8 zs = 2 f = 5
zc = 9 zm = 8 zs = 3 f = 5
Selecting parameters:
zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 19168
Output IDAT size = 19168 bytes (1243 bytes decrease)
Output file size = 19246 bytes (2047 bytes = 9.61% decrease)
--- finished re-building ‘wild_animals.Rmd’
--- re-building ‘Frank-Rmpfr.Rnw’ using Sweave
Loading required package: copula
Loading required package: Rmpfr
Loading required package: gmp
Attaching package: 'gmp'
The following objects are masked from 'package:copula':
Eulerian, Eulerian.all, Stirling1, Stirling1.all, Stirling2,
Stirling2.all
The following objects are masked from 'package:base':
%*%, apply, crossprod, matrix, tcrossprod
C code of R package 'Rmpfr': GMP using 64 bits per limb
Attaching package: 'Rmpfr'
The following object is masked from 'package:gmp':
outer
The following objects are masked from 'package:copula':
Bernoulli, log1mexp, log1pexp
The following objects are masked from 'package:stats':
dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm
The following objects are masked from 'package:base':
cbind, pmax, pmin, rbind
--- finished re-building ‘Frank-Rmpfr.Rnw’
--- re-building ‘nacopula-pkg.Rnw’ using Sweave
Loading required package: copula
Loading required package: lattice
Warning in pnacopula(C3joe.5, c(0.5, 0.5, 0.5)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C3joe.5, c(0.99, 0.99, 0.99)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C_9_clayton, rep(0.5, 9)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
Warning in pnacopula(C_9_clayton, rep(0.99, 9)) :
'pnacopula' is deprecated.
Use 'pCopula' instead.
See help("Deprecated")
--- finished re-building ‘nacopula-pkg.Rnw’
Warning: elapsed-time limit of 1 hours reached for sub-process
--- re-building ‘rhoAMH-dilog.Rnw’ using Sweave
Loading required package: copula
Loading required package: sfsmisc
Warning in xy.coords(x, y, xlabel, ylabel, log) :
190 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
1509 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
36 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
6323 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
7933 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
24289 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
148 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
2364 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE) :
6323 y values <= 0 omitted from logarithmic plot
Error: processing vignette 'rhoAMH-dilog.Rnw' failed with diagnostics:
Running 'texi2dvi' on 'rhoAMH-dilog.tex' failed.
LaTeX errors:
! Interruption.
\GenericError ...@ \else 6\fi \endcsname \protect
\GenericError
l.279 \end{align}
! Emergency stop.
\GenericError ...@ \else 6\fi \endcsname \protect
\GenericError
l.279 \end{align}
! ==> Fatal error occurred, no output PDF file produced!
--- failed re-building ‘rhoAMH-dilog.Rnw’
SUMMARY: processing the following file failed:
‘rhoAMH-dilog.Rnw’
Error: Vignette re-building failed.
Execution halted
Flavor: r-devel-linux-x86_64-fedora-gcc
Version: 1.1-4
Check: installed package size
Result: NOTE
installed size is 7.8Mb
sub-directories of 1Mb or more:
R 2.4Mb
doc 3.2Mb
Flavors: r-release-macos-arm64, r-release-macos-x86_64, r-oldrel-macos-arm64, r-oldrel-macos-x86_64
Version: 1.1-4
Flags: --no-vignettes
Check: installed package size
Result: NOTE
installed size is 7.3Mb
sub-directories of 1Mb or more:
R 2.1Mb
doc 3.2Mb
Flavors: r-release-windows-x86_64, r-oldrel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: ERROR: 1, OK: 12
Version: 0.5-9
Check: tests
Result: ERROR
Running ‘bd0-tst.R’ [5s/6s]
Running ‘chisq-nonc-ex.R’ [26s/33s]
Running ‘dgamma-tst.R’ [1s/1s]
Running ‘dnbinom-tst.R’ [25s/33s]
Running ‘dnchisq-tst.R’ [0s/1s]
Running ‘dt-ex.R’ [10s/15s]
Running ‘expm1x-tst.R’ [3s/4s]
Running ‘hyper-dist-ex.R’ [18s/22s]
Running ‘log4p1p-exp.R’ [3s/4s]
Running ‘pnbeta-tst.R’ [0s/1s]
Running ‘pnt-prec.R’ [7s/10s]
Running ‘pow-tst.R’ [4s/5s]
Running ‘ppois-ex.R’ [1s/2s]
Running ‘pqnorm_extreme.R’ [6s/7s]
Running ‘qPoisBinom-ex.R’ [1s/1s]
Running ‘qbeta-dist.R’ [6s/8s]
Running ‘qbeta-tst.R’ [0s/1s]
Running ‘qgamma-ex.R’ [13s/16s]
Running ‘stirlerr-tst.R’ [83s/94s]
Running ‘t-nonc-tst.R’ [14s/16s]
Running ‘wienergerm-pchisq-tst.R’ [0s/1s]
Running ‘wienergerm_nchisq.R’ [6s/6s]
Running the tests in ‘tests/stirlerr-tst.R’ failed.
Complete output:
> #### Testing stirlerr()
> #### =================== {previous 2nd part of this, now -->>> ./bd0-tst.R <<<---
> require(DPQ)
Loading required package: DPQ
> for(pkg in c("Rmpfr", "DPQmpfr"))
+ if(!requireNamespace(pkg)) {
+ cat("no CRAN package", sQuote(pkg), " ---> no tests here.\n")
+ q("no")
+ }
Loading required namespace: Rmpfr
Loading required namespace: DPQmpfr
> require("Rmpfr")
Loading required package: Rmpfr
Loading required package: gmp
Attaching package: 'gmp'
The following objects are masked from 'package:base':
%*%, apply, crossprod, matrix, tcrossprod
C code of R package 'Rmpfr': GMP using 64 bits per limb
Attaching package: 'Rmpfr'
The following object is masked from 'package:gmp':
outer
The following object is masked from 'package:DPQ':
log1mexp
The following objects are masked from 'package:stats':
dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm
The following objects are masked from 'package:base':
cbind, pmax, pmin, rbind
>
> source(system.file(package="DPQ", "test-tools.R", mustWork=TRUE))
> ## => showProc.time(), ... list_() , loadList() , readRDS_() , save2RDS()
> ##_ options(conflicts.policy = list(depends.ok=TRUE, error=FALSE, warn=FALSE))
> require(sfsmisc) # masking 'list_' *and* gmp's factorize(), is.whole()
Loading required package: sfsmisc
Attaching package: 'sfsmisc'
The following object is masked _by_ '.GlobalEnv':
list_
The following objects are masked from 'package:gmp':
factorize, is.whole
> ##_ options(conflicts.policy = NULL)o
>
> ## plot1cuts() , etc: ---> ../inst/extraR/relErr-plots.R <<<<<<<
> ## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> source(system.file(package="DPQ", "extraR", "relErr-plots.R", mustWork=TRUE))
>
> do.pdf <- TRUE # (manually)
> do.pdf <- !dev.interactive(orNone = TRUE)
> do.pdf
[1] TRUE
> if(do.pdf) {
+ pdf.options(width = 9, height = 6.5) # for all pdf plots {9/6.5 = 1.38 ; 4/3 < 1.38 < sqrt(2) [A4]
+ pdf("stirlerr-tst.pdf")
+ }
>
> showProc.time()
Time (user system elapsed): 0.08 0 0.079
> (doExtras <- DPQ:::doExtras())
[1] FALSE
> (noLdbl <- (.Machine$sizeof.longdouble <= 8)) ## TRUE when --disable-long-double or 'M1mac' ..
[1] FALSE
> (M.mac <- grepl("aarch64-apple", R.version$platform)) # Mac with M1, M2, ... proc
[1] FALSE
>
> abs19 <- function(r) pmax(abs(r), 1e-19) # cut |err| to positive {for log-plots}
>
> options(width = 100, nwarnings = 1e5, warnPartialMatchArgs = FALSE)
>
>
>
> ##=== Really, dpois_raw() and dbinom_raw() *both* use stirlerr(x) for "all" 'x > 0'
> ## ~~~~~~~~~~~ ~~~~~~~~~~~~ =========== ===== !
>
> ## below, 6 "it's okay, but *far* from perfect:" ===> need more terms in stirlerr() [
> ## April 20: MM added more terms up to S10; 2024-01: up to S12 ..helps a little only
> x <- lseq(1/16, 6, length=2048)
> system.time(stM <- DPQmpfr::stirlerrM(Rmpfr::mpfr(x,2048))) # 1.7 sec elapsed
user system elapsed
3.052 0.028 3.418
> plot(x, stirlerr(x, use.halves=FALSE) - stM, type="l", log="x", main="absolute Error")
> plot(x, stirlerr(x, use.halves=FALSE) / stM - 1, type="l", log="x", main="relative Error")
> plot(x, abs(stirlerr(x, use.halves=FALSE) / stM - 1), type="l", log="xy",main="|relative Error|")
> drawEps.h(-(52:50))
> ## lgammacor() does *NOT* help, as it is *designed* for x >= 10 ... (but is interesting there)
> ##
> ## ==> Need another chebyshev() or rational-approx. for x in [.1, 7] or so !!
>
> ##=============> see also ../Misc/stirlerr-trms.R <===============
> ## ~~~~~~~~~~~~~~~~~~~~~~~
>
> cutoffs <- c(15,35,80,500) # cut points, n=*, in the stirlerr() "algorithm"
> ##
> n <- c(seq(1,15, by=1/4),seq(16, 25, by=1/2), 26:30, seq(32,50, by=2), seq(55,1000, by=5),
+ 20*c(51:99), 50*(40:80), 150*(27:48), 500*(15:20))
> st.n <- stirlerr(n, "R3")# rather use.halves=TRUE; but here , use.halves=FALSE
> plot(st.n ~ n, log="xy", type="b") ## looks good now (straight line descending {in log-log !}
> nM <- mpfr(n, 2048)
> st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose
> all.equal(asNumeric(st.nM), st.n)# TRUE
[1] TRUE
> all.equal(st.nM, as(st.n,"mpfr"))# .. difference: 3.381400e-14 was 1.05884.........e-15
[1] "Mean relative difference: 3.317339e-14"
> all.equal(roundMpfr(st.nM, 64), as(st.n,"mpfr"), tolerance=1e-16)# (ditto)
[1] "Mean relative difference: 3.317339e-14"
>
>
> ## --- Look at the direct formula -- why is it not good for n ~= 5 ?
> ##
> ## Preliminary Conclusions :
> ## 1. there is *some* cancellation even for small n (how much?)
> ## 2. lgamma1p(n) does really not help much compared to lgamma(n+1) --- but a tiny bit in some cases
>
> ### 1. Investigating lgamma1p(n) vs lgamma(n+1) for n < 1 =============================================
>
> ##' @title Relative Error of lgamma(n+1) vs lgamma1p() vs MM's stirlerrD2():
> ##' @param n numeric, typically n << 1
> ##' @param precBits
> ##' @return relative error WRT mpfr(n, precBits)
> ##' @author Martin Maechler
> relE.lgam1 <- function(n, precBits = if(doExtras) 1024 else 320) {
+ M_LN2PI <- 1.837877066409345483 # ~ log(2*Const("pi",60)); very slightly more accurate than log(2*pi)
+ st <- lgamma(n +1) - (n +0.5)*log(n) + n - M_LN2PI/2
+ st. <- lgamma1p(n) - (n +0.5)*log(n) + n - M_LN2PI/2 # "lgamma1p"
+ st2 <- lgamma(n) + n*(1-(l.n <- log(n))) + (l.n - M_LN2PI)/2 # "MM2"
+ st0 <- -(l.n + M_LN2PI)/2 # "n0"
+ nM <- mpfr(n, precBits)
+ stM <- lgamma(nM+1) - (nM+0.5)*log(nM) + nM - log(2*Const("pi", precBits))/2
+ ## stM <- roundMpfr(stM, 128)
+ cbind("R3" = asNumeric(relErrV(stM, st))
+ , "lgamma1p"= asNumeric(relErrV(stM, st.))
+ , "MM2" = asNumeric(relErrV(stM, st2))
+ , "n0" = asNumeric(relErrV(stM, st0))
+ )
+ }
>
> n <- 2^-seq.int(1022, 1, by = -1/4)
> relEx <- relE.lgam1(n)
> showProc.time()
Time (user system elapsed): 6.067 0.051 6.956
>
> ## Is *equivalent* to 'new' stirlerr_simpl(n version = *) [not for <mpfr> though, see 'relEmat']:
> (simpVer <- eval(formals(stirlerr_simpl)$version))
[1] "R3" "lgamma1p" "MM2" "n0"
> if(is.null(simpVer)) { warning("got wrong old version of package 'DPQ':")
+ print(packageDescription("DPQ"))
+ stop("invalid outdated version package 'DPQ'")
+ }
> stir.allS <- function(n) sapply(simpVer, function(v) stirlerr_simpl(n, version=v))
> stirS <- stir.allS(n) # matrix
> nM <- mpfr(n, 256) # "high" precision = 256 should suffice!
> stirM <- stirlerr(nM)
> releS <- asNumeric(relErrV(stirM, stirS))
> all.equal(relEx, releS, tolerance = 0) # see TRUE on Linux
[1] TRUE
> stopifnot(all.equal(relEx, releS, tolerance = if(noLdbl) 2e-15 else 1e-15))
> simpVer3 <- simpVer[simpVer != "lgamma1p"] # have no mpfr-ified lgamma1p()!
> ## stirlerr_simpl(<mpfr>, *) :
> stirM2 <- sapplyMpfr(simpVer3, function(v) stirlerr_simpl(nM, version=v))
>
> ## TODO ?:
> ## apply(stirM2, 2, function(v) all.equal(v, stirS, check.class=FALSE))
> ## releS2 <- asNumeric(relErrV(stirM2, stirS))
> ## all.equal(relEx, releS, tolerance = 0) # see TRUE on Linux
> ## stopifnot(all.equal(relEx, releS, tolerance = 1e-15))
> relEmat <- matrix(NA, ncol(stirM2), ncol(stirS),
+ dimnames = list(simpVer3, colnames(stirS)))
> for(j in seq_len(ncol(stirM2)))
+ for(k in seq_len(ncol(stirS)))
+ relEmat[j,k] <- asNumeric(relErr(stirM2[,j], stirS[,k]))
> relEmat
R3 lgamma1p MM2 n0
R3 6.069585e-17 6.069957e-17 6.111712e-17 9.701665e-06
MM2 6.069585e-17 6.069957e-17 6.111712e-17 9.701665e-06
n0 9.701700e-06 9.701700e-06 9.701700e-06 6.054986e-17
> round(-log10(relEmat), 2) # well .. {why? / expected ?}
R3 lgamma1p MM2 n0
R3 16.22 16.22 16.21 5.01
MM2 16.22 16.22 16.21 5.01
n0 5.01 5.01 5.01 16.22
>
> cols <- c("gray30", adjustcolor(c(2,3,4), 1/2)); lwd <- c(1, 3,3,3)
> stopifnot((k <- length(cols)) == ncol(relEx), k == length(lwd))
> matplot(n, relEx, type = "l", log="x", col=cols, lwd=lwd, ylim = c(-1,1)*4.5e-16,
+ main = "relative errors of direct (approx.) formula for stirlerr(n), small n")
> mtext("really small errors are dominated by small (< 2^-53) errors of log(n)")
> ## very interesting: there are different intervals <---> log(n) Qpattern !!
> ## -- but very small difference, only for n >~= 1/1000 but not before
> drawEps.h(negative=TRUE) # abline(h= c(-4,-2:2, 4)*2^-53, lty=c(2,2,2, 1, 2,2,2), col="gray")
> legend("topleft", legend = colnames(relEx), col=cols, lwd=3)
>
> ## zoomed in a bit:
> n. <- 2^-seq.int(400,2, by = -1/4)
> relEx. <- relE.lgam1(n.)
> matplot(n., relEx., type = "l", log="x", col=cols, lwd=lwd, ylim = c(-1,1)*4.5e-16,
+ main = "relative errors of direct (approx.) formula for stirlerr(n), small n")
> drawEps.h(negative=TRUE)
> legend("topleft", legend = colnames(relEx.), col=cols, lwd=3)
>
> ##====> Absolute errors (and look at "n0") --------------------------------------
> matplot(n., abs19(relEx.), type = "l", log="xy", col=cols, lwd=lwd, ylim = c(4e-17, 5e-16),
+ main = quote(abs(relErr(stirlerr_simpl(n, '*')))))
> drawEps.h(); legend("top", legend = colnames(relEx.), col=cols, lwd=3)
> lines(n., abs19(relEx.[,"n0"]), type = "o", cex=1/4, col=cols[4], lwd=2)
>
> ## more zooom-in
> n.2 <- 2^-seq.int(85, 50, by= -1/100)
> stirS.2 <- sapply(c("R3", "lgamma1p", "n0"), function(v) stirlerr_simpl(n.2, version=v))
> releS.2 <- asNumeric(relErrV(stirlerr(mpfr(n.2, 320)), stirS.2))
>
> matplot(n.2, abs19(releS.2), type = "l", log="xy", col=cols, lwd=lwd, ylim = c(4e-17, 5e-16),
+ main = quote(abs(relErr(stirlerr_simpl(n, '*')))))
> drawEps.h(); legend("top", legend = colnames(releS.2), col=cols, lwd=3)
> abline(v = 5e-17, col=(cb <- adjustcolor("skyblue4", 1/2)), lwd=2, lty=3)
> axis(1, at=5e-17, col.axis=cb, line=-1/4, cex = 3/4)
>
> matplot(n.2, abs19(releS.2), type = "l", log="xy", col=cols, lwd=lwd, ylim = c(4e-17, 5e-16),
+ xaxt="n", xlim = c(8e-18, 1e-15), ## <<<<<<<<<<<<<<<<<<< Zoom-in
+ xlab = quote(n), main = quote(abs(relErr(stirlerr_simpl(n, '*')))))
> eaxis(1); drawEps.h(); legend("top", legend = colnames(releS.2), col=cols, lwd=3)
> abline(v = 5e-17, col=(cb <- adjustcolor("skyblue4", 1/2)), lwd=2, lty=3)
> mtext('stirlerr_simpl(*, "n0") is as good as others for n <= 5e-17', col=adjustcolor(cols[3], 2))
> ## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> ## ===> "all *but* "n0" approximations for "larger" small n:
> n2 <- 2^-seq.int(20,0, length.out=1000)
> relEx2 <- relE.lgam1(n2)[,c("R3", "lgamma1p", "MM2")] # "n0" is "bad": |relE| >= 2.2e-6 !
> cols <- c("gray30", adjustcolor(c(2,4), 1/2)); lwd <- c(1, 3,3)
> stopifnot((k <- length(cols)) == ncol(relEx2), k == length(lwd))
> matplot(n2, relEx2, type = "l", log="x", col=cols, lwd=lwd, ylim = c(-3,3)*1e-15, xaxt="n",
+ main = "relative errors of direct (approx.) formula for stirlerr(n), small n")
> eaxis(1, sub10=c(-3,0)); drawEps.h(negative=TRUE)
> legend("topleft", legend = colnames(relEx2), col=cols, lwd=3)
> ##==> "MM" is *NOT* good for n < 1 *but*
>
> ## "the same" -- even larger small n:
> n3 <- seq(.01, 5, length=1000)
> relEx3 <- relE.lgam1(n3)[,c("R3", "lgamma1p", "MM2")] # "no" is "bad" ..
> stopifnot((k <- length(cols)) == ncol(relEx3), k == length(lwd))
>
> matplot(n3, relEx3, type = "l", col=cols, lwd=lwd,
+ main = "relative errors of direct (approx.) formula for stirlerr(n), small n")
> legend("topleft", legend = colnames(relEx3), col=cols, lwd=3)
> drawEps.h(negative=TRUE)
>
> matplot(n3, abs19(relEx3), type = "l", col=cols, lwd=lwd,
+ log="y", ylim = 2^-c(54, 44), yaxt = "n", ylab = quote(abs(relE)), xlab=quote(n),
+ main = "|relative errors| of direct (approx.) formula for stirlerr(n), small n")
> eaxis(2, cex.axis=0.9); legend("topleft", legend = colnames(relEx3), col=cols, lwd=3)
> drawEps.h()
> lines(n3, smooth.spline(abs(relEx3)[,1], df=12)$y, lwd=3, col=cols[1])
> lines(n3, smooth.spline(abs(relEx3)[,2], df=12)$y, lwd=3, col=adjustcolor(cols[2], 1/2))
> lines(n3, smooth.spline(abs(relEx3)[,3], df=12)$y, lwd=4, col=adjustcolor(cols[3], offset = rep(.2,4)))
> ## ===> from n >~= 1, "MM2" is definitely better up to n = 5 !!
>
> ## Check log() only :
> plot(n, asNumeric(relErrV(log(mpfr(n, 256)), log(n))), ylim = c(-1,1)*2^-53,
+ log="x", type="l", xaxt="n") ## ===> indeed --- log(n) approximation pattern !!
> eaxis(1) ; drawEps.h(negative=TRUE)
> showProc.time()
Time (user system elapsed): 10.756 0.059 11.923
>
> ## =========== "R3" vs "lgamma1p" -------------------------- which is better?
>
> ## really for the very small n, all is dominated by -(n+0.5)*log(n); and lgamma1p() is unnecessary!
> i <- 1:20; ni <- n[i]
> lgamma1p(ni)
[1] -1.284347e-308 -1.527355e-308 -1.816342e-308 -2.160006e-308 -2.568695e-308 -3.054710e-308
[7] -3.632683e-308 -4.320013e-308 -5.137390e-308 -6.109421e-308 -7.265367e-308 -8.640026e-308
[13] -1.027478e-307 -1.221884e-307 -1.453073e-307 -1.728005e-307 -2.054956e-307 -2.443768e-307
[19] -2.906147e-307 -3.456010e-307
> - (ni +0.5)*log(ni) + ni
[1] 354.1982 354.1116 354.0249 353.9383 353.8516 353.7650 353.6783 353.5917 353.5051 353.4184
[11] 353.3318 353.2451 353.1585 353.0718 352.9852 352.8986 352.8119 352.7253 352.6386 352.5520
>
> ## much less extreme:
> n2 <- lseq(2^-12, 1/2, length=1000)
> relE2 <- relE.lgam1(n2)[,-4]
>
> cols <- c("gray30", adjustcolor(2:3, 1/2)); lwd <- c(1,3,3)
> matplot(n2, relE2, type = "l", log="x", col=cols, lwd=lwd)
> legend("topleft", legend=colnames(relE2), col=cols, lwd=2, lty=1:3)
> drawEps.h(negative=TRUE)
>
> matplot(n2, abs19(relE2), type = "l", log="xy", col=cols, lwd=lwd, ylim = c(6e-17, 1e-15),
+ xaxt = "n"); eaxis(1, sub10=c(-2,0))
> legend("topleft", legend=colnames(relE2), col=cols, lwd=2, lty=1:3)
> drawEps.h()
> ## "MM2" is *worse* here, n < 1/2
> for(j in 1:3) lines(n2, smooth.spline(abs(relE2[,j]), df=10)$y, lwd=3,
+ col=adjustcolor(cols[j], 1.5, offset = rep(-1/4, 4)))
> ## "lgammap very slightly better in [0.002, 0.05] ...
> ## "TODO": draw 0.90-quantile curves {--> cobs::cobs() ?} instead of mean-curves?
>
> ## which is better? ... "random difference"
> d.absrelE <- abs(relE2[,"R3"]) - abs(relE2[,"lgamma1p"])
> plot (n2, d.absrelE, type = "l", log="x", # no clear picture ...
+ main = "|relE_R3| - |relE_lgamma1p|", axes=FALSE, frame.plot=TRUE)
> eaxis(1, sub10=c(-2,1)); eaxis(2); axis(3, at=max(n2)); abline(v = max(n2), lty=3, col="gray")
> ## 'lgamma1p' very slightly better:
> lines(n2, smooth.spline(d.absrelE, df=12)$y, lwd=3, col=2)
>
> ## not really small n at all == here see, how "bad" the direct formula gets for 1 < n < 10 or so
> n3 <- lseq(2^-14, 2^2, length=800)
> relE3 <- relE.lgam1(n3)[, -4]
>
> matplot(n3, relE3, type = "l", log="x", col=cols, lty=1, lwd = c(1,3),
+ main = quote(rel.lgam1(n)), xlab=quote(n))
>
> matplot(n3, abs19(relE3), type = "l", log="xy", col=cols, lwd = c(1,3), xaxt="n",
+ main = quote(abs(rel.lgam1(n))), xlab=quote(n), ylim = c(2e-17, 4e-14))
> drawEps.h(); eaxis(1, sub10=c(-2,3))
> legend("topleft", legend=colnames(relE3), col=cols, lwd=2)
> ## very small difference --- draw the 3 smoothers :
> for(j in 1:3) {
+ ll <- lowess(log(n3), abs19(relE3[, j]), f= 1/12)
+ with(ll, lines(exp(x), y, col=adjustcolor(cols[j], 1.5), lwd=3))
+ }
> ## ==> lgamma1p(.) very slightly in n ~ 10^-4 -- 10^-2 --- but not where it matters: n ~ 0.1 -- 1 !!
> ## "MM2" gets best from n >~ 1 !
> abline(v=1, lty=3, col = adjustcolor(1, 3/4))
> showProc.time()
Time (user system elapsed): 1.142 0.004 1.472
>
>
> ### 2. relErr( stirlerr(.) ) ============================================================
>
> ##' Very revealing plot showing the *relative* approximation error of stirlerr(<dblprec>)
> ##'
> p.stirlerrDev <- function(n, precBits = if(doExtras) 2048L else 512L,
+ stnM = stirlerr(mpfr(n, precBits), use.halves=use.halves, verbose=verbose),
+ abs = FALSE,
+ ## cut points, n=*, in the stirlerr() algorithm; "FIXME": sync with ../R/dgamma.R <<<<
+ scheme = c("R3", "R4.4_0"),
+ cutoffs = switch(match.arg(scheme)
+ , R3 = c(15, 35, 80, 500)
+ , R4.4_0 = c(4.9, 5.0, 5.1, 5.2, 5.3, 5.4, 5.7,
+ 6.1, 6.5, 7, 7.9, 8.75, 10.5, 13,
+ 20, 26, 60, 200, 3300, 17.4e6)
+ ## {FIXME: need to sync} <==> ../man/stirlerr.Rd <==> ../R/dgamma.R
+ ),
+ use.halves = missing(cutoffs),
+ direct.ver = c("R3", "lgamma1p", "MM2", "n0"),
+ verbose = getOption("verbose"),
+ type = "b", cex = 1,
+ col = adjustcolor(1, 3/4), colnB = adjustcolor("orange4", 1/3),
+ log = if(abs) "xy" else "x",
+ xlim=NULL, ylim = if(abs) c(8e-18, max(abs(N(relE)))))
+ {
+ op <- par(las = 1, mgp=c(2, 0.6, 0))
+ on.exit(par(op))
+ require("Rmpfr"); require("sfsmisc")
+ st <- stirlerr(n, scheme=scheme, cutoffs=cutoffs, use.halves=use.halves, direct.ver=direct.ver,
+ verbose=verbose)
+ relE <- relErrV(stnM, st) # eps0 = .Machine$double.xmin
+ N <- asNumeric
+ form <- if(abs) abs(N(relE)) ~ n else N(relE) ~ n
+ plot(form, log=log, type=type, cex=cex, col=col, xlim=xlim, ylim=ylim,
+ ylab = quote(relErrV(stM, st)), axes=FALSE, frame.plot=TRUE,
+ main = sprintf("stirlerr(n, cutoffs) rel.error [wrt stirlerr(Rmpfr::mpfr(n, %d))]",
+ precBits))
+ eaxis(1, sub10=3)
+ eaxis(2)
+ mtext(paste("cutoffs =", deparse1(cutoffs)))
+ ylog <- par("ylog")
+ ## FIXME: improve this ---> drawEps.h() above
+ if(ylog) {
+ epsC <- c(1,2,4,8)*2^-52
+ epsCxp <- expression(epsilon[C],2*epsilon[C], 4*epsilon[C], 8*epsilon[C])
+ } else {
+ epsC <- (-2:2)*2^-52
+ epsCxp <- expression(-2*epsilon[C],-epsilon[C], 0, +epsilon[C], +2*epsilon[C])
+ }
+ dy <- diff(par("usr")[3:4])
+ if(diff(range(if(ylog) log10(epsC) else epsC)) > dy/50) {
+ lw <- rep(1/2, 5); lw[if(ylog) 1 else 3] <- 2
+ abline( h=epsC, lty=3, lwd=lw)
+ axis(4, at=epsC, epsCxp, las=2, cex.axis = 3/4, mgp=c(3/4, 1/4, 0), tck=0)
+ } else ## only x-axis
+ abline(h=if(ylog) epsC else 0, lty=3, lwd=2)
+ abline(v = cutoffs, col=colnB)
+ axis(3, at=cutoffs, col=colnB, col.axis=colnB,
+ labels = formatC(cutoffs, digits=3, width=1))
+ invisible(relE)
+ } ## p.stirlerrDev()
>
> showProc.time()
Time (user system elapsed): 0.006 0 0.007
>
> n <- lseq(2^-10, 1e10, length=4096)
> n <- lseq(2^-10, 5000, length=4096)
> ## store "expensive" stirlerr() result, and re-use many times below:
> nM <- mpfr(n, if(doExtras) 2048 else 512)
> st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose
>
> p.stirlerrDev(n=n, stnM=st.nM, use.halves = FALSE) # default cutoffs= c(15, 40, 85, 600)
> p.stirlerrDev(n=n, stnM=st.nM, use.halves = FALSE, ylim = c(-1,1)*1e-12) # default cutoffs= c(15, 40, 85, 600)
>
> ## show the zoom-in region in next plot
> yl2 <- 3e-14*c(-1,1)
> abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2)
>
> if(do.pdf) { dev.off() ; pdf("stirlerr-relErr_1.pdf") }
>
> ## drop n < 7:
> p.stirlerrDev(n=n, stnM=st.nM, xlim = c(7, max(n)), use.halves=FALSE) # default cutoffs= c(15, 40, 85, 600)
> abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2)
>
> ## The first plot clearly shows we should do better:
> ## Current code is switching to less terms too early, loosing up to 2 decimals precision
> if(FALSE) # no visible difference {use.halves = T / F }:
+ p.stirlerrDev(n=n, stnM=st.nM, ylim = yl2, use.halves = FALSE)
> p.stirlerrDev(n=n, stnM=st.nM, ylim = yl2, use.halves = TRUE)# exact at n/2 (n <= ..)
> abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2)
>
> showProc.time()
Time (user system elapsed): 3.059 0.008 3.184
>
>
> if(do.pdf) { dev.off(); pdf("stirlerr-relErr_6-fin-1.pdf") }
>
> ### ~19.April 2021: "This is close to *the* solution" (but see 'cuts' below)
> cuts <- c(7, 12, 20, 26, 60, 200, 3300)
> ## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> st. <- stirlerr(n=n , cutoffs = cuts, verbose=TRUE)
stirlerr(n, cutoffs = 7,12,20,26,60,200,3300) : case I (n <= 7), using direct formula for n= num [1:2354] 0.000977 0.00098 0.000984 0.000988 0.000991 ...
case II (n > 7 ), 7 cutoffs: ( 7, 12, 20, 26, 60, 200, 3300 ): n in cutoff intervals:
(7,12] (12,20] (20,26] (26,60] (60,200] (200,3.3e+03] (3.3e+03,Inf]
143 135 69 222 319 743 111
> st.nM <- stirlerr(n=nM, cutoffs = cuts, use.halves=FALSE) ## << on purpose
> relE <- asNumeric(relErrV(st.nM, st.))
> head(cbind(n, relE), 20)
n relE
[1,] 0.0009765625 -5.082434e-18
[2,] 0.0009802536 2.562412e-16
[3,] 0.0009839587 -1.229734e-16
[4,] 0.0009876777 1.527219e-16
[5,] 0.0009914108 8.168569e-17
[6,] 0.0009951581 1.722690e-16
[7,] 0.0009989195 -8.277734e-17
[8,] 0.0010026951 -1.706971e-16
[9,] 0.0010064850 9.143135e-17
[10,] 0.0010102892 1.008544e-16
[11,] 0.0010141077 2.920866e-17
[12,] 0.0010179408 -3.724266e-17
[13,] 0.0010217883 -2.367176e-16
[14,] 0.0010256503 -2.103384e-16
[15,] 0.0010295269 4.023359e-17
[16,] 0.0010334182 2.699887e-16
[17,] 0.0010373242 2.584752e-16
[18,] 0.0010412450 7.004536e-17
[19,] 0.0010451806 2.086952e-17
[20,] 0.0010491311 5.520460e-17
> ## nice printout :
> print(cbind(n = format(n, drop0trailing = TRUE),
+ stirlerr= format(st.,scientific=FALSE, digits=4),
+ relErr = signif(relE, 4))
+ , quote=FALSE)
n stirlerr relErr
[1,] 9.765625e-04 2.55398004 -5.082e-18
[2,] 9.802536e-04 2.55211721 2.562e-16
[3,] 9.839587e-04 2.55025446 -1.23e-16
[4,] 9.876777e-04 2.54839178 1.527e-16
[5,] 9.914108e-04 2.54652917 8.169e-17
[6,] 9.951581e-04 2.54466664 1.723e-16
[7,] 9.989195e-04 2.54280419 -8.278e-17
[8,] 1.002695e-03 2.54094181 -1.707e-16
[9,] 1.006485e-03 2.53907950 9.143e-17
[10,] 1.010289e-03 2.53721728 1.009e-16
[11,] 1.014108e-03 2.53535513 2.921e-17
[12,] 1.017941e-03 2.53349305 -3.724e-17
[13,] 1.021788e-03 2.53163106 -2.367e-16
[14,] 1.025650e-03 2.52976914 -2.103e-16
[15,] 1.029527e-03 2.52790730 4.023e-17
[16,] 1.033418e-03 2.52604553 2.7e-16
[17,] 1.037324e-03 2.52418385 2.585e-16
[18,] 1.041245e-03 2.52232224 7.005e-17
[19,] 1.045181e-03 2.52046071 2.087e-17
[20,] 1.049131e-03 2.51859926 5.52e-17
[21,] 1.053096e-03 2.51673789 2.175e-16
[22,] 1.057077e-03 2.51487659 1.455e-16
[23,] 1.061072e-03 2.51301538 1.371e-16
[24,] 1.065083e-03 2.51115425 -7.119e-17
[25,] 1.069108e-03 2.50929319 -3.203e-18
[26,] 1.073149e-03 2.50743222 -1.061e-16
[27,] 1.077206e-03 2.50557133 5.392e-17
[28,] 1.081277e-03 2.50371052 1.841e-16
[29,] 1.085364e-03 2.50184978 9.259e-17
[30,] 1.089466e-03 2.49998913 8.189e-17
[31,] 1.093584e-03 2.49812857 5.493e-17
[32,] 1.097718e-03 2.49626808 -3.044e-17
[33,] 1.101867e-03 2.49440767 -2.861e-16
[34,] 1.106031e-03 2.49254735 -7.993e-17
[35,] 1.110212e-03 2.49068711 6.438e-17
[36,] 1.114408e-03 2.48882695 6.849e-17
[37,] 1.118620e-03 2.48696687 -7.436e-17
[38,] 1.122848e-03 2.48510688 -6.001e-17
[39,] 1.127092e-03 2.48324697 2.464e-16
[40,] 1.131352e-03 2.48138715 2.368e-17
[41,] 1.135628e-03 2.47952741 6.221e-17
[42,] 1.139921e-03 2.47766775 6.605e-17
[43,] 1.144229e-03 2.47580818 6.717e-17
[44,] 1.148554e-03 2.47394869 -1.866e-16
[45,] 1.152895e-03 2.47208929 1.801e-16
[46,] 1.157253e-03 2.47022997 3.256e-16
[47,] 1.161627e-03 2.46837074 -1.514e-16
[48,] 1.166018e-03 2.46651159 -1.983e-18
[49,] 1.170425e-03 2.46465253 -1.39e-16
[50,] 1.174849e-03 2.46279355 1.634e-16
[51,] 1.179289e-03 2.46093467 8.901e-17
[52,] 1.183747e-03 2.45907586 1.956e-16
[53,] 1.188221e-03 2.45721715 3.932e-17
[54,] 1.192712e-03 2.45535852 2.802e-16
[55,] 1.197220e-03 2.45349998 -9.067e-18
[56,] 1.201745e-03 2.45164153 -1.149e-16
[57,] 1.206287e-03 2.44978317 4.78e-17
[58,] 1.210847e-03 2.44792489 -1.19e-16
[59,] 1.215423e-03 2.44606671 4.1e-17
[60,] 1.220017e-03 2.44420861 -2.046e-16
[61,] 1.224629e-03 2.44235060 -5.823e-17
[62,] 1.229257e-03 2.44049268 1.566e-16
[63,] 1.233903e-03 2.43863485 -1.991e-16
[64,] 1.238567e-03 2.43677711 7.107e-17
[65,] 1.243249e-03 2.43491947 -5.887e-17
[66,] 1.247948e-03 2.43306191 -1.285e-16
[67,] 1.252665e-03 2.43120444 -1.121e-16
[68,] 1.257399e-03 2.42934706 1.501e-16
[69,] 1.262152e-03 2.42748978 4.505e-17
[70,] 1.266922e-03 2.42563258 -4.205e-17
[71,] 1.271711e-03 2.42377548 1.292e-16
[72,] 1.276518e-03 2.42191847 -2.172e-17
[73,] 1.281342e-03 2.42006156 3.472e-16
[74,] 1.286186e-03 2.41820473 -1.962e-16
[75,] 1.291047e-03 2.41634800 -1.519e-16
[76,] 1.295927e-03 2.41449136 -1.752e-16
[77,] 1.300825e-03 2.41263482 -1.535e-17
[78,] 1.305742e-03 2.41077837 2.245e-17
[79,] 1.310677e-03 2.40892201 2.469e-16
[80,] 1.315631e-03 2.40706575 7.826e-17
[81,] 1.320604e-03 2.40520958 1.237e-16
[82,] 1.325595e-03 2.40335351 -1.321e-16
[83,] 1.330605e-03 2.40149754 1.9e-16
[84,] 1.335635e-03 2.39964166 -4.563e-17
[85,] 1.340683e-03 2.39778587 3.198e-17
[86,] 1.345750e-03 2.39593018 2.481e-16
[87,] 1.350837e-03 2.39407459 2.077e-16
[88,] 1.355943e-03 2.39221909 -7.773e-17
[89,] 1.361068e-03 2.39036370 4.031e-17
[90,] 1.366212e-03 2.38850839 1.41e-16
[91,] 1.371376e-03 2.38665319 1.129e-16
[92,] 1.376559e-03 2.38479809 1.782e-17
[93,] 1.381762e-03 2.38294308 -7.837e-17
[94,] 1.386985e-03 2.38108817 -6.103e-17
[95,] 1.392227e-03 2.37923336 -2.204e-18
[96,] 1.397489e-03 2.37737865 -3.985e-17
[97,] 1.402772e-03 2.37552404 9.959e-18
[98,] 1.408074e-03 2.37366953 4.462e-17
[99,] 1.413396e-03 2.37181512 9.567e-17
[100,] 1.418738e-03 2.36996081 2.97e-17
[101,] 1.424100e-03 2.36810660 5.213e-17
[102,] 1.429483e-03 2.36625249 -1.177e-16
[103,] 1.434886e-03 2.36439848 8.449e-17
[104,] 1.440309e-03 2.36254457 1.037e-16
[105,] 1.445753e-03 2.36069077 1.778e-16
[106,] 1.451218e-03 2.35883706 2.247e-17
[107,] 1.456703e-03 2.35698346 8.409e-17
[108,] 1.462209e-03 2.35512997 7.423e-17
[109,] 1.467736e-03 2.35327657 2.406e-16
[110,] 1.473283e-03 2.35142328 -1.224e-16
[111,] 1.478852e-03 2.34957010 -8.128e-17
[112,] 1.484441e-03 2.34771701 1.423e-16
[113,] 1.490052e-03 2.34586404 2.358e-16
[114,] 1.495684e-03 2.34401116 1.73e-16
[115,] 1.501337e-03 2.34215839 2.433e-17
[116,] 1.507012e-03 2.34030573 -1.479e-16
[117,] 1.512708e-03 2.33845317 1.394e-18
[118,] 1.518425e-03 2.33660072 2.797e-16
[119,] 1.524165e-03 2.33474838 9.285e-17
[120,] 1.529925e-03 2.33289614 -2.374e-17
[121,] 1.535708e-03 2.33104401 1.553e-16
[122,] 1.541513e-03 2.32919198 -5.306e-17
[123,] 1.547339e-03 2.32734006 -6.804e-17
[124,] 1.553188e-03 2.32548825 -5.164e-17
[125,] 1.559058e-03 2.32363655 -5.4e-17
[126,] 1.564951e-03 2.32178496 -2.546e-16
[127,] 1.570866e-03 2.31993348 9.653e-17
[128,] 1.576803e-03 2.31808210 1.293e-16
[129,] 1.582763e-03 2.31623084 -1.441e-16
[130,] 1.588746e-03 2.31437968 -8.2e-17
[131,] 1.594750e-03 2.31252864 -1.644e-16
[132,] 1.600778e-03 2.31067770 7.274e-17
[133,] 1.606829e-03 2.30882688 -1.791e-16
[134,] 1.612902e-03 2.30697617 -2.591e-16
[135,] 1.618998e-03 2.30512557 1.926e-16
[136,] 1.625118e-03 2.30327508 5.897e-17
[137,] 1.631260e-03 2.30142470 1.636e-16
[138,] 1.637426e-03 2.29957444 2.642e-16
[139,] 1.643615e-03 2.29772429 8.958e-17
[140,] 1.649827e-03 2.29587425 -5.138e-17
[141,] 1.656063e-03 2.29402432 2.726e-18
[142,] 1.662322e-03 2.29217451 1.624e-16
[143,] 1.668605e-03 2.29032482 2.081e-17
[144,] 1.674912e-03 2.28847524 -8.873e-17
[145,] 1.681243e-03 2.28662577 -1.437e-17
[146,] 1.687597e-03 2.28477642 2.161e-16
[147,] 1.693976e-03 2.28292718 2.451e-16
[148,] 1.700379e-03 2.28107806 1.237e-16
[149,] 1.706806e-03 2.27922906 8.671e-17
[150,] 1.713257e-03 2.27738017 1.924e-17
[151,] 1.719732e-03 2.27553140 -2.288e-16
[152,] 1.726232e-03 2.27368275 1.424e-16
[153,] 1.732757e-03 2.27183421 -6.027e-17
[154,] 1.739306e-03 2.26998579 2.736e-16
[155,] 1.745880e-03 2.26813749 -8.571e-18
[156,] 1.752479e-03 2.26628931 2.038e-17
[157,] 1.759103e-03 2.26444125 1.725e-16
[158,] 1.765752e-03 2.26259331 4.62e-17
[159,] 1.772426e-03 2.26074549 8.967e-17
[160,] 1.779125e-03 2.25889779 -1.87e-16
[161,] 1.785850e-03 2.25705021 2.779e-16
[162,] 1.792600e-03 2.25520275 4.373e-17
[163,] 1.799375e-03 2.25335541 7.847e-17
[164,] 1.806176e-03 2.25150819 1.403e-16
[165,] 1.813003e-03 2.24966110 4.483e-17
[166,] 1.819856e-03 2.24781412 -5.16e-17
[167,] 1.826734e-03 2.24596727 2.658e-16
[168,] 1.833639e-03 2.24412055 1.531e-16
[169,] 1.840569e-03 2.24227394 1.182e-16
[170,] 1.847526e-03 2.24042746 -1.273e-16
[171,] 1.854509e-03 2.23858111 1.501e-16
[172,] 1.861519e-03 2.23673487 8.684e-17
[173,] 1.868554e-03 2.23488877 6.754e-17
[174,] 1.875617e-03 2.23304279 -1.128e-16
[175,] 1.882706e-03 2.23119693 4.346e-17
[176,] 1.889822e-03 2.22935120 1.813e-16
[177,] 1.896965e-03 2.22750560 1.635e-16
[178,] 1.904135e-03 2.22566012 1.071e-16
[179,] 1.911332e-03 2.22381478 3.274e-16
[180,] 1.918557e-03 2.22196955 -8.211e-17
[181,] 1.925808e-03 2.22012446 5.732e-17
[182,] 1.933087e-03 2.21827950 8.192e-17
[183,] 1.940394e-03 2.21643466 -1.008e-16
[184,] 1.947728e-03 2.21458995 -1.671e-16
[185,] 1.955089e-03 2.21274537 -2.104e-17
[186,] 1.962479e-03 2.21090093 1.535e-16
[187,] 1.969897e-03 2.20905661 1.078e-16
[188,] 1.977342e-03 2.20721242 1.371e-16
[189,] 1.984816e-03 2.20536837 -2.04e-16
[190,] 1.992318e-03 2.20352444 2.151e-16
[191,] 1.999848e-03 2.20168065 -1.861e-16
[192,] 2.007407e-03 2.19983699 1.494e-16
[193,] 2.014995e-03 2.19799346 1.132e-16
[194,] 2.022611e-03 2.19615006 -1.717e-16
[195,] 2.030255e-03 2.19430680 2.281e-16
[196,] 2.037929e-03 2.19246367 2.363e-16
[197,] 2.045632e-03 2.19062068 2.262e-16
[198,] 2.053364e-03 2.18877782 -1.272e-17
[199,] 2.061125e-03 2.18693510 2.496e-16
[200,] 2.068915e-03 2.18509251 1.261e-16
[201,] 2.076735e-03 2.18325005 -6.126e-17
[202,] 2.084585e-03 2.18140774 5.53e-17
[203,] 2.092464e-03 2.17956556 2.26e-16
[204,] 2.100373e-03 2.17772351 -1.686e-16
[205,] 2.108311e-03 2.17588161 4.373e-17
[206,] 2.116280e-03 2.17403984 -9.225e-17
[207,] 2.124279e-03 2.17219821 1.872e-16
[208,] 2.132308e-03 2.17035672 1.467e-16
[209,] 2.140368e-03 2.16851536 -1.073e-16
[210,] 2.148457e-03 2.16667415 1.736e-16
[211,] 2.156578e-03 2.16483308 6.527e-17
[212,] 2.164729e-03 2.16299214 2.314e-16
[213,] 2.172911e-03 2.16115135 1.237e-16
[214,] 2.181124e-03 2.15931070 -1.756e-16
[215,] 2.189368e-03 2.15747019 2.711e-16
[216,] 2.197643e-03 2.15562982 1.188e-16
[217,] 2.205950e-03 2.15378960 -9.713e-17
[218,] 2.214287e-03 2.15194951 1.068e-16
[219,] 2.222657e-03 2.15010957 -5.873e-18
[220,] 2.231058e-03 2.14826978 2.034e-16
[221,] 2.239490e-03 2.14643012 1.031e-16
[222,] 2.247955e-03 2.14459062 2.195e-16
[223,] 2.256452e-03 2.14275125 -8.599e-18
[224,] 2.264980e-03 2.14091204 -1.438e-16
[225,] 2.273541e-03 2.13907296 1.433e-16
[226,] 2.282135e-03 2.13723404 1.483e-16
[227,] 2.290760e-03 2.13539526 1.834e-17
[228,] 2.299419e-03 2.13355663 -1.028e-16
[229,] 2.308110e-03 2.13171814 1.411e-16
[230,] 2.316834e-03 2.12987980 -1.209e-16
[231,] 2.325591e-03 2.12804162 -1.114e-16
[232,] 2.334381e-03 2.12620358 -7.032e-17
[233,] 2.343204e-03 2.12436569 7.023e-17
[234,] 2.352061e-03 2.12252794 6.216e-18
[235,] 2.360951e-03 2.12069035 -7.983e-17
[236,] 2.369874e-03 2.11885291 4.616e-17
[237,] 2.378832e-03 2.11701562 2.356e-16
[238,] 2.387823e-03 2.11517849 1.543e-16
[239,] 2.396848e-03 2.11334150 2.587e-16
[240,] 2.405907e-03 2.11150467 -9.167e-17
[241,] 2.415001e-03 2.10966798 -4.971e-17
[242,] 2.424129e-03 2.10783146 -4.516e-17
[243,] 2.433292e-03 2.10599508 1.246e-16
[244,] 2.442489e-03 2.10415886 2.32e-17
[245,] 2.451720e-03 2.10232280 -2.199e-16
[246,] 2.460987e-03 2.10048688 7.847e-17
[247,] 2.470289e-03 2.09865113 2.089e-16
[248,] 2.479626e-03 2.09681553 2.274e-16
[249,] 2.488998e-03 2.09498009 4.04e-17
[250,] 2.498406e-03 2.09314480 -2.338e-16
[251,] 2.507849e-03 2.09130967 -5.553e-17
[252,] 2.517328e-03 2.08947470 -4.654e-18
[253,] 2.526843e-03 2.08763989 1.603e-16
[254,] 2.536393e-03 2.08580523 -1.976e-16
[255,] 2.545980e-03 2.08397074 2.586e-16
[256,] 2.555603e-03 2.08213640 9.756e-17
[257,] 2.565263e-03 2.08030223 1.591e-16
[258,] 2.574958e-03 2.07846821 2.651e-16
[259,] 2.584691e-03 2.07663436 9.114e-17
[260,] 2.594460e-03 2.07480066 1.145e-16
[261,] 2.604267e-03 2.07296713 -6.184e-17
[262,] 2.614110e-03 2.07113377 -1.977e-16
[263,] 2.623990e-03 2.06930056 2.149e-17
[264,] 2.633908e-03 2.06746752 1.831e-16
[265,] 2.643864e-03 2.06563464 -2.117e-17
[266,] 2.653857e-03 2.06380193 -2.172e-16
[267,] 2.663887e-03 2.06196938 -4.925e-17
[268,] 2.673956e-03 2.06013699 -1.836e-16
[269,] 2.684063e-03 2.05830478 -1.418e-16
[270,] 2.694208e-03 2.05647272 -1.394e-16
[271,] 2.704391e-03 2.05464084 1.624e-16
[272,] 2.714613e-03 2.05280912 -5.128e-17
[273,] 2.724873e-03 2.05097757 1.935e-16
[274,] 2.735172e-03 2.04914619 -6.811e-17
[275,] 2.745511e-03 2.04731498 -1.034e-16
[276,] 2.755888e-03 2.04548393 1.337e-16
[277,] 2.766304e-03 2.04365306 2.121e-16
[278,] 2.776760e-03 2.04182235 3.608e-16
[279,] 2.787255e-03 2.03999182 1.898e-16
[280,] 2.797790e-03 2.03816146 1.461e-16
[281,] 2.808365e-03 2.03633127 -1.258e-16
[282,] 2.818980e-03 2.03450125 -4.698e-18
[283,] 2.829635e-03 2.03267140 2.759e-16
[284,] 2.840330e-03 2.03084173 1.781e-17
[285,] 2.851065e-03 2.02901223 1.557e-16
[286,] 2.861841e-03 2.02718291 1.138e-16
[287,] 2.872658e-03 2.02535375 2.081e-16
[288,] 2.883516e-03 2.02352478 4.027e-16
[289,] 2.894415e-03 2.02169598 3.325e-17
[290,] 2.905355e-03 2.01986736 -1.433e-16
[291,] 2.916336e-03 2.01803891 -9.769e-17
[292,] 2.927359e-03 2.01621064 3.246e-16
[293,] 2.938424e-03 2.01438255 1.564e-16
[294,] 2.949530e-03 2.01255464 -3.331e-17
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[1835,] 9.874963e-01 0.08203841 6.758e-17
[1836,] 9.912287e-01 0.08174437 -8.212e-16
[1837,] 9.949753e-01 0.08145129 8.057e-16
[1838,] 9.987360e-01 0.08115919 1.383e-15
[1839,] 1.002511 0.08086804 -4.681e-16
[1840,] 1.006300 0.08057786 3.158e-16
[1841,] 1.010104 0.08028864 -1.174e-15
[1842,] 1.013921 0.08000038 -2.007e-15
[1843,] 1.017754 0.07971307 -3.548e-15
[1844,] 1.021601 0.07942671 7.136e-16
[1845,] 1.025462 0.07914130 -6.84e-16
[1846,] 1.029338 0.07885684 -1.343e-15
[1847,] 1.033228 0.07857333 3.561e-16
[1848,] 1.037134 0.07829075 1.673e-15
[1849,] 1.041054 0.07800912 -2.801e-16
[1850,] 1.044989 0.07772842 -1.075e-15
[1851,] 1.048938 0.07744866 2.329e-15
[1852,] 1.052903 0.07716983 -1.756e-15
[1853,] 1.056883 0.07689193 1.56e-15
[1854,] 1.060877 0.07661496 1.04e-15
[1855,] 1.064887 0.07633891 -7.338e-16
[1856,] 1.068912 0.07606379 4.737e-16
[1857,] 1.072952 0.07578958 -1.814e-15
[1858,] 1.077008 0.07551630 -2.419e-15
[1859,] 1.081078 0.07524392 3.003e-16
[1860,] 1.085165 0.07497246 -6.242e-16
[1861,] 1.089266 0.07470191 -2.671e-15
[1862,] 1.093383 0.07443227 -7.352e-16
[1863,] 1.097516 0.07416353 -1.457e-15
[1864,] 1.101664 0.07389570 2.275e-15
[1865,] 1.105828 0.07362876 2.535e-15
[1866,] 1.110008 0.07336273 -1.42e-15
[1867,] 1.114203 0.07309758 -1.182e-15
[1868,] 1.118415 0.07283334 -3.873e-16
[1869,] 1.122642 0.07256998 2.524e-15
[1870,] 1.126885 0.07230751 -2.493e-16
[1871,] 1.131144 0.07204592 -3.711e-15
[1872,] 1.135420 0.07178522 -4.222e-16
[1873,] 1.139711 0.07152540 8.291e-16
[1874,] 1.144019 0.07126646 -7.988e-16
[1875,] 1.148343 0.07100839 -1.265e-16
[1876,] 1.152684 0.07075120 -1.558e-15
[1877,] 1.157040 0.07049487 -9.087e-16
[1878,] 1.161414 0.07023942 1.726e-15
[1879,] 1.165803 0.06998483 -5.183e-17
[1880,] 1.170210 0.06973111 -1.422e-15
[1881,] 1.174633 0.06947824 2.518e-15
[1882,] 1.179073 0.06922624 -7.119e-16
[1883,] 1.183529 0.06897509 9.497e-16
[1884,] 1.188002 0.06872480 -7.462e-16
[1885,] 1.192493 0.06847536 -2.578e-15
[1886,] 1.197000 0.06822676 2.651e-15
[1887,] 1.201524 0.06797902 -8.521e-16
[1888,] 1.206066 0.06773211 -2.211e-15
[1889,] 1.210624 0.06748606 1.676e-16
[1890,] 1.215200 0.06724084 1.965e-16
[1891,] 1.219793 0.06699645 1.441e-15
[1892,] 1.224404 0.06675291 -2.952e-15
[1893,] 1.229031 0.06651019 -2.416e-15
[1894,] 1.233677 0.06626830 -1.054e-15
[1895,] 1.238340 0.06602725 3.144e-15
[1896,] 1.243020 0.06578702 -1.917e-15
[1897,] 1.247718 0.06554761 -2.721e-15
[1898,] 1.252434 0.06530902 -1.939e-15
[1899,] 1.257168 0.06507125 -2.131e-15
[1900,] 1.261920 0.06483429 1.484e-15
[1901,] 1.266690 0.06459815 9.309e-16
[1902,] 1.271477 0.06436282 -3.867e-16
[1903,] 1.276283 0.06412830 -2.843e-15
[1904,] 1.281107 0.06389459 1.186e-15
[1905,] 1.285949 0.06366168 -4.652e-16
[1906,] 1.290810 0.06342957 -1.214e-15
[1907,] 1.295689 0.06319826 1.793e-16
[1908,] 1.300586 0.06296775 -7.672e-16
[1909,] 1.305502 0.06273803 1.388e-15
[1910,] 1.310436 0.06250911 4.136e-16
[1911,] 1.315389 0.06228098 3.217e-16
[1912,] 1.320361 0.06205363 -3.569e-15
[1913,] 1.325352 0.06182707 -1.09e-15
[1914,] 1.330361 0.06160129 1.838e-15
[1915,] 1.335389 0.06137630 5.138e-16
[1916,] 1.340437 0.06115208 -3.195e-15
[1917,] 1.345503 0.06092864 2.198e-15
[1918,] 1.350589 0.06070597 -5.86e-16
[1919,] 1.355694 0.06048408 9.79e-16
[1920,] 1.360818 0.06026295 3.056e-15
[1921,] 1.365961 0.06004259 2.699e-15
[1922,] 1.371124 0.05982300 4.03e-17
[1923,] 1.376306 0.05960416 -1.909e-15
[1924,] 1.381508 0.05938609 -1.619e-16
[1925,] 1.386730 0.05916878 7.599e-17
[1926,] 1.391972 0.05895222 2.312e-15
[1927,] 1.397233 0.05873642 -2.011e-15
[1928,] 1.402514 0.05852137 1.88e-16
[1929,] 1.407815 0.05830706 -1.501e-15
[1930,] 1.413136 0.05809350 8.322e-16
[1931,] 1.418477 0.05788069 -2.59e-15
[1932,] 1.423839 0.05766862 -1.602e-15
[1933,] 1.429220 0.05745729 -4.045e-15
[1934,] 1.434622 0.05724670 -5.737e-15
[1935,] 1.440045 0.05703684 -2.58e-15
[1936,] 1.445488 0.05682772 2.042e-15
[1937,] 1.450951 0.05661932 1.187e-15
[1938,] 1.456435 0.05641166 -3.626e-15
[1939,] 1.461940 0.05620472 2.141e-16
[1940,] 1.467466 0.05599851 9.299e-16
[1941,] 1.473013 0.05579302 3.592e-15
[1942,] 1.478580 0.05558824 4.964e-15
[1943,] 1.484169 0.05538419 -5.402e-15
[1944,] 1.489778 0.05518085 3.912e-16
[1945,] 1.495409 0.05497823 -6.289e-15
[1946,] 1.501061 0.05477631 2.456e-15
[1947,] 1.506735 0.05457511 4.12e-15
[1948,] 1.512430 0.05437461 2.574e-15
[1949,] 1.518147 0.05417482 -2.724e-15
[1950,] 1.523885 0.05397573 1.141e-15
[1951,] 1.529644 0.05377734 -1.981e-15
[1952,] 1.535426 0.05357965 -2.582e-15
[1953,] 1.541229 0.05338265 -9.349e-16
[1954,] 1.547055 0.05318635 1.021e-15
[1955,] 1.552902 0.05299073 -1.744e-15
[1956,] 1.558772 0.05279581 -1.408e-15
[1957,] 1.564663 0.05260158 -2.171e-15
[1958,] 1.570577 0.05240803 -8.398e-16
[1959,] 1.576514 0.05221516 -2.951e-15
[1960,] 1.582472 0.05202298 1.318e-15
[1961,] 1.588454 0.05183147 -2.924e-15
[1962,] 1.594458 0.05164064 -2.468e-16
[1963,] 1.600484 0.05145049 -5.71e-16
[1964,] 1.606533 0.05126100 8.692e-16
[1965,] 1.612606 0.05107219 2.484e-17
[1966,] 1.618701 0.05088404 1.327e-15
[1967,] 1.624819 0.05069657 -1.618e-15
[1968,] 1.630960 0.05050975 -2.173e-15
[1969,] 1.637125 0.05032360 -1.718e-15
[1970,] 1.643313 0.05013811 -2.544e-15
[1971,] 1.649524 0.04995327 1.617e-16
[1972,] 1.655759 0.04976909 -3.492e-15
[1973,] 1.662017 0.04958556 -7.871e-16
[1974,] 1.668299 0.04940269 -3.591e-16
[1975,] 1.674604 0.04922046 2.503e-16
[1976,] 1.680934 0.04903889 -3.363e-15
[1977,] 1.687287 0.04885795 -3.969e-16
[1978,] 1.693665 0.04867766 -2.458e-15
[1979,] 1.700066 0.04849802 -4.059e-15
[1980,] 1.706492 0.04831901 -2.201e-15
[1981,] 1.712942 0.04814063 3.177e-16
[1982,] 1.719416 0.04796290 -4.841e-15
[1983,] 1.725915 0.04778579 -6.591e-15
[1984,] 1.732439 0.04760932 1.521e-15
[1985,] 1.738987 0.04743347 -3.311e-15
[1986,] 1.745560 0.04725826 1.542e-15
[1987,] 1.752157 0.04708366 6.898e-16
[1988,] 1.758780 0.04690969 9.416e-17
[1989,] 1.765428 0.04673634 5.156e-15
[1990,] 1.772100 0.04656361 -1.637e-15
[1991,] 1.778798 0.04639150 -1.54e-15
[1992,] 1.785522 0.04622000 -5.768e-16
[1993,] 1.792270 0.04604912 -5.491e-15
[1994,] 1.799045 0.04587884 1.75e-16
[1995,] 1.805844 0.04570918 2.485e-15
[1996,] 1.812670 0.04554012 -7.234e-15
[1997,] 1.819521 0.04537167 -3.603e-15
[1998,] 1.826399 0.04520381 -1.532e-15
[1999,] 1.833302 0.04503657 -2.359e-15
[2000,] 1.840231 0.04486991 -4.735e-15
[2001,] 1.847187 0.04470386 -1.351e-16
[2002,] 1.854168 0.04453840 -8.021e-16
[2003,] 1.861177 0.04437354 -3.029e-15
[2004,] 1.868211 0.04420926 2.626e-15
[2005,] 1.875273 0.04404558 9.737e-16
[2006,] 1.882360 0.04388248 -1.996e-15
[2007,] 1.889475 0.04371997 -4.155e-15
[2008,] 1.896617 0.04355804 4.594e-15
[2009,] 1.903785 0.04339670 1.529e-15
[2010,] 1.910981 0.04323593 2.103e-15
[2011,] 1.918204 0.04307574 6.296e-16
[2012,] 1.925454 0.04291613 8.562e-16
[2013,] 1.932732 0.04275709 -1.49e-15
[2014,] 1.940037 0.04259863 -1.85e-15
[2015,] 1.947370 0.04244073 -8.186e-15
[2016,] 1.954730 0.04228340 1.494e-15
[2017,] 1.962119 0.04212664 6.517e-15
[2018,] 1.969535 0.04197044 2.445e-16
[2019,] 1.976979 0.04181481 -6.152e-15
[2020,] 1.984451 0.04165974 -3.198e-15
[2021,] 1.991952 0.04150522 9.752e-18
[2022,] 1.999481 0.04135127 -1.122e-15
[2023,] 2.007038 0.04119787 1.619e-15
[2024,] 2.014624 0.04104502 -3.315e-15
[2025,] 2.022239 0.04089272 -2.242e-15
[2026,] 2.029883 0.04074098 3.008e-15
[2027,] 2.037555 0.04058978 -5.591e-15
[2028,] 2.045256 0.04043912 -3.44e-15
[2029,] 2.052987 0.04028902 3.512e-15
[2030,] 2.060746 0.04013945 -1.344e-15
[2031,] 2.068535 0.03999043 -1.161e-14
[2032,] 2.076354 0.03984194 2.467e-16
[2033,] 2.084202 0.03969399 -4.227e-15
[2034,] 2.092079 0.03954658 -1.864e-16
[2035,] 2.099987 0.03939970 4.424e-15
[2036,] 2.107924 0.03925335 5.364e-15
[2037,] 2.115891 0.03910753 -4.937e-15
[2038,] 2.123889 0.03896224 2.674e-15
[2039,] 2.131916 0.03881748 -4.884e-15
[2040,] 2.139974 0.03867324 3.795e-15
[2041,] 2.148063 0.03852952 -1.041e-15
[2042,] 2.156182 0.03838633 3.173e-15
[2043,] 2.164332 0.03824365 -1.094e-14
[2044,] 2.172512 0.03810149 -1.747e-15
[2045,] 2.180724 0.03795985 -4.156e-15
[2046,] 2.188966 0.03781872 -8.631e-16
[2047,] 2.197240 0.03767811 8.76e-15
[2048,] 2.205544 0.03753800 -2.333e-17
[2049,] 2.213881 0.03739840 -4.512e-15
[2050,] 2.222249 0.03725931 1.637e-15
[2051,] 2.230648 0.03712073 1.094e-15
[2052,] 2.239079 0.03698265 -1.016e-15
[2053,] 2.247542 0.03684507 1.954e-15
[2054,] 2.256037 0.03670799 -7.343e-15
[2055,] 2.264564 0.03657141 8.815e-15
[2056,] 2.273124 0.03643533 -3.75e-15
[2057,] 2.281715 0.03629974 -1.163e-16
[2058,] 2.290340 0.03616464 2.287e-15
[2059,] 2.298996 0.03603004 2.322e-15
[2060,] 2.307686 0.03589593 2.393e-15
[2061,] 2.316408 0.03576231 -4.001e-15
[2062,] 2.325163 0.03562917 7.919e-15
[2063,] 2.333952 0.03549652 -6.088e-15
[2064,] 2.342774 0.03536435 7.692e-15
[2065,] 2.351628 0.03523266 -1.908e-15
[2066,] 2.360517 0.03510145 4.311e-15
[2067,] 2.369439 0.03497072 -1.847e-15
[2068,] 2.378395 0.03484047 -6.013e-16
[2069,] 2.387384 0.03471070 2.413e-15
[2070,] 2.396408 0.03458139 -5.676e-15
[2071,] 2.405466 0.03445256 -6.746e-15
[2072,] 2.414557 0.03432420 -6.183e-15
[2073,] 2.423684 0.03419631 -7.864e-15
[2074,] 2.432845 0.03406889 -1.31e-14
[2075,] 2.442040 0.03394193 5.082e-15
[2076,] 2.451270 0.03381543 6.294e-16
[2077,] 2.460535 0.03368940 -4.532e-15
[2078,] 2.469835 0.03356383 5.593e-17
[2079,] 2.479170 0.03343872 1.786e-15
[2080,] 2.488541 0.03331406 -3.706e-15
[2081,] 2.497947 0.03318986 3.486e-17
[2082,] 2.507388 0.03306612 9.84e-16
[2083,] 2.516866 0.03294282 6.226e-15
[2084,] 2.526378 0.03281998 -2.4e-15
[2085,] 2.535927 0.03269759 1.471e-15
[2086,] 2.545512 0.03257565 5.955e-16
[2087,] 2.555134 0.03245415 -3.394e-15
[2088,] 2.564791 0.03233310 -6.065e-16
[2089,] 2.574485 0.03221249 7.551e-15
[2090,] 2.584216 0.03209232 2.621e-15
[2091,] 2.593984 0.03197260 6.198e-16
[2092,] 2.603788 0.03185331 5.632e-15
[2093,] 2.613630 0.03173446 6.96e-15
[2094,] 2.623508 0.03161605 -1.768e-15
[2095,] 2.633425 0.03149807 1.225e-14
[2096,] 2.643378 0.03138052 -4.228e-15
[2097,] 2.653369 0.03126340 4.802e-15
[2098,] 2.663398 0.03114672 5.122e-15
[2099,] 2.673465 0.03103046 9.716e-15
[2100,] 2.683570 0.03091463 -2.628e-16
[2101,] 2.693713 0.03079922 -3.655e-15
[2102,] 2.703894 0.03068424 -1.083e-14
[2103,] 2.714114 0.03056968 -2.751e-15
[2104,] 2.724373 0.03045554 -5.199e-15
[2105,] 2.734670 0.03034182 -9.545e-15
[2106,] 2.745006 0.03022852 -2.001e-14
[2107,] 2.755381 0.03011564 -9.947e-15
[2108,] 2.765796 0.03000317 -2.573e-15
[2109,] 2.776250 0.02989111 1.086e-14
[2110,] 2.786743 0.02977946 1.437e-14
[2111,] 2.797276 0.02966823 2.901e-15
[2112,] 2.807849 0.02955740 1.141e-14
[2113,] 2.818462 0.02944699 -2.503e-15
[2114,] 2.829115 0.02933697 -9.145e-15
[2115,] 2.839808 0.02922737 -5.264e-15
[2116,] 2.850542 0.02911817 1.52e-14
[2117,] 2.861316 0.02900936 -1.32e-14
[2118,] 2.872131 0.02890096 -1.929e-15
[2119,] 2.882986 0.02879296 6.094e-15
[2120,] 2.893883 0.02868536 -1.819e-14
[2121,] 2.904821 0.02857815 1.729e-15
[2122,] 2.915801 0.02847134 -4.923e-15
[2123,] 2.926821 0.02836492 -1.957e-15
[2124,] 2.937884 0.02825889 -9.779e-15
[2125,] 2.948988 0.02815326 1.284e-15
[2126,] 2.960134 0.02804801 -1.668e-14
[2127,] 2.971323 0.02794315 -6.288e-15
[2128,] 2.982554 0.02783868 1.341e-14
[2129,] 2.993827 0.02773460 -1.762e-15
[2130,] 3.005142 0.02763089 2.047e-14
[2131,] 3.016501 0.02752757 -3.802e-15
[2132,] 3.027902 0.02742464 9.456e-15
[2133,] 3.039347 0.02732208 -8.935e-15
[2134,] 3.050835 0.02721990 2.3e-14
[2135,] 3.062366 0.02711809 8.832e-15
[2136,] 3.073941 0.02701667 -1.739e-14
[2137,] 3.085559 0.02691561 3.67e-14
[2138,] 3.097222 0.02681493 -1.292e-14
[2139,] 3.108928 0.02671463 1.277e-14
[2140,] 3.120679 0.02661469 -4.227e-14
[2141,] 3.132474 0.02651512 1.998e-15
[2142,] 3.144314 0.02641592 3.547e-14
[2143,] 3.156199 0.02631709 -3.097e-16
[2144,] 3.168128 0.02621862 -4.147e-14
[2145,] 3.180103 0.02612051 3.88e-15
[2146,] 3.192122 0.02602277 -2.751e-14
[2147,] 3.204188 0.02592539 -4.672e-15
[2148,] 3.216299 0.02582837 2.133e-14
[2149,] 3.228455 0.02573171 3.707e-15
[2150,] 3.240658 0.02563540 -2.907e-14
[2151,] 3.252906 0.02553946 5.333e-15
[2152,] 3.265201 0.02544386 -2.067e-14
[2153,] 3.277543 0.02534862 -1.225e-14
[2154,] 3.289931 0.02525374 -1.29e-15
[2155,] 3.302366 0.02515920 -1.76e-14
[2156,] 3.314848 0.02506501 -8.576e-15
[2157,] 3.327377 0.02497118 1.201e-14
[2158,] 3.339953 0.02487769 2.425e-15
[2159,] 3.352577 0.02478454 3.987e-15
[2160,] 3.365249 0.02469175 -1.137e-14
[2161,] 3.377969 0.02459929 -2.833e-14
[2162,] 3.390736 0.02450718 1.043e-14
[2163,] 3.403552 0.02441541 -1.381e-14
[2164,] 3.416417 0.02432397 2.764e-15
[2165,] 3.429330 0.02423288 -2.095e-14
[2166,] 3.442292 0.02414213 -2.777e-14
[2167,] 3.455302 0.02405171 -8.692e-15
[2168,] 3.468362 0.02396162 2.8e-14
[2169,] 3.481472 0.02387187 5.828e-15
[2170,] 3.494631 0.02378246 -2.806e-14
[2171,] 3.507839 0.02369337 -6.228e-15
[2172,] 3.521098 0.02360462 -1.116e-14
[2173,] 3.534406 0.02351619 6.554e-15
[2174,] 3.547765 0.02342809 5.027e-15
[2175,] 3.561175 0.02334032 -1.557e-14
[2176,] 3.574635 0.02325288 1.773e-14
[2177,] 3.588146 0.02316576 -3.626e-15
[2178,] 3.601708 0.02307896 5.965e-15
[2179,] 3.615321 0.02299248 5.202e-15
[2180,] 3.628986 0.02290633 -1.359e-14
[2181,] 3.642703 0.02282049 3.184e-15
[2182,] 3.656471 0.02273498 2.588e-15
[2183,] 3.670291 0.02264978 1.591e-14
[2184,] 3.684164 0.02256489 2.367e-15
[2185,] 3.698089 0.02248033 -1.583e-14
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[4051,] 4.219313e+03 0.00001975 1.626e-18
[4052,] 4.235261e+03 0.00001968 -6.848e-17
[4053,] 4.251269e+03 0.00001960 -1.644e-16
[4054,] 4.267337e+03 0.00001953 -3.362e-17
[4055,] 4.283467e+03 0.00001945 -1.294e-16
[4056,] 4.299657e+03 0.00001938 1.393e-17
[4057,] 4.315908e+03 0.00001931 -1.734e-17
[4058,] 4.332221e+03 0.00001924 -1.47e-16
[4059,] 4.348595e+03 0.00001916 -1.942e-16
[4060,] 4.365032e+03 0.00001909 -8.93e-17
[4061,] 4.381530e+03 0.00001902 -9.382e-17
[4062,] 4.398091e+03 0.00001895 -1.668e-16
[4063,] 4.414715e+03 0.00001888 -4.669e-17
[4064,] 4.431401e+03 0.00001881 -2.186e-16
[4065,] 4.448150e+03 0.00001873 -5.586e-17
[4066,] 4.464963e+03 0.00001866 -2.021e-16
[4067,] 4.481839e+03 0.00001859 -3.78e-17
[4068,] 4.498779e+03 0.00001852 -4.886e-17
[4069,] 4.515783e+03 0.00001845 -1.409e-16
[4070,] 4.532851e+03 0.00001838 -3.731e-17
[4071,] 4.549984e+03 0.00001832 -2.195e-16
[4072,] 4.567182e+03 0.00001825 -1.645e-17
[4073,] 4.584444e+03 0.00001818 -1.875e-17
[4074,] 4.601772e+03 0.00001811 7.383e-17
[4075,] 4.619165e+03 0.00001804 -1.858e-16
[4076,] 4.636624e+03 0.00001797 -6.538e-17
[4077,] 4.654149e+03 0.00001791 -4.84e-17
[4078,] 4.671740e+03 0.00001784 -9.022e-17
[4079,] 4.689398e+03 0.00001777 -4.602e-17
[4080,] 4.707123e+03 0.00001770 -9.452e-17
[4081,] 4.724914e+03 0.00001764 -1.064e-17
[4082,] 4.742773e+03 0.00001757 -7.592e-17
[4083,] 4.760699e+03 0.00001750 -5.355e-17
[4084,] 4.778693e+03 0.00001744 -1.003e-16
[4085,] 4.796755e+03 0.00001737 -7.795e-17
[4086,] 4.814885e+03 0.00001731 -2.51e-17
[4087,] 4.833084e+03 0.00001724 7.088e-17
[4088,] 4.851352e+03 0.00001718 -1.708e-16
[4089,] 4.869688e+03 0.00001711 -8.182e-17
[4090,] 4.888094e+03 0.00001705 4.589e-18
[4091,] 4.906570e+03 0.00001698 -3.178e-17
[4092,] 4.925115e+03 0.00001692 -1.18e-16
[4093,] 4.943731e+03 0.00001686 -1.146e-16
[4094,] 4.962416e+03 0.00001679 4.272e-17
[4095,] 4.981173e+03 0.00001673 -8.038e-17
[4096,] 5.000000e+03 0.00001667 1.57e-17
>
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts)
> ## and zoom in:
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim = yl2)
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim = yl2/20)
>
> if(do.pdf) { dev.off(); pdf("stirlerr-relErr_6-fin-2.pdf") }
>
> ## zoom in ==> {good for n >= 10}
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", ylim = 2e-15*c(-1,1),
+ cutoffs = cuts)## old default cutoffs = c(15,35, 80, 500)
>
> if(do.pdf) { dev.off(); pdf("stirlerr-relErr_6-fin-3.pdf") }
> showProc.time()
Time (user system elapsed): 3.33 0.02 3.532
>
>
> ##-- April 20: have more terms up to S10 in stirlerr() --> can use more cutoffs
> n <- n5m <- lseq(1/64, 5000, length=4096)
> nM <- mpfr(n, if(doExtras) 2048L # a *lot* accuracy for stirlerr(nM,*)
+ else 512L)
> ct10.1 <- c( 5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300)# till 2024-01-19
> ct10.2 <- c( 5.4, 7.9, 8.75,10.5 , 13, 20, 26, 60, 200, 3300)
> cuts <-
+ ct12.1 <- c(5.22, 6.5, 7.0, 7.9, 8.75,10.5 , 13, 20, 26, 60, 200, 3300)
> ## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> ## 5.25 is "too small" but the direct formula is already really bad there, ...
> st.nM <- roundMpfr(stirlerr(nM, use.halves=FALSE, ## << on purpose;
+ verbose=TRUE), precBits = 128)
stirlerr(n): As 'n' is "mpfr", using "mpfr" & stirlerrM():
> ## NB: for x=xM <mpfr>; `cutoffs` are *not* used.
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", scheme = "R4.4_0")
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", scheme = "R4.4_0", ylim = c(-1,1)*3e-15)
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", scheme = "R4.4_0", ylim = c(-1,1)*1e-15)
>
> p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", scheme = "R4.4_0", abs=TRUE)
> axis(1,at= 2:6, col=NA, col.axis=(cola <- "lightblue"), line=-3/4)
> abline(v = 2:6, lty=3, col=cola)
> if(FALSE)## using exact values sferr_halves[] *instead* of MPFR ones: ==> confirmation they lay on top
+ lines((0:30)/2, abs(stirlerr((0:30)/2, cutoffs=cuts, verbose=TRUE)/DPQ:::sferr_halves - 1), type="o", col=2,lwd=2)
>
> if(FALSE) ## nice (but unneeded) printout :
+ print(cbind(n = format(n, drop0trailing = TRUE),
+ stirlerr= format(st.,scientific=FALSE, digits=4),
+ relErr = signif(relE, 4))
+ , quote=FALSE)
>
> showProc.time()
Time (user system elapsed): 2.787 0.016 2.991
>
> <0c>
> ## ========== where should the cutoffs be ? ===================================================
>
> .stirl.cutoffs <- function(scheme)
+ eval(do.call(substitute, list(formals(stirlerr)$cutoffs, list(scheme = scheme))))
> drawCuts <- function(scheme, axis=NA, lty = 3, col = "skyblue", ...) {
+ abline(v = (ct <- .stirl.cutoffs(scheme)), lty=lty, col=col, ...)
+ if(is.finite(axis)) axisCuts(side = axis, at = ct, col=col, ...)
+ }
> axisCuts <- function(scheme, side = 3, at = .stirl.cutoffs(scheme), col = "skyblue", line = -3/4, ...)
+ axis(side, at=at, labels=formatC(at), col.axis = col, col=NA, col.ticks=NA, line=line, ...)
> mtextCuts <- function(cutoffs, scheme, ...) {
+ if(!missing(scheme)) cutoffs <- .stirl.cutoffs(scheme)
+ mtext(paste("cutoffs =", deparse1(cutoffs)), ...)
+ }
>
>
> if(do.pdf) { dev.off(); pdf("stirlerr-tst_order_k.pdf") }
>
> mK <- 20L # := max(k)
> ## order = k = 1:mK terms in series approx:
> k <- 1:mK
> n <- 2^seq(1, 28, by=1/16)
> nM <- mpfr(n, 1024)
> stnM <- stirlerr(nM) # the "true" values
>
> stirlOrd <- sapply(k, function(k.) stirlerr(n, order = k.))
> stirlO_lgcor <- cbind(stirlOrd, sapply(5:6, function(nal) lgammacor(n, nalgm = nal)))
> relE <- asNumeric(stirlO_lgcor/stnM -1) # "true" relative error
>
> ## use a "smooth" but well visible polette :
> palROBG <- colorRampPalette(c("red", "darkorange2", "blue", "seagreen"), space = "Lab")
> palette(adjustcolor(palROBG(mK+2), 3/4))
> ## -- 2 lgamcor()'s
>
> (tit.k <- substitute(list( stirlerr(n, order=k) ~~"error", k == 1:mK), list(mK = mK)))
list(stirlerr(n, order = k) ~ ~"error", k == 1:20L)
> (tit.kA <- substitute(list(abs(stirlerr(n, order=k) ~~"error"), k == 1:mK), list(mK = mK)))
list(abs(stirlerr(n, order = k) ~ ~"error"), k == 1:20L)
> lgammacorTit <- function(...) mtext("+ lgammacor(x, 5) [bad] + lgammacor(x, 6) [good]", col=1, ...)
>
> matplotB(n, relE, cex=2/3, ylim = c(-1,1)*1e-13, col=k,
+ log = "x", xaxt="n", main = tit.k)
> lgammacorTit()
> eaxis(1, nintLog = 20)
> drawCuts("R4.4_0")
>
> ## zoom in (ylim)
> matplotB(n, relE, cex=2/3, ylim = c(-1,1)*5e-15, col=k,
+ log = "x", xaxt="n", main = tit.k)
> lgammacorTit()
> eaxis(1, nintLog = 20); abline(h = (-2:2)*2^-53, lty=3, lwd=1/2)
> drawCuts("R4.4_0", axis = 3)
>
> ## log-log |rel.Err| -- "linear"
> matplotB(n, abs19(relE), cex=2/3, col=k, ylim = c(8e-17, 1e-7), log = "xy", main=tit.kA)
> mtext(paste("k =", deparse(k))) ; abline(h = 2^-(53:51), lty=3, lwd=1/2)
> lgammacorTit(line=-1)
> drawCuts("R4.4_0", axis = 3)
>
> ## zoom in -- still "large" {no longer carry the lgammacor() .. }:
> n2c <- 2^seq(2, 8, by=1/256)
> nMc <- mpfr(n2c, 1024)
> stnMc <- stirlerr(nMc) # the "true" values
> stirlOrc <- sapply(k, function(k.) stirlerr(n2c, order = k.))
> relEc <- asNumeric(stirlOrc/stnMc -1) # "true" relative error
>
> matplotB(n2c, relEc, cex=2/3, ylim = c(-1,1)*1e-13, col=k,
+ log = "x", xaxt="n", main = tit.k)
> eaxis(1, sub10 = 2)
> drawCuts("R4.4_0", axis=3)
>
> ## log-log |rel.Err| -- "linear"
> matplotB(n2c, abs19(relEc), cex=2/3, col=k, ylim = c(8e-17, 1e-3), log = "xy", main=tit.kA)
> mtext(paste("k =", deparse(k))) ; abline(h = 2^-(53:51), lty=3, lwd=1/2)
> drawCuts("R4.4_0", axis = 3)
>
>
> ## zoom into the critical n region
> nc <- seq(3.5, 11, by=1/128)
> ncM <- mpfr(nc, 256)
> stncM <- stirlerr(ncM) # the "true" values
> stirlO.c <- sapply(k, function(k) stirlerr(nc, order = k))
> relEc <- asNumeric(stirlO.c/stncM -1) # "true" relative error
>
>
> ## log-log |rel.Err| -- "linear"
> matplotB(nc, abs19(relEc), cex=2/3, col=k, ylim = c(2e-17, 1e-8),
+ log = "xy", xlab = quote(n), main = quote(abs(relErr(stirlerr(n, order==k)))))
> mtext(paste("k =", deparse(k))) ; drawEps.h(lwd = 1/2)
> lines(nc, abs19(asNumeric(stirlerr_simpl(nc, "R3" )/stncM - 1)), lwd=1.5, col=adjustcolor("thistle", .6))
> lines(nc, abs19(asNumeric(stirlerr_simpl(nc, "MM2")/stncM - 1)), lwd=4, col=adjustcolor(20, .4))
> ## lines(nc, abs19(asNumeric(stirlerr_simpl(nc,"MM2")/stncM - 1)), lwd=3, col=adjustcolor("purple", 2/3))
> legend(10^par("usr")[1], 1e-9, legend=paste0("k=", k), bty="n", lwd=2,
+ col=k, lty=1:5, pch= c(1L:9L, 0L, letters)[seq_along(k)])
> drawCuts("R4.4_0", axis=3)
>
> ## Zoom-in [only]
> matplotB(nc, abs19(relEc), cex=2/3, col=k, ylim = c(4e-17, 1e-11), xlim = c(4.8, 6.5),
+ log = "xy", xlab = quote(n), main = quote(abs(relErr(stirlerr(n, order==k)))))
> mtext(paste("k =", deparse(k))) ; drawEps.h(lwd = 1/2)
> lines(nc, abs19(asNumeric(stirlerr_simpl(nc, "R3" )/stncM - 1)), lwd=1.5, col=adjustcolor("thistle", .6))
> lines(nc, abs19(asNumeric(stirlerr_simpl(nc, "MM2")/stncM - 1)), lwd=4, col=adjustcolor(20, .4))
>
> k. <- k[-(1:6)]
> legend("bottomleft", legend=paste0("k=", k.), bty="n", lwd=2,
+ col=k., lty=1:5, pch= c(1L:9L, 0L, letters)[k.])
> drawCuts("R4.4_0", axis=3)
>
> showProc.time()
Time (user system elapsed): 3.711 0.016 4.303
>
> ##--- Accuracy of "R4.4_0" -------------------------------------------------------
>
> for(nc in list(seq(4.75, 28, by=1/512), # for a bigger pix
+ seq(4.75, 9, by=1/1024)))
+ {
+ ncM <- mpfr(nc, 1024)
+ stncM <- stirlerr(ncM) # the "true" values
+ stirl.440 <- stirlerr(nc, scheme = "R4.4_0")
+ stirl.3 <- stirlerr(nc, scheme = "R3")
+ relE440 <- asNumeric(relErrV(stncM, stirl.440))
+ relE3 <- asNumeric(relErrV(stncM, stirl.3 ))
+ ##
+ plot(nc, abs19(relE440), xlab=quote(n), main = quote(abs(relErr(stirlerr(n, '"R4.4_0"')))),
+ type = "l", log = "xy", ylim = c(4e-17, 1e-13))
+ mtextCuts(scheme="R4.4_0", cex=4/5)
+ drawCuts("R4.4_0", lty=2, lwd=2, axis=4)
+ drawEps.h()
+ if(max(nc) <= 10) abline(v = 5+(0:20)/10, lty=3, col=adjustcolor(4, 1/2))
+ if(TRUE) { # but just so ...
+ c3 <- adjustcolor("royalblue", 1/2)
+ lines(nc, pmax(abs(relE3), 1e-18), col=c3)
+ title(quote(abs(relErr(stirlerr(n, '"R3"')))), adj=1, col.main = c3)
+ drawCuts("R3", lty=4, col=c3); mtextCuts(scheme="R3", adj=1, col=c3)
+ }
+ addOrd <- TRUE
+ addOrd <- dev.interactive(orNone=TRUE)
+ if(addOrd) {
+ if(max(nc) >= 100) {
+ i <- (15 <= nc & nc <= 85) # (no-op in [4.75, 7] !)
+ ni <- nc[i]
+ } else { i <- TRUE; ni <- nc }
+ for(k in 8:17) lines(ni, abs19(asNumeric(relErrV(stncM[i], stirlerr(ni, order=k)))), col=adjustcolor(k, 1/3))
+ title(sub = "stirlerr(*, order k = 8:17)")
+ }
+ } ## for(nc ..)
>
> if(FALSE)
+ lines(nc, abs19(relE440))# *re* draw!
>
> showProc.time()
Time (user system elapsed): 11.923 0.008 13.367
>
>
> palette("Tableau")
>
> ## Focus more:
> stirlerrPlot <- function(nc, k, res=NULL, legend.xy = "left", full=TRUE, precB = 1024,
+ ylim = c(3e-17, 2e-13), cex = 5/4) {
+ stopifnot(require("Rmpfr"), require("graphics"))
+ if(is.list(res) && all(c("nc", "k", "relEc","splarelE") %in% names(res))) { ## do *not* recompute
+ list2env(res, envir = environment())
+ } else { ## compute
+ stopifnot(is.finite(nc), nc > 0, length(nc) >= 100, k == as.integer(k), 0 <= k, k <= 20)
+ ncM <- mpfr(nc, precB)
+ stncM <- stirlerr(ncM) # the "true" values
+ stirlO.c <- sapply(k, function(k) stirlerr(nc, order = k))
+ relEc <- asNumeric(stirlO.c/stncM -1) # "true" relative error
+ ## log |rel.Err| -- "linear"
+ ## smooth() on log-scale {and transform back}:
+ splarelE <- apply(log(abs19(relEc)), 2, function(y) exp(smooth.spline(y, df=4)$y))
+ ## the direct formulas (default "R3", "MM2"):
+ arelEs0 <- abs(asNumeric(stirlerr_simpl(nc )/stncM - 1))
+ arelEs2 <- abs(asNumeric(stirlerr_simpl(nc, "MM2")/stncM - 1))
+ }
+ pch. <- c(1L:9L, 0L, letters)[k]
+ if(full)
+ matplotB(nc, abs19(relEc), col=k, pch = pch., cex=cex, ylim=ylim, log = "y",
+ xlab = quote(n), main = quote(abs(relErr(stirlerr(n, order==k)))))
+ else ## smooth only
+ matplotB(nc, splarelE, col=adjustcolor(k,2/3), pch=pch., lwd=2, cex=cex, ylim=ylim, log = "y",
+ xlab = quote(n), main = quote(abs(relErr(stirlerr(n, order==k)))))
+ mtext(paste("k =", deparse(k))) ; abline(h = 2^-(53:51), lty=3, lwd=1/2)
+ legend(legend.xy, legend=paste0("k=", k), bty="n", lwd=2, col=k, lty=1:5, pch = pch.)
+ abline(v = 5+(0:20)/10, lty=3, col=adjustcolor(10, 1/2))
+ drawCuts("R4.4_0", axis=3)
+ if(full) {
+ matlines(nc, splarelE, col=adjustcolor(k,2/3), lwd=4)
+ lines(nc, pmax(arelEs0, 1e-19), lwd=1.5, col=adjustcolor( 2, 0.2))
+ lines(nc, pmax(arelEs2, 1e-19), lwd=1, col=adjustcolor(10, 0.2))
+ }
+ lines(nc, smooth.spline(arelEs0, df=12)$y, lwd=3, col= adjustcolor( 2, 1/2))
+ lines(nc, smooth.spline(arelEs2, df=12)$y, lwd=3, col= adjustcolor(10, 1/2))
+ invisible(list(nc=nc, k=k, relEc = relEc, splarelE = splarelE, arelEs0=arelEs0, arelEs2=arelEs2))
+ }
>
> rr1 <- stirlerrPlot(nc = seq(4.75, 9.0, by=1/1024),
+ k = 7:20)
> stirlerrPlot(res = rr1, full=FALSE, ylim = c(8e-17, 1e-13))
> if(interactive())
+ stirlerrPlot(res = rr1)
>
> rr <- stirlerrPlot(nc = seq(5, 6.25, by=1/2048), k = 9:18)
> stirlerrPlot(res = rr, full=FALSE, ylim = c(8e-17, 1e-13))
>
> showProc.time()
Time (user system elapsed): 8.074 0.103 8.708
> <0c>
>
> palette("default")
>
> if(do.pdf) { dev.off(); pdf("stirlerr-tst_order_k-vs-k1.pdf") }
>
> ##' Find 'cuts', i.e., a region c(k) +/- s(k) i.e. intervals [c(k) - s(k), c(k) + s(k)]
> ##' where c(k) is such that relE(n=c(k), k) ~= eps)
>
> ##' 1. Find the c1(k) such that |relE(n, k)| ~= c1(k) * n^{-2k}
> findC1 <- function(n, ks, e1 = 1e-15, e2 = 1e-5, res=NULL, precBits = 1024, do.plot = TRUE, ...)
+ {
+ if(is.list(res) && all(c("n", "ks", "arelE") %in% names(res))) { ## do *not* recompute, take from 'res':
+ list2env(res, envir = environment())
+ } else { ## compute
+ stopifnot(require("Rmpfr"),
+ is.numeric(ks), ks == (k. <- as.integer(ks)), length(ks <- k.) >= 1,
+ length(e1) == 1L, length(e2) == 1L, is.finite(c(e1,e2)), e1 >= 0, e2 >= e1,
+ 0 <= ks, ks <= 20, is.numeric(n), n > 0, is.finite(n), length(n) >= 100)
+ nM <- mpfr(n, precBits)
+ stirM <- stirlerr(nM) # the "true" values
+ stirlOrd <- sapply(ks, function(k) stirlerr(n, order = k))
+ arelE <- abs(asNumeric(stirlOrd/stirM -1)) # "true" relative error
+ }
+ arelE19 <- pmax(arelE, 1e-19)
+ ## log |rel.Err| -- "linear"
+ ## on log-scale {and transform back; for linear fit, only use values inside [e1, e2]
+ if(do.plot) # experi
+ matplotB(n, arelE19, log="xy", ...)
+ ## matplot(n, arelE19, type="l", log="xy", xlim = c(min(n), 20))
+
+ ## re-compute these, as they *also* depend on (e1, e2)
+ c1 <- vapply(seq_along(ks), function(i) {
+ k <- ks[i]
+ y <- arelE19[,i]
+ iUse <- e1 <= y & y <= e2
+ if(sum(iUse) < 10) stop("only", sum(iUse), "values in [e1,e2]")
+ ## .lm.fit(cbind(1, log(n[iUse])), log(y[iUse]))$coefficients
+ ## rather, we *know* the error is c* n^{-2k} , i.e.,
+ ## log |relE| = log(c) - 2k * log(n)
+ ## <==> c = exp( log|relE| + 2k * log(n))
+ exp(mean(log(y[iUse]) + 2*k * log(n[iUse])))
+ }, numeric(1))
+ if(do.plot) {
+ drawEps.h()
+ for(i in seq_along(ks))
+ lines(n, c1[i] * n^(-2*ks[i]), col=adjustcolor(i, 1/3), lwd = 4, lty = 2)
+ }
+ invisible(list(n=n, ks=ks, arelE = arelE, c1 = c1))
+ } ## findC1()
>
> c1.Res <- findC1(n = 2^seq(2, 26, by=1/128), ks = 1:18)
> (s.c1.fil <- paste0("stirlerr-c1Res-", myPlatform(), ".rds"))
[1] "stirlerr-c1Res-R-d_87286_unix_DbnGNU_Ltrx_.rds"
> saveRDS(c1.Res, file = s.c1.fil)
>
>
> if(!exists("c1.Res")) {
+ c1.Res <- readRDS(s.c1.fil)
+ ## re-do the "default" plot of findC1():
+ findC1(res = c1.Res, xaxt="n"); eaxis(1, sub10=2)
+ }
>
> ## the same, zoomed in:
> findC1(res = c1.Res, xlim = c(4, 40), ylim = c(2e-17, 1e-12))
> ks <- c1.Res$ks; pch. <- c(1L:9L, 0L, letters)[ks]
> legend("left", legend=paste0("k=", ks), bty="n", lwd=2, col=ks, lty=1:5, pch = pch.)
>
> ## smaller set : larger e1 :
> c1.r2 <- findC1(res = c1.Res, xlim = c(4, 30), ylim = c(4e-17, 1e-13), e1 = 4e-15)
> legend("left", legend=paste0("k=", ks), bty="n", lwd=2, col=ks, lty=1:5, pch = pch.)
>
> print(digits = 4,
+ cbind(ks, c1. = c1.Res$c1, c1.2 = c1.r2$c1,
+ relD = round(relErrV(c1.r2$c1, c1.Res$c1), 4)))
ks c1. c1.2 relD
[1,] 1 3.326e-02 3.331e-02 -0.0017
[2,] 2 9.532e-03 9.511e-03 0.0022
[3,] 3 7.042e-03 7.049e-03 -0.0009
[4,] 4 9.845e-03 9.811e-03 0.0035
[5,] 5 2.172e-02 2.169e-02 0.0015
[6,] 6 7.028e-02 6.967e-02 0.0088
[7,] 7 3.061e-01 3.041e-01 0.0066
[8,] 8 1.771e+00 1.744e+00 0.0156
[9,] 9 1.275e+01 1.259e+01 0.0128
[10,] 10 1.156e+02 1.129e+02 0.0235
[11,] 11 1.242e+03 1.224e+03 0.0152
[12,] 12 1.638e+04 1.592e+04 0.0294
[13,] 13 2.466e+05 2.427e+05 0.0162
[14,] 14 4.434e+06 4.331e+06 0.0238
[15,] 15 8.994e+07 8.846e+07 0.0167
[16,] 16 2.134e+09 2.082e+09 0.0253
[17,] 17 5.608e+10 5.515e+10 0.0169
[18,] 18 1.704e+12 1.655e+12 0.0292
>
> c1.. <- c1.r2[c("ks", "c1")] # just the smallest part is needed here:
> (s.c1.fil <- paste0("stirlerr-c1r2-", myPlatform(), ".rds"))
[1] "stirlerr-c1r2-R-d_87286_unix_DbnGNU_Ltrx_.rds"
> saveRDS(c1.., file = s.c1.fil) # was "stirlerr-c1.rds"
>
> ## 2. Now, find the n(k) +/- se.n(k) intervals
> ## Use these c1 from above
>
> ##' Given c1-results relErr(n,k); |relE(n,k) ~= c1 * n^{-2k} , find n such that
> ##' |relE(n,k)| line {in log-log scale} cuts y = eps, i.e., n* such that |relE(n,k)| <= eps for all n >= n*
> n.ep <- function(eps, c1Res, ks = c1Res$ks, c1 = c1Res$c1, ...) {
+ stopifnot(is.finite(eps), length(eps) == 1L, eps > 0,
+ length(ks) == length(c1), is.numeric(c1), is.integer(ks), ks >= 1)
+ ## n: given k, the location where the |relE(n,k)| line {in log-log} cuts y = eps
+ ## |relE(n,k) ~= c1 * n^{-2k} <==>
+ ## log|relE(n,k)| ~= log(c1) - 2k* log(n) <==>
+ ## c := mean{ exp( log|relE(n,k)| + 2k* log(n) ) } ------- see findC1()
+ ## now, solve for n :
+ ## c1 * n^{-2k} == eps
+ ## log(c1) - 2k* log(n) == log(eps)
+ ## log(n) == (log(eps) - log(c1)) / (-2k) <==>
+ ## n == exp((log(c1) - log(eps)) / 2k)
+ exp((log(c1) - log(eps))/(2*ks))
+ }
>
> ## get c1..
> if(!exists("c1..")) c1.. <- readRDS("stirlerr-c1.rds")
>
> ne2 <- n.ep(2^-51, c1Res = c1..) ## ok
> ne1 <- n.ep(2^-52, c1Res = c1..)
> ne. <- n.ep(2^-53, c1Res = c1..)
>
> form <- function(n) format(signif(n, 3), scientific=FALSE)
> data.frame(k = ks, ne2 = form(ne2), ne1 = form(ne1), ne. = form(ne.),
+ cutoffs = form(rev(.stirl.cutoffs("R4.4_0")[-1])))
k ne2 ne1 ne. cutoffs
1 1 8660000.00 12200000.00 17300000.00 17400000.00
2 2 2150.00 2560.00 3040.00 3700.00
3 3 159.00 178.00 200.00 200.00
4 4 46.60 50.80 55.40 81.00
5 5 23.40 25.10 26.90 36.00
6 6 15.20 16.10 17.10 25.00
7 7 11.50 12.10 12.70 19.00
8 8 9.43 9.85 10.30 14.00
9 9 8.20 8.53 8.86 11.00
10 10 7.42 7.68 7.95 9.50
11 11 6.89 7.11 7.34 8.80
12 12 6.53 6.72 6.92 8.25
13 13 6.27 6.44 6.62 7.60
14 14 6.10 6.25 6.41 7.10
15 15 5.98 6.12 6.26 6.50
16 16 5.90 6.03 6.16 6.50
17 17 5.85 5.97 6.10 6.50
18 18 5.83 5.95 6.06 6.50
>
> ## ------- Linux F 36/38 x86_64 (nb-mm5|v-lynne)
> ## k ne2 ne1 ne. cutoffs
> ## 1 8660000.00 12200000.00 17300000.00 17400000.00
> ## 2 2150.00 2560.00 3040.00 3700.00
> ## 3 159.00 178.00 200.00 200.00
> ## 4 46.60 50.80 55.40 81.00
> ## 5 23.40 25.10 26.90 36.00
> ## 6 15.20 16.10 17.10 25.00
> ## 7 11.50 12.10 12.70 19.00
> ## 8 9.43 9.85 10.30 14.00
> ## 9 8.20 8.53 8.86 11.00
> ## 10 7.42 7.68 7.95 9.50
> ## 11 6.89 7.11 7.34 8.80
> ## 12 6.53 6.72 6.92 8.25
> ## 13 6.27 6.44 6.62 7.60
> ## 14 6.10 6.25 6.41 7.10
> ## 15 5.98 6.12 6.26 6.50 * (not used)
> ## 16 5.90 6.03 6.16 6.50 * " "
> ## 17 5.85 5.97 6.10 6.50 * " "
> ## 18 5.83 5.95 6.06 6.50 << used all the way down to 5.25
>
> ## ok --- correct order of magnitude ! --- good!
>
>
> ## 2b. find *interval* around the 'n(eps)' values
>
> ## -- Try simply
> d.k <- ne. - ne1
> ## interval
> int.k <- cbind(ne1 - d.k,
+ ne1 + d.k)
> ## look at e.g.
> data.frame(k=ks, `n(k)` = form(ne1), int = form(int.k))
k n.k. int.1 int.2
1 1 12200000.00 7180000.00 17300000.00
2 2 2560.00 2070.00 3040.00
3 3 178.00 156.00 200.00
4 4 50.80 46.20 55.40
5 5 25.10 23.30 26.90
6 6 16.10 15.20 17.10
7 7 12.10 11.40 12.70
8 8 9.85 9.41 10.30
9 9 8.53 8.19 8.86
10 10 7.68 7.41 7.95
11 11 7.11 6.88 7.34
12 12 6.72 6.52 6.92
13 13 6.44 6.27 6.62
14 14 6.25 6.10 6.41
15 15 6.12 5.98 6.26
16 16 6.03 5.90 6.16
17 17 5.97 5.85 6.10
18 18 5.95 5.83 6.06
> ## k n.k. int.1 int.2
> ## 1 12200000.00 7180000.00 17300000.00
> ## 2 2560.00 2070.00 3040.00
> ## 3 178.00 156.00 200.00
> ## 4 50.80 46.20 55.40
> ## 5 25.10 23.30 26.90
> ## 6 16.10 15.20 17.10
> ## 7 12.10 11.40 12.70
> ## 8 9.85 9.41 10.30
> ## 9 8.53 8.19 8.86
> ## 10 7.68 7.41 7.95
> ## 11 7.11 6.88 7.34
> ## 12 6.72 6.52 6.92
> ## 13 6.44 6.27 6.62
> ## 14 6.25 6.10 6.41
> ## 15 6.12 5.98 6.26
> ## 16 6.03 5.90 6.16
> ## 17 5.97 5.85 6.10
> ## 18 5.95 5.83 6.06
>
> ##' as function {well, *not* computing c1.k from scratch
> nInt <- function(k, c1.k, ep12 = 2^-(52:53)) {
+ if(length(k) == 1L) { # special convention to call for *one* k, with c1.k vector
+ stopifnot(k == (k <- as.integer(k)), k >= 1, length(c1.k) >= k)
+ c1.k <- c1.k[k]
+ }
+
+ ## see n.ep() above
+ n_ <- function(eps, k, c1) {
+ stopifnot(is.finite(eps), length(eps) == 1L, eps > 0,
+ length(k) == length(c1), is.numeric(c1), is.integer(k), k >= 1)
+ exp((log(c1) - log(eps))/(2*k))
+ }
+
+ ne1 <- n_(ep12[1], k, c1.k)
+ ne. <- n_(ep12[2], k, c1.k)
+ d.k <- ne. - ne1
+ stopifnot(d.k > 0)
+ ## interval: {"fudge" 0.5 / 2.5} from results -- also 'noLdbl' gives *quite* different pic!:
+ odd <- k %% 2 == 1
+ cbind(ne1 - ifelse( odd & noLdbl, 1.5, 0.5) * d.k,
+ ne1 + ifelse(!odd , 8, 2.5) * d.k)
+ }
>
> nInt(k= 1, c1..$c1)
[,1] [,2]
[1,] 9711838 24932455
> nInt(k= 2, c1..$c1)
[,1] [,2]
[1,] 2316.237 6430.581
> nInt(k=18, c1..$c1)
[,1] [,2]
[1,] 5.888326 6.870896
>
> nints.k <- nInt(ks, c1..$c1)
> ## for printing
> form(as.data.frame( nints.k ))
V1 V2
1 9710000.00 24900000.00
2 2320.00 6430.00
3 167.00 232.00
4 48.50 87.50
5 24.20 29.60
6 15.70 23.80
7 11.70 13.60
8 9.63 13.30
9 8.36 9.36
10 7.54 9.85
11 7.00 7.68
12 6.62 8.29
13 6.36 6.88
14 6.17 7.51
15 6.05 6.48
16 5.96 7.09
17 5.91 6.28
18 5.89 6.87
>
> ## (-.5 , +2.5) ## originally ( -1, +1)
> ## 1 9710000.00 24900000.00 # 7180000.00 17300000.00
> ## 2 2320.00 3770.00 # 2070.00 3040.00
> ## 3 167.00 232.00 # 156.00 200.00
> ## 4 48.50 62.30 # 46.20 55.40
> ## 5 24.20 29.60 # 23.30 26.90
> ## 6 15.70 18.50 # 15.20 17.10
> ## 7 11.70 13.60 # 11.40 12.70
> ## 8 9.63 10.90 # 9.41 10.30
> ## 9 8.36 9.36 # 8.19 8.86
> ## 10 7.54 8.36 # 7.41 7.95
> ## 11 7.00 7.68 # 6.88 7.34
> ## 12 6.62 7.21 # 6.52 6.92
> ## 13 6.36 6.88 # 6.27 6.62
> ## 14 6.17 6.64 # 6.10 6.41
> ## 15 6.05 6.48 # 5.98 6.26
> ## 16 5.96 6.36 # 5.90 6.16
> ## 17 5.91 6.28 # 5.85 6.10
> ## 18 5.89 6.24 # 5.83 6.06
>
> ## 3. Then for each of the intervals, compare order k vs k+1
> ## -- ==> optimal cutoff { how much platform dependency ?? }
>
> ### Here, compute only
> find1cuts <- function(k, c1,
+ n = nInt(k, c1), # the *set* of n's or the 'range'
+ len.n = 1000,
+ precBits = 1024, nM = mpfr(n, precBits),
+ stnM = stirlerr(nM),
+ stirlOrd = sapply(k+(0:1), function(.k.) stirlerr(n, order = .k.)),
+ relE = asNumeric(stirlOrd/stnM -1), # "true" relative error for the {k, k+1}
+ do.spl=TRUE, df.spline = 9, # df = 5 gives 2 cutpoints for k==1
+ do.low=TRUE, f.lowess = 0.2,
+ do.cobs = require("cobs", quietly=TRUE), tau = 0.90)
+ {
+ ## check relErrV( stirlerr(n, order=k ) vs
+ ## stirlerr(n, order=k+1)
+ if(length(n) == 2L)
+ if(n[1] < n[2]) n <- seq(n[1], n[2], length.out = len.n)
+ else stop("'n' must be *increasing")
+ force(relE)
+ y <- abs19(relE)
+ ## NB: all smoothing --- as in stirlerrPlot() above -- should happen in log-space
+ ## (log(abs19(relEc)), 2, function(y) exp(smooth.spline(y, df=4)$y))
+ ly <- log(y) # == log(abs19(relE)) == log(max(|r|, 1e-19))
+ if(do.spl) {##
+ s1 <- exp(smooth.spline(ly[,1], df=df.spline)$y)
+ s2 <- exp(smooth.spline(ly[,2], df=df.spline)$y)
+ }
+ if(do.low) { ## lowess
+ s1l <- exp(lowess(ly[,1], f=f.lowess)$y)
+ s2l <- exp(lowess(ly[,2], f=f.lowess)$y)
+ }
+ ## also use cobs() splines for the 90% quantile !!
+ EE <- environment() # so can set do.cobs to FALSE in case of error
+ if(do.cobs) { ## <==> require("cobs") # yes, this is in tests/
+ cobsF <- function(Y) cobs(n, Y, tau=tau, nknots = 6, lambda = -1,
+ print.warn=FALSE, print.mesg=FALSE)
+ ## sparseM::chol(<matrix.csr>) now gives error when it gave warning {about singularity}
+ cobsF <- function(Y) {
+ r <- tryCatch(cobs(n, Y, tau=tau, nknots = 6, lambda = -1,
+ print.warn=FALSE, print.mesg=FALSE),
+ error = identity)
+ if(inherits(r, "error")) {
+ assign("do.cobs", FALSE, envir = EE) # and return
+ list(fitted = FALSE)
+ }
+ else
+ r
+ }
+ cs1 <- exp(cobsF(ly[,1])$fitted)
+ cs2 <- exp(cobsF(ly[,2])$fitted)
+ }
+ smooths <- list(spl = if(do.spl ) cbind(s1, s2 ),
+ low = if(do.low ) cbind(s1l,s2l),
+ cobs= if(do.cobs) cbind(cs1,cs2))
+ ## diffL <- list(spl = if(do.spl ) s2 -s1,
+ ## low = if(do.low ) s2l-s1l,
+ ## cobs= if(do.cobs) cs2-cs1)
+ ### FIXME: simplification does not always *work* -- (i, n.) are not always ok
+ ### ------ notably within R-devel-no-ldouble {hence probably macOS M1 ... ..}
+ sapply(smooths, function(s12) { d <- s12[,2] - s12[,1]
+ ## typically a (almost or completely) montone increasing function, crossing zero *once*
+ ## compute cutpoint:
+ ## i := the first n[i] with d(n[i]) >= 0
+ i <- which(d >= 0)[1]
+ if(length(i) == 1L && !is.na(i) && i > 1L) {
+ i_ <- i - 1L # ==> d(n[i_]) < 0
+ ## cutpoint must be in [n[i_], n[i]] --- do linear interpolation
+ n. <- n[i_] - (n[i] - n[i_])* d[i_] / (d[i] - d[i_])
+ } else {
+ if(length(i) != 1L) i <- -length(i)
+ n. <- NA_integer_
+ }
+ c(i=i, n.=n.)
+ }) -> n.L
+
+ list(k=k, n=n, relE = unname(relE), smooths=smooths, i.n = n.L)
+ } ## find1cuts()
>
> k. <- 1:15
> system.time(
+ ## Failed on lynne [2024-06-04, R 4.4.1 beta] with
+ ## Error in .local(x, ...) : insufficient space ---> SparseM :: chol(<..>)
+ ## ==> now we catch this inside find1cuts():
+ resL <- lapply(setNames(,k.), function(k) find1cuts(k=k, c1=c1..$c1))
+ ) ## -- warnings, notably from cobs() not converging
user system elapsed
24.641 0.015 29.172
There were 34 warnings (use warnings() to see them)
> ## needs 12 sec (!!) user system elapsed =
> (s.find15.fil <- paste0("stirlerr-find1_1-15_", myPlatform(), ".rds"))
[1] "stirlerr-find1_1-15_R-d_87286_unix_DbnGNU_Ltrx_.rds"
> ## now we catch cobs() errors {from SparseM::chol},
> ## okCuts <- !inherits(resL, "error")
> ## if(okCuts) {
> saveRDS(resL, file = s.find15.fil) # was "stirlerr-find1_1-15.rds"
> ## } else traceback()
> ## 11: stop(mess)
> ## 10: .local(x, ...)
> ## 9: chol(e, tmpmax = tmpmax, nsubmax = nsubmax, nnzlmax = nnzlmax)
> ## 8: chol(e, tmpmax = tmpmax, nsubmax = nsubmax, nnzlmax = nnzlmax)
> ## 7: rq.fit.sfnc(Xeq, Yeq, Xieq, Yieq, tau = tau, rhs = rhs, control = rqCtrl)
> ## 6: drqssbc2(x, y, w, pw = pw, knots = knots, degree = degree, Tlambda = if (select.lambda) lambdaSet else lambda,
> ## constraint = constraint, ptConstr = ptConstr, maxiter = maxiter,
> ## trace = trace - 1, nrq, nl1, neqc, niqc, nvar, tau = tau,
> ## select.lambda = select.lambda, give.pseudo.x = keep.x.ps,
> ## rq.tol = rq.tol, tol.0res = tol.0res, print.warn = print.warn)
> ## 5: cobs(n, Y, tau = tau, nknots = 6, lambda = -1, print.warn = FALSE,
> ## print.mesg = FALSE) at stirlerr-tst.R!udBzpT#32
> ## 4: cobsF(ly[, 1]) at stirlerr-tst.R!udBzpT#34
> ## 3: find1cuts(k = k, c1 = c1..$c1) at #1
> ## 2: FUN(X[[i]], ...)
> ## 1: lapply(setNames(, k.), function(k) find1cuts(k = k, c1 = c1..$c1))
>
> ok1cutsLst <- function(res) {
+ stopifnot(is.list(res), sapply(res, is.list)) # must be list of lists
+ cobsL <- lapply(lapply(res, `[[`, "smooths"), `[[`, "cobs")
+ vapply(cobsL, is.array, NA)
+ }
> (resLok <- ok1cutsLst(resL))
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> ## 1 2 3 4 5 6 ...... 15
> ## FALSE TRUE TRUE TRUE TRUE TRUE ...... TRUE
>
>
> if(FALSE) {
+ ## e.g. in R-devel-no-ldouble:
+ (r1 <- find1cuts(k=1, c1=c1..$c1))$i.n # list --- no longer ok {SparseM::chol -> insufficient space}
+ (r2 <- find1cuts(k=2, c1=c1..$c1))$i.n # "good"
+ (r3 <- find1cuts(k=3, c1=c1..$c1))$i.n # 3-vector: only 3x 'i' == 1
+ }
>
> ## if(okCuts) {
> mult.fig(15, main = "stirlerr(n, order=k) vs order = k+1")$old.par -> opar
> invisible(lapply(resL[resLok], plot1cuts))
> ## plus the "last" ones {also showing that k=15 is worse here anyway than k=17}
> str(r17 <- find1cuts(k=17, n = seq(5.1, 6.5, length.out = 1500), c1=c1..$c1))
List of 5
$ k : num 17
$ n : num [1:1500] 5.1 5.1 5.1 5.1 5.1 ...
$ relE : num [1:1500, 1:2] 5.31e-14 5.29e-14 5.25e-14 5.21e-14 5.19e-14 ...
$ smooths:List of 3
..$ spl : num [1:1500, 1:2] 5.29e-14 5.26e-14 5.23e-14 5.19e-14 5.16e-14 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
.. .. ..$ : chr [1:2] "s1" "s2"
..$ low : num [1:1500, 1:2] 5.29e-14 5.26e-14 5.23e-14 5.20e-14 5.17e-14 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
.. .. ..$ : chr [1:2] "s1l" "s2l"
..$ cobs: NULL
$ i.n : int [1:2, 1:3] 1 NA 1 NA NA NA
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:2] "i" "n."
.. ..$ : chr [1:3] "spl" "low" "cobs"
Warning messages:
1: In min(sol1["k", i.keep]) :
no non-missing arguments to min; returning Inf
2: In min(sol1["k", i.keep]) :
no non-missing arguments to min; returning Inf
> plot1cuts(r17) # no-ldouble is *very* different than normal: k *much better* than k+1
Error in stopifnot(is.list(smooths), (nS <- length(smooths)) >= 1L, sapply(smooths, :
'list' object cannot be coerced to type 'integer'
Calls: plot1cuts -> stopifnot -> eval -> eval -> stopifnot
Execution halted
Flavor: r-devel-linux-x86_64-debian-clang
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: WARN: 2, NOTE: 1, OK: 10
Version: 1.1-3
Check: re-building of vignette outputs
Result: WARN
Error(s) in re-building vignettes:
--- re-building ‘BspecFGN.Rnw’ using Sweave
Loading required package: longmemo
Error: processing vignette 'BspecFGN.Rnw' failed with diagnostics:
Running 'texi2dvi' on 'BspecFGN.tex' failed.
LaTeX errors:
! TeX capacity exceeded, sorry [input stack size=10000].
\GenericWarning ...tchoice@ \else 4\fi \endcsname
\protect \GenericWarning
l.170 ... always fulfilled for $x in \{1,2,\dots\}
$, as
! ==> Fatal error occurred, no output PDF file produced!
--- failed re-building ‘BspecFGN.Rnw’
SUMMARY: processing the following file failed:
‘BspecFGN.Rnw’
Error: Vignette re-building failed.
Execution halted
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.1-3
Check: tests
Result: NOTE
Running 'FEXP-ex.R' [1s]
Comparing 'FEXP-ex.Rout' to 'FEXP-ex.Rout.save' ... OK
Running 'ceta-ex.R' [3s]
Comparing 'ceta-ex.Rout' to 'ceta-ex.Rout.save' ...75c75
< [2,] -8.5705517 13.00507 -5.2497156
---
> [2,] -8.5705518 13.00507 -5.2497156
86c86
< [1,] 7.4008136 -7.25886 0.0763714
---
> [1,] 7.4008136 -7.25886 0.0763715
88c88
< [3,] 0.0763714 -5.38985 6.8074697
---
> [3,] 0.0763715 -5.38985 6.8074697
111c111
< [2,] -6.6156657 11.346062 -5.4359093
---
> [2,] -6.6156658 11.346062 -5.4359093
116c116
< [1,] 6.6254802 -6.577171 0.1320888
---
> [1,] 6.6254801 -6.577171 0.1320888
Running 'sim-ex.R' [0s]
Comparing 'sim-ex.Rout' to 'sim-ex.Rout.save' ... OK
Running 'spec-ex.R' [14s]
Flavor: r-devel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: NOTE: 3, OK: 10
Version: 0.9-5
Check: Rd cross-references
Result: NOTE
Found the following Rd file(s) with Rd \link{} targets missing package
anchors:
mpfr-class.Rd: is.whole
mpfr-utils.Rd: asNumeric
mpfr.Rd: asNumeric
mpfrArray.Rd: asNumeric
mpfrMatrix-utils.Rd: asNumeric
pbetaI.Rd: bigq
utils.Rd: is.whole
Please provide package anchors for all Rd \link{} targets not in the
package itself and the base packages.
Flavors: r-devel-linux-x86_64-debian-clang, r-devel-linux-x86_64-debian-gcc, r-devel-windows-x86_64
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: OK: 13
Current CRAN status: ERROR: 2, OK: 11
Version: 1.4-4
Check: PDF version of manual
Result: WARN
LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! TeX capacity exceeded, sorry [input stack size=10000].
\@latex@warning #1->\GenericWarning
{\space \space \space \@spaces \@spaces ...
l.739 \eqn{j \in \{0,1,\dots\}}{}
, as these are rational
! ==> Fatal error occurred, no output PDF file produced!
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.4-4
Check: PDF version of manual without index
Result: ERROR
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc
Version: 1.4-4
Check: for non-standard things in the check directory
Result: NOTE
Found the following files/directories:
‘VLMC-manual.tex’
Flavors: r-devel-linux-x86_64-fedora-clang, r-devel-linux-x86_64-fedora-gcc