Last updated on 2024-11-18 10:53:03 CET.
| Flavor | Version | Tinstall | Tcheck | Ttotal | Status | Flags |
|---|---|---|---|---|---|---|
| r-devel-linux-x86_64-debian-clang | 1.3-8 | 10.26 | 115.07 | 125.33 | ERROR | |
| r-devel-linux-x86_64-debian-gcc | 1.3-8 | 7.76 | 86.31 | 94.07 | OK | |
| r-devel-linux-x86_64-fedora-clang | 1.3-8 | 198.59 | ERROR | |||
| r-devel-linux-x86_64-fedora-gcc | 1.3-8 | 203.68 | OK | |||
| r-devel-windows-x86_64 | 1.3-8 | 14.00 | 132.00 | 146.00 | OK | |
| r-patched-linux-x86_64 | 1.3-8 | 10.52 | 114.41 | 124.93 | OK | |
| r-release-linux-x86_64 | 1.3-8 | 10.40 | 114.40 | 124.80 | OK | |
| r-release-macos-arm64 | 1.3-8 | 69.00 | OK | |||
| r-release-macos-x86_64 | 1.3-8 | 96.00 | OK | |||
| r-release-windows-x86_64 | 1.3-8 | 15.00 | 134.00 | 149.00 | OK | |
| r-oldrel-macos-arm64 | 1.3-8 | 74.00 | OK | |||
| r-oldrel-macos-x86_64 | 1.3-8 | 160.00 | OK | |||
| r-oldrel-windows-x86_64 | 1.3-8 | 17.00 | 167.00 | 184.00 | OK |
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’ [2s/3s]
Running ‘ex1.R’ [4s/4s]
Running ‘ex2-long.R’ [10s/12s]
Running ‘ex3.R’ [2s/3s]
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [4s/5s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [4s/5s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ... OK
Running ‘small-ex.R’ [3s/3s]
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’ [8s/10s]
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 ...
> 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] 0.1976 0.063 0.0491 -0.0626 -0.0868 ...
$ fitted : num [1:50] 0.0278 0.0287 0.0312 0.0354 0.0414 ...
$ coef : num [1:4] 0.0278 0.0278 0.8154 1
$ 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 7
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -6.77514e-02 -0.029701622 0.0278152 0.0853320 0.123382
2 -6.41787e-02 -0.027468888 0.0280224 0.0835138 0.120224
3 -6.04433e-02 -0.024973163 0.0286442 0.0822615 0.117732
4 -5.65412e-02 -0.022212175 0.0296803 0.0815728 0.115902
5 -5.24674e-02 -0.019182756 0.0311310 0.0814447 0.114729
6 -4.82149e-02 -0.015880775 0.0329961 0.0818729 0.114207
7 -4.37751e-02 -0.012301110 0.0352757 0.0828524 0.114326
8 -3.91381e-02 -0.008437641 0.0379697 0.0843771 0.115077
9 -3.42918e-02 -0.004283290 0.0410782 0.0864397 0.116448
10 -2.92233e-02 0.000169901 0.0446012 0.0890325 0.118426
11 -2.39179e-02 0.004930665 0.0485387 0.0921467 0.120995
12 -1.83600e-02 0.010008360 0.0528906 0.0957728 0.124141
13 -1.25335e-02 0.015412811 0.0576570 0.0999012 0.127847
14 -6.42140e-03 0.021154129 0.0628378 0.1045216 0.132097
15 -6.81378e-06 0.027242531 0.0684332 0.1096238 0.136873
16 6.72715e-03 0.033688168 0.0744430 0.1151978 0.142159
17 1.37970e-02 0.040500961 0.0808672 0.1212335 0.147938
18 2.12185e-02 0.047690461 0.0877060 0.1277215 0.154193
19 2.90068e-02 0.055265726 0.0949592 0.1346527 0.160912
20 3.71760e-02 0.063235225 0.1026269 0.1420185 0.168078
21 4.57390e-02 0.071606758 0.1107090 0.1498113 0.175679
22 5.47075e-02 0.080387396 0.1192056 0.1580238 0.183704
23 6.40921e-02 0.089583438 0.1281167 0.1666500 0.192141
24 7.39018e-02 0.099200377 0.1374422 0.1756841 0.200983
25 8.41444e-02 0.109242876 0.1471823 0.1851216 0.210220
26 9.48262e-02 0.119714746 0.1573367 0.1949588 0.219847
27 1.05952e-01 0.130618921 0.1679057 0.2051925 0.229859
28 1.17526e-01 0.141957438 0.1788891 0.2158208 0.240253
29 1.29548e-01 0.153731401 0.1902870 0.2268426 0.251026
30 1.42021e-01 0.165940947 0.2020994 0.2382578 0.262178
31 1.54941e-01 0.178585191 0.2143262 0.2500672 0.273711
32 1.68306e-01 0.191662165 0.2269675 0.2622729 0.285629
33 1.82111e-01 0.205168744 0.2400233 0.2748778 0.297936
34 1.96348e-01 0.219100556 0.2534935 0.2878865 0.310639
35 2.11008e-01 0.233451886 0.2673782 0.3013046 0.323748
36 2.26079e-01 0.248215565 0.2816774 0.3151392 0.337276
37 2.41547e-01 0.263382876 0.2963910 0.3293992 0.351235
38 2.57393e-01 0.278943451 0.3115191 0.3440948 0.365645
39 2.73599e-01 0.294885220 0.3270617 0.3592382 0.380524
40 2.90023e-01 0.311080514 0.3429107 0.3747410 0.395798
41 3.06194e-01 0.327075735 0.3586411 0.3902065 0.411088
42 3.22074e-01 0.342831649 0.3742095 0.4055873 0.426345
43 3.37676e-01 0.358355597 0.3896158 0.4208761 0.441556
44 3.53012e-01 0.373655096 0.4048602 0.4360653 0.456709
45 3.68094e-01 0.388737688 0.4199426 0.4511475 0.471791
46 3.82936e-01 0.403610792 0.4348630 0.4661151 0.486790
47 3.97549e-01 0.418281590 0.4496214 0.4809611 0.501694
48 4.11944e-01 0.432756923 0.4642177 0.4956786 0.516491
49 4.26133e-01 0.447043216 0.4786521 0.5102611 0.531172
50 4.40124e-01 0.461146429 0.4929245 0.5247027 0.545725
51 4.53927e-01 0.475072016 0.5070350 0.5389979 0.560143
52 4.67551e-01 0.488824911 0.5209834 0.5531418 0.574416
53 4.81002e-01 0.502409521 0.5347698 0.5671300 0.588538
54 4.94287e-01 0.515829730 0.5483942 0.5809587 0.602501
55 5.07412e-01 0.529088909 0.5618566 0.5946243 0.616302
56 5.20381e-01 0.542189933 0.5751571 0.6081242 0.629933
57 5.33198e-01 0.555135196 0.5882955 0.6214558 0.643393
58 5.45867e-01 0.567926630 0.6012719 0.6346172 0.656677
59 5.58390e-01 0.580565721 0.6140864 0.6476070 0.669782
60 5.70769e-01 0.593053527 0.6267388 0.6604241 0.682708
61 5.83005e-01 0.605390690 0.6392293 0.6730679 0.695454
62 5.95098e-01 0.617577451 0.6515577 0.6855380 0.708017
63 6.07048e-01 0.629613656 0.6637242 0.6978347 0.720400
64 6.18854e-01 0.641498766 0.6757287 0.7099586 0.732603
65 6.30515e-01 0.653231865 0.6875711 0.7219104 0.744627
66 6.42028e-01 0.664811658 0.6992516 0.7336916 0.756475
67 6.53391e-01 0.676236478 0.7107701 0.7453037 0.768149
68 6.64600e-01 0.687504287 0.7221266 0.7567489 0.779653
69 6.75652e-01 0.698612675 0.7333211 0.7680295 0.790991
70 6.86541e-01 0.709558867 0.7443536 0.7791483 0.802166
71 6.97262e-01 0.720339721 0.7552241 0.7901084 0.813186
72 7.07810e-01 0.730951740 0.7659326 0.8009134 0.824055
73 7.18179e-01 0.741391078 0.7764791 0.8115671 0.834779
74 7.28361e-01 0.751653555 0.7868636 0.8220736 0.845367
75 7.38348e-01 0.761734678 0.7970861 0.8324375 0.855824
76 7.48134e-01 0.771629669 0.8071466 0.8426636 0.866160
77 7.57709e-01 0.781333498 0.8170452 0.8527568 0.876382
78 7.67065e-01 0.790840929 0.8267817 0.8627224 0.886499
79 7.76192e-01 0.800146569 0.8363562 0.8725659 0.896520
80 7.85083e-01 0.809244928 0.8457688 0.8822926 0.906455
81 7.93727e-01 0.818130488 0.8550193 0.8919081 0.916312
82 8.02116e-01 0.826797774 0.8641079 0.9014179 0.926100
83 8.10240e-01 0.835241429 0.8730344 0.9108274 0.935829
84 8.18091e-01 0.843456291 0.8817990 0.9201417 0.945507
85 8.25661e-01 0.851437463 0.8904015 0.9293656 0.955142
86 8.32942e-01 0.859180385 0.8988421 0.9385038 0.964742
87 8.39928e-01 0.866680887 0.9071207 0.9475605 0.974313
88 8.46612e-01 0.873935236 0.9152373 0.9565393 0.983862
89 8.52989e-01 0.880940170 0.9231918 0.9654435 0.993395
90 8.59054e-01 0.887692913 0.9309844 0.9742760 1.002915
91 8.64803e-01 0.894191180 0.9386150 0.9830389 1.012427
92 8.70233e-01 0.900433167 0.9460836 0.9917341 1.021934
93 8.75343e-01 0.906417527 0.9533902 1.0003629 1.031437
94 8.80130e-01 0.912143340 0.9605348 1.0089263 1.040939
95 8.84594e-01 0.917610075 0.9675174 1.0174248 1.050441
96 8.88735e-01 0.922817542 0.9743381 1.0258586 1.059942
97 8.92551e-01 0.927765853 0.9809967 1.0342275 1.069442
98 8.96045e-01 0.932455371 0.9874933 1.0425312 1.078941
99 8.99218e-01 0.936886669 0.9938279 1.0507692 1.088438
100 9.02069e-01 0.941060487 1.0000006 1.0589406 1.097932
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0278152 0.0278152 0.8153868 1.0000006
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
{tau=0.5}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:4]: -1.000002, -0.632653, 0.183673, 1.000002
with 3 pointwise constraints
coef[1:4]: 0.0504467, 0.0504467, 0.6305155, 1.0000009
R^2 = 93.83% ; empirical tau (over all): 21/50 = 0.42 (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%)
........................
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.
> with(coS, cbind(pp.lambda, pp.sic, k0, ifl, icyc))
pp.lambda pp.sic k0 ifl icyc
[1,] 3.54019e-05 -2.64644 22 1 21
[2,] 6.92936e-05 -2.64644 22 1 21
[3,] 1.35631e-04 -2.64644 22 1 20
[4,] 2.65477e-04 -2.64644 22 1 22
[5,] 5.19629e-04 -2.64644 22 1 22
[6,] 1.01709e-03 -2.64644 22 1 23
[7,] 1.99080e-03 -2.68274 21 1 20
[8,] 3.89667e-03 -2.75212 19 1 18
[9,] 7.62711e-03 -2.73932 19 1 14
[10,] 1.49289e-02 -2.85261 16 1 13
[11,] 2.92209e-02 -2.97873 12 1 12
[12,] 5.71953e-02 -3.01058 11 1 12
[13,] 1.11951e-01 -3.04364 10 1 11
[14,] 2.19126e-01 -3.11242 8 1 12
[15,] 4.28904e-01 -3.17913 6 1 12
[16,] 8.39512e-01 -3.18824 5 1 11
[17,] 1.64321e+00 -3.01467 5 1 12
[18,] 3.21633e+00 -3.01380 4 1 11
[19,] 6.29545e+00 -3.01380 4 1 10
[20,] 1.23223e+01 -3.01380 4 1 11
[21,] 2.41190e+01 -3.01380 4 1 11
[22,] 4.72092e+01 -3.01380 4 1 10
[23,] 9.24046e+01 -3.01380 4 1 10
[24,] 1.80867e+02 -3.01380 4 1 10
[25,] 3.54019e+02 -3.01380 4 1 10
> with(coS, plot(pp.sic ~ pp.lambda, type = "b", log = "x", col=2,
+ main = deparse(call)))
> ##-> very nice minimum close to 1
>
> summaryCobs(coS)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", lambda = -1, pointwise = con, trace = 3)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : NULL
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi TRUE
$ 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] 0.2254 0.0829 0.062 -0.0562 -0.0862 ...
$ fitted : num [1:50] 0 0.00869 0.01837 0.02906 0.04075 ...
$ coef : num [1:22] 0 0.00819 0.03365 0.06662 0.10458 ...
$ knots : num [1:20] -1 -0.918 -0.796 -0.714 -0.592 ...
$ k0 : int [1:25] 22 22 22 22 22 22 21 19 19 16 ...
$ k : int 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : Named num 0.84
..- attr(*, "names")= chr "lambda"
$ icyc : int [1:25] 21 21 20 22 22 23 20 18 14 13 ...
$ ifl : int [1:25] 1 1 1 1 1 1 1 1 1 1 ...
$ pp.lambda : num [1:25] 0 0 0 0 0.001 0.001 0.002 0.004 0.008 0.015 ...
$ pp.sic : num [1:25] -2.65 -2.65 -2.65 -2.65 -2.65 ...
$ i.mask : logi [1:25] TRUE TRUE TRUE TRUE TRUE TRUE ...
cb.lo ci.lo fit ci.up cb.up
1 -0.07071332 -0.03907635 -3.77249e-07 0.0390756 0.0707126
2 -0.06555125 -0.03435600 4.17438e-03 0.0427048 0.0739000
3 -0.06016465 -0.02940203 8.59400e-03 0.0465900 0.0773526
4 -0.05455349 -0.02421442 1.32585e-02 0.0507314 0.0810704
5 -0.04871809 -0.01879334 1.81678e-02 0.0551289 0.0850537
6 -0.04265897 -0.01313909 2.33220e-02 0.0597831 0.0893029
7 -0.03637554 -0.00725134 2.87210e-02 0.0646934 0.0938176
8 -0.02986704 -0.00112966 3.43649e-02 0.0698595 0.0985969
9 -0.02313305 0.00522618 4.02537e-02 0.0752812 0.1036404
10 -0.01617351 0.01181620 4.63873e-02 0.0809584 0.1089481
11 -0.00898880 0.01864020 5.27658e-02 0.0868914 0.1145204
12 -0.00157983 0.02569768 5.93891e-02 0.0930806 0.1203581
13 0.00605308 0.03298846 6.62573e-02 0.0995262 0.1264615
14 0.01391000 0.04051257 7.33704e-02 0.1062282 0.1328307
15 0.02199057 0.04826981 8.07283e-02 0.1131867 0.1394660
16 0.03029461 0.05626010 8.83310e-02 0.1204020 0.1463675
17 0.03882336 0.06448412 9.61787e-02 0.1278732 0.1535339
18 0.04757769 0.07294234 1.04271e-01 0.1355999 0.1609646
19 0.05655804 0.08163500 1.12608e-01 0.1435819 0.1686589
20 0.06576441 0.09056212 1.21191e-01 0.1518192 0.1766169
21 0.07519637 0.09972344 1.30018e-01 0.1603120 0.1848391
22 0.08485262 0.10911826 1.39090e-01 0.1690610 0.1933266
23 0.09473211 0.11874598 1.48406e-01 0.1780668 0.2020807
24 0.10483493 0.12860668 1.57968e-01 0.1873294 0.2111011
25 0.11516076 0.13870015 1.67775e-01 0.1968489 0.2203882
26 0.12570956 0.14902638 1.77826e-01 0.2066253 0.2299421
27 0.13648327 0.15958645 1.88122e-01 0.2166576 0.2397608
28 0.14748286 0.17038090 1.98663e-01 0.2269453 0.2498433
29 0.15870881 0.18140998 2.09449e-01 0.2374880 0.2601892
30 0.17016110 0.19267368 2.20480e-01 0.2482859 0.2707984
31 0.18183922 0.20417172 2.31755e-01 0.2593391 0.2816716
32 0.19374227 0.21590361 2.43276e-01 0.2706482 0.2928095
33 0.20587062 0.22786955 2.55041e-01 0.2822129 0.3042118
34 0.21822524 0.24007008 2.67051e-01 0.2940328 0.3158776
35 0.23080666 0.25250549 2.79306e-01 0.3061075 0.3278063
36 0.24361488 0.26517577 2.91806e-01 0.3184370 0.3399979
37 0.25664938 0.27808064 3.04551e-01 0.3310217 0.3524530
38 0.26990862 0.29121926 3.17541e-01 0.3438624 0.3651730
39 0.28339034 0.30459037 3.30775e-01 0.3569602 0.3781603
40 0.29709467 0.31819405 3.44255e-01 0.3703152 0.3914146
41 0.31102144 0.33203019 3.57979e-01 0.3839275 0.4049363
42 0.32517059 0.34609876 3.71948e-01 0.3977971 0.4187252
43 0.33954481 0.36040126 3.86162e-01 0.4119224 0.4327789
44 0.35414537 0.37493839 4.00621e-01 0.4263028 0.4470958
45 0.36897279 0.38971043 4.15324e-01 0.4409381 0.4616757
46 0.38402708 0.40471738 4.30273e-01 0.4558281 0.4765184
47 0.39930767 0.41995895 4.45466e-01 0.4709732 0.4916245
48 0.41479557 0.43541678 4.60887e-01 0.4863568 0.5069780
49 0.43039487 0.45099622 4.76442e-01 0.5018872 0.5224885
50 0.44609197 0.46668362 4.92117e-01 0.5175506 0.5381422
51 0.46188684 0.48247895 5.07913e-01 0.5333471 0.5539392
52 0.47773555 0.49833835 5.23786e-01 0.5492329 0.5698357
53 0.49336687 0.51398935 5.39461e-01 0.5649325 0.5855550
54 0.50873469 0.52938518 5.54891e-01 0.5803975 0.6010480
55 0.52383955 0.54452615 5.70077e-01 0.5956277 0.6163143
56 0.53868141 0.55941225 5.85018e-01 0.6106231 0.6313539
57 0.55325974 0.57404316 5.99714e-01 0.6253839 0.6461673
58 0.56757320 0.58841816 6.14165e-01 0.6399109 0.6607558
59 0.58161907 0.60253574 6.28371e-01 0.6542056 0.6751223
60 0.59539741 0.61639593 6.42332e-01 0.6682680 0.6892665
61 0.60890835 0.62999881 6.56048e-01 0.6820980 0.7031884
62 0.62215175 0.64334429 6.69520e-01 0.6956957 0.7168882
63 0.63512996 0.65643368 6.82747e-01 0.7090597 0.7303634
64 0.64784450 0.66926783 6.95729e-01 0.7221893 0.7436126
65 0.66029589 0.68184700 7.08466e-01 0.7350841 0.7566352
66 0.67248408 0.69417118 7.20958e-01 0.7477442 0.7694313
67 0.68440855 0.70624008 7.33205e-01 0.7601699 0.7820014
68 0.69606829 0.71805313 7.45207e-01 0.7723617 0.7943465
69 0.70746295 0.72961016 7.56965e-01 0.7843198 0.8064670
70 0.71859343 0.74091165 7.68478e-01 0.7960438 0.8183620
71 0.72946023 0.75195789 7.79746e-01 0.8075332 0.8300309
72 0.74006337 0.76274887 7.90769e-01 0.8187883 0.8414738
73 0.75040233 0.77328433 8.01547e-01 0.8298091 0.8526911
74 0.76047612 0.78356369 8.12080e-01 0.8405963 0.8636839
75 0.77028266 0.79358583 8.22368e-01 0.8511510 0.8744542
76 0.77982200 0.80335076 8.32412e-01 0.8614732 0.8850020
77 0.78909446 0.81285866 8.42211e-01 0.8715627 0.8953269
78 0.79809990 0.82210946 8.51765e-01 0.8814196 0.9054292
79 0.80683951 0.83110382 8.61074e-01 0.8910433 0.9153076
80 0.81531459 0.83984244 8.70138e-01 0.9004329 0.9249608
81 0.82352559 0.84832559 8.78957e-01 0.9095884 0.9343884
82 0.83147249 0.85655324 8.87531e-01 0.9185095 0.9435903
83 0.83915483 0.86452515 8.95861e-01 0.9271968 0.9525671
84 0.84657171 0.87224082 9.03946e-01 0.9356505 0.9613196
85 0.85372180 0.87969951 9.11786e-01 0.9438715 0.9698492
86 0.86060525 0.88690131 9.19381e-01 0.9518597 0.9781558
87 0.86722242 0.89384640 9.26731e-01 0.9596149 0.9862389
88 0.87357322 0.90053476 9.33836e-01 0.9671371 0.9940986
89 0.87965804 0.90696658 9.40696e-01 0.9744261 1.0017347
90 0.88547781 0.91314239 9.47312e-01 0.9814814 1.0091460
91 0.89103290 0.91906239 9.53683e-01 0.9883028 1.0163323
92 0.89632328 0.92472655 9.59808e-01 0.9948904 1.0232937
93 0.90134850 0.93013464 9.65689e-01 1.0012443 1.0300304
94 0.90610776 0.93528622 9.71326e-01 1.0073650 1.0365434
95 0.91060065 0.94018104 9.76717e-01 1.0132527 1.0428331
96 0.91482784 0.94481950 9.81863e-01 1.0189071 1.0488987
97 0.91878971 0.94920179 9.86765e-01 1.0243279 1.0547400
98 0.92248624 0.95332789 9.91422e-01 1.0295152 1.0603569
99 0.92591703 0.95719761 9.95833e-01 1.0344692 1.0657498
100 0.92908136 0.96081053 1.00000e+00 1.0391902 1.0709194
knots :
[1] -1.0000020 -0.9183673 -0.7959184 -0.7142857 -0.5918367 -0.5102041
[7] -0.3877551 -0.2653061 -0.1836735 -0.0612245 0.0204082 0.1428571
[13] 0.2244898 0.3469388 0.4693878 0.5510204 0.6734694 0.7551020
[19] 0.8775510 1.0000020
coef :
[1] -4.01161e-07 8.18714e-03 3.36534e-02 6.66159e-02 1.04576e-01
[6] 1.50032e-01 2.00486e-01 2.70027e-01 3.35473e-01 4.05918e-01
[11] 4.83858e-01 5.64259e-01 6.37163e-01 7.05069e-01 7.77561e-01
[16] 8.30474e-01 8.78390e-01 9.18810e-01 9.54232e-01 9.87743e-01
[21] 1.00000e+00 5.99960e-01
>
> plot(x, y, main = "cobs(x,y, constraint=\"increase\", pointwise = *)")
> matlines(x, cbind(fitted(coR), fitted(coR1), fitted(coS)),
+ col = 2:4, lty=1)
>
> ##-- real data example (still n = 50)
> data(cars)
> attach(cars)
> co1 <- cobs(speed, dist, "increase")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> co1.1 <- cobs(speed, dist, "increase", knots.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> co1.2 <- cobs(speed, dist, "increase", knots.add = TRUE, repeat.delete.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> ## These three all give the same -- only remaining knots (outermost data):
> ic <- which("call" == names(co1))
> stopifnot(all.equal(co1[-ic], co1.1[-ic]),
+ all.equal(co1[-ic], co1.2[-ic]))
> 1 - sum(co1 $ resid ^2) / sum((dist - mean(dist))^2) # R^2 = 64.2%
[1] 0.642288
>
> co2 <- cobs(speed, dist, "increase", lambda = -1)# 6 warnings
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-debian-clang
Version: 1.3-8
Check: examples
Result: ERROR
Running examples in ‘cobs-Ex.R’ failed
The error most likely occurred in:
> ### 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-fedora-clang
Version: 1.3-8
Check: tests
Result: ERROR
Running ‘0_pt-ex.R’
Running ‘ex1.R’
Running ‘ex2-long.R’ [12s/16s]
Running ‘ex3.R’
Comparing ‘ex3.Rout’ to ‘ex3.Rout.save’ ... OK
Running ‘multi-constr.R’ [7s/11s]
Comparing ‘multi-constr.Rout’ to ‘multi-constr.Rout.save’ ... OK
Running ‘roof.R’ [6s/12s]
Comparing ‘roof.Rout’ to ‘roof.Rout.save’ ... OK
Running ‘small-ex.R’
Comparing ‘small-ex.Rout’ to ‘small-ex.Rout.save’ ... OK
Running ‘spline-ex.R’
Comparing ‘spline-ex.Rout’ to ‘spline-ex.Rout.save’ ... OK
Running ‘temp.R’
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 : 20
35,42c32,35
<
< **** ERROR in algorithm: ifl = 20
<
<
< {tau=0.5}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.40707639, -0.31455702, 0.05463725, -0.05314932, 0.29190009
< R^2 = 72.54% ; empirical tau (over all): 56/113 = 0.4955752 (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$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.47054145, -0.01648649, -0.01648649, 0.27562279
> R^2 = 70.37% ; empirical tau (over all): 56/113 = 0.4955752 (target tau= 0.5)
72,75c58,61
< {tau=0.1}-quantile; dimensionality of fit: 5 from {5}
< x$knots[1:5]: 1880, 1908, 1936, 1964, 1992
< coef[1:5]: -0.5515010, -0.4255000, -0.1700000, -0.1700000, 0.1300024
< empirical tau (over all): 11/113 = 0.09734513 (target tau= 0.1)
---
> {tau=0.1}-quantile; dimensionality of fit: 4 from {4}
> x$knots[1:4]: 1880, 1936, 1964, 1992
> coef[1:4]: -0.5700016, -0.1700000, -0.1700000, 0.1300024
> empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
78,80d63
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
84,91c67,70
<
< **** ERROR in algorithm: ifl = 22
<
<
< {tau=0.9}-quantile; dimensionality of fit: 5 from {5}
< x$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)
94,96c73
< [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
98c75
< [1] 5 8 25 38 39 77 85 86 92 95 97
---
> [1] 5 8 25 28 38 39 85 86 92 95 97 113
103,215c80,192
< [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
218,330c195,307
< [1,] 1880 -0.551500000 -0.8692435 -0.233756532 -0.74079307 -0.362206927
< [2,] 1881 -0.547000000 -0.8504667 -0.243533314 -0.72778780 -0.366212204
< [3,] 1882 -0.542500000 -0.8319198 -0.253080242 -0.71491945 -0.370080546
< [4,] 1883 -0.538000000 -0.8136378 -0.262362171 -0.70220898 -0.373791017
< [5,] 1884 -0.533500000 -0.7956627 -0.271337305 -0.68968128 -0.377318719
< [6,] 1885 -0.529000000 -0.7780442 -0.279955841 -0.67736602 -0.380633979
< [7,] 1886 -0.524500000 -0.7608416 -0.288158389 -0.66529858 -0.383701418
< [8,] 1887 -0.520000000 -0.7441258 -0.295874209 -0.65352111 -0.386478893
< [9,] 1888 -0.515500000 -0.7279807 -0.303019336 -0.64208362 -0.388916382
< [10,] 1889 -0.511000000 -0.7125052 -0.309494803 -0.63104507 -0.390954927
< [11,] 1890 -0.506500000 -0.6978147 -0.315185325 -0.62047415 -0.392525847
< [12,] 1891 -0.502000000 -0.6840410 -0.319959029 -0.61044942 -0.393550580
< [13,] 1892 -0.497500000 -0.6713309 -0.323669122 -0.60105832 -0.393941676
< [14,] 1893 -0.493000000 -0.6598415 -0.326158511 -0.59239445 -0.393605547
< [15,] 1894 -0.488500000 -0.6497316 -0.327268365 -0.58455243 -0.392447572
< [16,] 1895 -0.484000000 -0.6411491 -0.326850877 -0.57762031 -0.390379695
< [17,] 1896 -0.479500000 -0.6342149 -0.324785091 -0.57167014 -0.387329858
< [18,] 1897 -0.475000000 -0.6290072 -0.320992831 -0.56674851 -0.383251488
< [19,] 1898 -0.470500000 -0.6255495 -0.315450451 -0.56286950 -0.378130499
< [20,] 1899 -0.466000000 -0.6238074 -0.308192629 -0.56001245 -0.371987550
< [21,] 1900 -0.461500000 -0.6236932 -0.299306846 -0.55812524 -0.364874755
< [22,] 1901 -0.457000000 -0.6250795 -0.288920492 -0.55713199 -0.356868008
< [23,] 1902 -0.452500000 -0.6278154 -0.277184649 -0.55694269 -0.348057313
< [24,] 1903 -0.448000000 -0.6317413 -0.264258680 -0.55746239 -0.338537611
< [25,] 1904 -0.443500000 -0.6367018 -0.250298234 -0.55859837 -0.328401628
< [26,] 1905 -0.439000000 -0.6425525 -0.235447498 -0.56026474 -0.317735261
< [27,] 1906 -0.434500000 -0.6491648 -0.219835216 -0.56238479 -0.306615211
< [28,] 1907 -0.430000000 -0.6564265 -0.203573485 -0.56489174 -0.295108256
< [29,] 1908 -0.425500000 -0.6642417 -0.186758271 -0.56772843 -0.283271568
< [30,] 1909 -0.416375000 -0.6444420 -0.188308043 -0.55224402 -0.280505976
< [31,] 1910 -0.407250000 -0.6249490 -0.189550984 -0.53694241 -0.277557591
< [32,] 1911 -0.398125000 -0.6058089 -0.190441134 -0.52185096 -0.274399035
< [33,] 1912 -0.389000000 -0.5870750 -0.190924973 -0.50700158 -0.270998423
< [34,] 1913 -0.379875000 -0.5688095 -0.190940499 -0.49243118 -0.267318816
< [35,] 1914 -0.370750000 -0.5510835 -0.190416485 -0.47818222 -0.263317783
< [36,] 1915 -0.361625000 -0.5339779 -0.189272139 -0.46430281 -0.258947192
< [37,] 1916 -0.352500000 -0.5175825 -0.187417468 -0.45084657 -0.254153431
< [38,] 1917 -0.343375000 -0.5019952 -0.184754769 -0.43787171 -0.248878295
< [39,] 1918 -0.334250000 -0.4873183 -0.181181668 -0.42543921 -0.243060793
< [40,] 1919 -0.325125000 -0.4736540 -0.176596039 -0.41360991 -0.236640086
< [41,] 1920 -0.316000000 -0.4610972 -0.170902819 -0.40244046 -0.229559541
< [42,] 1921 -0.306875000 -0.4497278 -0.164022164 -0.39197841 -0.221771591
< [43,] 1922 -0.297750000 -0.4396023 -0.155897699 -0.38225735 -0.213242652
< [44,] 1923 -0.288625000 -0.4307468 -0.146503154 -0.37329293 -0.203957073
< [45,] 1924 -0.279500000 -0.4231543 -0.135845678 -0.36508089 -0.193919112
< [46,] 1925 -0.270375000 -0.4167851 -0.123964922 -0.35759761 -0.183152393
< [47,] 1926 -0.261250000 -0.4115719 -0.110928148 -0.35080301 -0.171696986
< [48,] 1927 -0.252125000 -0.4074273 -0.096822686 -0.34464508 -0.159604916
< [49,] 1928 -0.243000000 -0.4042525 -0.081747527 -0.33906484 -0.146935158
< [50,] 1929 -0.233875000 -0.4019444 -0.065805632 -0.33400095 -0.133749048
< [51,] 1930 -0.224750000 -0.4004021 -0.049097883 -0.32939331 -0.120106687
< [52,] 1931 -0.215625000 -0.3995310 -0.031718987 -0.32518550 -0.106064496
< [53,] 1932 -0.206500000 -0.3992449 -0.013755146 -0.32132617 -0.091673830
< [54,] 1933 -0.197374999 -0.3994669 0.004716902 -0.31776960 -0.076980402
< [55,] 1934 -0.188249999 -0.4001299 0.023629911 -0.31447572 -0.062024276
< [56,] 1935 -0.179124999 -0.4011756 0.042925575 -0.31140981 -0.046840186
< [57,] 1936 -0.169999999 -0.4025537 0.062553694 -0.30854196 -0.031458039
< [58,] 1937 -0.169999999 -0.3920506 0.052050575 -0.30228481 -0.037715186
< [59,] 1938 -0.169999999 -0.3818799 0.041879911 -0.29622572 -0.043774276
< [60,] 1939 -0.169999999 -0.3720919 0.032091902 -0.29039460 -0.049605402
< [61,] 1940 -0.169999999 -0.3627449 0.022744854 -0.28482617 -0.055173829
< [62,] 1941 -0.169999999 -0.3539060 0.013906014 -0.27956050 -0.060439496
< [63,] 1942 -0.169999999 -0.3456521 0.005652118 -0.27464331 -0.065356687
< [64,] 1943 -0.169999999 -0.3380694 -0.001930632 -0.27012595 -0.069874048
< [65,] 1944 -0.169999999 -0.3312525 -0.008747527 -0.26606484 -0.073935158
< [66,] 1945 -0.169999999 -0.3253023 -0.014697685 -0.26252008 -0.077479916
< [67,] 1946 -0.169999999 -0.3203219 -0.019678148 -0.25955301 -0.080446986
< [68,] 1947 -0.169999999 -0.3164101 -0.023589921 -0.25722261 -0.082777393
< [69,] 1948 -0.169999999 -0.3136543 -0.026345677 -0.25558089 -0.084419112
< [70,] 1949 -0.169999999 -0.3121218 -0.027878154 -0.25466793 -0.085332072
< [71,] 1950 -0.169999999 -0.3118523 -0.028147699 -0.25450735 -0.085492652
< [72,] 1951 -0.169999999 -0.3128528 -0.027147163 -0.25510341 -0.084896591
< [73,] 1952 -0.169999999 -0.3150972 -0.024902819 -0.25644046 -0.083559541
< [74,] 1953 -0.169999999 -0.3185290 -0.021471038 -0.25848491 -0.081515086
< [75,] 1954 -0.169999999 -0.3230683 -0.016931668 -0.26118921 -0.078810793
< [76,] 1955 -0.169999999 -0.3286202 -0.011379769 -0.26449670 -0.075503294
< [77,] 1956 -0.169999999 -0.3350825 -0.004917467 -0.26834657 -0.071653431
< [78,] 1957 -0.169999999 -0.3423529 0.002352862 -0.27267781 -0.067322192
< [79,] 1958 -0.169999999 -0.3503335 0.010333515 -0.27743222 -0.062567783
< [80,] 1959 -0.169999999 -0.3589345 0.018934501 -0.28255618 -0.057443816
< [81,] 1960 -0.169999999 -0.3680750 0.028075027 -0.28800158 -0.051998422
< [82,] 1961 -0.169999999 -0.3776839 0.037683867 -0.29372596 -0.046274035
< [83,] 1962 -0.169999999 -0.3876990 0.047699017 -0.29969241 -0.040307591
< [84,] 1963 -0.169999999 -0.3980670 0.058066957 -0.30586902 -0.034130975
< [85,] 1964 -0.169999999 -0.4087417 0.068741729 -0.31222843 -0.027771567
< [86,] 1965 -0.159285714 -0.3857122 0.067140801 -0.29417746 -0.024393969
< [87,] 1966 -0.148571428 -0.3632362 0.066093356 -0.27645622 -0.020686639
< [88,] 1967 -0.137857142 -0.3414096 0.065695360 -0.25912188 -0.016592404
< [89,] 1968 -0.127142857 -0.3203446 0.066058909 -0.24224123 -0.012044485
< [90,] 1969 -0.116428571 -0.3001699 0.067312749 -0.22589096 -0.006966182
< [91,] 1970 -0.105714285 -0.2810296 0.069601066 -0.21015697 -0.001271599
< [92,] 1971 -0.095000000 -0.2630795 0.073079509 -0.19513199 0.005131993
< [93,] 1972 -0.084285714 -0.2464789 0.077907440 -0.18091096 0.012339531
< [94,] 1973 -0.073571428 -0.2313788 0.084235942 -0.16758388 0.020441022
< [95,] 1974 -0.062857142 -0.2179067 0.092192406 -0.15522664 0.029512358
< [96,] 1975 -0.052142857 -0.2061500 0.101864313 -0.14389137 0.039605655
< [97,] 1976 -0.041428571 -0.1961435 0.113286338 -0.13359871 0.050741570
< [98,] 1977 -0.030714285 -0.1878634 0.126434838 -0.12433459 0.062906020
< [99,] 1978 -0.020000000 -0.1812316 0.141231635 -0.11605243 0.076052428
< [100,] 1979 -0.009285714 -0.1761272 0.157555775 -0.10868017 0.090108739
< [101,] 1980 0.001428572 -0.1724023 0.175259450 -0.10212975 0.104986896
< [102,] 1981 0.012142857 -0.1698981 0.194183828 -0.09630656 0.120592277
< [103,] 1982 0.022857143 -0.1684575 0.214171819 -0.09111701 0.136831296
< [104,] 1983 0.033571429 -0.1679338 0.235076625 -0.08647364 0.153616502
< [105,] 1984 0.044285714 -0.1681949 0.256766379 -0.08229790 0.170869332
< [106,] 1985 0.055000000 -0.1691258 0.279125791 -0.07852111 0.188521107
< [107,] 1986 0.065714286 -0.1706273 0.302055897 -0.07508430 0.206512868
< [108,] 1987 0.076428572 -0.1726156 0.325472731 -0.07193745 0.224794593
< [109,] 1988 0.087142857 -0.1750198 0.349305552 -0.06903842 0.243324139
< [110,] 1989 0.097857143 -0.1777807 0.373494972 -0.06635184 0.262066125
< [111,] 1990 0.108571429 -0.1808483 0.397991187 -0.06384803 0.280990883
< [112,] 1991 0.119285714 -0.1841810 0.422752400 -0.06150208 0.300073511
< [113,] 1992 0.130000000 -0.1877435 0.447743468 -0.05929307 0.319293073
---
> [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
333,445c310,422
< [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
468,470d444
< Warning message:
< In cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 19
480,482d453
< Warning message:
< In cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1, constraint = "none", :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
486,489d456
<
< **** ERROR in algorithm: ifl = 22
<
<
492,493c459,460
< 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)
499,502d465
<
< **** ERROR in algorithm: ifl = 22
<
<
505,507d467
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
512,515d471
<
< **** ERROR in algorithm: ifl = 22
<
<
518,520d473
< Warning message:
< In cobs(year, temp, nknots = length(a50$knots), knots = a50$knot, :
< drqssbc2(): Not all flags are normal (== 1), ifl : 22
522,524c475
< [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
526,529c477
< [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/12s]
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 ...
> 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] 0.1976 0.063 0.0491 -0.0626 -0.0868 ...
$ fitted : num [1:50] 0.0278 0.0287 0.0312 0.0354 0.0414 ...
$ coef : num [1:4] 0.0278 0.0278 0.8154 1
$ 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 7
$ ifl : int 1
$ pp.lambda : NULL
$ pp.sic : NULL
$ i.mask : NULL
cb.lo ci.lo fit ci.up cb.up
1 -6.77514e-02 -0.029701622 0.0278152 0.0853320 0.123382
2 -6.41787e-02 -0.027468888 0.0280224 0.0835138 0.120224
3 -6.04433e-02 -0.024973163 0.0286442 0.0822615 0.117732
4 -5.65412e-02 -0.022212175 0.0296803 0.0815728 0.115902
5 -5.24674e-02 -0.019182756 0.0311310 0.0814447 0.114729
6 -4.82149e-02 -0.015880775 0.0329961 0.0818729 0.114207
7 -4.37751e-02 -0.012301110 0.0352757 0.0828524 0.114326
8 -3.91381e-02 -0.008437641 0.0379697 0.0843771 0.115077
9 -3.42918e-02 -0.004283290 0.0410782 0.0864397 0.116448
10 -2.92233e-02 0.000169901 0.0446012 0.0890325 0.118426
11 -2.39179e-02 0.004930665 0.0485387 0.0921467 0.120995
12 -1.83600e-02 0.010008360 0.0528906 0.0957728 0.124141
13 -1.25335e-02 0.015412811 0.0576570 0.0999012 0.127847
14 -6.42140e-03 0.021154129 0.0628378 0.1045216 0.132097
15 -6.81378e-06 0.027242531 0.0684332 0.1096238 0.136873
16 6.72715e-03 0.033688168 0.0744430 0.1151978 0.142159
17 1.37970e-02 0.040500961 0.0808672 0.1212335 0.147938
18 2.12185e-02 0.047690461 0.0877060 0.1277215 0.154193
19 2.90068e-02 0.055265726 0.0949592 0.1346527 0.160912
20 3.71760e-02 0.063235225 0.1026269 0.1420185 0.168078
21 4.57390e-02 0.071606758 0.1107090 0.1498113 0.175679
22 5.47075e-02 0.080387396 0.1192056 0.1580238 0.183704
23 6.40921e-02 0.089583438 0.1281167 0.1666500 0.192141
24 7.39018e-02 0.099200377 0.1374422 0.1756841 0.200983
25 8.41444e-02 0.109242876 0.1471823 0.1851216 0.210220
26 9.48262e-02 0.119714746 0.1573367 0.1949588 0.219847
27 1.05952e-01 0.130618921 0.1679057 0.2051925 0.229859
28 1.17526e-01 0.141957438 0.1788891 0.2158208 0.240253
29 1.29548e-01 0.153731401 0.1902870 0.2268426 0.251026
30 1.42021e-01 0.165940947 0.2020994 0.2382578 0.262178
31 1.54941e-01 0.178585191 0.2143262 0.2500672 0.273711
32 1.68306e-01 0.191662165 0.2269675 0.2622729 0.285629
33 1.82111e-01 0.205168744 0.2400233 0.2748778 0.297936
34 1.96348e-01 0.219100556 0.2534935 0.2878865 0.310639
35 2.11008e-01 0.233451886 0.2673782 0.3013046 0.323748
36 2.26079e-01 0.248215565 0.2816774 0.3151392 0.337276
37 2.41547e-01 0.263382876 0.2963910 0.3293992 0.351235
38 2.57393e-01 0.278943451 0.3115191 0.3440948 0.365645
39 2.73599e-01 0.294885220 0.3270617 0.3592382 0.380524
40 2.90023e-01 0.311080514 0.3429107 0.3747410 0.395798
41 3.06194e-01 0.327075735 0.3586411 0.3902065 0.411088
42 3.22074e-01 0.342831649 0.3742095 0.4055873 0.426345
43 3.37676e-01 0.358355597 0.3896158 0.4208761 0.441556
44 3.53012e-01 0.373655096 0.4048602 0.4360653 0.456709
45 3.68094e-01 0.388737688 0.4199426 0.4511475 0.471791
46 3.82936e-01 0.403610792 0.4348630 0.4661151 0.486790
47 3.97549e-01 0.418281590 0.4496214 0.4809611 0.501694
48 4.11944e-01 0.432756923 0.4642177 0.4956786 0.516491
49 4.26133e-01 0.447043216 0.4786521 0.5102611 0.531172
50 4.40124e-01 0.461146429 0.4929245 0.5247027 0.545725
51 4.53927e-01 0.475072016 0.5070350 0.5389979 0.560143
52 4.67551e-01 0.488824911 0.5209834 0.5531418 0.574416
53 4.81002e-01 0.502409521 0.5347698 0.5671300 0.588538
54 4.94287e-01 0.515829730 0.5483942 0.5809587 0.602501
55 5.07412e-01 0.529088909 0.5618566 0.5946243 0.616302
56 5.20381e-01 0.542189933 0.5751571 0.6081242 0.629933
57 5.33198e-01 0.555135196 0.5882955 0.6214558 0.643393
58 5.45867e-01 0.567926630 0.6012719 0.6346172 0.656677
59 5.58390e-01 0.580565721 0.6140864 0.6476070 0.669782
60 5.70769e-01 0.593053527 0.6267388 0.6604241 0.682708
61 5.83005e-01 0.605390690 0.6392293 0.6730679 0.695454
62 5.95098e-01 0.617577451 0.6515577 0.6855380 0.708017
63 6.07048e-01 0.629613656 0.6637242 0.6978347 0.720400
64 6.18854e-01 0.641498766 0.6757287 0.7099586 0.732603
65 6.30515e-01 0.653231865 0.6875711 0.7219104 0.744627
66 6.42028e-01 0.664811658 0.6992516 0.7336916 0.756475
67 6.53391e-01 0.676236478 0.7107701 0.7453037 0.768149
68 6.64600e-01 0.687504287 0.7221266 0.7567489 0.779653
69 6.75652e-01 0.698612675 0.7333211 0.7680295 0.790991
70 6.86541e-01 0.709558867 0.7443536 0.7791483 0.802166
71 6.97262e-01 0.720339721 0.7552241 0.7901084 0.813186
72 7.07810e-01 0.730951740 0.7659326 0.8009134 0.824055
73 7.18179e-01 0.741391078 0.7764791 0.8115671 0.834779
74 7.28361e-01 0.751653555 0.7868636 0.8220736 0.845367
75 7.38348e-01 0.761734678 0.7970861 0.8324375 0.855824
76 7.48134e-01 0.771629669 0.8071466 0.8426636 0.866160
77 7.57709e-01 0.781333498 0.8170452 0.8527568 0.876382
78 7.67065e-01 0.790840929 0.8267817 0.8627224 0.886499
79 7.76192e-01 0.800146569 0.8363562 0.8725659 0.896520
80 7.85083e-01 0.809244928 0.8457688 0.8822926 0.906455
81 7.93727e-01 0.818130488 0.8550193 0.8919081 0.916312
82 8.02116e-01 0.826797774 0.8641079 0.9014179 0.926100
83 8.10240e-01 0.835241429 0.8730344 0.9108274 0.935829
84 8.18091e-01 0.843456291 0.8817990 0.9201417 0.945507
85 8.25661e-01 0.851437463 0.8904015 0.9293656 0.955142
86 8.32942e-01 0.859180385 0.8988421 0.9385038 0.964742
87 8.39928e-01 0.866680887 0.9071207 0.9475605 0.974313
88 8.46612e-01 0.873935236 0.9152373 0.9565393 0.983862
89 8.52989e-01 0.880940170 0.9231918 0.9654435 0.993395
90 8.59054e-01 0.887692913 0.9309844 0.9742760 1.002915
91 8.64803e-01 0.894191180 0.9386150 0.9830389 1.012427
92 8.70233e-01 0.900433167 0.9460836 0.9917341 1.021934
93 8.75343e-01 0.906417527 0.9533902 1.0003629 1.031437
94 8.80130e-01 0.912143340 0.9605348 1.0089263 1.040939
95 8.84594e-01 0.917610075 0.9675174 1.0174248 1.050441
96 8.88735e-01 0.922817542 0.9743381 1.0258586 1.059942
97 8.92551e-01 0.927765853 0.9809967 1.0342275 1.069442
98 8.96045e-01 0.932455371 0.9874933 1.0425312 1.078941
99 8.99218e-01 0.936886669 0.9938279 1.0507692 1.088438
100 9.02069e-01 0.941060487 1.0000006 1.0589406 1.097932
knots :
[1] -1.00000 -0.22449 1.00000
coef :
[1] 0.0278152 0.0278152 0.8153868 1.0000006
> coR1 <- cobs(x,y,constraint = "increase", pointwise = con, degree = 1)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> summary(coR1)
COBS regression spline (degree = 1) from call:
cobs(x = x, y = y, constraint = "increase", degree = 1, pointwise = con)
{tau=0.5}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:4]: -1.000002, -0.632653, 0.183673, 1.000002
with 3 pointwise constraints
coef[1:4]: 0.0504467, 0.0504467, 0.6305155, 1.0000009
R^2 = 93.83% ; empirical tau (over all): 21/50 = 0.42 (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%)
........................
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.
> with(coS, cbind(pp.lambda, pp.sic, k0, ifl, icyc))
pp.lambda pp.sic k0 ifl icyc
[1,] 3.54019e-05 -2.64644 22 1 21
[2,] 6.92936e-05 -2.64644 22 1 21
[3,] 1.35631e-04 -2.64644 22 1 20
[4,] 2.65477e-04 -2.64644 22 1 22
[5,] 5.19629e-04 -2.64644 22 1 22
[6,] 1.01709e-03 -2.64644 22 1 23
[7,] 1.99080e-03 -2.68274 21 1 20
[8,] 3.89667e-03 -2.75212 19 1 18
[9,] 7.62711e-03 -2.73932 19 1 14
[10,] 1.49289e-02 -2.85261 16 1 13
[11,] 2.92209e-02 -2.97873 12 1 12
[12,] 5.71953e-02 -3.01058 11 1 12
[13,] 1.11951e-01 -3.04364 10 1 11
[14,] 2.19126e-01 -3.11242 8 1 12
[15,] 4.28904e-01 -3.17913 6 1 12
[16,] 8.39512e-01 -3.18824 5 1 11
[17,] 1.64321e+00 -3.01467 5 1 12
[18,] 3.21633e+00 -3.01380 4 1 11
[19,] 6.29545e+00 -3.01380 4 1 10
[20,] 1.23223e+01 -3.01380 4 1 11
[21,] 2.41190e+01 -3.01380 4 1 11
[22,] 4.72092e+01 -3.01380 4 1 10
[23,] 9.24046e+01 -3.01380 4 1 10
[24,] 1.80867e+02 -3.01380 4 1 10
[25,] 3.54019e+02 -3.01380 4 1 10
> with(coS, plot(pp.sic ~ pp.lambda, type = "b", log = "x", col=2,
+ main = deparse(call)))
> ##-> very nice minimum close to 1
>
> summaryCobs(coS)
List of 24
$ call : language cobs(x = x, y = y, constraint = "increase", lambda = -1, pointwise = con, trace = 3)
$ tau : num 0.5
$ degree : num 2
$ constraint : chr "increase"
$ ic : NULL
$ pointwise : num [1:3, 1:3] 1 -1 0 -1 1 0 0 1 0.5
$ select.knots : logi TRUE
$ select.lambda: logi TRUE
$ 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] 0.2254 0.0829 0.062 -0.0562 -0.0862 ...
$ fitted : num [1:50] 0 0.00869 0.01837 0.02906 0.04075 ...
$ coef : num [1:22] 0 0.00819 0.03365 0.06662 0.10458 ...
$ knots : num [1:20] -1 -0.918 -0.796 -0.714 -0.592 ...
$ k0 : int [1:25] 22 22 22 22 22 22 21 19 19 16 ...
$ k : int 5
$ x.ps :Formal class 'matrix.csr' [package "SparseM"] with 4 slots
$ SSy : num 6.19
$ lambda : Named num 0.84
..- attr(*, "names")= chr "lambda"
$ icyc : int [1:25] 21 21 20 22 22 23 20 18 14 13 ...
$ ifl : int [1:25] 1 1 1 1 1 1 1 1 1 1 ...
$ pp.lambda : num [1:25] 0 0 0 0 0.001 0.001 0.002 0.004 0.008 0.015 ...
$ pp.sic : num [1:25] -2.65 -2.65 -2.65 -2.65 -2.65 ...
$ i.mask : logi [1:25] TRUE TRUE TRUE TRUE TRUE TRUE ...
cb.lo ci.lo fit ci.up cb.up
1 -0.07071332 -0.03907635 -3.77249e-07 0.0390756 0.0707126
2 -0.06555125 -0.03435600 4.17438e-03 0.0427048 0.0739000
3 -0.06016465 -0.02940203 8.59400e-03 0.0465900 0.0773526
4 -0.05455349 -0.02421442 1.32585e-02 0.0507314 0.0810704
5 -0.04871809 -0.01879334 1.81678e-02 0.0551289 0.0850537
6 -0.04265897 -0.01313909 2.33220e-02 0.0597831 0.0893029
7 -0.03637554 -0.00725134 2.87210e-02 0.0646934 0.0938176
8 -0.02986704 -0.00112966 3.43649e-02 0.0698595 0.0985969
9 -0.02313305 0.00522618 4.02537e-02 0.0752812 0.1036404
10 -0.01617351 0.01181620 4.63873e-02 0.0809584 0.1089481
11 -0.00898880 0.01864020 5.27658e-02 0.0868914 0.1145204
12 -0.00157983 0.02569768 5.93891e-02 0.0930806 0.1203581
13 0.00605308 0.03298846 6.62573e-02 0.0995262 0.1264615
14 0.01391000 0.04051257 7.33704e-02 0.1062282 0.1328307
15 0.02199057 0.04826981 8.07283e-02 0.1131867 0.1394660
16 0.03029461 0.05626010 8.83310e-02 0.1204020 0.1463675
17 0.03882336 0.06448412 9.61787e-02 0.1278732 0.1535339
18 0.04757769 0.07294234 1.04271e-01 0.1355999 0.1609646
19 0.05655804 0.08163500 1.12608e-01 0.1435819 0.1686589
20 0.06576441 0.09056212 1.21191e-01 0.1518192 0.1766169
21 0.07519637 0.09972344 1.30018e-01 0.1603120 0.1848391
22 0.08485262 0.10911826 1.39090e-01 0.1690610 0.1933266
23 0.09473211 0.11874598 1.48406e-01 0.1780668 0.2020807
24 0.10483493 0.12860668 1.57968e-01 0.1873294 0.2111011
25 0.11516076 0.13870015 1.67775e-01 0.1968489 0.2203882
26 0.12570956 0.14902638 1.77826e-01 0.2066253 0.2299421
27 0.13648327 0.15958645 1.88122e-01 0.2166576 0.2397608
28 0.14748286 0.17038090 1.98663e-01 0.2269453 0.2498433
29 0.15870881 0.18140998 2.09449e-01 0.2374880 0.2601892
30 0.17016110 0.19267368 2.20480e-01 0.2482859 0.2707984
31 0.18183922 0.20417172 2.31755e-01 0.2593391 0.2816716
32 0.19374227 0.21590361 2.43276e-01 0.2706482 0.2928095
33 0.20587062 0.22786955 2.55041e-01 0.2822129 0.3042118
34 0.21822524 0.24007008 2.67051e-01 0.2940328 0.3158776
35 0.23080666 0.25250549 2.79306e-01 0.3061075 0.3278063
36 0.24361488 0.26517577 2.91806e-01 0.3184370 0.3399979
37 0.25664938 0.27808064 3.04551e-01 0.3310217 0.3524530
38 0.26990862 0.29121926 3.17541e-01 0.3438624 0.3651730
39 0.28339034 0.30459037 3.30775e-01 0.3569602 0.3781603
40 0.29709467 0.31819405 3.44255e-01 0.3703152 0.3914146
41 0.31102144 0.33203019 3.57979e-01 0.3839275 0.4049363
42 0.32517059 0.34609876 3.71948e-01 0.3977971 0.4187252
43 0.33954481 0.36040126 3.86162e-01 0.4119224 0.4327789
44 0.35414537 0.37493839 4.00621e-01 0.4263028 0.4470958
45 0.36897279 0.38971043 4.15324e-01 0.4409381 0.4616757
46 0.38402708 0.40471738 4.30273e-01 0.4558281 0.4765184
47 0.39930767 0.41995895 4.45466e-01 0.4709732 0.4916245
48 0.41479557 0.43541678 4.60887e-01 0.4863568 0.5069780
49 0.43039487 0.45099622 4.76442e-01 0.5018872 0.5224885
50 0.44609197 0.46668362 4.92117e-01 0.5175506 0.5381422
51 0.46188684 0.48247895 5.07913e-01 0.5333471 0.5539392
52 0.47773555 0.49833835 5.23786e-01 0.5492329 0.5698357
53 0.49336687 0.51398935 5.39461e-01 0.5649325 0.5855550
54 0.50873469 0.52938518 5.54891e-01 0.5803975 0.6010480
55 0.52383955 0.54452615 5.70077e-01 0.5956277 0.6163143
56 0.53868141 0.55941225 5.85018e-01 0.6106231 0.6313539
57 0.55325974 0.57404316 5.99714e-01 0.6253839 0.6461673
58 0.56757320 0.58841816 6.14165e-01 0.6399109 0.6607558
59 0.58161907 0.60253574 6.28371e-01 0.6542056 0.6751223
60 0.59539741 0.61639593 6.42332e-01 0.6682680 0.6892665
61 0.60890835 0.62999881 6.56048e-01 0.6820980 0.7031884
62 0.62215175 0.64334429 6.69520e-01 0.6956957 0.7168882
63 0.63512996 0.65643368 6.82747e-01 0.7090597 0.7303634
64 0.64784450 0.66926783 6.95729e-01 0.7221893 0.7436126
65 0.66029589 0.68184700 7.08466e-01 0.7350841 0.7566352
66 0.67248408 0.69417118 7.20958e-01 0.7477442 0.7694313
67 0.68440855 0.70624008 7.33205e-01 0.7601699 0.7820014
68 0.69606829 0.71805313 7.45207e-01 0.7723617 0.7943465
69 0.70746295 0.72961016 7.56965e-01 0.7843198 0.8064670
70 0.71859343 0.74091165 7.68478e-01 0.7960438 0.8183620
71 0.72946023 0.75195789 7.79746e-01 0.8075332 0.8300309
72 0.74006337 0.76274887 7.90769e-01 0.8187883 0.8414738
73 0.75040233 0.77328433 8.01547e-01 0.8298091 0.8526911
74 0.76047612 0.78356369 8.12080e-01 0.8405963 0.8636839
75 0.77028266 0.79358583 8.22368e-01 0.8511510 0.8744542
76 0.77982200 0.80335076 8.32412e-01 0.8614732 0.8850020
77 0.78909446 0.81285866 8.42211e-01 0.8715627 0.8953269
78 0.79809990 0.82210946 8.51765e-01 0.8814196 0.9054292
79 0.80683951 0.83110382 8.61074e-01 0.8910433 0.9153076
80 0.81531459 0.83984244 8.70138e-01 0.9004329 0.9249608
81 0.82352559 0.84832559 8.78957e-01 0.9095884 0.9343884
82 0.83147249 0.85655324 8.87531e-01 0.9185095 0.9435903
83 0.83915483 0.86452515 8.95861e-01 0.9271968 0.9525671
84 0.84657171 0.87224082 9.03946e-01 0.9356505 0.9613196
85 0.85372180 0.87969951 9.11786e-01 0.9438715 0.9698492
86 0.86060525 0.88690131 9.19381e-01 0.9518597 0.9781558
87 0.86722242 0.89384640 9.26731e-01 0.9596149 0.9862389
88 0.87357322 0.90053476 9.33836e-01 0.9671371 0.9940986
89 0.87965804 0.90696658 9.40696e-01 0.9744261 1.0017347
90 0.88547781 0.91314239 9.47312e-01 0.9814814 1.0091460
91 0.89103290 0.91906239 9.53683e-01 0.9883028 1.0163323
92 0.89632328 0.92472655 9.59808e-01 0.9948904 1.0232937
93 0.90134850 0.93013464 9.65689e-01 1.0012443 1.0300304
94 0.90610776 0.93528622 9.71326e-01 1.0073650 1.0365434
95 0.91060065 0.94018104 9.76717e-01 1.0132527 1.0428331
96 0.91482784 0.94481950 9.81863e-01 1.0189071 1.0488987
97 0.91878971 0.94920179 9.86765e-01 1.0243279 1.0547400
98 0.92248624 0.95332789 9.91422e-01 1.0295152 1.0603569
99 0.92591703 0.95719761 9.95833e-01 1.0344692 1.0657498
100 0.92908136 0.96081053 1.00000e+00 1.0391902 1.0709194
knots :
[1] -1.0000020 -0.9183673 -0.7959184 -0.7142857 -0.5918367 -0.5102041
[7] -0.3877551 -0.2653061 -0.1836735 -0.0612245 0.0204082 0.1428571
[13] 0.2244898 0.3469388 0.4693878 0.5510204 0.6734694 0.7551020
[19] 0.8775510 1.0000020
coef :
[1] -4.01161e-07 8.18714e-03 3.36534e-02 6.66159e-02 1.04576e-01
[6] 1.50032e-01 2.00486e-01 2.70027e-01 3.35473e-01 4.05918e-01
[11] 4.83858e-01 5.64259e-01 6.37163e-01 7.05069e-01 7.77561e-01
[16] 8.30474e-01 8.78390e-01 9.18810e-01 9.54232e-01 9.87743e-01
[21] 1.00000e+00 5.99960e-01
>
> plot(x, y, main = "cobs(x,y, constraint=\"increase\", pointwise = *)")
> matlines(x, cbind(fitted(coR), fitted(coR1), fitted(coS)),
+ col = 2:4, lty=1)
>
> ##-- real data example (still n = 50)
> data(cars)
> attach(cars)
> co1 <- cobs(speed, dist, "increase")
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
> co1.1 <- cobs(speed, dist, "increase", knots.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> co1.2 <- cobs(speed, dist, "increase", knots.add = TRUE, repeat.delete.add = TRUE)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
> ## These three all give the same -- only remaining knots (outermost data):
> ic <- which("call" == names(co1))
> stopifnot(all.equal(co1[-ic], co1.1[-ic]),
+ all.equal(co1[-ic], co1.2[-ic]))
> 1 - sum(co1 $ resid ^2) / sum((dist - mean(dist))^2) # R^2 = 64.2%
[1] 0.642288
>
> co2 <- cobs(speed, dist, "increase", lambda = -1)# 6 warnings
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
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): 0.002 0.001 0.002
>
> 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): 0.681 0.035 1.101
>
> 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 0.05
>
> ## 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): 2.83 0.017 3.206
>
> 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